INSTRUCTOR’S MANUAL
Charles I. Jones
Macroeconomics
FOURTH EDITION
Anthony Laramie
BOSTON COLLEGE
B
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TABLE OF CONTENTS
Part 1
Preliminaries
Chapter 1 | Introduction to Macroeconomics
1
Chapter 2 | Measuring the Macroeconomy
7
Part 2
The Long Run
Chapter 3 | An Overview of Long-Run Economic Growth
16
Chapter 4 | A Model of Production
24
Chapter 5 | The Solow Growth Model
35
Chapter 6 | Growth and Ideas
45
Chapter 7 | The Labor Market, Wages, and Unemployment
53
Chapter 8 | Inflation
62
Part 3
The Short Run
Chapter 9 | An Introduction to the Short Run
71
Chapter 10 | The Great Recession: A First Look
79
Chapter 11 | The IS Curve
85
Chapter 12 | Monetary Policy and the Phillips Curve
95
Chapter 13 | Stabilization Policy and the AS/AD Framework
104
Chapter 14 | The Great Recession and the Short-Run Model
116
Chapter 15 | DSGE Models: The Frontier of Business Cycle Research
123
iii
iv | Contents
Part 4
Applications and Microfoundations
Chapter 16 | Consumption
132
Chapter 17 | Investment
137
Chapter 18 | The Government and the Macroeconomy
144
Chapter 19 | International Trade
151
Chapter 20 | Exchange Rates and International Finance
158
Chapter 21 | Parting Thoughts
163
CHAPTER 1
Introduction to Macroeconomics
CHAPTER OVERVIEW
This is a conventional first textbook chapter: it defines macroeconomics, it mentions a few interesting topics, it says what a
model is, and it lays out the book’s separation into Long
Run, Short Run, and Applications and Microfoundations. It
is quite a short chapter with few surprises, so rather than summarizing it, I will instead talk a little about what makes this
book different and lay out a few different ways you can use
it in your course.
WHAT MAKES THIS BOOK DIFFERENT?
It offers solid long-run growth coverage—including endogenous growth—while simplifying the New Keynesian business cycle dramatically, and it does all this without any
calculus. Chad shows how long-run macroeconomic growth
models have evolved and how tweaking the assumptions of
the model can lead to new and interesting insights and policy conclusions. Moreover, Chad easily deduces a short-run
model from the long-run model and therefore links short-run
and long-run economic analyses. By streamlining the coverage while teaching surprisingly solid microfoundations,
Chad’s text offers you a solid chance to spend more time on
intelligent, model-driven policy discussions about growth and
business cycles.
HOW TO USE THIS TEXTBOOK
our students learn, and how they learn. Most students who
have recently had a principles course and who are comfortable with a little algebra should be able to handle Chapters 1–14 in a semester. How much time you spend on these
chapters, whether you omit coverage of any of these chapters, and the nature and skill level of your students will
influence your coverage of the later chapters.
Moreover, if you want to leave room for a few supplementary articles, a nontechnical book, or a major empirical project or two, then you might have to tread lightly over some of
the math in the growth- and labor-market models, which are
self-contained and don’t directly come up again later in the
semester. Advice on how to do this is given in later chapters
of this manual.
This fourth edition of the book provides an innovative
chapter on dynamic stochastic general equilibrium (DSGE)
models. This chapter provides a bridge between long-run economic growth and short-run economic fluctuations, and it
fits in nicely at the end of Part 3 of the textbook to remind us
of the links between the long run and the short run. I’d recommend that you make time in the semester to include Chapter 15 as a capstone to a semester course.
ONE-QUARTER COURSE OR ONE-SEMESTER COURSE WITH
MANY OUTSIDE READINGS AND PROJECTS
Chapters 1–4 (Introduction through the basics of growth and
productivity), 8–11, 15 (inflation, business cycles, and DGSE
models), and two of the following: Chapters 5, 6.1–6.3, and
7; or 12–14 and 18–20.
CONVENTIONAL ONE-SEMESTER CLASS
TWO-QUARTER COURSE OR TWO-SEMESTER COURSE
In this day and age of assessment, we are ever conscious of
what we teach, how we teach it, who our students are, what
The entire book— one quarter on long-run growth, labor markets, inflation, consumption, and investment (Chapters 1–8,
1
2 | Chapter 1
16, and 17); one quarter on short-run business cycles, the
Great Recession, monetary policy, the Phillips curve, fiscal
policy, the aggregate demand/aggregate supply model, DSGE
models, international trade, exchange rates, and international
finance (Chapters 9–15, 18–21)—with enough time for a supplementary book each quarter and a few articles and data
projects. This would be a great way to teach this course.
CHAPTERS THAT MAY BE OMITTED
I include this list because instructors often want to know if
they can leave out a chapter without omitting facts or theories
that come back in later chapters. These chapters each build on
previous chapters, but none are directly used in later chapters:
6 Growth and Ideas (the last growth chapter)
7 The Labor Market, Wages, and Unemployment
15 Dynamic Stochastic General Equilibrium (DSGE)
Models
16 Consumption
17 Investment
18 The Government and the Macroeconomy
19 International Trade
20 Exchange Rates and International Finance
21 Parting Thoughts
In particular, the International Trade chapter (19) is independent of the Foreign Exchange chapter (20), so you can
choose just one or the other depending upon your needs.
For math-averse students, Chapter 5 (Solow) may be omitted if necessary, while key parts of Chapter 6 (Growth and
Ideas) may be covered without difficulty (Sections 6.1–6.3).
This means instructors can still teach the economics of ideas
(a largely math-free topic) yet avoid the math of the Solow
model.
HOW TO USE THIS INSTRUCTION MANUAL
Chad provides excellent summaries at the end of each chapter, and the student study guide performs much the same
function. This instruction manual does something different:
it is written to help you do a better job teaching with this innovative textbook.
In this manual, we walk through each chapter from beginning to end, discussing how you might approach topics that
students often find troublesome—for instance, the Solow
steady state, making sense of the three ways to measure gross
domestic product (GDP), or what the Fisher equation really
means.
Also, we sometimes recommend that you orga nize your
lecture differently than the text does—some topics just flow
together particularly well when you’re up there at the chalkboard. We always try to point out which topics you can safely
gloss over or omit, and we often mention an illustration or
two that might make your lectures a bit more relevant.
Every chapter in this manual also has a sample lecture that
you can use, written on a topic with which students typically
have a tough time. Finally, each chapter of this manual also
contains a few case studies, often building on Chad’s own
case studies. In the case studies, we provide some additional
facts or theories that might help to flesh out a lecture or
provoke classroom discussion. We hope you find this manual useful in getting the most out of Charles Jones’s
Macroeconomics.
SAMPLE LECTURE: GIVING YOU ALL
THE ANSWERS UP FRONT
Of great concern to the economics profession is the economic
literacy of our students. In par ticular, do our students really
understand the subject matter or do they simply borrow an
understanding for the course? One of my teaching objectives
is to ensure, as much as possible, that students own an understanding of economics. To that end, I begin the introductory
class with a set of unfolding questions. I start with the most
basic question, What is economics? The better students
respond with the textbook definition given in Principles,
which is fine. But then I ask the question, Would your brother
or sister, friend or parent understand that answer? Most students respond by saying no. Loosely following the late great
Robert Heilbroner, I’ll say that economics is the study of the
economy (and I’ll get a laugh) and students will relax. But
then that compels the question, What is the economy? We go
around on different definitions, and we work up to the point,
again following Heilbroner, that the economy is a set of
social institutions/relationships devised to produce and distribute goods and bads. Then we pull that definition apart (to
produce—to transform nature into something useful; to
distribute—to decide who gets what; the goods and the bads—
things that are literally good and/or bad.)
So, the next question is, Why study economics? Because
of the economic problem. What economic problem? Scarcity.
What is scarcity? Not having enough resources or goods to
meet needs and desires. What causes scarcity? Resource constraints inherent in nature and the process of social interaction that create wants and desires for goods. Again, via
modified Heilbroner, How does a society, regardless of space
and time, confront scarcity? People must be induced to work
more when they want to work less; people must be induced
to consume less when they want to consume more; and technology (the art of production) must be modified/improved.
What economic system does most of the world use today to
confront scarcity? Students will say capitalism or markets.
What are markets? Markets are the process whereby buyers
and sellers interact to determine prices and quantities. What
two approaches do we have for studying markets? Microeco-
Introduction to Macroeconomics | 3
nomics, the study of the individual parts of the economy, and
macroeconomics, the study of the economy as a whole with
emphasis on factors like economic growth, economic fluctuations, unemployment, inflation, and international economic
relations.
Microeconomics is rooted in the writings of Adam Smith
in An Inquiry into the Nature and Causes of the Wealth of
Nations (1776) (I like to say the full title—it sums up what
most of economics is about). Smith showed that markets promote order and stability by allowing individuals to freely
express self-interest through markets and that the expression
of self-interest promotes the social good. (Most students will
be familiar with the “invisible hand” but not familiar with
its strong political implications.) Of course, if Smith is correct, then markets, as a set of institutions, become a set of
goods that promote social welfare. Well, what about macroeconomics? Where did it come from?
Macroeconomics’ origins can be traced to the Great
Depression, the writings of John Maynard Keynes, World
War II, and the Employment Act of 1946. If anything, macroeconomics was the consequence of market failures as evidenced by the Great Depression. To illustrate the market
failures, Keynes invoked fallacies of composition in reasoning, like the paradox of thrift (that wage deflation in isolation can stabilize a labor market, but wage deflation in the
economy as a whole will do little to reduce unemployment
and may actually destabilize the economy). Keynes’s ideas
were too revolutionary to gain acceptance, but World War II
taught my parents’ generation that government coordination
of the economy to ensure high levels of spending and the
national defense of the United States ended the Great Depression. The World War II generation, wanting to eliminate
future unemployment, had the Employment Act of 1946
passed. According to this legislation, government should pursue policies to promote maximum employment, production,
and purchasing power. In addition, this legislation created the
Council of Economic Advisors and the Joint Economic Committee to advise the president and Congress on the economy.
Subsequently, macroeconomics, along with microeconomics,
became part of every core economics curriculum. Although
there is little disagreement as to how to teach microeconomics, tension remains as to how to teach macroeconomics. In
particular, conflict occurs over whether to emphasize the long
run or the short run. Chad’s textbook gives you the flexibility of emphasizing either concept or both.
Today, the global economy continues to recover from the
Great Recession— the greatest recession since the Great
Depression. Clearly the emphasis in policy has shifted to the
short run, but long-run concerns remain. The U.S. unemployment rate rose from 4.6 percent in 2007 to 5.8 percent in
2008 and 9.6 percent in 2010 (the year after the Great Recession officially ended); it declined from 7.4 percent in 2013 to
5.3 in 2013 and 4.9 percent in June 2016. While the financial
markets have largely recovered, still fresh in the public’s
mind is that the Dow Jones Industrial stock index, along with
many other stock indexes, lost 40 percent of its value in a
matter of weeks; housing prices in many markets collapsed;
record numbers of bankruptcies and foreclosures were
recorded; banks, insurance companies, and brokerage houses
became insolvent as their assets proved insufficient to cover
their liabilities; and a chain of bankruptcies threatened the
strength and stability of the United States and global economies. Prior to the financial crisis, the price of crude oil rose
from under $70 in August 2007 to over $140 by July 2008.
Two of the big three U.S. automakers were on the brink of
bankruptcy. Unprecedented steps were taken by the Federal
Reserve and the U.S. Treasury to bail out the financial sector and to save the automakers. An economic stimulus bill
was passed that included tax credits for first-time homebuyers, cash for clunkers, tax cuts, and funding for so-called
shovel-ready projects (to name a few). The economic stimulus bill, combined with the War on Terrorism and the downturn in the economy, subsequently increased the federal
government budget deficit from around $160 billion in 2007
to about $460 billion in 2008 and over $1.5 trillion in 2010 to
almost $1.4 trillion in 2011. Moreover, despite bailouts and
the stimulus, we have seen the money supply (M2) grow by
8 percent in 2009, 2.5 percent in 2010, 7.3 percent in 2011,
8.5 percent in 2012, and about 6 percent in 2015. The threat
of worldwide recession remains even as oil prices have collapsed, and the Federal Reserve contemplates the speed at
which short-term interest rates should increase as corporate
profits remain weak. Even as of this writing in 2016, the
recovery remains slow and fragile, and the debate over austerity versus stimulus continues to rage (see John Cassidy,
“The Reinhart and Rogoff Controversy: A Summing Up,”
New Yorker, available at http://www.newyorker.com /online
/ blogs / johncassidy / 2013 / 04 / the - rogoff - and - reinhart
-controversy-a-summing-up.html). This experience, now
compounded by the Greek financial crisis, the European refugee crisis, and Brexit, has taken the economics profession
by surprise and is currently causing us to reevaluate what we
think about how economies work.
In this course, we’ll spend the first half of the semester
talking about why some countries are richer than others and
why the average person today lives so much better than someone one or two hundred years ago. A generation ago, such
topics would barely have been mentioned, but with the rise
of globalization, the spread of markets around the world, and
a new concern about global growth prospects, a new emphasis in economics has emerged.
In the second half of the semester, we’ll talk about economic busts and booms, which economists often call the
“business cycle” or “economic fluctuations.” The book’s goal
is to provide a framework for understanding the nature, causes,
and solutions to both short-run and long-run fluctuations.
A generation ago, the business cycle section would’ve been
almost the whole course. Back then, many macroeconomists
4 | Chapter 1
thought they could control the overall level of GDP on a yearto-year basis. That’s certainly what the textbooks taught
back then. In those days, we spent the semester talking about
how to control the demand for goods and ser vices in the
economy. Back then, we thought we actually could control
things.
Today’s macroeconomics is largely about teaching
macroeconomists—myself and my colleagues—to be
humble. We’ll learn that the Federal Reserve can have an
impact on the average rate of inflation. There are increases
in the overall price level, but at the same time we’ll see that
the Federal Reserve has a limited impact on reducing the
average rate of unemployment—the fraction of workers who
can’t find jobs. (The Federal Reserve might be able to temporarily reduce the unemployment rate below some “natural”
rate but subsequently risk high inflation without any long-run
reduction in the unemployment rate.)
One point to take away from the semester is this: the Federal Reserve might be able to smooth out the bumps in the
road— emphasis on “might”—but it can’t make the trip go
any faster. For the average American to have a better standard of living in the long run, we must focus on something
other than interest-rate policy.
That’s why we’ll spend quite a bit of time in the first half
of the semester on the “supply side” of the economy: the supply of people willing to work; the supply of machines,
equipment, and natural resources; and the supply of useful,
practical ideas. Economists tend to think that if you have a
good supply of those four things—people, machines, natural resources, and ideas—then in a market economy, those
“inputs” will usually get combined to create “outputs” that
we really want, like cars and movies and doctor’s appointments and books and vacations and food. By spending time
in the first half of the semester talking about the supply side,
the hope is that when you’re voting or when you’re serving
in government, you’ll remember that how well people live
doesn’t depend on whether there’s a demand for goods—as
you learned in Principles or by talking with your friends,
people’s demands are basically unlimited. The key problem
of economics is scarcity—and the miracle of long-term economic growth is that most of the things people want are a
little bit less scarce each year.
SAMPLE LECTURE: MODELS AND THEIR
SOLUTIONS
In section 1.2, Chad offers the four-step approach that unifies macroeconomics: document the facts, develop a model,
compare the predictions of the model with the original facts,
and use the model to make additional predictions. Students
in intermediate theory still can be a little uncertain and ill at
ease in developing models. One possible way to make students comfortable in the process of developing models is to
remind them that central to their study in Principles was the
supply and demand (the market) model. A quick review of
that supply and demand model goes a long way in clearing
up the vocabulary used throughout much of the text (and economics, in general). For example, describing the market
model as a process whereby buyers and sellers interact to
determine price and quantity provides a structural model
where the buyer’s behavior is modeled as a demand equation,
the seller’s behavior is modeled as a supply equation, and the
model of solved is by specifying an equilibrium equation, that
is, in general functional form (an idea that is good to introduce early on) where demand is Qd = Qd(P, NPDs), supply is
Qs = Qs(P, NPDs) (where the NPDs = the relevant nonprice
determinants of demand or supply and where an example or
two of the respective NPDs quickly refreshes students’ memories), and where equilibrium is Qd = Qs. After specifying
the model, remind students that the model has to be signed
(and explain what that means)—putting a “−” under “P” in
the demand equation and a “+” under P in the supply
equation—meanwhile explaining what the signs mean. A
quick graph illustrates the equilibrium solution; the equilibrium price and quantity are shown as endogenous variables;
and the NPDs are the exogenous variables that determine
equilibrium levels. As a further example, you might consider
moving the market analysis into specific functional form,
where Qd = a − bP and Qs = α + βP, the NPDs are reflected in
the slope and intercept parameters, and the equilibrium price
and quantities are P* = (a − α)/(b + β) and Qd* = a − bP* and
Qs* = α + βP*. Students quickly learn that much of what they
were doing in principles is nicely summarized in Figure 1.6:
the parameters/exogenous variables determine the solutions
to the endogenous variables, equilibrium price, and quantity,
and tweaking those parameters/exogenous variables modifies
the solutions to the models.
CASE STUDY: HOW MUCH WOULD YOU PAY
TO GET RID OF RECESSIONS?
Given that the U.S. economy has just emerged from the socalled Great Recession and is perhaps teetering on the brink
of another recession, Nobel Prize–winner Robert Lucas’s
question, How much would you pay to get rid of recessions?
remains apropos. Lucas’s answer to this question was, “Not
much.”
As is well described in “After the Blowup” by John Cassidy (New Yorker, January 11, 2010), Lucas won the Nobel
Prize, in part, for reinventing the notion that markets are
self-regulating. So Lucas’s answer is not surprising. Lucas
noticed that consumer spending—the part of our incomes we
use to buy happiness— doesn’t really change that much for
the average person from year to year. It only fluctuates from
year to year by about 1.5 percent (aside: that’s the standard
deviation of real consumption) for the average person. There’s
Introduction to Macroeconomics | 5
a strong annual upward trend of about 2 percent, but around
that trend there’s a small wiggle, averaging about 1.5 percent
per year.
So how much would you, personally, be willing to pay for
an insurance policy that promised that you’d never risk those
1.5 percent up-and-down shocks to your consumer spending?
Lucas ran some estimates and found that the average person would be willing to pay about 0.06 percent per year for
an insurance policy like that. For a person earning $50,000
per year, it would cost $30 annually to guarantee a steady
growth in his or her standard of living. Even when considering that it is hard to buy goods when you lose your job—you
just might not be able to borrow the money to put food on
the table—he found that in the United States, unemployment
insurance benefits are usually good enough that the average
person still wouldn’t want to pay a lot for insurance to get
rid of his or her consumption risk. This suggests that modern unemployment insurance is pretty good insurance
already.
Quite possibly, the average poor person in the United States
would pay more than $30 per year for that kind of insurance
policy. For poorer people, every dollar counts more. But
Lucas was trying to come up with an average estimate of how
much the typical American would pay to get rid of business
cycles. And he just couldn’t find a way to make that number
look big.
Economists David Romer and Lawrence Ball1 think that
Lucas is missing the point entirely. They think that the big
cost of economic fluctuations isn’t the fact that you can’t go
to restaurants as often during a recession but that you might
not have a job. They’ve run some estimates based on what
they think the average person is like and they find that economic fluctuations have a much higher cost than Lucas
believes. They agree that the average person doesn’t get hit
hard on the consuming side during a recession, but they think
that people really don’t like going in and out of the workforce.
They find that people would rather work a steady 40-hour
week than work 45 hours most of the time with some random layoffs thrown in. And of course, surveys and common
sense do show that people hate being out of work.
Over the course of fifty years, the economics profession
has gone from the notion that business cycles could be tamed
(Samuelson and the Keynesians) to the ideas of Lucas and
others that markets are self-regulating and that government
intervention has ill or nil effects. In light of current events,
you will be challenged throughout this course with questions
regarding what should be done to end recessions and reduce
unemployment.
For a nice review of the current debate, see the aforementioned New Yorker article.
1. Laurence Ball and David Romer, “Real Rigidities and the Nonneutrality of Money,” Review of Economic Studies 57, no. 2 (April 1990):
183–203.
CASE STUDY: THE OECD REPORT ON INCOME
INEQUALITY AND ECONOMIC GROWTH
Chad, in section 1.1, examines some of the big questions in
macroeconomics. Some students might be wondering where
income inequality fits into macroeconomics, as, in recent
years, the issue of income inequality has risen to the forefront of both political and economic discussions. A good
primer on this topic can be found in the report published in
December 2015 by the OECD, Income Inequality: The Gap
Between Rich and Poor (see: http://www.oecd.org/social/
income-inequality-9789264246010-en.htm). In section 4.1
of the report, a summary of what economists “think about
inequality is provided.” First, the Kuznets hypothesis is discussed. Economic growth, through industrialization and the
development specializations, raises living standards above
the subsistence levels and generates ever-widening gaps in the
income distribution that are then moderated by redistributive
fiscal policies. With economic development, over time,
inequality is expected to rise and then fall. However, in looking back over the last 100 years or so, as economies have
developed, inequality has fallen, then increased. Second, in
attempting to provide a link between economic growth and
inequality, a “complex and dynamic” relationship is considered that depends upon (where Sara Voitchovsky’s insights are
mentioned) how different income groups behave and how
different income groups interact. For example, inequality
affects how the poor invest in education, how the middle class
demand goods and services, or how the rich save and investment and alter the direction of public investment or services.
Inequality also affects the way groups interact by altering
trust (which impacts transaction costs), social capital (creating insider and outsider networks), social unrest (increasing
governance costs), and volatility (generating sudden policy
shifts). In short, the report hedges on the issue of income
equality, arguing that inequality is the by-product of an
incentives-driven process that stimulates growth while recognizing the rising income inequality can generate underinvestment in education and skills, as, for example, evidenced
in the decline in numeracy skills of low-income people as
income inequality increases. The OECD suggests that the
solution to the dual problem of growth and income inequality
is a radical rethink of the educational process: providing more
equal and meaningful educational opportunity to the poor.
REVIEW QUESTIONS
1–3. Based on personal preference.
4. Ingredients: Inputs, the model itself, and outputs. We can
call these “exogenous variables,” “equations or words,” and
“endogenous variables,” respectively. The best short summary of the power of models is Robert Lucas’s speech
“What Economists Do.” It is available widely on the Web.
6 | Chapter 1
This is possibly his best line: “I’m not sure whether you
will take this as a confession or a boast, but we are basically
storytellers, creators of make-believe economic systems.”
Lucas explains that if you want to be a matter-of-fact person
who understands how the world works, you actually need to
be creative and imaginative.
the wage. (Of course, you could just collapse this to equilibrium labor supply and equilibrium wage without losing
much interest.)
EXERCISES
Now might be a good time to review the importance of the
associative rule—students often forget about the importance
of parentheses when doing algebra.
1–2. Based on personal preference.
3. (a) From www.stanford.edu/~chadj/snapshots.pdf (data is
available through 2010):
Ethiopia: 1.9 percent
India: 8.9 percent
Mexico: 28.5 percent
Japan: 75.6 percent
(b) Botswana’s per capita growth rate between 1960 and 2010
was about 6.07 percent. China’s per capita growth rate was
somewhere between 4.38 percent (as reported on “Snapshots,” from 1953 to 2010) and about 6.02 percent (between
1960 and 2010, if calculated from the data provided by Chad
on the related Excel spreadsheet).
(c) Population as of 2010, biggest to smallest: USA (313.7
million), Indonesia (242.3 million), Brazil (196.7 million),
Nigeria (162.5 million), Bangladesh (156.5 million), Russia
(148.2 million).
(d) Government purchases are larger in poor countries, while
investment expenditures are higher in rich countries.
(e) Although there are many exceptions, it appears that money
in poorer countries has less value per unit compared to rich
countries. This is largely because some poor countries have
a history of high inflation, so that one unit of their currency
becomes worth very little compared to the dollar. High inflation is rare in rich countries and much more common in
poor countries.
4. Based on personal preference.
5. This is a worked exercise. Please see the text for the
solution.
6. (a) ā tells us how the quantity of labor supplied responds
to wages. Informally, it tells us how sensitive workers are to
wages when deciding how much to work.
(b) This is the same as in 5: quantity of labor supplied,
quantity of labor demanded, equilibrium labor supply, and
(c) w* = ( − )/(1 + ā)
L* = ( − w*)
(d) If increases, the wage falls, and the equilibrium quantity of labor increases. This is just what we expect: the labor
supply increased exogenously, and workers were willing to
work the same hours at a lower wage. In equilibrium, firms
decided to hire more workers at a new, lower wage.
(e) This is an increase in demand: the quantity and wage of
labor will both rise in equilibrium. The wage rises a bit, to
which workers respond by supplying more labor.
7. (a) QD = demand for computers = F(P, )
is exogenous and captures consumers’ understanding
of how to use computers.
QS = supply of computers = G(P, )
is exogenous and captures the manufacturing skill of
the computer industry.
In equilibrium QS = QD = Q*, so this model is really two
equations and two variables. If the demand and supply functions are straight lines, then there must be a unique solution.
(b) QD = demand for classical music = F(P, )
is exogenous and captures consumers’ interest in classical music.
QS = supply of classical music = G(P, )
is exogenous and captures the technology for recovering and cleaning up old classical music recordings.
(c) QD = demand for dollars = F(P, )
is exogenous and captures the domestic and foreign
beliefs about the relative safety of the dollar versus the yen,
the euro, and the pound.
QS = supply of dollars = G(P, )
is exogenous and captures the Federal Reserve’s supply
of currency.
CHAPTER 2
Measuring the Macroeconomy
CHAPTER OVERVIEW
By and large, this is a conventional “What is gross domestic
product (GDP)?” chapter. Jones runs through the production,
expenditure, and income approaches, and emphasizes that the
labor share in the United States is roughly constant (well
worth emphasizing, since it helps justify the Cobb-Douglas
production function that plays a major role later).
There’s a particularly clear discussion of how to compare
GDP numbers across countries; even if you don’t plan to
cover international topics in your course, this is probably
worth discussing, since cross-country GDP comparisons are
so central to the economic growth chapters (and many students have an intuition that prices differ across countries).
Interest rates and the unemployment rate are deferred to
later chapters, so you can focus your energies on an intellectual triumph that we economists usually take for granted:
the definition of GDP.
2.1 Introduction
Chad starts off by emphasizing just how hard it is to measure “an economy.” What should we include? What should
we leave out? How can we add up things that are wildly
dissimilar— automobile production and grocery store
employment and resales of homes and on and on—into one
number that tells us what is happening?
Simon Kuznets found a reasonable way to do this and
was awarded the 1971 Nobel Prize in economics largely for
creating the definition of GDP that we use today. Economists and citizens take GDP for granted—but it really is
one of the great intellectual contributions to economics.
What did we ever do without it? Bad macro policy—that’s
what we did without it. Throughout this chapter, you may
want to look for ways to emphasize how many bad ways
there are to count economic activity—this lets students
know that you’re not just belaboring the obvious. In addition, you may want to emphasize that the system of national
accounts constitutes a set of accounting identities—
statements that are true by definition. These definitions are
impor tant in framing questions and finding answers. For
example, if we define “spending” as C + I + G + NX, then we
will ask how C, I, G, and NX changed to cause spending to
change. In contrast, if we define “spending” as the money
supply times velocity (M × V), then we will ask how the
money supply and velocity changed to cause spending to
change. Definitions are an essential part of economic theory. The national accounts provide ample definitions for
asking questions.
A useful analogy comes from medicine. How can you tell
whether a human being is healthy? Doctors have settled on a
few key variables for summing up human health: body temperature, blood pressure, heart rate, and breathing rate. The
first two of the vital signs could be measured in a number of
ways—so doctors had to settle on the one best way to measure body temperature and blood pressure. Over the centuries, many different “vital signs” were put forward as being
the key to measuring health, but only these four passed the
test. Even today, many doctors push to include a fifth or sixth
vital sign— oxygen levels in the blood, pupil size, emotional
distress, pain— but the profession as a whole resists these
efforts.
So too with GDP: we’re always tinkering with ways to
improve the GDP measure. We remind students of its limitations; we look at other numbers as well, but we keep coming
back to GDP because it seems to be one of the vital signs of
the nation’s economic health. GDP is also the most complicated vital sign to explain—not unlike blood pressure in that
regard—so we spend a whole chapter explaining it.
7
8 | Chapter 2
2.2 Measuring the State of the Economy
Let’s start with Chad’s phrasing of the definition of GDP:
“Gross domestic product is defined as the market value of the
final goods and ser vices produced in an economy over a
certain period.” The words of this definition that can be
emphasized are “market value,” “final,” “ser vices,” and
“produced.”
By emphasizing “market value,” we stress that GDP is valued in some currency, such as dollars, and that unalike quantities of goods cannot be added up to measure the nation’s
output.
By highlighting “final” I emphasize that one key to accurately measuring GDP is to avoid double counting. I like to
use examples in which common sense conflicts with Kuznets’s
GDP measure, as in the sample lecture below.
By highlighting “produced” I emphasize that GDP doesn’t
include sales of used items (such as homes and cars) and
doesn’t include purely financial transactions (such as buying
stocks or moving money between bank accounts). Moreover,
GDP is a flow. A flow represents an economic variable that
is measured through time, for example, how much income
was earned or spent last week. In contrast, economic variables measured at a point in time are called stocks. These
variables are found in our balance sheets (our statements of
assets, liabilities, and net worth). How much money you hold
is a question about an economic stock.
By highlighting “services” I emphasize that a large part of
economic activity in the United States isn’t about making
things—it’s about providing valuable services. If we leave out
the ambiguous “housing services” part of GDP, the remaining service items—transportation, medical care, tourism, and
“other”—add up to about $3.5 trillion, about one-fourth of
our $13 trillion U.S. economy. Consumer services represent
the largest category of consumer spending in the United
States, about two-thirds of total consumer spending. In short,
consumer ser vices are almost half (around 47 percent) of
GDP.
PRODUCTION = EXPENDITURE = INCOME
A clear example about Homer and Marge running a farm
makes the point that if you measure correctly, there are three
equivalent ways to measure GDP. You can remind students
that this is the same “circular flow” idea they saw back in
Principles: you can take the economy’s pulse when products
flow to final users, when revenue flows to firms, or when
income flows to the firm’s workers, owners, and lenders.
It may be worth emphasizing that Chad’s “profits” are what
Principles texts often call “accounting profits.” They’re different from “economic profits,” which don’t come into play
at all when measuring GDP (recall that the difference between
accounting and economic profits is the opportunity cost of
the entrepreneur’s time and the investor’s capital). It’s worth
remembering that GDP is by and large an accounting measure, using accounting intuition.
The rhetoric of macroeconomists often confuses students.
A case in point arises here. Macroeconomists often use the
terms “real income,” “output,” and “GDP” interchangeably.
Since the value of output, as realized through sales, is distributed in the form of various incomes, output, GDP, and
income are identical.
THE EXPENDITURE APPROACH TO GDP
Here we run through C, I, G, and NX just as in Principles.
Fortunately, Chad places less emphasis on the minutiae of the
four categories and instead focuses on how these shares have
changed over time—and by emphasizing time series, he gives
the students stylized facts for macroeconomic theory to
explain.
In one case he begins a theoretical explanation immediately. He draws attention to the rise in the U.S. consumption
share, noting that it could reflect the fact that it’s been easier
for average consumers to borrow in recent decades. Alternatively, the rise in today’s consumption share could reflect an
expected rise in future income.
A few points that might be worth noting include the
following:
• It’s always worth emphasizing the difference between
government purchases (measured in GDP) and government spending (which is what the media cares about, and
what matters for many fiscal policy questions, but is not
a formal category of GDP). As Chad notes, Social Security, Medicare, and interest on the debt are not included
in G. They are transfer payments, and in practice most
Social Security and all Medicare payments are used to
purchase C, consumer goods and services.
• It’s worth noting that composition of spending is sensitive to where the economy is during the business cycle.
During the current downturn in the economy, we see
investment’s share of GDP falling, as consumption and
government purchases’ shares are increasing.
It’s also worth emphasizing what NX really does: it makes
sure we count everything exactly once. For example, C contains all purchases of consumer goods within the United
States, not all production of consumer goods within the
United States. So, some of the C in GDP is really produced in
Germany or China or Canada—and if our final measure of
GDP is really going to measure U.S. production, we must subtract that to make sure it doesn’t show up in our final number.
So, when an American buys a $400 Chinese TV from the
local appliance store, it shows up twice on the right-hand side
of the national income identity: as +$400 in C and again as
−$200 in NX. That’s how we make sure that the portion of the
TVs produced abroad doesn’t show up in U.S. gross domestic
product.
Measuring the Macroeconomy | 9
The surprise is that C, I, G, and NX all reflect purchases
by different groups, but they are defined in such a way that
they sum up to U.S. production.
THE INCOME APPROACH TO GDP
This section gives just enough information for students to
learn that the labor share is fairly stable across time within
the United States. The only point I might emphasize is that
the two forms of business income (net operating surplus and
depreciation) are actually one item: income going to owners
of capital, which we might call “gross operating surplus of
business.” The “depreciation” item is imputed (that is, scientifically made up) based on assumptions about the decay of
the U.S. capital stock.
And just why is there an item called “indirect business
taxes” if so many other forms of taxes—income and payroll
taxes, in particular— don’t show up here? The easy answer
is probably the right one: it’s because the creators of the
national accounts are following accounting methods. In
accounting terms, the answer to “Who pays a sales-type tax?”
is empirically ambiguous: in the typical case, the customer
“pays” the tax, since it’s added onto the bill, but in reality,
the business owner sends the proceeds on to the government.
By lumping these ambiguous taxes together, we reduce the
ambiguity of the other income categories.
THE PRODUCTION APPROACH TO GDP
Once again, this gives you another chance to emphasize the
importance of counting everything exactly once. In the production method, you have only two choices:
1. Either only measure final goods and ser vices, or
2. Only measure the value added at each stage of production as a good moves from firm to firm to final
purchaser.
Why bother with choice number 2? For an economist (or
businessperson) trying to figure out which industries are most
productive, it is useful to know which industries add the most
value to their inputs. In Chad’s example, you could use the
value-added method to answer the question, “Where does
most of a car’s value come from—the raw materials or the
assembly of those materials?” In the diamond jewelry industry, the answer might be quite different (if the “raw” material is cut diamonds).
I often emphasize that when measuring the size of a local
economy, common sense and economic sense are likely to
conflict. Common sense says, “Measure the size of the local
economy by adding up the sales of all the local businesses.”
But that would include massive double counting—just think
of all the products that are sold from one local business to
the next before they reach their final user (farm products are
a good example, as is anything locally made and then sold
in a local store).
Economic sense says something different: “Measure the
size of the local economy by summing up the value added
by each local business.” To do that, you need to know the cost
of each company’s outputs and inputs, and then just sum all
the values of the outputs while subtracting the sum of all the
values of the inputs.
WHAT IS INCLUDED IN GDP AND WHAT IS NOT?
Of course, we must explain the limitations of GDP— Chad’s
discussion differs from many by pointing to recent research
showing that health matters more than is measured in GDP,
while environmental degradation likely matters very little. In
addition, you might emphasize the importance of leisure as
a good that is excluded from GDP.
In this fourth edition of the textbook, Chad provides a case
study in which a nation’s welfare is linked to consumption
(government and personal) per person, life expectancy, leisure, and consumption inequality. The resulting measure of
welfare is contrasted to relative per capita GDP. When comparing the welfare measures across countries, two impor tant
results emerge. First, relative to the United States, in developed countries like those of Northern Europe, welfare rises
in comparison to per capita GDP because of (1) more government consumption, (2) more leisure, (3) higher life
expectancy, and (4) less consumption inequality. Second, in
poorer countries relative welfare decreases in comparison to
relative per capita GDP for the opposite reasons. Chad’s
case study complements and provides results similar to the
United Nations Development Programme’s Human Development Index (available at http:// hdr.undp.org/en /statistics
/ hdi).
2.3 Measuring Changes Over Time
Now we get to the distinction between nominal and real
GDP. In Section 2.3.1, Jones runs through a simple applesand-computers example, yielding what you really need to
cover: Nominal GDP and Real GDP.
In Sections 2.3.2, 2.3.3, and 2.3.5, he runs through the various types of price indexes—Laspeyres, Paasche, and chainweighted. If you want to avoid these price-index details, that’s
easy: just cover 2.3.1 to teach the old standby of “Real GDP
in Year X Prices.” Then use the basic equation at the beginning of 2.3.1 (nominal GDP = real GDP × price level) to back
out the price level.
From there, proceed directly to 2.3.4 and to the definition of inflation, which is probably what you care about
anyway. Chain weighting doesn’t ever come up again aside
from a parenthetical reference between equations 2.3
and 2.4.
10 | Chapter 2
Chad’s coverage of the three types of price indexes is quite
clear and brief, so if you do want to cover it, it shouldn’t take
more than half an hour in class.
2.4 Comparing Economic Performance
across Countries
Students often have a strong intuition that prices vary
across countries, and since cross-country GDP comparisons will play a major role in the next four chapters, it may
be worthwhile to spend a little time on this section. There is
one par ticular point that I would expand on a bit with most
students, and that is the meaning of the final equation in
this section:
real Chinese GDP in U.S. prices = (U.S. price level/
Chinese price level) × Chinese nominal GDP
The easiest way to make sense of this equation is to first convert Chinese nominal GDP from yuan into dollars. Students
can then see, given the exchange rate, how much those many
trillion yuan are worth in dollars. Then you can point out that
goods cost less in China than in the United States, and therefore those dollars purchase more goods than they would
have purchased in the United States. If those dollars purchase
more goods, real GDP in China is increased. This real Chinese GDP in U.S. dollars can then simply be found by dividing China’s nominal dollar GDP by the ratio of the Chinese
price level to the U.S. price level (multiplying nominal dollar GDP by the ratio of the U.S. price level to the Chinese
price level).
The key takeaway here should be that if prices are “lower”
in China than in the United States, then Chinese real GDP is
higher than Chinese nominal GDP.
Compare actual, uncorrected, right-off-the-website U.S.
prices (in dollars) for certain goods and ser vices against
actual, uncorrected, right-off-the-website Chinese prices (in
yuan) for the same goods and services. Convert those yuan
prices into dollars at the actual, uncorrected nominal dollar/
yuan exchange rate, and you’ve got a commonsense measure
of where prices are lower. Add in a big budget and dozens of
well-meaning bureaucrats, and you’ve got the United Nations
International Comparisons Program.
If goods and services cost less in China than in the United
States (in fact they do, after you convert yuan into dollars),
then that means the price level is lower in China than in the
United States. So, while China’s nominal GDP may look relatively small at $5.8 trillion (when converted into dollars),
when adjusting for relative prices, the Chinese real GDP is
relatively large at $10.8 trillion.
Figuring out why the same goods and services are more or
less expensive in some countries than in others is a task usually left to international economics, so I won’t attempt even a
quick explanation here. Chad closes this section (and for prac-
tical purposes, the chapter) by noting that the same goods and
services are often cheaper in the poorest countries—haircuts
are a classic example. Also, the Economist’s Big Mac Index is
always worth a mention, since students can grasp that idea
quickly.
So, though on paper the world’s wealthiest countries may
appear 100 times richer than the world’s poorest countries,
the actual difference is closer to 30 times richer. That is still
a massive difference that demands explanation—and that is
the topic of the next few chapters.
2.5 Concluding Thoughts
Just as a reminder, there are two popular topics that Chad
(mercifully) leaves out of this chapter in order to get us away
from the economic anatomy and toward the economic models that are our field’s strength. These are the Consumer Price
Index (CPI) and how price indexes measure quality changes.
Chad provides coverage of the former in Chapter 8, while this
manual provides some coverage on quality changes when discussing that chapter.
You may want to mention these topics in class at some
point, to let the students know you’ll come back to them:
• The Consumer Price Index’s “basket” method is different from the other price indexes covered in this chapter.
(The CPI is used to index tax brackets and Social Security payments, so it has policy relevance.)
• It’s difficult to measure changes in quality over time (key
in a new-economy world). The Census Bureau’s hedonic
price indexes for computers and Alan Greenspan’s
speech on the falling real price of cataract surgery come
to mind.
Finally, students might be interested to know that national
accounts provide a wealth of useful definitions that can be
used as a starting point for analyzing impor tant questions
such as what causes the national budget deficit and what role
the national budget deficit plays in affecting national savings
and gross savings.
SAMPLE LECTURE: PRODUCTION,
EXPENDITURE, AND INCOME IN
A TRUCK ECONOMY
In this lecture, you can tie together all three GDP measurement methods in a simple economy with one output good.
Since I find that most misunderstandings and most of the
insights in national income accounting come from the production/value-added method, we’ll use Chad’s example of
steel being used to make trucks. Let’s consider the economy
of Pickupia. The only two companies in Pickupia produce
steel (SteelCo) and trucks (TruckCo).
Measuring the Macroeconomy | 11
SteelCo
Wages
Sales Tax
Cost of Inputs
+ Profit
Total Steel Sales
70
0
0
30
100
TruckCo
Wages
Sales Tax
Cost of Inputs
+ Profit
250
30
100
120
Total Truck Sales
500
There are four different customers for TruckCo’s trucks:
Pickupia’s consumers buy $200 worth of trucks for personal use;
Pickupia’s businesses buy $100 worth of trucks to haul
products and workers;
Pickupia’s government buys $150 worth of trucks to haul
products and workers; and
Foreign countries buy $50 worth of trucks for unknown
reasons.
Emphasize how different this answer is from “common
sense.” If I wanted a commonsense answer to how much is
produced in this economy, I’d add up SteelCo’s 100 in sales
plus TruckCo’s 500 in sales to get my answer: 600.
The commonsense answer—which is what you’d get if you
just surveyed both businesses and added their answers—
turns out to be completely wrong, because it double counts
the steel. Making sure you count everything exactly once is
the key to a good accounting system—and that’s harder to
do than you might think.
CASE STUDY: CAPITAL GAINS—WHY AREN’T
THEY PART OF GDP?
Income:
total wages: 320
total sales tax (an “indirect tax”): 30
total profits: 150
total income = 320 + 30 + 150 (assuming no depreciation
of capital) = 500
(This 64 percent wage share is close to the true U.S. value,
which may be a surprise to many students who suspect that
the vast majority of GDP is profits.)
If you buy a share of Microsoft stock for $100 and then sell
it a year later for $150, common sense tells you that you’ve
earned $50. The $50 increase is called a “capital gain.” Similarly, if you bought a house for $100,000 and sell it two years
later for $125,000, that $25,000 sure feels like income to
you—it’s money you can spend just as if you had received a
$25,000 bonus at work.
But economists’ measure of GDP doesn’t include capital
gains at all—so we have a case of “economists versus common sense.” If we focus on the income approach to GDP, we
include labor income, capital income, and a few adjustments.
“Capital gains” sounds a lot like “capital income,” so why
aren’t capital gains counted as part of capital income?
The short answer is that capital gains can’t be part of capital income because capital gains (or losses) merely reflect a
change in the future profitability of an asset. For example, a
stock price might rise because people believe their company
will earn more profits in the future. And if those people are
correct, those future profits will show up in future GDP.
Of course, stock prices rise and fall for many reasons, and
in a course on asset pricing you can cover that topic. But the
main point holds: a rise in the price of a home, a painting, or
the collection of machines and workers we call “Microsoft”
doesn’t reflect any current-year production. And remember,
GDP is all about current-year production.
Capital gains aren’t part of the government’s measure of
“national income,” but many capital gains are still taxed by
the state and federal income tax.
Production:
Value Added by SteelCo: Somehow, it gets its raw ore for
free, so its value added is just:
CASE STUDY: ROBERT HALL AND
“INTANGIBLE CAPITAL”
Pickupia’s consumers also import $100 worth of other
goods and services from foreign countries.
This is a complete description of the Pickupia economy.
Now, let’s work out the GDP measures based on the expenditure, income, and production methods.
Expenditure:
GDP = C + I + G + total exports − total imports
GDP = (200 on trucks + 100 on imports)
+ 100 + 150 + 50 − 100 on imports = 500
There’s no trick here—just a reminder that C includes all purchases by domestic consumers, regardless of whether those
goods are made here or overseas.
revenue − cost of inputs = 100 − 0 = 100.
Value Added by TruckCo:
revenue − cost of inputs = 500 − 100 = 400
total domestic production = value added by all firms
in the economy = 100 + 400 = 500
According to some economists—most prominently Robert
Hall1 of Stanford— the previous case study is completely
wrong for an economically important reason. Hall shows that
1. Robert E. Hall, “The Stock Market and Capital Accumulation,”
American Economic Review 9, no. 5 (December 2001): 1185–1202.
12 | Chapter 2
under some fairly strict assumptions (inter alia, that a company’s stock price doesn’t reflect either future monopoly profits or changes in the rate of time preference), changes in the
stock price must reflect changes in the size of the nation’s
total stock of capital. That would mean that an increase in
a stock’s price must reflect corporate investment, while
stock price decreases must reflect decay of past corporate
investment.
But clearly, stock prices change too often and by too large
an amount to reflect changes in the physical amount of corporate capital—roughly measured by the I part of GDP—so
Hall argues that many changes in stock price must reflect
changes in the stock of the nation’s “intangible capital.”
Intangible capital might include a corporation’s ability to
create new ideas, its form of corporate organization, its ability to motivate employees to work hard, and many other
things that a corporation can do today to help it to produce
more output in the future. That, after all, is what investment
goods do, right? What we call “investment goods” are just
products we create today in order to reap a benefit down the
road. Perhaps we can think of “intangible investment” as services we create today in order to reap a benefit in the future.
In Hall’s view, then, the rise in the stock market in the late
1990s reflected the market’s guess that modern technology
would enable firms to create much more output in the future
with very few workers— something that sounds quite a bit
like the “new economy” in a nutshell. Of course, since the
NASDAQ (a tech-heavy stock market index) plummeted by
75 percent between 2000 and 2003, the big question is, Where
did all of that intangible capital go? Did hundreds of billions
in “intangible capital” somehow get destroyed?
There is much literature on “intangible capital,” also
known as “organizational capital.” In the future, economists
may find a coherent, practical way to include these important
forms of investment activity in the I part of GDP.
If Hall’s view has merit, then accurately measured GDP
should include some portion of capital gains income. If these
improved measures are even half as volatile as the stock market, then GDP is much more volatile than we currently
believe.
CASE STUDY: “ONE QUARTER OF GDP
IS PERSUASION”
As we saw before, ser vices are about one-quarter of U.S.
GDP. That means that much economic activity isn’t about
making things but about interacting with other people. There
are two other ways of slicing up GDP that might be of
interest:
1. John Wallis and Nobel laureate Douglass North estimate
that “transactions costs, that is, expenditures to negotiate and enforce contracts, rose from a quarter of national
income in 1870 to over half of national income in 1970”
(cited in McCloskey and Klamer, 1995).2
Transaction costs include attorneys’ fees, the cost of
the legal system, most of the cost of running the nation’s
banking and financial systems, auditors, office workers
who do accounts payable and receivable, locks on doors,
security guards, and almost anything else that makes it
possible for you to (1) keep your property, (2) feel enough
trust to transfer your property to someone else, or (3)
receive property from someone else. Transaction costs
aren’t just part of G: as the list above shows, there are a
lot of private-sector purchases involved, so they show up
in C, I, and NX as well. According to Wallis and North,
about half of GDP gets spent just so that we can interact
and exchange with each other.
2. McCloskey and Klamer go further: they estimate how
much of GDP is just devoted to “sweet talk,” or persuasion. Even when a person is providing information, much
of the work isn’t just about giving raw data but about selling the audience on the data. “Why should I listen to
you?” That’s the question persuasion answers. The father
of economics himself noted the importance of persuasion. Adam Smith, in his Lectures on Jurisprudence,
noted, “Everyone is practicing oratory on others through
the whole of his life” (cited in McCloskey and Klamer).
Broadly, McCloskey and Klamer want to count all
human communication that isn’t about providing either
information (for example, telephone operators or college
professors) or commands (such as much of the work of
police officers and CEOs). They count lawyers, actors,
and members of the clergy; three-quarters of the work
done by salespeople, therapists, and job supervisors; and
half the work done by police officers, technical writers,
and nurses. Their rough estimate is the title of their paper:
one-quarter of GDP is persuasion.
CASE STUDY: ACCOUNTING FOR CHANGES
IN PROFITS: THE GREAT RECESSION
AND ITS AFTERMATH
The national income and product accounts are a wonderful
device. Not only are these accounts used to measure an economy’s performance but the accounts can be used to structure
economic analyses—just like the financial accounts of any
business. For example, these accounts can be used to measure savings, the source of wealth creation—where gross sav2. Donald McCloskey and Arjo Klamer, “One-Quarter of GDP Is Persuasion,” American Economic Review 85, no. 2 (May 1995): 191–95.
John Joseph Wallis and Douglass North, “Measur ing the Transaction
Sector in the American Economy, 1870–1970,” in S. L. Engerman and R.
E. Gallman, eds., Long-Term Factors in American Economic Growth (Chicago: University of Chicago Press, 1986).
Measuring the Macroeconomy | 13
Table 1. CORPORATE PROFITS (2014)— DERIVED
FROM TABLE 5.1 FROM THE NATIONAL INCOME
AND PRODUCT ACCOUNTS OF THE UNITED STATES
(BILLIONS OF DOLLARS, AUTHORS’ CALCULATIONS)
Line 4, Table 5.1
Domestic business savings
Line 16, Table 1.12 + Net dividends
Line 4, Table 7.5
+ Corporate business consumption of fixed capital
Equals
= Corporate Profits4
699
860
1467.3
.
.
.
3026.3
22, Table 5.1
Gross Private Domestic
Investment
Line 25, Table 5.1
Line 10, Table 5.1
Line 32, Table 5.1
Gross government investment
− Net government saving
+ Government current account
balance net
− Government consumption of
fixed capital
= Government Budget Deficit
595.8
−799.2
−5
Net Lending or Net Borrowing (–),
NIPAs
+ Capital account transactions
(net) 1
−401.6
Line 17, Table 5.1
Equals
Line 35, Table 5.1
Line 28, Table 5.1
Equals
2860
.
.
.
516.8
873.2
.
.
Current Account Balance
.
−401.1
Line 32, Table 5.1 Government Capital Account
Transactions (net)
.
Line 16, Table 1.12 Net dividends
Line 14, Table 5.1
Line 4, Table 7.5
Equals
Line 9, Table 5.1
.
.
REVIEW QUESTIONS
Noncorporate Consumption of
Fixed Capital
Corporate Profits
= Gross private domestic
investment + Government Budget Deficit
+ Current Account Balance −
Government Capital Account
Transactions (net)
+ Net dividends − Noncorporate
Consumption of Fixed Capital
− Personal saving
− Statistical discrepancy
2229.9
1467.3
762.6
620.2
Line 42, Table 5.1 Statistical Discrepancy
Equals
−5
860
Private consumption of fixed
capital
Corporate business consumption
of fixed capital
Personal Saving
0.5
ment, government purchases, and net exports. Recognizing
that GDP measured in income equals GDP in expenditures,
adding and subtracting government transfers payments to the
expenditure side, and solving for profits yields the following:
Profits = Investment + Government Purchases + Transfer Payments − Wage Taxes − Profit Taxes + Net Exports + Consumption − Wages − Transfer Payments.3 Using the National
Income and Product Accounts of the United States, corporate profits can be similarly accounted for as described
in Table 1. Using data on the right-hand side of the corporate profit equation, Laramie and Mair (2016, see note 3)
show that gross domestic private investment decreased in
2007 through 2009, and, therefore, made negative contributions to the growth in corporate profits, and that these
decreases were dampened by increases in the government
budget deficit. Since the beginning of the economic recovery
in 2009, gross domestic private investment has made positive
contributions to the growth in corporate profits, but these
increases have been significantly dampened by decreases in
the government budget deficit and increases in personal savings. For example, Laramie and Mair show that in 2013, corporate profits increased by 2.42 percent, while investments,
the government budget deficits, and personal savings’ contributions to the growth rate in corporate profits were 5.16 percent,
−18.13 percent (fiscal drag effect), and −12 percent (as
household savings continued to increase through the economic
recovery), respectively.
.
.
−212
3026.3
ings, the sum of private savings, public savings, and foreign
savings equals gross domestic private investment. In addition,
a less well-known use of the national income and product
accounts is accounting for business or corporate profits. For
example, if GDP mea sured in terms of income can be
approximated as the sum of “wages,” “wage taxes,” “profits,” “profits taxes,” and recognizing that GDP in terms of
expenditures is given as the sum of consumption, invest-
1–4. These essentially summarize the entire chapter, so I will
refrain from answering them.
EXERCISES
1. (a) Real GDP 2015 is $16,348.9 billion, nominal GDP 2015
is $17,947 billion—these numbers are different because real
GDP is valued in 2009 (chained) prices whereas nominal
GDP is valued in 2015 (current) prices.
(b) Real GDP 1970 is $4,722 billion; nominal GDP 1970 is
$1075.9 billion.
3. This accounting identity has been attributed to M. Kalecki (1943),
Studies in Economic Dynamics, Allen and Unwin, and Jerome Levy. See
S. J. and D. A. Levy (1983), Profits and the Future of American Society,
New York, Harper and Row. Kalecki, a colleague of Keynes, a progenitor
of early business cycle theory, took this accounting identity and turned it
into a theory of profits by noting that businesses cannot predetermine their
profits, but they can determine how much they spend, and, therefore concluded that profits are determined by profits and augmented by the other
right-hand-side variables.
4. This definition is the same as the BEA’s Table 1.12 definition of corporate cash flow plus net dividends plus capital transfers (net).
14 | Chapter 2
(c) The ratio of real GDP 2015 to real GDP 1970 is 3.46; the
ratio of nominal GDP 2015 to nominal GDP 1970 is 16.68.
(d) The difference between the two ratios can be explained
by inflation factor between 1970 and 2015, reflected in the
growth of the GDP deflator. Letting Pt = GDP deflator in time
t, and Yt = Real GDP in time t, we know that P2015Y2015/
P1970Y1970 = 16.68, and that Y2015/Y1970 = 3.46, so that P2015/
P1970 = 4.82; that is, the GDP deflator has grown by a factor
of 4.82.
Here GDP growth only shows a tiny difference between the
various methods.
6. We’ll use Chad’s shortcut from Section 2.3:
growth in nominal GDP = growth in price level
(a.k.a. inflation) + growth in real GDP
This isn’t exact, as Chad notes, but it’s good enough for our
purposes. This implies
2. This is a worked exercise. Please see the text for the
solution.
growth in nominal GDP − growth in real GDP
= inflation rate.
3. (a) GDP rises by $2 million (final sale price of computers).
(b) GDP rises by the $6,000 commission (capital gains—an
increase in the price of an asset like a home, car, or painting—
are not part of GDP since the asset wasn’t produced that
year. They aren’t part of national income, either).
(c) No impact. This is a government transfer payment, not a government purchase of a good or service. If the government hired
the unemployed and paid them to dig ditches or program in
C++, then their wages would count as a government purchase.
(d) No impact. I rises by $50 million, but NX falls by $50 million, so the two effects cancel out and have no impact on GDP.
(e) U.S. GDP rises by $50 million; NX rises by $50 million.
(Incidentally, this has no impact on European GDP for the
same reason as in part (d)).
(f) GDP rises by $25,000; NX falls by $100,000 but C rises
by $125,000. The store added $25,000 of value to the U.S.
economy, so it shows up in GDP.
All we need to do is add in our three definitions of “growth
in real GDP” and we’ll have our three answers:
4. Real GDP in 2020 in 2018 prices: 5,950; 19 percent growth
between 2019 and 2020
Real GDP in 2018 in 2010 prices: 6,500
Real GDP in chained prices, benchmarked to 2020: 6,483
(Note: output of apples and computers didn’t change between
2018 and 2019, so the average of the Paasche and Laspeyres
zero growth rates is still zero.)
5.
2020
Quantity of oranges
Quantity of
boomerangs
Price of oranges
(dollars)
Price of boomerangs
(dollars)
Nominal GDP
Real GDP in 2020 prices
Real GDP in 2021 prices
Real GDP in chained
prices, benchmarked
to 2021
100
20
2021
105
22
1
1.10
3
3.10
160
160
172
171.9
183.7
171
183.7
183.7
Percent change
2020–2021
5
10
10
3.33
14.8
6.9
6.8
6.85
Paasche: 14.8 percent − 6.9 percent = 7.9 percent
Laspeyres: 14.8 percent − 6.8 percent = 8 percent
Chained: 14.8 percent − 6.85 percent = 7.95 percent
7. (a) Without taking relative price differences into account,
India’s economy is 11.8 percent the size of the U.S. economy
(119 trillion rupees/61)/16.5 trillion = $1.95 trillion/$16.5
trillion.
(b) Given that prices in the United States are higher by a
factor of 3.57 (= 1/.28), and India’s GDP in U.S dollars in U.S
prices equals $1.95 trillion, India’s GDP in U.S. prices is
$1.95 × 3.57 = $6.96 trillion. Taking relative price differences
into account, India’s economy is 42.2 percent of the U.S.
economy ($6.96 trillion/$16.5 trillion).
(c) The numbers are different because many consumer
goods—food, haircuts, and medical visits—are very cheap
in India when you are measuring in U.S. dollars. This is usually true in poor countries. As we’ll see in Chapter 20, when
we look at The Economist’s “Big Mac Index” of exchange
rates, the same McDonald’s hamburger is much cheaper in
poor countries than in rich countries when you compare
prices in U.S. dollars. Wages, rents, and taxes cost less in
poor countries, which makes it cheaper to produce a hamburger or a haircut or even a doctor’s visit.
That means that although India is a very poor country, the
Indian economy is not one-tenth the size of the U.S. economy. It is closer to one-third.
8. (a) $5.68 trillion/$16.2 trillion = 35 percent
(b) ($5.86 trillion/1.307)/$16.2 trillion = 27.7 percent
(c) The numbers are different because many goods are more
expensive in Japan than in the United States.
9. (a) If fewer people have homes, then the average person
must be worse off when it comes to homeownership—after
Measuring the Macroeconomy | 15
all, now people must share homes or live in less desirable
places. People will be working to rebuild things that they
already had before. This is a loss, not a benefit. It is likely
that if there hadn’t been an earthquake, most of the people
rebuilding these lost homes would have been able to build
something new and valuable, rather than rebuilding something old and valuable.
(b) Measured GDP will likely rise—people will want to work
hard and quickly to rebuild homes, or they will pay a high
price to have other workers rebuild their homes. These wages
for workers and purchases of materials (which are mostly
wages for other workers, probably) all show up in GDP.
This question illustrates a famous parable in economics,
the “fallacy of the broken window.” 5 If a person breaks a
shop window, the shop owner must pay to repair that window. If we only look at the direct effect, we will only notice
that the person who broke the window has “created new
jobs” in the windowmaking industry. That’s true, but what
4
5. Henry Hazlitt, Economics in One Lesson, Chapters 1 and 2.
we don’t see is that if the window hadn’t been broken, the
shop owner would have bought a new suit later that week.
Now, he doesn’t get the suit since he must replace his window. So, he would’ve “created new jobs” in the suitmaking
industry, but now he won’t get that new and valuable suit.
Instead, he’ll spend his scarce dollars replacing something
old and valuable.
So, our earthquake is like the broken window: workers
who could have created something new instead must replace
something. It would have been better for citizens if the earthquake had not happened.
CHAPTER 3
An Overview of Long-Run Economic Growth
CHAPTER OVERVIEW
This short chapter lays out the basic facts of the wealth of
nations. Chad makes it clear that higher GDP per person
usually means real improvements in people’s lives—
something that more than a few undergrads might need to
remember.
He also covers the simple and increasingly common
mathematical shortcuts that macroeconomists and finance
professors use to think about growth rates. You’ll get to use
these shortcuts in the growth and inflation chapters, and
they’ll likely come in handy in unexpected places elsewhere—
it’s surprising how often we unconsciously use these
shortcuts.
This chapter shouldn’t take more than an hour to cover—
even with plenty of examples. Push your students to read it
rather than just listen to it, since the stylized facts come back
time and again in the rest of the growth chapters.
3.1 Introduction
Chad starts off with an excellent gimmick: describing a very
poor country and asking the reader to guess which country
it is. It turns out to be the United States of 100 years ago.
There are many ways to emphasize the surprise of economic
progress, and Chad hits a few of them quite quickly: higher
levels of education, greater life expectancy, and vast numbers
of new goods.
When I teach about long-term economic change, I use the
same word that Robert Lucas used repeatedly and without
shame: “miracle.” In fact, he said that the goal of economic
growth research should be to create “a theory of economic
miracles” (“Making a Miracle,” Econometrica [1993]: 253).
When something wonderful that has never happened before
16
in human history begins to happen, not once but repeatedly
in many countries, the word “miracle” seems entirely appropriate. So, you may want to emphasize that over the next four
chapters, your students are going to learn a little about where
miracles come from.
3.2 Growth over the Very Long Run
This section covers the broad sweep of prehistory and history. We learn that prosperity is a new phenomenon, and that
growth in living standards started at different times in different places. Argentina, China, Ghana, the United Kingdom,
Japan, and the United States receive par ticular attention, if
you are looking for countries to highlight with additional data
or online photos.
We also learn that centuries-long peaks and valleys have
occurred in the past—which raises the question of whether
the developed world’s current prosperity could be just
another local maximum. (Two case studies that follow
cover the Roman economy’s golden age and collapse— a
cautionary tale as well as one of the great puzzles of human
history.)
Finally, Chad introduces the term “Great Divergence,”
coined by Harvard’s Lant Pritchett to summarize the enormous new gap in living standards between the world’s richest and poorest inhabitants.
An expanded case study later in the chapter looks at
whether the world really is experiencing a great divergence:
as Steven Parente and Nobel Prize–winner Ed Prescott have
shown in their work, and as Xavier Sala-i-Martin has shown
in separate work, the rapid growth in East and South Asia
throws doubt on the Great Divergence—or at least makes a
strong case for nuance.
An Overview of Long-Run Economic Growth | 17
3.3 Modern Economic Growth
Here, Chad defines growth rates and shows how to calculate
them. In my experience, the growth rate students understand
best is the interest they earn on money at the bank—they probably were taught about that back in elementary and secondary
school—so you may want to start with that intuition and
expand upon it. A sample lecture on interest rates and growth
rates appears later in this chapter of the manual and is further
illustrated in a worked exercise at the end of the chapter.
Through the rest of this section, Chad shows that when
variables are growing exponentially (that is, at roughly constant growth rates), it’s often handier to look at them in a ratio
scale, which economists usually call the log scale. The terms
“ratio scale” and “log scale” are both widely used (Microsoft
Excel uses the term “logarithmic scale” in its graphing tools,
while the term “ratio scale” has tens of thousands of Google
hits), so it is a good idea to familiarize students with them.
The benefit of using a ratio scale, of course, is that constant growth always looks like a straight line. That makes
breaks in trend growth quite easy to see—breaks that would
be invisible if the y-axis were measured the usual way. In
both long-term growth and inflation, we’ll see examples of
such breaks, so a little practice now will pay off quite soon.
The last equation in this section shows how to back out
annualized growth rates from long-term data: it requires taking a fractional exponent, but since most students have either
high-tech calculators or Excel readily available, it’s not technically difficult.
If we start with the constant growth rule
yt = y0 (1 + ḡ)t
and consider a case where we know the start and end values,
but don’t know ḡ, we can rearrange this to get:
country, but since about 1900 the United States has been on
top (tiny Luxembourg’s GDP is actually higher). Other rich
countries are about 25 percent below the U.S. peak.
He also shows that cross-sectionally, rich countries have
grown faster in recent decades (although the relationship isn’t
perfect), and a dozen or so countries have had declines in
GDP per capita since 1960.
3.5 Some Useful Properties of
Growth Rates
Here, Chad runs through the shortcuts that are increasingly
common in intermediate macro texts. It is an exceptionally
transparent section, with plenty of clear examples.
The one thing you may want to do before you begin this is
point out that one of the simplest ideas in economics—the
law of diminishing returns— can’t be explained with straight
lines. The law of diminishing returns—whether we’re talking about the utility from consumption or the efficiency of
production—implies a falling slope as the variable gets
bigger.
The easiest way to talk about diminishing returns ends up
being exponents—in par ticular, exponents between 0 and 1.
You may want to use the example of a square root—which
students probably should recall from algebra courses. Or, you
may want to skip straight to the cube root—which is part of
the Cobb-Douglas production function that figures prominently in Chapters 4 and 5.
Show them that an exponent between 0 and 1 means
diminishing returns, while an exponent of 1 means constant
returns. That way, at least they’ll understand that there’s a reason you’re teaching them these rules about the growth of
variables raised to a power.
(yt / y0)1/t − 1 = ḡ.
Remind your students that because growth is exponential,
if they’re calculating a ten-year growth rate, they can’t just
take the total growth rate (y2020 − y2010)/y2010 = ḡ) and divide
by 10. That will result in a number that’s too big: it’ll include
the compounding.
For example, consider the case where a worker’s wage doubles in ten years. What was the average annual growth rate?
“Common sense” would tell us that it had to grow 10 percent
per year: [(2–1)/1]/10. But the rule of 70 tells us that if something doubles in ten years, considering compounding, it
must’ve grown 7 percent per year—so which is it? An exact
calculation gets us 7.177 percent—pretty close to the rule of
70’s guideline.
3.6 The Costs of Economic Growth
Chad is quite sanguine about the benefits of economic growth
and emphasizes that in the views of most macroeconomists,
the world’s poor need more growth rather than less. He briefly
mentions the Kuznets-type relationship (a U-shaped relationship) between living standards and environmental health:
middle-income countries are the dirtiest. If this relationship
holds, then the way to reduce pollution is for all countries to
be either poor or rich. Chad’s preference between the two
options is rather clear.
3.7 Conclusion and a Long-Run Road Map
3.4 Modern Growth around the World
Here, Chad presents some more stylized facts. The British
used to have the world’s highest GDP per capita of any large
Chad closes with Lucas’s famous quote: “Once one starts
to think about [economic growth], it is hard to think about
anything else.” You may want to consider assigning your
18 | Chapter 3
students a nontechnical essay by Lucas entitled, “The Industrial Revolution: Past, Present, and Future,” available at
https://www.minneapolisfed.org/publications/the-region/
the-industrial-revolution-past-and-future.
SAMPLE LECTURE: INTEREST RATES AND
GROWTH RATES
Suppose you have $100 in 2016 that you want to deposit. You
can earn 5 percent annual interest at the bank (compounded
annually, to make the math easy). That means that at the end
of the year, you’ll have this much money:
y2017 = 100 + 0.05 × 100 = 100 + 5 = 105.
You start off with 100, you earn five bucks in interest, and
you wind up with 105 at the end. If we wanted to turn this
into a general formula, we’d write it this way:
y2017 = y2016 + g × y2016.
This is the general way to know how much money you’ll have
in a year if it grows at g percent per year. There are two ways
we can rewrite this to get some good insights. First, let’s see
how to calculate a growth rate (here, the interest rate) when
you only have information on raw balances. Isolate the g term
on one side to get
(y2017 − y2016)/y2016 = g.
I tell my students this: “The growth rate is the change over
where you started.” With that, it’s always easy to calculate a
growth rate if you have raw data. If you can answer, How
much did this variable change this month/year/century?, and,
What did it start off as?, then you can calculate a percentage
growth rate over that period. Examples include height, income,
employment levels, and crime levels.
You may want to emphasize how the growth rates that
come out of this calculation must be shifted over two decimal places if you want to report them as percentages. For
example, “0.02” becomes “2 percent.” I’ve seen “0.02 percent”
show up as an exam answer all too often.
Some students make these decimal point errors because
they don’t know what they’re doing, while others do so
because they don’t realize that reporting in proper units is the
mathematical equivalent of using good grammar: it’s polite,
and it helps your reader understand you. Badger them a little
now—it’ll save you a lot of corrections on the final exam, and
it may save you thousands if your student becomes an analyst at your bank.
Here is a second way to rewrite the above equation. A little
factoring gets us
y2017 = y2016(1 + g).
With this version, we can easily ask what happens if this
grows at the same percentage rate, g, for many periods.
That’s what Section 3.3.2 does, with an exceptionally clear
example: population growth. Let’s call the starting period
“time 0” and the ending period “time t.” If t = 1, then we’ve
got the previous equation. If t = 2, we have y2 = y1(1 + g) and
y1 = y0(1 + g). That quickly collapses to y2 = y0(1 + g)2.
Emphasize that only the 1 + g gets squared, not the y 0:
many students forget the order of operations, particularly
when exponents are in the mix.
If we let t be any number, rather than just 1 or 2, this yields
something Chad comes back to repeatedly— the constant
growth rule:
yt = y0 (1 + ḡ)t
Note that the “t” means the same thing on both sides of the
equal sign: it is the number of years of growth, when growth
starts in period 0. (Students often have trouble knowing
whether to count periods inclusive or exclusive of the initial
period— Chad’s symmetric “t” notation makes it easy to see
the right answer.)
In Section 3.3.3, Chad teaches what may well be one of the
most useful concepts your students learn this semester: the
rule of 70. If something grows at a rate of X percent per year,
it takes 70/X years to double. So, something that grows at
10 percent per year doesn’t take ten years to double; it only
takes seven.
Whether they’re thinking about retirement planning, economic growth, or inflation, the rule of 70 (or 72) comes in
handy. Any shortcut that gives students a good intuition for
a counterintuitive idea like exponential growth can only be a
good thing.
The hardest thing about the rule of 70 is getting the units
right: if something grows at 5 percent, it takes about 70/5 years
to double, not 70/.05 years.
The second-hardest thing about the rule of 70 is figuring out
what happens when something doubles again and again. If
your standard of living grows 5 percent per year on average (a
reasonable estimate of China’s growth in recent decades), then
living standards double every fourteen years. But how long
does it take for living standards to be eight times higher?
14 years for 2 times.
28 years for 4 times.
42 years for 8 times more than the starting value.
Even with good students, many will think the progression is
2, 4, 6, 8 (so 56 years until octupling) rather than 2, 4, 8, 16.
Humans just seem to have bad intuition for continuous exponential growth. The rule of 70 can help us overcome that.
CASE STUDY: RULE OF 70 VERSUS
THE RULE OF 72
Having finance students, either double majoring or minoring
in economics, in this class is quite common. Many finance
An Overview of Long-Run Economic Growth | 19
professors will “correct” our economics students’ use of the
rule of 70, and, instead, insist that the rule of 72 be used in
class. As a result, students will often ask you which rule they
should use: the rule of 70 or rule of 72. A quick Google of
“rule of 70 vs rule of 72” will generate the sort of explanations given below, if this question comes up in your class.
You can refer to a simple example and give the sort of “it
depends” answer with which economic students have become
familiar. In the table below, various growth rates are provided
in the first column, the actual number of years for an initial
amount to double is provided in the second column, the ruleof-70 approximation is in the third column, the error in the
rule-of-70 approximation is in the fourth column, the ruleof-72 approximation is the fifth column and the rule-of-72approximation error is in the last column. An examination
of this table reveals four conclusions you can share with your
students: (1) For growth rates less than 5 percent, the rule of
70 generates a smaller approximation error than the rule of
72; (2) For a growth rate of 5 percent, the approximation error
is about the same for both rules; (3) For growth rates greater
5 percent, the rule of 72 generates a smaller approximation
error than the rule of 70, and (4) The rule of 72, when 72 is
divided by an integer, generates more whole numbers than
does the rule of 70. In discussing the average (per capita)
growth rates of most countries, we expect growth rates to be
5 percent or less, and the rule of 70 works as the best approximation (in these cases).
Growth Rate
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%
10.00%
Years
Rule
of 70
Rule
of 70
Rule
of 72
Rule
of 72
to Double
70/g
Error
72/g
Error
69.66
35.00
23.45
17.67
14.21
11.90
10.24
9.01
8.04
7.27
70.00
35.00
23.33
17.50
14.00
11.67
10.00
8.75
7.78
7.00
−0.34
0.00
0.12
0.17
0.21
0.23
0.24
0.26
0.27
0.27
72
36
24
18
14.4
12
10.29
9
8
7.2
−2.34
−1.00
−0.55
−0.33
−0.19
−0.10
−0.04
0.01
0.04
0.07
EXPANDED CASE STUDY: PEOPLE VERSUS
COUNTRIES
In Figure 3.7—a typical “convergence”-style graph—it looks
like the rich countries are growing faster than the poor countries, which implies a massive increase in long-term global
inequality. If present trends continue, the rich countries will
tend to pull further away from the poor countries—and the
miracle of compounding really will create unimaginable differences between rich and poor countries.
But in Figure 3.8 Chad points to the famous result, showing that if we measure economic progress on a per-person
rather than a per-country basis, a different picture emerges:
living standards have dramatically risen for the median
human over the past four-plus decades.
Recent market-oriented economic reforms in China and
India apparently caused much of this, which created massive
new middle and lower-middle classes where none existed
before. Tens of millions of people in these countries now live
in a world where owning a car or taking a trip on an airplane
is no longer a dream. And while it might not be reality, either,
at least it’s a real possibility. A quick Googling of “China” or
“India” and “traffic” will yield enough hits to convince your
students that life really has changed in these countries, countries that Westerners used to think of as bicycle nations.
Another part of the explanation for the difference between
Figures 3.7 and 3.8 is this: while there are many countries
that have grown slowly, relatively few people live in those
countries. Africa, the poorest inhabited continent by far, has
quite a low population density, and a quick glance at the map
will confirm that it has many small countries. So, while conventional wisdom might point to “overpopulation” as a reason
for Africa’s plight, Africa has fewer people per square mile
than any inhabited continent except Australia. Thus, Africa
weighs heavi ly when we look at the country level, but it
receives less weight when we look at the human level.
In a footnote, Chad refers to Sala-i-Martin’s Quarterly
Journal of Economics piece, “The World Distribution of
Income: Falling Poverty, and . . . Convergence, Period.” That
article demonstrates that Figure 3.8’s result is quite robust
compared to what you believe about income inequality within
the countries of the world. So overall, Sala-i-Martin’s story
is an optimistic one about the recent past of GDP per capita.
But the future may not be as rosy: as Sala-i-Martin notes, if
Africa doesn’t start growing quickly quite soon, enough
people in Africa will be poor enough that global income
inequality will start rising again.
A broader point to make in this case study is that for most
purposes, what we should really focus on is people, not countries. Thus, good news for India and China, if broadly shared
within these countries, is really good news for one-third of
all of humanity. It’s not just good news for one-ninetieth of
the world’s countries.
EXPANDED CASE STUDY: GROWTH RATES
IN A FAMOUS EXAMPLE
As another opportunity to teach about diminishing returns,
consider asking your students how much GDP rises as
employment rises by 1 percent, 10 percent, or 100 percent.
Fixing this idea in their heads now will create some surprise
when they see that in the Solow model of Chapter 5,
endogenous capital formation takes us from a world of diminishing returns to a factor into a world of constant returns to
scale.
20 | Chapter 3
CASE STUDY: THE ANCIENT ROMAN ECONOMY
Peter Temin’s 2006 article “The Economy of the Early Roman
Empire”1 showed that the successful Roman economy was
built on a few key innovations (cement, arches, and so on)
combined with surprisingly developed labor and financial
markets.
Though the Hollywood stereotype is that Roman success
was built on forced labor, and although slavery was indeed
very common, most public works in Rome were built by paid
labor. Some of those paid laborers were free, some enslaved—
but slaves generally kept their wages. Indeed, Roman slavery, while brutal and contrary to modern ideas of human
rights, was generally less brutal than American slavery.
(Students may be interested to know that a Roman
gladiator—a type of slave—had only about a 10 percent
chance of dying in any given fight. It was expensive to kill
such highly trained performers. Indeed, individual gladiators
had their own separate fan bases, so the owner of a gladiator
wouldn’t want to place his popular investment at such a high
risk of depreciation. But note that if a gladiator has a 10 percent
chance of dying per fight, and he fights 10 times, he only has a
0.910 = 35 percent chance of surviving to an 11th fight. Thus,
gladiator careers were probably quite short, all the same.)
Another important economic fact about the Roman Empire
is that the Pax Romana created a free-trade area throughout
the Mediterranean, something that does not exist today. And
as economists can predict, where there is free trade, there is
specialization and exchange— unique goods were created
throughout the Roman Empire and beyond and were traded
everywhere in developed markets.
CASE STUDY: THE FALL OF ROME AND THE
END OF CIVILIZATION
The widely praised book The Fall of Rome and the End of
Civilization, written in 2006 by archeologist Bryan WardPerkins, shows that once the Roman empire collapsed in
the west in the 400s a collapse in living standards soon
followed. Importantly, the collapse in living standards
apparently occurred after the collapse of government,
after the barbarian invasions.
Some of your better-read students may have heard ideas
such as “empires collapse from within,” “Rome weakened
from within before the barbarians came and destroyed it,”
and the like. That could be true politically— Gibbon surely
thought so—but economically, the records appear quite clear.
The quality of pottery in the homes of the poor, the existence
of tile rather than thatched grass roofs, the long-distance trad1. Peter Temin, “The Economy of the Early Roman Empire,” Journal of
Economic Perspectives 20, no. 1 (Winter 2006): 133–51.
ing networks, all held up until the decades after the forced
retirement of the last western Roman emperor, Augustulus.
Another interesting piece of evidence includes ice core
samples from Greenland. These samples show that during
the period of the western Roman Empire, pollution levels
were quite high—but after the fall of the western empire,
the air become much less sooty. This is more evidence that
something major occurred.
Ward-Perkins says that after the collapse of the western
empire, living standards fell to genuinely prehistoric levels:
things became worse than in the still relatively poor Greek
and Etruscan civilizations. The scale of the calamity was then
unprecedented and perhaps can only be compared to modern North Korea. Even modern Zimbabwe, where land and
capital confiscations have destroyed productivity under
Robert Mugabe’s regime, seems an inadequate comparison.
What is the lesson to take away from this? Let’s at least
consider Ward-Perkins’s conclusion: economic interdependence was a key to Roman prosperity. When the empire fell, it
was more dangerous and more difficult to trade with foreigners, so less trade occurred. That means less specialization
occurred.
It also means that the magic of Adam Smith’s pin factory—
where each person specializes in one small task and lets
others produce other goods and other services—went away.
Western Europeans went to a genuine Robinson Crusoe economy, with every family—or at best every village—for itself.
Surely this quaint, medieval world must have looked charming to an outsider, but it was a very poor world all the same.
REVIEW QUESTIONS
1. The first sustained economic growth occurred in England
in the late 1700s and spread across western Europe over the
next few decades. A thousand years ago, living standards
were quite equal across countries—Robert Lucas summed
it up by saying incomes differed by a factor of maybe two.
Today, living standards differ by a factor of 30, perhaps as
high as 50, across countries.
2. The average forty-year-old today in the United States is
about twice as rich as the same person thirty-five years ago.
This is confirmed by applying the rule of 70: living standards
grew about 2 percent per year, so 70/2 = 35 years.
The text notes that South Korea and Japan have grown at
between 4 percent and 6 percent per capita per year in recent
decades. Let’s take 5 percent as the average. By the rule of
70, that would mean it would take 70/5 = 14 years to double.
At that rate, in twenty-eight years it would quadruple, and in
forty-two years it would octuple. Thirty-five years is in
between—so let’s say incomes have increased by about six
times over that period. (In fact, 1.0535 is about 5.62, so this
rough estimate only slightly overstates.)
An Overview of Long-Run Economic Growth | 21
6. The costs are environmental losses and perhaps the loss
of the simpler lives our ancestors used to live. The benefits
include longer lives for almost everyone, greater health, and
the ability to explore other cultures through travel, reading,
and multimedia.
EXERCISES
1. 2050 is thirty-six years from 2014.
So, if Ethiopian living standards grew as fast as in China or
South Korea—6 percent per year, in thirty-six years people
there wouldn’t be as well off as in Mexico today.
2. (a) 135 billion
(b) Now: 7 billion. One year: 7.21 billion. Two years: 7.43
billion. Ten years: 9.41 billion. Twenty-five years: 14.66 billion. Fifty years: 30.69 billion.
30
25
20
15
10
5
0
8
100
10
1
1
(d)
15 22 29 36 43 50
Year
(c)
5. The growth rate of population plus the growth rate of GDP
per capita equals the growth rate of GDP.
(a) $2,146
(b) $3,060
(c) $6,156
(d) $12,221
35
1
Population in billions of people
4. The rule of 70 gets us in the ballpark of the right answer,
and it makes it easy to remember just how powerful a force
compound growth really is.
The ratio scale helps us to see when something is growing
at a constant percentage rate. In a normal, nonratio scale,
something that grows 2 percent just goes up and up, and it’s
hard to see if the growth rate is constant or not. In a ratio
scale, a constant growth rate is a straight line.
They’ll naturally be used together whenever you’re discussing fairly constant exponential growth: the first takes
care of the simple math and the second takes care of the
simple graphs.
Population in billions of people
3. This is an exciting and active area of research. I’ll let you
try out some answers on your own, but I generally direct students to two things: (a) the development of trade and markets; and (b) a shift in epistemology—the Galileo example.
8
15 22 29 36 43 50
Year
3. This is a worked exercise. Please see the text for the
solution.
4. (a) Age 25: $33,455. Age 30: $44,771. Age 40: $80,178. Age
50: $143,587. Age 65: $344,115.
(b) 5 percent: Age 25: $31,907. Age 30: $40,722. Age 40:
$66,332. Age 50: $108,048. Age 65: $224,625.
(c) 7 percent: Age 25: $35,063. Age 30: $49,178. Age 40:
$96,742. Age 50: $190,306. Age 65: $525,061.
The shift from 5 percent to 7 percent more than doubles the
value of the retirement portfolio by age 65.
$600,000
$10,000,000
$500,000
$1,000,000
$400,000
$100,000
$300,000
Per capita GDP
Balance
22 | Chapter 3
5%
6%
7%
$200,000
$100,000
$10,000
$1,000
$100
$10
$0
0
10
20
(c)
30
40
Age
50
60
70
$1
2000
$1,000,000
$100,000
Balance
$1,000
5%
6%
7%
$100
United States
Canada
France
United Kingdom
Italy
Germany
Japan
Ireland
Mexico
Brazil
Indonesia
Kenya
China
India
Ethiopia
$1
0
10
20
30
40
Age
50
60
70
5.
$1,000,000
Per capita GDP
$100,000
$10,000
$1,000
$100
$10
$1
2000
(a)
2250
1980
2014
Ave. Annual
Growth Rate
29,288
24,716
22,557
20,044
19,912
19,617
19,147
12,845
11,954
5,297
2,249
2,049
1,578
1,169
690
51,958
43,376
37,360
38,083
34,876
45,320
35,574
52,186
15,521
17,459
9,797
2,971
12,514
5,451
1,505
1.70%
1.67%
1.50%
1.91%
1.66%
2.49%
1.84%
4.21%
0.77%
3.57%
4.42%
1.10%
6.28%
4.63%
2.32%
8. This is an essay question.
2020
2040 2060
Year
2080
2100
$1,000,000
$100,000
Per capita GDP
2200
7. Note:
Country
$10
$10,000
$1,000
9. These are all approximations. (Note: students often have
problems with this question because they fail to recognize the
equation as a growth process as the initial value of x and y
are implied as 1.) It might help to remind students of this
point and that gx is 4 percent and gy is 2 percent.
(a) 6 percent
(b) 2 percent
(c) −2 percent
$100
$10
(b)
2100 2150
Year
6. This is a worked exercise. Please see the text for the
solution.
$10,000
(d)
2050
(c)
$1
2000 2020 2040 2060 2080 2100 2120 2140
Year
(d) 3 percent
(e) 4 percent
(f) 0 percent
An Overview of Long-Run Economic Growth | 23
10. (a) (1/3) × gk
(c) Time 0: 1.68. Time 1: 1.73. Time 2: 1.78. Time 10: 2.20.
Time 17: 2.66. Time 35: 4.33.
(b) (1/3) × gk + (2/3) × gl
(c) gm + (1/3) × gk + (2/3) × gl
(d) gm + (1/4) × gk + (3/4) × gl
(e) gm + (3/4) × gk + (1/4) × gl
(f) (1/2) × (gm + gk + gl)
(g) (1/4) × gk + (1/4) × gl − (3/4) × gm
11. (a) Time 0: 2. Time 1: 2.04. Time 2: 2.081. Time 10: 2.44.
Time 17: 2.8. Time 35: 4.
(b) Time 0: 1. Time 1: 1.05. Time 2: 1.1025. Time 10: 1.638.
Time 17: 2.29. Time 35: 5.52.
12. This method always yields a larger answer. That’s because
it forgets about the miracle of compound growth.
For example, if this method is used to measure a variable that
doubles in ten years, it concludes that the variable must have
grown 10 percent per year. In reality, it only grew 7 percent
per year. Seven percent annual growth is all you need to double in ten years—not 10 percent.
13. (a) About 260 years (= ln(51000/300)/ln(1.02))
(b) About $86 (= 51000/(1.03)216). That is not plausible—
people could not have lived on that tiny amount. This is very
strong evidence that the U.S. economy has not grown at a
3 percent rate for 216 years.
CHAPTER 4
A Model of Production
CHAPTER OVERVIEW
This chapter puts the Cobb-Douglas production function
front and center in our study of economic growth. At the
same time, it provides the opportunity to tell your students
an honest yet understandable general equilibrium story as
well as the chance to show how productivity accounting can
give real insight into the reasons why some countries are so
rich while others are so poor.
4.1 Introduction
The real world looks complex and often incomprehensible,
so can we hope to explain it with just a few simple equations?
In many cases, the answer seems to be a surprising yes. Macroeconomists make “toy models” of a complex world and
then check to see if the model matches the real world. We
push a lever inside the toy model (raise the savings rate) and
watch what happens (the economy grows faster for a while,
then slows down). If that matches what seems to happen in
the real world, then we trust the model a bit more. That gives
us some faith that the model will give us good answers even
when we can’t easily compare the model to the data, such as
when a government tries a new economic policy.
In practice, what macroeconomists do is build many different toy models of the economy and then compare them to
some key facts about the real world. This textbook tells us
about the models that have survived that brutal contest.
4.2 A Model of Production
This covers the work horse model of macroeconomics, the
Cobb-Douglas production function. It is widely used at
24
the World Bank, by many branches of the U.S. government and by economists around the world. Chad uses the
explicit form Y = Ā × K1/3 × L 2/3 throughout, so you can dispense with the alphas. He illustrates the constant returns
property before taking us to a simple general equilibrium
setup.
The only real maximization problem to consider is profit
maximization for the firm. Since Chad assumes labor and
capital are in fixed supply, it’s a very straightforward setup.
He assumes no calculus, so you can just hand students the
formula for the marginal product of labor or capital, show that
it’s intuitive, and then move on to the real economics that
grow out of the model.
There are a few immediate payoffs: we can show students
that when markets are competitive, labor productivity determines wages. So when productivity rises, so does the typical
worker’s wage. This goes against a lot of people’s quasiLuddite intuition, so it may be a point worth driving home.
Also, as I show below, you can test the “toy model” by seeing if it gets labor’s share of income right—and the toy model
passes the test pretty well.
Finally, we show students a real general equilibrium
model. In practice, that means we can show them that under
some plausible assumptions, the interest rate and the average wage depend on the shape of the production function
and the supply of production factors. This Solow-type world
depends much less on demand-side forces like animal spirits, preference parameters, and the like. Students often come
to macroeconomics with the folk wisdom that macroeconomic outcomes like wages and prices are about psychology: optimism, pessimism, manias, greed, and the like.
Here, and in the next four chapters, we abstract from these
ideas and focus our energies on the supply-side factors, such
as the supply of savings, the supply of ideas, and the supply
of labor.
A Model of Production | 25
4.3 Analyzing the Production Model
Here, we take the model to the data. First, we check to see if
differences in capital per worker can explain why some countries are richer than others. In other words, was Marx
right—is modern capitalism mostly about “Das Kapital”?
The answer is a clear no. As Lucas long ago noted, capital
differences just can’t do the job. Poor countries have less capital than rich ones, to be sure, but differences in capital
aren’t big enough to explain differences in output per worker
(as long as our model is the right one).
At this point, we turn to the neglected term in the production function, which now rightly takes its place at center
stage: A. If we’re going to stick with this model, then
A—which growth scholar Moses Abramovitz called “a measure of our ignorance”— deserves to be a focus of our attention. And if our model is right, then A—also known as the
Solow residual— differs by a factor of 10 between the richest and poorest countries. This is a massive difference.
4.4 Understanding TFP Differences
Our model seems to be telling us that if we put 100 machines
per worker in Japan and 100 machines per worker in China,
we’re going to get a lot more output in Japan. Why?
This brings us to the list of possible reasons why the residual differs so much across countries. Human capital, genuine technological differences, and market-oriented institutions
all get their due. You likely have well-formed opinions on
which of these is most impor tant, and Chad refers to some
of the leading authors in this literature if you’re looking for
supplemental readings.
SAMPLE LECTURE: EXAMPLES
OF PRODUCTION FUNCTIONS
A good approach for students to become acquainted with the
characteristics of the Cobb-Douglas production function is
to consider what sort of production functions do not fit the
diminishing returns and constant-returns-to-scale assumptions. For example, in Table 4.1 below, we illustrate a linear
production function. With some numerical examples, we easily show that the assumptions of diminishing returns and
constant returns to scale are violated.
Table 4.1
a) Y = bK + cL
hold L constant, L = 0
hold K constant, K = 0
let b = 1
Y
K
MPK
Y
L
MPL
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
1
1
1
1
1
1
1
1
1
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
1
1
1
1
1
1
1
1
1
scale, let b = c = 1
Y
K
L
2
4
8
16
32
64
1
2
4
8
16
32
1
2
4
8
16
32
4.5 Evaluating the Production Model
Our model tells us that differences in living standards are
caused by one of two things: differences in capital per worker
and differences in how efficiently that capital is used. The
data tell us that the second cause is more impor tant. Inefficiency is the cause of global poverty—not a lack of machines
and equipment. This implies that the cure for global poverty
will be found when we find ways to make workers in poor
countries just as efficient as workers in places like Japan,
France, and Canada.
Moreover, we consider a nonlinear production function in
Table 4.2. In this case, each exponent is equal to 1, and again
we show that the diminishing returns and scale assumptions
are violated.
26 | Chapter 4
Table 4.2
Table 4.3
Cobb-Douglas Production Function
Y = ĀKbLc
Y = ĀK L
let A = 1, b = (1/3), c = (2/3)
let A = b = c = 1
hold L constant, L = 1
b c
Hold L constant, L = 1
y=K
Hold K constant, K = 1
Y
K
MPK
Y
L
MPL
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
1
1
1
1
1
1
1
1
1
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
1
1
1
1
1
1
1
1
1
Scale: a = b = c = 1
Y
K
L
1
4
9
16
25
36
49
64
81
100
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
Finally, in Table 4.3 we present the popular ized CobbDouglas production function presented in the textbook. We
easily show that both diminishing returns and constant
returns to scale are evidenced.
hold K constant, K = 1
Y
K
MPK
Y
L
MPL
1
1.259921
1.44225
1.587401
1.709976
1.817121
1.912931
2
2.080084
2.154435
1
2
3
4
5
6
7
8
9
10
1
0.259921
0.182329
0.145151
0.122575
0.107145
0.095811
0.087069
0.080084
0.074351
1
1.587401
2.080084
2.519842
2.924018
3.301927
3.659306
4
4.326749
4.641589
1
2
3
4
5
6
7
8
9
10
0.587401
0.492683
0.439758
0.404176
0.37791
0.357378
0.340694
0.326749
0.31484
Scale
Y
K
L
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
SAMPLE LECTURE: RUNNING SOME
EXPERIMENTS—SHIFTING PARAMERS
Back in Chapter 1, Chad described the research methods of
macroeconomics: (1) document the facts; (2) develop a model;
(3) compare the model’s predictions with the original facts;
and (4) use the model to make other predictions . . . to be
tested. A good calisthenics to prepare students for this process is learning how the pa rameters/exogenous variables
solve the model and how shifts or changes in the parameters
result in changes to the model’s solutions. Shifting the parameters in the production model not only provides an excellent calisthenics but also helps students to distinguish between
the sort of partial equilibrium analysis they are used to in
principles from the sort of macroeconomics to which they
are exposed in this course. To help students learn how
parameter shifts affect the model’s solutions, restate the production model:
(1) Y = Ā K(1/3) × L(2/3);
(2) w = MPL =(2/3)(Y/L);
(3) r = MPK = (1/3)(Y/K);
(4) L = ; and
( 5) K = ,
A Model of Production | 27
where the model has five equations and five unknowns and
three parameters (ignoring the distribution parameters):
Ā, , and . In addition, recall that per capita output can be
written as
(6) Y/L = Ā(K/L)
(1/3)
Once the model is set up, consider a simple numerical example: let Ā = = = 1, and solve the model: Y = Y/L = 1,
w = 2/3, r = 1/3. The solution to the model can be easily illustrated in four graphs: (a) the production function (labor on
the horizontal axis); (b) the per capita output function; (c) the
labor market—where labor demand is the MPL and labor
supply is ; and (d) the capital goods market—where capital
demand is the MPK and capital goods supply is . Given this
basic set up, let each of the parameters change, in turn, holding the other parameters constant, and illustrate graphically
the consequence of each change. For example, let = 2. The
result is Y = 1.59, Y/L = 0.79, w = 0.53, and r = 1.06. Due to
the assumption of diminishing returns, output increases at a
decreasing rate and per capita output decreases. The increase
in labor supply creates an excess supply of labor, this drives
the real wage rate down to 0.53 to eliminate the excess supply of labor, and the increase in the supply of labor makes
capital more productive, increasing capital’s marginal product and increasing the demand for and price of capital goods.
Here students learn that the labor and capital goods markets
are interrelated and that the interrelationships of markets
are commonly studied in macroeconomics. You can repeat
this exercises by resetting labor’s value back to one and letting = 2. You will show that Y/L = 1.26, w = 0.84, and
r = 0.42. In this case, the increase in the supply of capital
creates an excess supply of capital driving down the real
price of capital, while the increase in the supply of capital
makes labor more productive, increasing the demand for
labor while driving up the real wage rate. Next consider the
effect of technological change. Let Ā = 2. The effect is such
that Y = Y/L = 2, w = 1.33, and r = 0.67. Technological change
increases the demand for both capital and labor, driving up
the prices of capital and labor. Finally, consider the problem
of scale. Let both capital and labor double. Because of the
constant returns to scale assumption, Y = 2, Y/L = 1, w = 0.66,
and r = 0.33. To test how well students really understand the
model, you can tease out as to why the prices of labor and
capital are unchanged following a doubling of the inputs.
Most students will still be thinking in the partial equilibrium world, so you will have to be careful to explain that as
the supply of labor increases, capital is more productive,
increasing the demand for capital, and that as the supply of
capital increases, labor is more productive, increasing the
demand for labor (more of those interrelationships [interdependent shift factors]), and these combination of shifts leave
factor prices unchanged.
SAMPLE LECTURE: WAGES IN GENERAL
EQUILIBRIUM
Many macroeconomists think that a nation’s economy is like
this:
Y = Ā × K1/3 × L2/3.
Of course, this is just a model—it’s a major oversimplification of how machines, workers, and technology combine to
make all of the goods and services a real-world economy creates. But let’s see if this oversimplification can take us somewhere interesting.
Here, Y is GDP, also known as “output,” K stands for the
capital (machines, equipment, and tools) in the economy, and
L is the amount of labor—think of it as the number of fulltime workers. What is A? We’ll spend a lot of time thinking
about that later— Chad Jones has had a major impact on the
study of A—but for now, let’s call it technology. If we spend a
moment to look at this equation (and perhaps draw a chart or
two), you can see that more capital creates more output, and
more labor creates more output. And both capital and labor
run into diminishing returns—so more inputs are always better, but the first input is worth more than the hundredth one.
So far, this doesn’t really involve any economics—it’s
more of an engineering story: if I want to make a lot of stuff,
it’s no surprise to hear that I’ll need lots of machines and lots
of workers.
But here’s a uniquely economic question we should care
about: if you create a free-market system, will all of the workers get jobs, and will all of the machines get used? Or is a
free-market system instead likely to create something like the
Great Depression, where lots of workers and machines are
unemployed? And perhaps most importantly, from the typical voter’s point of view, how much will workers earn in a
competitive economy? In the long-run framework, markets
are assumed to operate as if an impersonal auctioneer is present. The auctioneer sets the price to equate quantity demanded
and quantity supplied.
We can use the auctioneer metaphor to answer these questions. Let’s think about this equation as telling us about how
to grow potatoes. To keep it simple, let’s only think about the
plight of workers. What we’d like to know is how much these
workers “sell” for and whether all of them will get sold. Of
course, the price of workers is their wage—think of an annual
wage.
When you studied microeconomics, you learned how
prices get set in perfectly competitive markets: by supply and
demand. But supply and demand is just for finding out the
price of one product (potatoes or workers), assuming that you
already know the price of apples, and workers, and machines,
and everything else in the economy. What happens when you
don’t know the price of anything? What if you just have some
“capital” and some “labor”? Will a competitive market create prices that ensure all the capital and labor get used?
28 | Chapter 4
(Note: To macroeconomists, “capital” generally refers to
machines and equipment [not to stocks and bonds], and
“labor” means any kind of worker [not just unionized workers]. Some students will think “capital and labor” means “the
moneyed classes and the unions”—so a little explanation
might be in order.)
To make things even more concrete, let’s consider a simple
farm economy, with 100 workers and 10 farm owners. Capital and technology are fixed.
First, draw the production function. (Don’t draw the tangency line yet.)
Total output
Production
function
Slope of production
function = Marginal
product of labor =
5,000 potatoes per
year
N ∗ = 100 workers
Number of workers
Let’s assume an inelastic labor supply of 100 workers. Sounds
like a recipe for exploitation, since even if the wage is bare
minimum for survival, all the workers must still work.
ASSUMPTIONS
100 workers working full-time, regardless of the wage
10 farms trying to hire the workers
Diminishing returns to labor
Marginal product of labor: 5,000 potatoes
Start off with everyone working, 10 workers per farm.
Let’s also assume, quite reasonably, that farm owners start
off trying to pay a wage of 3,000 potatoes per year—barely
enough for a person to survive on. They might all meet at the
general store one day and agree to keeping the wage at the
bare minimum. Adam Smith knew these kinds of price-fixing
schemes happened all the time. As he said in Wealth of
Nations: “People of the same trade seldom meet, even for
merriment and diversion, but the conversation ends in a conspiracy against the public.”
So, they agree on a wage of 3,000 per year. What happens
next?
By the time the farm owners get back to their plots of land,
they’ve done the math. Farmer #7, for example, reasons that
if he can hire one more worker at the going wage, he can get
5,000 more potatoes per year, but at a cost of only 3,000 potatoes per year. That’s a 2,000 potato profit per worker! So, he
tries to hire one more worker.
But where can he get one more worker? Only from another
farm! So, he tries to hire a worker away by offering 10 more
potatoes a year—he breaks the general store agreement, but
just this once . . .
Of course, this doesn’t happen just once. Farmer #2 and
Farmer #8 and all the rest get the same idea—they’ll just get
one or two more workers and make a lot of money. But the
only way to get more workers is to bid up the wage just a bit,
so the asking price goes from 3,000 to 3,010 to 3,040 and on
and on—not because the owners are kind to the workers but
because the owners are greedy. The owners fight against each
other—acting in their individual self-interest—and unintentionally raise the wage of workers.
This cycle continues, each farmer bidding up the price of
the cheap workers, until the wage is at 5,000. Why does it
stop at this point? Because once the wage is 5,000, each
farmer is content with the number of workers he or she has—
the benefit of hiring one more worker is just equal to the cost
of hiring one more worker. In economic jargon, we’d say that
at this point, the marginal product of labor (benefit) equals
the wage (cost).
That’s a surprising result, isn’t it? We’re concluding that
in a competitive market, the wage depends on a fact of engineering, agriculture, and the nature of farming. The wage
depends on how many more potatoes you could produce if
you had one more worker. It doesn’t depend at all on how
desperate workers are. It’s this simple: Slope = Wage.
So, we started off with an assumption—fixed labor
supply— that made it look like workers would be ripe for
exploitation. But there are two sides to a fixed number of
workers: it also means that business owners can’t bring in
workers to work at lower wages. The fixed labor supply
puts farm owners in a ruthless competition against each
other, which helps push farm wages far above the starvation level.
EXTRA TOPICS YOU COULD DEVELOP IN THIS LECTURE
A. In this model, how do you increase wages? You do so by
getting rid of workers or by shifting the production function
upward (through extra capital or technology). Both would
make it more valuable to have one extra worker—which
pushes up the wage for every single worker. So, how have
wages increased in the rich countries over the last two centuries? Clearly, through the second method: by shifting the
production function up. Anything that raises the slope raises
the wage. In the real world, we obviously have many more
workers, both in the rich countries and around the world—
but wages have risen over the decades.
A Model of Production | 29
poorest. Only in the very poorest countries is there much of
a difference from the two-thirds value our model predicts.
1.0
0.9
0.8
0.7
Fraction of GDP
B. Why don’t the farm owners stick to the agreement they
made at the general store? Because they are trapped in a prisoner’s dilemma (a concept many students will have seen in
Principles or in an introductory political science class, if
you’re inclined to cover such a topic). Each farm owner hopes
all of the other farm owners are “honorable” enough to stick
to the agreement, but whether the other farm owners stick to
the agreement or not, it’s in each farm owner’s self-interest
to undercut the others. In competitive markets, fi rm/farm
owners are playing a prisoner’s dilemma against each other.
In this course, we’ll often return to the competitive markets
assumption, so it’s worth keeping this in mind as we start off.
0.6
0.5
0.4
0.3
0.2
C. So, am I saying the farm owners aren’t making any profit?
I am saying that they’re not making any profit on their tenth
worker— each farmer is just indifferent between hiring and
firing that last worker. But they’re making profit—or more
accurately, a return on their capital equipment—on each of
the other nine workers. How much of a profit? It’s actually
easy to draw that on this graph. (Just shift the tangency line
down so that it crosses the origin, and it instantly becomes
the “wage bill” line.) Now we can see how much (accounting) profit the farm owner makes on each worker at this wage.
For any given number of workers, the gap between the production function and the wage bill line is the profit the farm
owners would have if they hired that many workers.
CASE STUDY: LABOR’S SHARE OF OUTPUT
ACROSS TIME AND ACROSS COUNTRIES
We’re going to rely heavily on the Cobb-Douglas equation;
in fact, we’re going to treat it as a basic model of a national
economy. If it’s going to be so central, it would be nice to have
some evidence that such a simple equation actually can sum
up something as complex as an entire national economy. So
is there a simple way to check and see if this equation actually makes some good predictions? Yes, there is. As Chad
notes, the Cobb-Douglas model (combined with competitive
markets) has a clear prediction about how much of a nation’s
income goes to the workers and how much goes to the firms.
It’s surprisingly simple, actually. Recall the function:
Y = Ā × K1/3 × L2/3.
Cobb-Douglas makes the following prediction: the exponent
on labor is the fraction of the nation’s income going to workers. That means that in every country in the world, about twothirds of the income should go to the workers, and about
one-third should go to owners of capital. In Chapter 2, he
shows that in the United States, this share has been stable for
decades. But can this possibly be true around the world?
As the chart below shows, the answer is a rough yes. Each
dot represents one country, ranging from the richest to the
0.1
0.0
0
4,000
8,000
12,000
16,000
20,000
Real per capita GDP
Estimates of labor share are derived using an adjustment to
account for income of self-employed persons and proprietors,
combined cross-country and time-series data. The adjustment involves assigning the operating surplus of private
unincorporated enterprises to labor and capital income in the
same proportions as other portions of GDP.1
It turns out that the hardest thing to measure when looking at these data from different countries is the wages of
small-business owners—for the most part individual farmers, people scraping out a bare existence on their own plots
of land. It’s hard to decide how much of a small farmer’s
income should count as “capital income” and how much as
“wage income.” But Gollin sweated the details for years to
create this chart, and in doing so he gave good evidence that
for the vast majority of countries, Cobb-Douglas does a good
job predicting how much of GDP gets paid to workers. Our
simple model passes a big test.
This is a surprising result—after all, we often hear in the
news about how the power of workers seems to rise or fall in
different countries or in different decades. You might think,
for example, that western Europe, with its strong unions,
would have a much higher labor share than the capitalistfriendly United States. But that isn’t the case; all of the
world’s rich countries are right around the magical two-thirds
labor share. Despite these findings, rising wage inequality
remains an important source of increasing income inequality
in the United States. The functional income distribution data
does pick up this factor. (For example, see James Galbraith,
Created Unequal: The Crisis in American Pay [New York:
Free Press, 1998].)
1. Raw data are taken from United Nations (1994). Data on real per
capita GDP are taken from the Penn World Tables, Version 5.6.
Douglas Gollin, “Getting Income Shares Right,” Journal of Political
Economy 110 (April 2002): 458–74.
30 | Chapter 4
CASE STUDY: THE QUALITY OF HUMAN CAPITAL
We all know that just sitting in a classroom isn’t enough to
make a person smart, and it certainly isn’t enough to make a
person rich. But when we talk about “human capital,” it often
sounds like economists are saying that if we can just give students more years of education, we can make those students
more productive. But don’t results matter? Recent work by
Eric Hanushek and Dennis Kimko tell us that results do
matter. Looking at data from dozens of countries, they find
that even after they control for years of schooling and other
important factors, “international math and science test scores
are strongly related to [a nation’s economic] growth.”2
So, can we raise these math and science scores by spending more money on education in poor countries? William
Easterly, in his excellent, readable book The Elusive Quest
for Growth (Cambridge, MA: MIT Press, 2001) points out
just how hard that is to do. In poor countries, it’s hard for
weak governments to keep track of teachers and resources.
That means that teachers often show up half the time or less
(but still get paid), and teachers often sell the books— and
even the pencils!—meant for the students.
After all, just think about how much a box of 50 textbooks
costs—perhaps $2,500—and then consider that the annual
salary of a teacher in a poor country is perhaps even less than
that. How tempting is it for a teacher to sell those books
on the black market (even for $1,000) rather than give them
to the students? The incentives to teach just aren’t there.
The solutions to many of these institutional problems lie
not in macroeconomics but in microeconomics. In your
microeconomics courses you’ll learn more about how to give
people good incentives so that teachers will be more likely
to educate their students.
sus about what those factors mean in practice. Is elementary
education more important than college education? Are political rights more impor tant than property rights in driving
long-run growth? There is even less agreement about whether
we need to include factors beyond these three—factors like
geography, health, and culture.
Xavier Sala-i-Martin, Gernot Doppelhofer, and Ronald
Miller have tried to do something about that: they ran literally millions of statistical tests, using data from 1960 to 2000,
to see which factors consistently predicted good economic
performance over those decades.3 They looked at 67 different factors and ranked them by how well they predicted good
economic per for mance. Let’s look at the top ten—which
surely deserve more attention than we can provide. (Note: I’m
omitting the log 1960 GDP measure, since that’s the convergence variable, which we’ll get into in Chapter 5. The plus
or minus sign indicates whether more of that factor is good
or bad for long-term performance.)
SALA-I-MARTIN, DOPPELHOFER, AND MILLER’S TOP 10
1. Whether a country is in East Asia (+)
2. Amount of K–6 schooling in 1960 (+)
3. Price of capital goods (–)
4. Fraction of tropical area (–)
5. Fraction of a nation’s population living near a coastline
in the 1960s (+)
6. Malaria prevalence in the 1960s (–)
7. A person’s life expectancy in 1960 (+)
8. Fraction of the population that is Confucian (+)
9. Whether a country is in sub-Saharan Africa (–)
CASE STUDY: WHAT PREDICTS GOOD
LONG-TERM ECONOMIC PERFORMANCE?
Economists have put great effort into finding the root causes
behind the massive differences we see in living standards
across countries. After all, Adam Smith’s classic book is
called The Wealth of Nations. Over the centuries, geography,
government policy, health, education, and many more factors
have been proposed. Have economists come to a final conclusion? The answer is simple: no. After decades of work, no
clear consensus has emerged.
So, although most economists will agree that the broad
factors that Chad discusses as drivers of TFP play a big role
in driving income differences—human capital, institutions,
and technological innovations—there is much less consen2. Eric Hanushek and Dennis D. Kimko, “Schooling, Labor-Force Quality, and the Growth of Nations,” American Economic Review 90, no. 5
(December 2000): 1184–1208.
10. Whether a country is in Latin America (–)
Surprisingly, none of the top ten are what we think of as
“institutional” variables, even though the authors used a number of tests to see if various measures of political freedom
and capitalism were good predictors of economic per formance. Those measures largely failed the test. One reason
may be because, through no fault of their own, the authors
didn’t include any communist countries in their database (it’s
hard to get trustworthy long-term data on countries under
communism; perhaps future researchers will go back into the
archives and create good historical data on that).
So, the top ten are mostly about geography, disease, and
longevity, with one bright light shining for human capital:
3. Xavier Sala-i-Martin, Gernot Dopplehofer, and Ronald Miller,
“Determinants of Long-Term Growth: A Bayesian Averaging of Classical
Estimates (BACE) Approach,” American Economic Review 94, no. 4
(September 2004): 813–35.
A Model of Production | 31
K–6 education. Other education measures like level of high
school and college education generally seem to do poorly in
these cross-country comparisons (as Sala-i-Martin said in
1996, “I just ran two million regressions”).4 Perhaps this is
because too much education really can be wasteful for society as a whole, or perhaps because many governments just
don’t know how to give people practical skills beyond reading and writing. Again, it will take good microeconomic
studies to help sort out many of these questions that are so
impor tant for macroeconomic outcomes.
Regarding disease, health, and economic growth, the tropical regions of the planet are hotbeds of health-destroying
infectious diseases. Modern growth researchers such as
David Weil have considered the link between disease and
economic growth and have found that indeed, sick people are
worse workers, and people with short life spans won’t consider education a good long-run investment. Again, the incentive for investing in human capital—which we’ll look at
again later in the text—appears to play a key role.
CASE STUDY: SETTLER MORTALITY AND
EXTRACTIVE INSTITUTIONS
In a famous paper, Acemoglu, Johnson, and Robinson tried to
find out whether institutions really do matter.5 In economics,
it’s often hard to separate cause and effect—do countries have
good economies because they have good governments, or is it
vice versa? Or does high education really cause both? Acemoglu, Johnson, and Robinson try to get around these kinds of
puzzles by looking at what happened to countries after 1492,
when Europeans started colonizing the rest of the world.
Europeans quickly found that some countries were easier
to colonize than others. In some countries—generally those
near the equator—tropical diseases were so deadly that few
Europeans went there. Other places, like North Amer ica,
Australia, and New Zealand, were easier for Europeans to
settle. Acemoglu, Johnson, and Robinson argue that in places
where colonizers died at high rates, Europeans set up “extractive” government institutions—gold mines and slaveryintensive plantations, for example. These institutions required
only a few Europeans to stick around and endure the deadly
environment. In these countries, Europeans generally didn’t
worry about creating incentives for long-term investments in
education or about creating stable property rights. They just
needed enough political power to control the mines, plantations, and other physical sources of wealth—that was all.
4. Xavier Sala-i-Martin, “I Just Ran Two Million Regressions,” American Economic Review 87, no. 2 (May 1997): 178–83.
5. Daron Acemoglu, Simon Johnson, and James A. Robinson, “The
Colonial Origins of Comparative Development: An Empirical Investigation,” American Economic Review 91, no. 5 (December 2001): 1369–1401.
By contrast, in places that were less deadly to Europeans,
many of them created institutions with strong property rights,
personal freedoms, and mass education. This led, they argue,
to centuries of prosperity for these countries. The combination of disease and power relations that existed centuries ago
appears to have had very real implications for living standards hundreds of years later.
REVIEW QUESTIONS
1. Macroeconomic models are also “toy versions” of the real
world that (hopefully) contain the key moving parts to give
us an idea about how the real world really works.
In order to generate real insights, a model of ice cream production only needs a few key features in common with the real
economy. For example, the more workers you have, the more
ice cream you can produce, and if you have more machines,
you can produce more, as well. If you get a new idea for
improving the machines, you can make even more ice cream
with fewer workers.
The model can easily capture positive and diminishing
returns to a factor, constant returns to scale, and increasing
returns to ideas, but it is incredibly simple. It helps us forget
about the (hopefully) extraneous details about real life—the
human emotions, the need for health care and nutrition, the
distribution of income, natural resources, and so forth. Economics has progressed as a science when it has left things out.
Economists are reluctant to add new tools to their toolkit—
we work with the small number of tools we have.
2. Hire workers until the cost of one more worker (in wages)
is just equal to the benefit of having one more worker (in extra
output). When you have few workers, the cost of one more
worker will be much less than the benefit. But as more workers arrive, the benefit of extra workers falls and falls, until
extra workers aren’t worth the cost.
The same argument holds for capital: buy machines until
the marginal rental cost of one more machine equals the marginal benefit of one more machine.
3. An equilibrium occurs when businesses want to hire
exactly the number of workers they have and want to rent
exactly the number of machines they have.
In our model the number of workers and machines in society is fixed (or perfectly inelastic)—so what really adjusts
isn’t the quantity of machines and workers but the price of
machines and workers. Prices adjust so that the quantity supplied equals the quantity demanded. (Later we’ll see that the
price of output—ice cream—adjusts as well, to ensure that
all output gets sold.)
4. This ice cream economy is a closed economy. The only
thing people make is ice cream, and the only thing they consume is ice cream, and although workers and capital owners
32 | Chapter 4
may get paid in money, there’s only one thing they can buy
with that money: ice cream. That means that production (Y)
must equal income (wages and rental payments).
9
More formally, Y = w × L + r × K,
output = total wages + total rental payments
6
(Note: if you want to keep the economy money-free at this
point, the simplest way to do it is to assume that workers and
capital owners get paid in ice cream. All real output, Y, goes
to pay off the factors of production, w × L + r × K. None is kept
for the owners of the firm—and incidentally, none is “sold”
to any separate “public” either— since the workers are the
public.)
8
7
Y/L
Y/L if 3/4
Y/L if 1/3
5
4
3
2
1
0
0
2. (a)
5
10
K/L
15
20
Y/L = K/L
5. Capital differences really are huge across countries, but
our model says that can’t drive big income differences.
Why? Because our usual model assumes that diminishing
returns to capital set in rapidly. That’s what the one-third
exponent on capital means: capital just isn’t that impor tant.
If you run through a simple example, you can show students
that a 1 percent rise in capital causes only a 1/3 percent rise
in output—a small effect.
The case study on labor shares shows that there’s actually
some good evidence of capital not being all that impor tant
in practice.
Y/L
(b)
6. Your guess is as good as mine. But Douglass North’s guess
is probably better than both of our guesses put together.
K/L
Y/L = K/L + A
Y/L = K/L − A
EXERCISES
1. (a) Constant
(b) Increasing
(c) Increasing
(d) Constant
(e) In decreasing returns to scale, the K term has constant
returns, but the K1/3L1/3 term has decreasing returns. When
you put them together, the term with the exponents wins out:
this production function has decreasing returns.
(f) Decreasing returns to scale at the beginning, but moving
toward constant returns as inputs increase (Hint: The Ā term
gives a little extra productivity whose impact diminishes as
K and L rise.)
(g) Increasing returns to scale at the beginning, but moving
toward constant returns as inputs increase
Y/L
(c)+(d)
K/L
3. This is a worked exercise. Please see the text for the
solution.
4. (a) Y = ĀK3/4L1/4
Rule for hiring capital: (3/4) × Y/K = r
Rule for hiring labor: (1/4) × Y/L = w
Capital demand equals capital supply: K = .
Labor demand equals labor supply: L = .
(b) The interesting answers are as follows:
r* = (3/4)Ā × (L/K)1/4 (more workers or ideas equals a higher
interest rate!)
A Model of Production | 33
w* = (1/4)Ā × (K/L)3/4 (more machines or fewer workers equals
higher wages!)
(c) Y/L = Ā × (K/L)3/4
5. (a)–(c) Please see the table below.
Implied
Capital
Per Capital Per
Pre- TFP to
per
capita
per
capita dicted match
person GDP person GDP
y*
data
United
States
Canada
France
Hong
Kong
South
Korea
Indonesia
Argentina
Mexico
Kenya
Ethiopia
141842
51958 1
1
1
1
128667 43376 0.9071 0.8348 0.9680 0.8624
162207 37360 1.1435 0.7190 1.0457 0.6876
159247 45095 1.1226 0.8679 1.0393 0.8351
120472
41044
53821
45039
4686
3227
7. (a) In the first column, we’re now saying that the United
States is X times richer than a par ticular country. In the second column, we’re saying that capital differences alone make
the United States Y times richer than that country. In the third
column, we’re saying that TFP differences alone make the
United States Z times richer than that country.
(b)
34961 0.8493 0.6729 0.9470 0.7105
9797
20074
15521
2971
1505
0.2893
0.3794
0.3175
0.0330
0.0227
0.1886
0.3864
0.2987
0.0572
0.0290
0.6614
0.7239
0.6822
0.3209
0.2833
0.2851
0.5337
0.4379
0.1782
0.1022
(d) As the text says, differences in TFP (“technology,” “ideas,”
“residual”) are bigger than differences in capital in driving
income differences. K/L differences are big, but in our model,
capital runs into diminishing returns quickly, so it can’t
matter that much.
6.
Implied
Capital
Per Capital Per
Pre- TFP to
per
capita
per
capita dicted match
person GDP person GDP
y*
data
United
States
Canada
France
Hong
Kong
South
Korea
Indonesia
Argentina
Mexico
Kenya
Ethiopia
Problems 5 and 6 are useful in showing students how a
choice we make early on—the choice of exponent—has a big
impact down the road when we try to draw conclusions from
the model. Assumptions matter.
141,842 51,958 1
1
1
1
United States
Canada
France
Hong Kong
South Korea
Indonesia
Argentina
Mexico
Kenya
Ethiopia
Per capita
GDP
Predicted
y*
1.00
1.20
1.39
1.15
1.49
5.30
2.59
3.35
17.49
34.52
1.00
1.03
0.96
0.96
1.06
1.51
1.38
1.47
3.12
3.53
Implied TFP
to match data
1.00
1.16
1.45
1.20
1.41
3.51
1.87
2.28
5.61
9.78
(c) America’s bigger capital stock makes it 3.12 times richer
than Kenya. Amer ica’s higher level of TFP makes it 5.61
times richer than Kenya.
(d) America’s bigger capital stock makes it 3.53 times richer
than Ethiopia. America’s higher level of TFP makes it 9.78
times richer than Ethiopia.
8. (a)
128,667 43,376 0.9071 0.8348 0.9295 0.8982
162,207 37,360 1.1435 0.7190 1.1058 0.6502
159,247 45,095 1.1226 0.8679 1.0906 0.7958
120,472 34,961 0.8493 0.6729 0.8847 0.7606
41,044 9,797 0.2893 0.1886 0.3945
53,821 20,074 0.3794 0.3864 0.4834
45,039 15,521 0.3175 0.2987 0.4230
4,686 2,971 0.0330 0.0572 0.0775
3227
1505 0.0227 0.0290 0.0586
0.4779
0.7992
0.7062
0.7379
0.4945
Since we now assume that capital doesn’t run into diminishing returns that quickly, the big capital differences now predict big output differences. With the change in the capital
exponent, the implied total factor productivity coefficient
increases for South Korea, Indonesia, Argentina, Mexico,
Kenya, and Ethiopia.
(b) For the first quarter of 2016, the index was 100.878. The
index from 1965 to 1980 was about 107.5, so labor’s share for
the first quarter of 2016 was about 62.5 percent. The production can still be Cobb-Douglas, however the exponents on
capital and labor have been shifting—with capital getting a
higher share of income and labor getting a smaller share of
income than in the past.
34 | Chapter 4
9. Olson is referring to the fact that even if people are individually smart, they may make poor (or nonsensical) group
decisions. The classic simple example would be Condorcet’s
paradox, which many students will have seen in Principles
of Microeconomics or an introductory political science
course. But Olson is speaking much more broadly: he’s noticing that while individual people are doing the best they can
to be as productive as possible (even going so far as to migrate
to the United States to improve their productivity), entire
countries are foolishly leaving “big bills on the sidewalk” and
staying poor.
This fact puzzles him, since it violates one of economists’
favorite ideas: the Coase theorem. At its broadest level, the
Coase theorem is the idea that if a group of people disagree
about how to divide any valuable item, they should be able
to negotiate a settlement that leaves everyone better off. (I’m
intentionally oversimplifying so that Coase is as relevant as
possible to the topic at hand.) So why can’t people in poor
countries come to some agreement to start acting more like
the rich countries? If they need to change government poli-
cies, culture, or education levels, there ought to be a way to
work things out, according to the (intentionally) naïve view
of the Coase theorem.
Here is an example: countries like Singapore or China,
which grew quickly in recent decades, created enough new
wealth to compensate just about everyone who could possibly be hurt in the transition to prosperity. Few people in those
countries would look back longingly to the “good old days”
when they were poorer. Government bureaucrats, union officials, older workers, schoolteachers—almost all are better off
now that their country has decided to pick up the “big bills.”
Few rational people would stand in the way of that kind of
prosperity—it would be economically irrational. This makes it
all the more puzzling that many countries leave those bills
right there on the sidewalk. They spend time fighting over who
will win and who will lose in the transition to prosperity (Will
I lose my government job? Will I get laid off at the factory?
Will my education in communist economics become worthless?) rather than creating the prosperity in the first place.
This, to Olson, is a puzzle that deserves further study.
CHAPTER 5
The Solow Growth Model
CHAPTER OVERVIEW
Chad lays out the simplest possible version of the Solow
model—with no technology growth and with no population
growth—and works through it extensively. By the end of the
chapter, your students should understand the catch-up principle, which he calls “The Principle of Transition Dynamics.”
This principle helps explain why postwar or newly capitalist
countries grow quickly for a while and then slow down. At
the same time, students will understand why long-term
growth in living standards in capitalist societies can’t really
be explained by growth in capital. In addition, your students
will learn the importance of assumptions in constructing
models, how assumptions generate conclusions, and how
“tweaking” assumptions will modify conclusions.
The math is surprisingly light—and since you’ve already
worked out the model’s microfoundations in the last chapter,
you should find it relatively painless to reach back and convert these “dynamic general equilibrium” results into insights
about how wages (definitely) and interest rates (maybe) should
change over time in the world’s transitional economies.
While this is the longest chapter of the book, it goes back
and forth between model and data in an organic way that
resists a simple breakdown into “model” and “application”
units. I would suggest that you teach the chapter roughly the
same way that Chad builds it out. If you absolutely have to
omit some of this chapter, Sections 1–3, 5, 7, and 8 cover the
“traditional” undergraduate Solow model.
5.1 Introduction
Chad’s introductory quote by Solow can’t be emphasized
enough: many of your students will just be taking this course
to get a grade, and they’ll be grinding through the models to
do okay on the midterm and final. But Solow’s quote—like
many of the methodological comments that Chad slips in
from time to time—might actually help sell your students on
the idea that macroeconomic models really are a way to look
at the real world.
The reason we keep using the Solow model is because it
gives a lot of insights into a lot of different situations. For
example, if we expand “capital” to mean “physical and
human capital,” the Solow model’s main results hold. If we
add in population growth and technology growth and even
some migration, the results still hold. If we open up international capital flows, so that domestic savings needn’t equal
domestic investment—well, things get a little tougher there,
but since the Feldstein-Horioka savings puzzle (that a country’s savings rate tends to be quite close to its investment rate)
is still with us, that seems to be a minor empirical matter,
one that you can omit in this course without feeling too
deceptive.
The key point I emphasize when introducing the Solow
model is that we’re going to use it to explain where the capital stock comes from. Where did all of these machines and
construction equipment and office buildings and factories
come from? And why are they so much more common in
some countries than in others?
We’re also going to learn why a higher savings rate can’t
permanently raise a nation’s growth rate. In the media, we
often hear that Americans spend too much and that if we only
taxed capital less we could grow faster. There may be slivers
of truth in each of these ideas, but can we save our way into
a higher growth rate?
The Solow model says no, and the proof is ingenious:
Solow takes a very simple assumption— diminishing returns
to capital— and shows us that if we believe in the law of
diminishing returns, then we can’t believe that higher savings
cause higher permanent growth.
35
36 | Chapter 5
5.2 Setting Up the Model
Here, Chad sets up the simplest Solow model possible: no
technology growth, no population growth, no government,
and no international trade. He uses the metaphor that output
is “corn,” so that saved corn becomes part of next year’s productive capital stock of seed corn.
PRODUCTION
Here is the Cobb-Douglas production function again, and the
simplified national income identity: GDP = Y = C + I. You may
want to remind students that I is what builds up the capital
stock.
CAPITAL ACCUMULATION
computer chip factory to make investment goods. So, if
society is deciding it wants more computer chips (raising
“s”), it is deciding that it is going to give up some potato
chips, at least in the short run. Ultimately, the savings rate is
simultaneously a decision about private family savings and
about how many people are going to make consumer versus
capital goods.
Students have pressed me on this issue a few times, so a
little general equilibrium hand-waving might be appropriate
on that point. In the simplest case, we’re thinking about a
corn economy, so saving more literally means setting more
corn aside to plant next year. Savings = Investment in a physical sense. For slightly more realistic coverage, consider the
case study below.
5.3 Prices and the Real Interest Rate
This is the big one, in my experience.
Kt + 1 = Kt + It − đKt.
Next year’s capital stock equals last year’s plus your new
investment, minus the amount of capital that wore out. Chad
notes that in practice, đ seems to be about 7 percent
to 10 percent. We saw back in Table 2.2 that depreciation was
roughly $2.8 trillion in 2015, about 15.7 percent of gross
domestic product (GDP)—so a lot of investment effort in the
U.S. economy is devoted to just replacing this worn-out capital
stock. This implies that the productive (i.e., nonhousing) U.S.
capital stock is at least $18 trillion.
The case study that accompanies this subsection conveys
the intuition about what it means to be in a steady state. That’s
because students will see that more capital means more
depreciation. As I note in an expanded case study below, if
you have extremely math-averse students, you could choose
to cover this subsection rigorously and then hand-wave your
way through the rest of the Solow model’s algebra.
LABOR, INVESTMENT, AND THE MODEL SUMMARIZED
Labor supply is mercifully fixed, and as usual, Chad assumes
that people save a fixed percentage of their incomes.
I often point out that the fixed savings assumption seems
to fit the real world quite well: some countries are high savers and some are low savers, but whatever a country’s saving
rate is, it seems to keep it for decade after decade in most
cases. Big tax changes, government reforms, changes in living standards—none seem to have overwhelming impacts on
a nation’s savings rate. That’s why this is a big puzzle for macroeconomists to explain, but fortunately we keep that outside our model.
You may want to give intuition about the fixed savings
rate by telling your students to imagine that a fixed number
of workers go to the potato chip factory every day to make
consumer goods, while the rest of the workers go to the
As a simplifying assumption, the factor prices, the rental
price of capital and the wage rate, are left out of the Solow
model. As we know from the production model, firms adjust
the employment of an input until the marginal product of the
factor equals the factor price. This section of the chapter
introduces students to the concept of the real rate of interest.
The real interest rate is introduced again in Chapter 8 in the
context of the Fisher equation.
Chad defines the real rate of interest as the amount a person can earn by saving a unit of output per year or the amount
that has to be paid if a unit of output is borrowed. The interest rate is termed “real” because the inflation component of
the earnings (or the expense) has been removed from the
interest rate. To illustrate the role of the real rate of interest
as a rental price of capital in the Solow model, Chad returns
to the family farm metaphor. For example, the family farm
may decide to forego consumption of some of its corn (foregone consumption equals savings) and set it aside as next
year’s seed (investment). In this case, the savings becomes
the investment, and the investment becomes the additional
unit of capital, and the marginal product of that capital
becomes the return on savings, the real rate of interest.
5.4 Solving the Solow Model
This is fully covered in a sample lecture to come.
5.5 Looking at Data through the Lens
of the Solow Model
This innovative section speaks for itself—it shows that the
Solow model does a good job explaining the real-world “capital intensity” of different economies, and it shows that TFP
differences matter enormously, just as in Chapter 4. It’s a
The Solow Growth Model | 37
practical undergraduate application of quantitative economic
theory— the kind of thing we should see more of in our
textbooks.
5.6 Understanding the Steady State
By now, you will have likely made this point in a lecture—
that the reason Solow heads to a steady-state living standard
is because diminishing returns to capital run up against a
constant rate of depreciation.
5.7. Economic Growth in the
Solow Model
There is no long-run growth in GDP per capita in the Solow
model. Chad also notes that population growth doesn’t change
the story about GDP per capita (he leaves out the capitaldiluting effect of population growth completely, so you don’t
ever have to mention “n + đ” in your lecture).
5.8 Some Economic Experiments
This section covers two popular experiments showing how
permanent policy changes have temporary effects on GDP
growth rates but permanent effects on GDP levels. A permanent increase in the savings rate (perhaps caused by a fall in
the budget deficit or some investment-targeted tax breaks)
can’t create a permanent increase in the economic growth
rate; diminishing returns are to blame. It is likewise with a
permanent fall in the depreciation rate (perhaps caused by
better weather or cheaper repair methods).
5.9 The Principle of Transition Dynamics
In this section Chad illustrates the principle of transition
dynamics. You may want to consider covering this material
earlier than it appears in the book—perhaps after Section 5.4
or so. In Section 5.4, you can easily show how the growth rate
is related to the difference between the steady capital stock
and actual capital stock due to diminishing returns to capital.
For example, assuming the actual capital stock is below the
steady capital stock, the greater that difference, the greater
the growth rate. This section shows in detail and with intuition how permanent changes in deep Solow parameters have
only temporary out-of-steady-state changes on the growth
rate. A simple Excel spreadsheet simulation, with time on the
x-axis, can do wonders for building this kind of intuition. The
case study provides an easy illustration by comparing highsaving South Korea with the low-saving Philippines. In an
expanded case study below, we look at another transition
dynamic: a capital stock destroyed by war and then quickly
rebuilt afterward.
Chad uses the Solow model to provide a possible explanation for differences in growth rates. For example, different
countries experience different growth rates because of differences in each country’s actual capital stock relative to its
steady capital stock. He then uses this principle to make a
quite remarkable conclusion: since the average poor country
actually grows at the same rate as the average rich country,
then it is likely that both kinds of countries are in similar
positions relative to their steady states. Rich countries appear
to be in high-TFP steady states, while poor countries are in
low-TFP steady states. This gets us looking at deep parameters like TFP levels and savings rates as root causes of
long-term differences in living standards. The average poor
country frankly isn’t on the road to prosperity—fast-growing
China and India are oddities in that regard.
5.10 Strengths and Weaknesses
of the Solow Model
These sections read clearly enough that many students will
be tempted to skip the models and just read these two parts—
let them know that would be a big mistake. In this chapter,
more than most, I’d encourage you to assign quite a few
homework questions so that students will develop Solow-style
intuition, which will serve them well whenever they read
news articles about economic performance in this or another
country.
SAMPLE LECTURE
I can’t emphasize the point Chad makes at the beginning
of Section 5.4 enough: students need to spend some time
working out the Solow model’s steady state for themselves. I
would set aside one hour for this section and some
applications.
If you’ve already spent some time on the “Capital Accumulation” case study, you should remind your students that
more capital means more depreciation. Double the capital, in
fact, means double the depreciation. But since we have diminishing returns, double the capital will not mean double the
new investment goods. Therefore, the more capital goods
society creates, the harder it will become to replace the decaying capital goods. The key endogenous variable in this
model is the capital stock— everything else depends on it—
so let’s focus on the capital accumulation equation:
ΔKt + 1 = Yt − đKt.
The two halves of the right-hand side are the real story here.
Every period, the change in capital comes from the war
between savings (that is, investment) and depreciation. Our
38 | Chapter 5
production function tells us how output (Y) is produced by
capital and labor, so let’s substitute:
ΔKt + 1 = ĀKt1/3
2/3
− đKt.
The right-hand side of the equation gets you the two halves
of the Solow diagram, Figure 5.1. As long as the first term is
larger than the second term, new investment goods are winning in their battle against depreciation, so the capital stock
rises. Chad does a great job explaining the intuition of this
result— his presentation has the feel of well-honed lecture
notes—so let me just mention that a case study below shows
how this diagram can be used to explain the futility of some
foreign-aid programs.
Solving for the steady state takes a little algebra (particularly, it requires some actions with exponents that might be
unfamiliar to your students). As before, we’re in steady state
when ΔK = 0, so we can start with the previous equation
ΔKt + 1 = ĀKt1/3 2/3 − đKt; but in steady state, K is now something special: K*. Solve for K* and you’re done:
K* = ( Ā/đ)3/2 .
This looks a little like “Saddle,” if you’re into mnemonic
devices. Higher depreciation hurts your long-term capital
stock—there’s no vulgar-Keynesian story here where you
can break the capital stock to get richer in the long run—
and everything else helps. Once you plug this into the production function and make it per capita, you get something
simple and familiar:
y* = Y*/L* = Ā3/2( /đ)1/2.
Comparing 5.7 with 5.9 yields some insights: technology
matters more in the second equation, while savings and
depreciation matter less. One reason is that capital just isn’t
all that useful in creating output, since it runs into diminishing returns. Another reason is that (as we’ll see in the endof-chapter exercises) higher technology levels raise GDP in
two ways: directly by making existing capital more productive, and indirectly by raising the steady-state capital stock.
(Note: In the Solow model, steady-state living standards
don’t depend on the population size! Faculty often forget this
point. The steady-state capital stock is endogenous with
respect to labor supply.)
EXPANDED CASE STUDY: AN EXAMPLE
OF CAPITAL ACCUMULATION
Chad’s case study of capital accumulation emphasizes that
“capital stock is simply the sum of past investments.” We’ll
run into many stock-and-flow metaphors, and this is probably
your first chance to use that metaphor this semester. The
river/dam/lake/evaporation metaphor is always a handy one
in this context— evaporation can be a fixed percentage of the
lake’s volume, just like depreciation.
Chad runs through some actual numbers in Table 5.1, but
rather than running it through the real production function,
he picks a hypothetical case: start with a certain capital stock
(1,000 units) and add 200 units of new investment each year.
I find that when students’ algebra is rusty, it helps to run
through the first two rows of calculations by hand. Emphasize that the only “exogenous” variables here are 0 (one
period) and It (all periods).
Let students know that if you give them a table with just
those two facts (and the deep pa rameter of đ the depreciation rate), they should be able to fill out a whole table, for
thousands of periods. In the full Solow model, of course,
we’ll even make It endogenous, since that’s what good economic theory does—it explains more by assuming less.
What we quickly see in Table 5.1 is that as the capital stock
gets bigger every year, so does the amount of depreciation—
an insight that explains why the full Solow model always
heads toward a steady state. More capital means more capital wearing out. If you want to work out this non-Solow
steady state, you may want to call it the “constant units of
investment steady state.” That will contrast with the “constant
percentage of investment steady state” that is key to Solow’s
model.
As we just noted, Chad’s Table 5.1 shows that depreciation
increases as the capital stock rises. But will this continue, or
will it level off at some point?
Focus on Chad’s case, where It stays the same every period.
Just call it I in this case. You can run a simple Excel spreadsheet to chart some numbers, or if you like, you can proceed
directly to the steady state. In this case, a steady state means
that the capital stock will stay fixed at some value we’ll call
K*. So, Kt+1 will equal Kt, which will equal K*, and the change
in K will equal 0.
ΔK = 0 = I − đK*
Solving this for K* yields K* = I/đ So, for our example in
Table 5.1, Kt would rise until Kt equals 200/0.1 = 2,000.
You may want to have the students see how K* is impacted
by a rise in I or a fall in đ The fall in đ will have an especially large impact on K*.
So here, you can get many of the Solow model’s insights
at a low cost. This is a reminder that any change in plans that
you stick with for a long time can have a massive permanent
(“steady state”) impact. It’s also a reminder that the fixed rate
of depreciation drives so much in the Solow model and (presumably) in the real world.
An additional possibility is this: you could integrate the
“Kindness of Strangers” case study (below) into this part of
the lecture to show that a one-time massive gift of capital
will have absolutely no impact on the steady-state level of
capital. More capital means more capital wearing out.
In fact, you cover enough of Solow’s big insights in this
case study that if your students are extremely math averse,
you could just make this the only rigorous, quantitative cov-
The Solow Growth Model | 39
erage of steady states and convergence. After covering this,
you could just hand-wave your way through the rest of this
chapter without too much difficulty.
EXPANDED CASE STUDY: DO IMMIGRANTS CUT
WAGES? ONE-TIME POPULATION INCREASES
IN THE SOLOW MODEL
Chad worked out the model as an aggregate model in Section 5.4, and only at the end did he convert it to a per-capita
model. If you take a moment to divide the equation (5.5) in
the text (ΔKt + 1 = Yt − đKt) by L, the fixed number of workers, you can instantly turn this into a per-capita Solow
model.
That lets us look at Figure 5.1, the Solow diagram, in a new
light. Now, the x-axis is capital per worker, and the y-axis is
savings and depreciation per worker. With these, we can
answer an impor tant question: What happens if a lot of new
workers show up one day? We’ve already seen from the last
chapter that the instant effect (with a fixed capital stock) is
that all the workers get jobs at new, lower wages—you’re just
moving down the fixed demand curve.
But in the long run, something interesting happens: K/L
shifts sharply to the left in the Solow diagram, while the deep
parameters of the model—reflected in the savings and depreciation curves— don’t budge at all. That means that as soon
as the immigrants arrive, they ease the force of diminishing
returns to capital. Now we are back in a world where net
investment is positive. In simpler terms, more labor makes
capital more productive.
That builds up the capital stock until, in the new steady
state, society is right back where it started. The immediate
impact of immigrants is bad for wages but good for investors (since the interest rate rises). The long-term impact of
immigrants is no impact on wages or the interest rate.
The surprising result here is that a big rise in the supply of
labor has no impact whatsoever on the long-run wage. This
result comes from the fact that our principles-level supplyand-demand story is a static model, while the Solow model
is a dynamic model. In the dynamic model, a fall in the wage
draws in more capital, which ironically raises the productivity of workers, raising their wages right back to the preimmigration level.
EXPANDED CASE STUDY: WAR, CAPITAL
DESTRUCTION, AND RECOVERY
Germany, Japan, France, and England all suffered massive
damage to their capital stocks during World War II, and all
grew quickly in the decades after the war. Popular history
gives much of the credit to the Marshall Plan, a U.S. aid plan
for war-ravaged Europe (the classic Orson Welles film The
Third Man gives an idea of just how terrible things were in
immediate postwar Western Europe). Though this aid likely
prevented much suffering, the Solow model reminds us that
whenever you destroy a country’s capital stock, as long as the
deep parameters haven’t changed—as long as the savings and
depreciation rates, and the level of technology are the same
as before the war—then the economy will grow quite quickly
and will converge to its old steady state.
As a rough estimate, that is just what happened after the
war in western Europe. Western Europe was not quite as rich
as the United States before World War II, and decades later,
it is now about 75 percent as productive as the U.S. economy.
The more interesting case is Japan. It was much poorer
than the United States before World War II—about 25 percent
of prewar U.S. output per worker. But after the war, Japan
grew extremely rapidly—growth built on a reputation for
mass-produced low-quality goods. Now Japan is in the same
economic league as western Europe, about 75 percent as productive as the United States. Why the change? That’s a topic
for a book in itself, but Solow tells us to look for big changes
in technology, depreciation rates, and savings rates. You
might ask students to read up on the subject to find out which
of Solow’s ideas explain Japan’s new, higher postwar productivity level.
CASE STUDY: THE KINDNESS OF STRANGERS:
FOREIGN AID IN THE SOLOW MODEL
Let’s return to Figure 5.1, the classic Solow model chart. Consider a country that starts off in steady state, at K*, and let’s
imagine that this country receives a massive gift of foreign
aid, no strings attached, funded by (name of the celebritydriven aid-concert-du-jour). Let’s imagine that all of the aid
is used to buy productive new capital equipment—no money
is wasted, none is funneled into the secret bank accounts of
government officials, and all is right with the world.
At this point, something wonderful happens: the economy
is more productive! Since the capital stock is higher, GDP per
person is higher, and living standards are higher. There’s no
doubt about that whatsoever.
But what will happen to the capital stock over the next few
years? Remember: more capital means more capital depreciation. And at any point to the right of K*, the amount of
capital wearing out is greater than the amount of new investment capital that society is making each year. Machines are
wearing out faster than they can be replaced, and the capital
stock falls. People are still richer than before the gift of aid,
but each year, they are a little less rich than before. The capital stock keeps declining until it is right back at its old level,
K*. Keeping the capital stock at the postgift level was just too
wearying, too expensive.
The lesson is this: a temporary change in the capital stock
only leads to a temporary change in living standards.
40 | Chapter 5
A bonus lesson is that the only way to keep society at the
new higher postaid capital level would be to permanently
change some deep parameter in the model—the savings rate,
the depreciation rate, or the level of technology. That means
that serious economic reform efforts should probably focus
on these kinds of changes, if our goal is to permanently
increase living standards in the world’s poorest countries.
Perhaps a wise society could use aid to buy some time to
make long-lasting changes in those deep parameters.
CASE STUDY: HOW MORE SAVINGS CREATES
MORE CAPITAL IN A MARKET ECONOMY
In a relatively realistic economy, with families making a decision to consume or save, there’s a bit more to the story than
in a world of corn.
As in the real world, let’s assume there are families who
consume and save, and who work as well. When it comes to
saving, let’s omit the middleman of banks and let’s just
remember that all the capital is really owned by the families.
We could make it fancy and assume that families own firms
indirectly through stocks, but it’s easier if they just own the
capital directly and rent the capital out each period to the
firms.
There are two industries in the economy: the consumer
goods industry and the investment goods industry. Both
industries hire workers each period and rent capital each
period. When the savings rate (exogenously) rises, families
are demanding fewer consumer goods. That means fewer
consumer goods get produced, which leaves lots of workers
(and machines) with very little to do.
What do the families do with their extra savings? Well,
they use them to buy investment goods from the investment
goods industry, of course—and the investment goods industry expands, hiring the unused consumer-industry employees
and renting the unused consumer-industry capital stock to
make those new investment goods. The extra savings is
just large enough to pay the extra salary to the extra workers and to pay the extra rent on the extra machines:
Δs × Y = Δs × (wage × L + interest rate × K).
If you want to tell an even more realistic story in which
families own shares of stock, it goes like this: a boost in savings means that revenues fall in the consumer-goods industry.
Families lend their savings to the consumer-good-producing
and investment-good-producing fi rms (perhaps through
banks). Firms in both industries use the funds to place orders
for the only thing they can: extra investment goods, produced
by the investment goods industry. The investment-goods
industry rents (or, with some complication, buys) unused capital from the consumer goods industry for the period, and it
hires the unused consumer-goods workers for the period.
Now, the investment-goods industry has the means to make
the extra investment goods.
Afterward, both the C and I industries are a little more
profitable with their extra capital, so they have the means to
pay a little more interest to the families.
So, just to review, where does that extra savings go? The
firms borrow that extra supply of savings from families, and
the funds get used (directly or indirectly) to pay the wages of
the extra investment-good-producing workers and to pay the
rent on the extra investment-good-producing capital. And
those new investment goods will generate a stream of profits
that will flow as interest payments for the savers. And that
is how the industry expansion is funded by the high savings
level.
In brief, the fall in demand for consumer goods plus the
inelastic labor supply means consumer-industry workers and
capital are going to wind up somewhere, and since there’s
only one place for them to go, they’ll wind up making investment goods. This is worth keeping in mind when students
worry about rising unemployment.
CASE STUDY: HOW LONG IS THE LONG RUN?
An interesting question arises in the Solow model. Suppose
one of the determinants of the steady-state changes, or suppose the economy is out of the steady state. How long, how
many years, does it take for the economy to adjust to the
steady state? One way to give students a sense of this answer
is to simulate the simple Solow model and then allow changes
in the parameters. For example, given that Y* = (Ā)(3/2) ×
( /đ)(1/2) × L, let L = Ā = 1. = đ = .1, show that Y* = 1, show
that if o = 1, Y = đK, and ΔK = 0, and the steady-state condition is satisfied. Now set up the production function, where
Y = Ā × K(1/3) × (2/3), given values of Ā, K, and , Y = Y*. Now
illustrate, using a spreadsheet, some out-of-steady-state situations. Consider the case where K = 2 > K* = 1. Illustrate how
the capital stock and the level of output decline over time.
Given the parameters, the adjustment will take over fifty years
to get within 1 percentage point of the steady-state capital
stock. Consider the case where K = .1 < K* = 1. Through the
same exercise, students will see that adjustment to steady
state will take over seventy years. Now let the parameters ,
đ, Ā, and change. For example, if s increases by 10 percent
from 0.10 to 0.11, show how the capital stock and output
grow over time. Students will learn that adjustment toward
the steady state will take over fifty years with over half of
the adjustment taking place in the first eleven years. Similar
stories can be told for a 10 percent decline in the depreciation rate and a 10 percent increase in the level of employment. For those 10 percent shifts in the parameters, the first
decade captures about half of the adjustment toward the
steady state, but the adjustment toward the steady state goes
on for decades. Given the amount of time involved in adjusting to the steady state, we can reasonably expect parameter
shifts to shock that path over time.
The Solow Growth Model | 41
CASE STUDY: THE GOLDEN RULE OF CAPITAL
ACCUMULATION
Edmund Phelps (1966) asked the question, “What savings
rate maximizes steady state per-capita consumption?”1 The
answer to this question generated what was commonly known
as the “golden rule of capital accumulation.” To illustrate this
rule, using Chad’s version of the Solow model, recall that
steady-state consumption is the difference between steadystate output and depreciation:
C* = Y* − đK*.
Given that the labor supply is fixed in Chad’s model, percapita consumption is simply maximized when
ΔC*/ΔK = 0 = (ΔY* − ΔđK*)ΔK
or
ΔC*/ΔK = 0 = MPK − đ.
To find the savings rate that maximizes per-capita consumption, recall the steady-state condition that sY* = dK*, solve for
the savings rate, s, by substituting the MPK for d, and divide
both sides by Y*; that is,
s* = MPK(K*/Y*),
where s* is the savings rate that maximizes per-capita consumption. If we use our standard production function where
MPK* = (1/3)(Y*/K*), and substitute this into s*, then s* = 1/3.
See the solution to Review Question 4.
REVIEW QUESTIONS
1. Capital accumulation delivers growth. This makes sense
because we can see by looking around ourselves that machines
help us produce more output in the same amount of time. Also,
since our economic system is called “capitalism,” we might
reasonably assume that the reason our economy grows is
because of growth in capital.
However, the law of diminishing returns to capital combined
with the fact that capital depreciates at a constant rate means
that it is hard to keep the capital stock growing. The bigger
the capital stock gets, the harder it is to produce more (diminishing returns), while a larger amount of capital depreciates
(constant depreciation rate). Together, these two forces mean
that capital can’t be the true cause of long-run growth in a
capitalist economy.
2. K6 = 1,469
I6 = 200
1. Edmund Phelps, Golden Rules of Economic Growth (New York: W. W.
Norton, 1966).
đK6 = 147
Change in capital: 53 = 200 − 147
3. The gap is “net investment” or “how much the capital stock
grows this period.”
4. (1 − )Ā3/2( /đ)1/2.
A higher depreciation rate raises steady-state consumption
(since it’s only in the denominator), while a higher technology level increases it (since it’s only in the numerator).
The savings rate is ambiguous. A higher savings rate helps
build a bigger capital stock (good for raising consumption),
but it means there’s less to consume. In a more advanced
course, you will find an optimal savings rate if your goal is
to maximize long-run consumption—and that rate is equal
to the exponent on the capital stock. Since, in our examples,
the exponent is 1/3, the optimal savings rate would be 33 1/3
percent. If it goes above or below that level, steady-state
consumption will be below the maximum possible level.
5. Now we see that technology differences can drive capital
differences. In the last chapter, we saw that high-capital countries were also high-technology countries—but now we
realize that part of the reason for that was because high-tech
economies find it easier to create more capital.
(Note: Our model assumes that the reverse is not true. Dropping capital on an economy does not create high levels of
technology in the Solow framework: it’s a one-way street
running from tech to capital. Some economists focus on the
capital-creates-technology route, but most researchers currently think that’s a less impor tant channel.)
6. If or đ or Ā shift, then a curve shifts. If K or shift,
then you’re moving along the fixed savings and depreciation curves. and Ā shift the savings curve (more of each
pushes it up), while a rise in đ makes the depreciation curve
steeper.
7. The principle of transition dynamics is that any time an
economy is away from the steady-state capital-labor ratio,
forces will naturally return the economy to the steady state.
When the economy is far from steady state, it will move there
quickly, but as it gets closer to steady state, the process slows
down.
The Solow model has this property because of two features:
diminishing returns to capital combined with the constant
depreciation rate. The more capital rich the economy gets, the
harder it is to build those extra units of capital—that’s diminishing returns. Also, the richer the economy gets, the bigger
its capital stock must be—and the more capital you have, the
more capital you have wearing out. So, capital-rich economies
42 | Chapter 5
Thus, a capital-rich economy faces two barriers to building
up the capital stock: diminishing returns and depreciation.
EXERCISES
1. The capital stock will immediately start falling toward its
new steady-state level. At first, the drop will be rapid, but then
it will slow down, and eventually it will come to rest at the
new, lower level.
250
Investment, Depreciation, and Output
must replace enormous amounts of capital each year, and
that eats up a lot of social effort.
200
Low A Y
High A Y
Low A s ∗Y
High A s ∗Y
d ∗K
150
100
50
0
0
50
100
150
200
250
K
(b) Output per person increases as the total economy
approaches a new higher steady-state level of output.
Depreciation Line
Hi s
Yt
Lo s
(c) Here are two graphs that show how the output growth
reacts to the technology transfer. In the first graph, we can see
that output grows at a decreasing rate as the economy transitions to a new (higher) steady state. In the second graph, we
see directly how the growth rate asymptotically approaches
zero as the steady state is approached.
Old K ∗
New K ∗
Time
Before the drop in savings, the capital stock was at Old K*.
Then, people became more impatient, and immediately the
savings curve dropped to “Lo s.” The capital stock does not
make the same immediate drop, but it does start dropping
quickly.
The double-thick dashed line shows the immediate gap
that opens up that year between the massive amount of depreciation and the lower amount of saved capital. That shows
how much the capital stock will fall that year. Clearly, as the
capital stock drops next year, the gap between the high level
of depreciation and the lower level of savings will also drop—
imagine pushing that double-thick dashed line to the left,
and you’ll see that it will be a shorter line. So, the first year’s
drop is the biggest. Society eventually converges to the new,
lower capital stock.
Investment, Depreciation,
and Output
180.00
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
0
10
20
30
Time
40
50
60
0.8
0.7
0.6
0.5
g 0.4
0.3
0.2
0.1
2. (a) Following the technology transfer to China, the total
factor productivity coefficient, Ā, permanently increases. The
increase in Ā has a direct effect of increasing current output
and an indirect effect, whereby the increase in current output increases the level of savings and investment above the
level of depreciation— the resulting change in the capital
stock leads to further changes in output, subject to diminishing returns, as the economy then adjusts to new higher
steady levels.
0
0
10
20
30
Time
40
50
60
(d) A one-time technology transfer stimulates growth, but
the growth rate will diminish to zero as the economy moves
into a new higher steady state. For the economy to continue
to grow, in this case, new technology transfers must be
continuous.
The Solow Growth Model | 43
3. This is a worked exercise. Please see the text for the
solution.
capital-creating earthquake rather than a capital-destroying
one. It has no long-run impact on the steady-state capital stock.
4. This question can be answered in two complementary
ways. First, note that, as in the case study, Chad’s diagrams
always label the x-axis as “capital,” not “capital per worker.”
But in fact, the story doesn’t change at all if we divide everything through by , the labor force. We can keep the same
curves— depreciation line and savings line—and just label
them on a per-person basis. That means that a rise in workers works just like the earthquake: there is a one-time drop
in K/ , but now that’s happening not because K falls but
because rises. The economy starts growing rapidly to build
up K/L to its old level. This assumes, of course, that the
immigrants have the same savings rate as the old citizens.
Second, we can recognize that the capital stock is endogenous with respect to changes in the labor force, and that constant returns to scale are present in production. As a result,
the percent change in the labor force equals the percent
change in the capital stock, which, in turn, equals the percent
change in output, leaving per-capita output unchanged.
(b) The precise answer: Consumption will immediately
increase by 6.3 percent, since that’s (600/500)1/3. But then the
economy will start declining, just like when the savings rate
fell in exercise 1. In the long run, consumption will, of course,
not change at all.
5. A version of this is addressed in a case study. In answering these questions, recall that students will be tempted to
use the growth rules learned in Chapter 3— but as noted
in footnote 5 in Section 3.5, those rules work well for small
growth rates, but not as well for large changes in growth rates,
as in this question. So, if you want to reinforce the growth
rate rules and sacrifice some precision, you might encourage
students to simply apply the growth rate rules to derive the
answers. Thus, both sets of answers are provided below.
(a) The precise answer: Immediately, of course, the capital
stock rises to $400 billion. Before the gift, the economy was
growing rapidly toward its steady state of $500 billion in capital. But now that it’s been given a big boost, and it’s now
closer to the steady state, the capital stock and the economy
will grow more slowly.
Consumption increases by the ratio of the capital stocks,
raised to the 1/3 power (400/300)1/3. That’s 10 percent. So,
consumption increases by 10 percent.
(How did I get this? I looked at the formula for consumption in the Solow model, (1 − ) × Y = (1 − )ĀK1/3L2/3 and
made a before-and-after ratio, a little like in 5.12: (1 − )
Y after/[(1 − ) × Y before]. Since , Ā and are all the same for
“before” and “after,” they cancel out. All that is left in the
ratio is the difference in K.)
The approximate answer: If the growth rules are used, then
recall that the gY = (1/3) × gk , and that gK = 33%, so that
gY = 11%, and gC = gY = 11%.
Long-run consumption will not change at all. That’s a key
insight here: since the savings and depreciation lines haven’t
changed, this is just like the earthquake story—except it’s a
The approximate answer using the growth rate rules:
gy = (1/3) × (20%) = 6.66% = gC
(c) Foreign aid that shifts only the capital stock will only help
an economy temporarily. It will only raise consumer spending temporarily.
We can hope that the Solow model is too simple. Perhaps
a rise in foreign aid could help an economy to raise its level
of technology, or it could be used to educate people in the
value of saving money. If the aid can somehow permanently
raise A or s, then aid could have a permanent impact on living standards and consumer spending.
If we want foreign aid to have a permanent impact, then it
needs to be used to change the deep parameters, not the size
of the capital stock.
6. This is a worked exercise. Please see the text for the
solution.
7. (a)
(b) The average reported in the graph is below the average,
21 percent, reported in the textbook; see footnote 9 in the
textbook.
(c) The investment continues to recover from its trough during the Great Recession, but it is still below the average
levels around 18 percent. In 2015, gross domestic private
investment’s share of GDP was about 16.8 percent.
8. As in exercise 5, students will be tempted to use the growth
rate rules and ignore the warning in footnote 5 in Section 3.5.
If you want students to use the growth rate rules, then you
should allow for both answers.
(a) 21/2 = 1 + gy*, so gy* = 41.42%, or, given that y* = ( /đ).5
(Ā)1.5, gy* = 0.5(gs − gd) + 1.5 × gA = 50%
44 | Chapter 5
(b) 0.9−1/2 = 1 + gy*, so gy* = −5.1%, or gy* = .5(gs − gd) + 1.5 ×
gA = 5%
(c) 1.13/2 = 1 + gy*, so gy* = 15.4%, or gy* = 0.5(gs − gd) + 1.5 ×
gA = 15%
(d) Not at all
(b) For countries that have growth rates greater than that of
the United States, such as China and India, we expect relative per-capita output to rise.
12. This is known, unsurprisingly, as an “AK model.” Much
theoretical work has been done on this kind of growth model.
(a) The slope of the savings line is sA.
(e) Not at all
9. (a) growth rate of GDP = 1/3 × growth rate of capital stock
The key is to substitute the solution for K*, equation 5.7, into
the final footnote equation.
(Note: As Kt goes to zero, the growth of output goes to infinity—so, very poor economies [with decent savings rates and
technology levels] should grow extremely quickly. On the
other end, as Kt goes to infinity [through generous foreign aid,
for example], the growth rate of output can only be as low as
one-third of đ, the depreciation rate [where đ = sY*/K*]. No
matter how rich you get, the only way to grow poorer is to
wear down your capital stock.)
10. Note that the question asks about the growth rate of GDP
per person, not the growth rate of capital.
(a) 3.33 percent
(b) 10 percent
(d) Note that our growth equation is not in per-capita terms,
yet the question asks about growth in per-capita income.
Using our growth shortcuts, we see that the growth rate in
Y/L equals the growth rate of Y minus the growth rate of L.
The right answer using that shortcut is
growth rate in Y = 2/3 of 100% = 66.66%;
growth rate in L = 100%; and
growth rate in Y/L = −33.33%. That’s the immediate fall in
Y/L from the immigrants.
11. (a)
United States
Argentina
Mexico
Brazil
China
India
Uganda
K0
Depreciation Line
Capital
(b) As long as the savings line is higher than the depreciation
line—in other words, as long as sA is greater than đ—then
the economy will grow forever. The dashed line represents
what happens if you start off at some capital stock K0. As you
can see, regardless of where we draw K0, the savings line is
above the depreciation line.
(c) This economy will grow forever, at rate Ā − đ. That is
also the growth rate of the capital stock.
(c) −25 percent
Country
Investment, depreciation
(b) growth rate of Y/L = (1/3) × [(s(Y*/K*) × [(K*/Kt)2/3 − 1]
Savings
Line
Relative
Per- Capita
GDP in
2004
Growth
Rate during
2004–2014
Relative
Per- Capita
Steady- State
GDP
100
27
24
18
12
5
3
2.00
4.00
2.50
5.00
8.00
8.00
4.00
100.00
52.59
28.35
48.93
88.67
36.95
5.84
Proof:
Kt + 1 = Kt + It − đKt (by definition of capital stock),
Kt + 1 = Kt + Yt − đKt (by definition of investment),
Kt + 1 = Kt + ĀKt − đKt (by definition of production function),
(Kt + 1−Kt)/Kt = Ā − đ (moved Kt over,
divided both sides by Kt).
And by our growth shortcuts, we know that since the exponent on Kt is one in the production function, the growth rate
of capital equals the growth rate of output.
CHAPTER 6
Growth and Ideas
CHAPTER OVERVIEW
Here, we discuss a key source of productivity growth: new
ideas. Most textbooks cover this material with a bit of handwaving, but Chad takes the time to outline two simple models that will let students understand the basics of the
economics of innovation. These two models underlie Paul
Romer’s now-classic model of endogenous growth.
The first model shows how an entrepreneur has a strong
incentive to spend money to discover profitable new ideas. At
the same time, this model shows that since idea discovery
creates a (perhaps temporary) monopoly, the invisible hand
fails, and we land in a world of the second best. The second
model illustrates a key trade-off society faces: How many
workers should make ideas rather than final products? The
chapter concludes by pointing out how the Romer and Solow
models together can explain much of what we see, and also
runs through the basics of growth accounting (the last is easily eliminated, if you prefer).
6.1 and 6.2 Introduction and the Economics
of Ideas
We want to understand long-term economic growth, and
Chapter 5 just told us that long-term growth is driven by technological progress, which in turn is (usually? always?)
driven by creation of new ideas. We need to show students
that the economics of ideas works quite differently from the
usual supply-and-demand model that they’re used to. Chad
emphasizes throughout just how different ideas are and
repeatedly uses Romer’s distinction between “objects” (subject to diminishing returns) and “ideas” (subject to increasing returns).
These sections sound a lot like microeconomics, and some
instructors will be tempted to give them short shrift in their
rush to cover the simple general-equilibrium Romer model.
My sense is that you’ll really do your students a disservice if
you omit Sections 6.1 and 6.2, which cover the economics of
ideas at a solid microprinciples level. These are microfoundations that undergraduates can handle.
The idea diagram at the beginning of Section 6.2 probably
deserves a spot at the top of your chalkboard—and it should
probably stay there as long as you’re teaching these two sections of the chapter:
ideas → nonrivalry → increasing returns
→ problems with pure competition
The idea diagram outlines what you’ll need to cover in these
two sections. You probably have your own ideas about how
to cover the fi rst two parts of the idea diagram, so I won’t
spend much time on that.
I like to spend some time talking about actual food recipes
when discussing ideas as recipes. That really drives home the
point that a small set of ingredients can make many different kinds of food. Students probably have some experience
with that. The recipe model raises an interesting question that
you might turn to afterward: Would today’s food taste better
if chefs in the past had been able to effectively patent recipes?
And if not, why not? (Perhaps the fixed costs of recipe innovation are low enough that trade secrets and the warm glow
of creation get us an efficient amount of innovation.)
Another example I use is sand: by combining it with heat
in a certain way, you get glass (a window that actually blocks
the wind); by combining it with heat and the knowledge of
optics, you get corrective eyeglasses; by combining it with a
few other ingredients and a mountain of knowledge, you get
silicon computer chips.
45
46 | Chapter 6
David Landen notes in his book The Wealth and Poverty
of Nations1 that simple lenses to correct nearsightedness
doubled the working life of skilled European craftsmen. This
was especially impor tant in fields involving detail work like
clock making and other fine machinery.
As we’ll see in Chapter 7, when a worker’s career is
expected to last longer, the worker has a stronger incentive
to invest in education. So eyeglasses (and penicillin, and
wheelchair ramps, and anything else that increases the length
of one’s career) may be a driving force behind the higher levels of education we see in the modern world.
In a world driven by inventions, society often faces increasing returns to scale— doubling the inputs creates more than
double the outputs. But how can we fit that fact into this
course when our standard Cobb-Douglas production function
has diminishing returns to each factor (capital, labor) and
constant returns to scale?
Chad does this with a little sleight of hand that I’ve gotten
away with as well: he doesn’t sweat any microfoundational
story about how to aggregate these monopolies into a CobbDouglas form (he does that in his Introduction to Economic
Growth, however). What he does instead is point out that our
Cobb-Douglas form already has increasing returns built into
it—if we open our eyes to the fact that A is really a factor of
production.
I’d run through Chad’s math on this (equation 6.1 and following) and use a couple of simple numerical examples with
students. It pays off well in my experience. Students start to
see quite readily that ideas really are very different. In fact,
this works so well that I might even start off the chapter with
this story— and then talk about nonrivalry and build the
monopoly pill story afterward.
6.3 The Romer Model
Chad presents a true Romer-style “endogenous growth”
model, not Chad’s own, more difficult “semiendogeous
growth” model. In other words, in this book’s model, a change
in the number of researchers impacts the long-run growth rate
of gross domestic product (GDP), not the long-run level of
GDP. He drops capital from the discussion to make it simpler, so the real focus becomes the idea production function:
ΔAt+1 = AtL at.
The number of new ideas in each period depends on how
many ideas already exist (more ideas help create more ideas)
and how many researchers are looking for new ideas (note
the “a” subscript on the labor term). is a fixed parameter on
which we don’t spend any time. The At term is a “standing
1. David Landen, The Wealth and Poverty of Nations (New York: W. W.
Norton, 1999).
on shoulders” effect, based on Sir Isaac Newton’s statement
that “I have seen as far as I have only because I stood on the
shoulders of giants.”
If you just divide both sides by At, you see this section’s
main result: the growth rate of technology depends on the
number of researchers. This gets you thinking about how
many “researchers” the world has (since this is best thought
of as a model of the global stock of productive ideas) and what
a “researcher” is: A lab scientist? An innovative human
resources manager? A novelist imagining new ways for
people to cooperate with strangers? Or most outlandishly, a
macroeconomic theorist?
Our simplified Romer model helps students look at the
world in a new way: they should see workers as either “workers who make goods and services” or “workers who make
new ideas.” Who fits into which category? This should be
able to generate some good Q&A in the classroom.
If you like, you can work through the rest of the math in
this unit—the Romer model is indeed quite elegant, and I love
teaching it in a growth course—but I hear the siren song of
inflation calling over in Chapter 8 and we’ve still got to cover
business cycles, so I’d be in a hurry to get through the rest of
the chapter.
GROWTH VERSUS LEVEL EFFECTS
Some of Chad’s research has been devoted to reminding
people that although the number of researchers in the world
has increased dramatically in recent decades, the world’s economic growth rate hasn’t. This means that the simplest versions of the Romer model—like the one covered above— can’t
strictly be true.
So, perhaps more researchers don’t create permanent faster
growth but instead raise GDP per worker to a permanently
higher level. That would be like a shift in the y-intercept, not
in the slope. More researchers, in the Romer model, would
work just like a higher savings rate in the Solow model: you
grow faster for a while as you rise to your new, better steadystate path. That’s probably more realistic—and that realism
goes by the name “semiendogenous growth.”
6.4 Combining Solow and Romer:
Overview
I think this section’s a pleasure to read since it ties together
so much—and the nice part is, you can probably just handwave your way through it in lecture. Romer tells us about A
and Solow tells us about K; Romer tells us about long-run
growth while Solow tells us about transitions. That’s pretty
much it, right?
The appendix to this chapter combines the two models
rigorously—great fun for theoretically inclined students.
Growth and Ideas | 47
6.5 Growth Accounting
This is another payoff for the time you spent back in Section 3.5 on properties of growth rates. If you practiced with
the case study back in that section, students won’t be surprised to see that a 1 percent rise in capital yields a 1/3 percent
increase in output. Chapter 4’s microfoundations also make
the same point—that the capital share equals the capital elasticity of output. This lets you march through the famous facts
in Table 6.2 about the productivity slowdown and the new
economy. The cynicism of undergrads knows few bounds, so
it may be worth reminding students that, all hype aside, they
really are living in a rare age of rapid technological progress.
6.6–6.8 Concluding Our Study
of Long-Run Growth
The last chapter showed us that we can’t save our way to economic growth. This chapter taught us that we need to worry
about idea creation. So the Solow model takes one hypothesis
off the list, and the Romer model puts ideas right at the top.
Now, we know something about the sources of growth at
the frontier. But why are some countries so much richer than
others? Why isn’t everyone at the frontier? That’s something
on which we’ve spent little time— capital differences explain
a little, but most of the difference is clearly in TFP, the “measure of our ignorance.” The short sections at the end of
Chapter 4 and a few case studies in this manual are all the
time we have to spend on this impor tant issue—an issue that
really demands a course in itself.
The additional readings that Chad recommends are all
excellent, but you probably don’t want to assign your students
demanding reading assignments. If that’s the case, I particularly recommend one of the books on the list—it’s a breezy,
enjoyable read that actually manages to teach a surprising
amount of economics along the way. William Easterly’s book
The Elusive Quest for Growth is an excellent application of
growth models to real-world questions. He has a par ticular
emphasis on micro-based incentive stories. Students seem to
enjoy reading it since it makes economic models feel relevant.
It’s completely nontechnical, but for students who have
already covered these growth chapters, it will make the models come alive. Few students would complain about having
this book added to their syllabus— Easterly’s such a good
writer that it just doesn’t feel that demanding to them.
6.9 Appendix: Combining the Solow and Romer
Models (Algebraically)
Reviewing this appendix will be useful for more advanced
macroeconomics theory students who want more of a feel for
Romer’s model when the capital stock is included. The simplified Romer model is modified by making the production
function Cobb-Douglas and by including Solow’s capital
accumulation equation. That is,
Yt = AtKt1/3Lyt2/3
ΔKt + 1 = Yt − đKt
ΔAt + 1 = AtL at
Lyt + L at =
L at = ,
where the first two equations reflect the modifications to the
model and the latter three equations are the same as in the
chapter. The main difference between this model and
the Solow model presented in Chapter 5 is the treatment
of the total factor productivity coefficient, A. In this variant
of the model, A continuously grows at a rate equal to
as
in the chapter. Given that A continuously grows, output, savings, investment, and capital stock continuously grow. In
short, due to endogenous changes in A, the steady-state capital stock and output change over time.
To illustrate the endogenous nature of long-run growth, the
balanced-growth path is examined. The balanced-growth
path is defined as the situation where all the endogenous variables grow at constant rates. From the Cobb-Douglas production function, the Romer model, and the Solow model, the
growth rates in output, the total factor productivity coefficient, and the capital stock are given as
gyt = gAt + (1/3)gkt + (2/3)gLyt
gAt =
gKt = (Yt /Kt) − đ.
From these three equations, an expression for the balance
rate of growth is easily derived. Assume that gLyt = 0, and if
gKt is constant, then gYt = gKt, so that
gyt = gAt + (1/3)gyt; or : gyt = (3/2)gAt = (3/2)
.
Our results can be compared to the simple (no capital
stock) Romer model presented in the chapter. In the simple
(no capital stock) Romer model, gyt = gAt = L. Now the
growth rate has increased by 50 percent (by a factor of 1.5)
due to inclusion of capital accumulation effects. With capital
accumulation, the effects of technological change on output
are augmented. With technological change, output increases,
which in turn increases savings, investment, and the capital
stock. In short, technological change increases output directly
through the total factor productivity coefficient and indirectly
through changes in income, savings, and investment, and this
process happens continuously because technological change
occurs continuously. As Chad says in the appendix, the capital stock amplifies the effects of technological change on the
output growth rate.
48 | Chapter 6
Now output per person along the balanced-growth path
can be found. To find output per person, derive the capital
stock, K, from gKt = (Yt/Kt) − đ; that is, K = ( /(gy + đ))Y,
where gy = gk, and recall Ly = (1 − ) . Substitution and solving for Y/ yields yt = Yt/ = [s/(gy + d)]1/2(At)3/2(1 − ). This
result shows that both Solow and Romer variables determine output per person (along the balanced-growth path).
Romer’s variables are reflected in the determinants of the
total factor productivity coefficient, At, and in gyt = gAt = L;
Solow’s variables are reflected in the savings (investment)
and depreciation rates: and đ.
With balanced-growth per-capita output determined,
transition dynamics can be revisited. Given the stock of
ideas around the world, we expect all countries’ growth
paths to converge to gyt = (3/2) gAt = 3/2( L;). Shocks to , đ,
, , and , given initial values for the capital stock and the
total factor productivity coefficient, will shock the economy
off its balanced-growth path, creating transition dynamics,
where the economy would eventually transition back to the
balanced rate of growth.
SAMPLE LECTURE: TEACHING THE INCREASING
RETURNS MODEL LIKE A MICROECONOMIST
This follows Section 6.2. Here, as an alternative to Chad’s
presentation, I’ll lay out the charts and diagrams in a microoriented manner, with a focus on average cost curves. This
may be more familiar to most students.
The underlying story here is simple: the pill costs $800 million
to invent, but after that the marginal cost is $10 per pill. Falling
average costs mean that perfect competition is impossible—so
price has to be above marginal cost and the society will produce an inefficiently low amount of pills. This is a metaphor
for many idea-creation industries—and it helps explain why
citizens are so often frustrated by the high cost of prescription
drugs, music, movies, books, and other idea-intensive products
subject to increasing returns.
Average cost per pill
= total cost/quantity
= total fixed cost/quantity + total variable cost/quantity
= $800,000,000/quantity + $10 × quantity/quantity
= $800,000,000/quantity + $10.
This means the average cost curve is a hyperbola with asymptotes at quantity = 0 and average cost = 10. Of course, since
you must make at least one pill for the story to make sense,
I’d only start drawing the curve at quantity = 1.
Average cost of pill
$800,000,010
$400,000,010
$200,000,010
1 2
4
Quantity of pills
COST OF A PILL BY QUANTITY
Quantity
1
2
4
8
...
800,000,000
Infinite
Average Cost
$800,000,010
$400,000,010
$200,000,010
$100,000,010
$11
Approaching $10
By definition, if a company is going to avoid losing money, it
has to set its price at or above average cost. And a quick
glance at the table or the chart will show that the average cost
is always going to be above the marginal cost of $10 per pill.
So in any kind of free market, the price of this pill is going
to be greater than its marginal cost.
We don’t need to worry about whether the price is at average cost or above average cost (that is, whether the firm can
turn its market power into profits). All that matters for our
purposes is that price is greater than marginal cost (P > MC;
an idea that might ring a bell with many students).
Can this be efficient? To answer that, we’ll have to take a
moment to explain what economists mean by “efficient.” If
something is efficient, it means that nobody in society could
be made better off without making at least one person worse
off. (Strictly speaking, this is Pareto efficiency, which Chad
mentions in footnote 6 to the chapter.)
To see if this pill market is efficient, let’s look at an extreme
case where the company produces just one pill—the firm has
looked at the market’s demand for this pill, and it has decided (presumably accurately) that the way to make the most
profit is to sell just one pill to an extremely wealthy person
for, say, $1 billion. It will never make the pill again.
Can this possibly be efficient? Not as long as there are
some people who are willing to pay at least $10 for an additional pill—something that is almost obviously going to be
true. Any pill for which one person, however rich, would pay
a billion dollars is going to be of some substantial worth to
others.
Growth and Ideas | 49
This means that some potential customers could be made
better off (willingly buying the pill for at least $10) without
making anyone else worse off (since the company would get
paid at least the marginal cost for making the pill). Thus,
there are gains from trade that aren’t “getting got.”
Of course, it’s no surprise that a one-pill-for-a-billiondollars equilibrium is inefficient. It just sounds inefficient.
But surprisingly, the same inefficiency is still there even if
the company sells 800 million pills. The price at that point
has to be greater than or equal to $11 per pill. Let’s assume
that there’s a big demand for this pill, so consumers are willingly paying the market price for all 800 million pills. Is this
an efficient outcome? Not if there are some extra customers
who’d buy the pill at a slightly lower price. It’s quite likely
that some more people would buy the pill if the price were
equal to the marginal cost of $10 per pill.
So, for example, if 800 million pills really do get sold at
$12 per pill, and then an extra (marginal) million customers
walk in the door offering to buy one pill each at $10 per pill,
wouldn’t society be better off if the firm sold those extra million pills at $10 each? Yes, it would. The firm would be no
worse off—it’s selling at marginal cost—and those million
consumers would be better off. If you have a chance to make
one party better off without making anyone else worse off,
and you don’t take that chance, then you’re being inefficient,
according to economists. And that’s a bad thing to do.
But that’s what markets like this one do all the time: in
markets where most of the good’s value shows up in ideas,
this is quite common. As I mentioned above, books, music,
movies, and, above all, prescription drugs are all cases where
the market equilibrium is likely to be inefficient since P > MC.
(At this point, I’d continue teaching Problems with Pure
Competition, and then double back for the remainder of
Section 6.2.3; that’s what I’m doing in these notes.)
But it’s not just that this market is inefficient in some
obscure technical sense—if that were the case, then perhaps
some small government intervention could fix the inefficiency. It goes deeper than that: if government tries to make
things efficient by forcing the company to set the price at
marginal cost, then it destroys the company’s ability to innovate. If the company knows it will only get $10 per pill, it
knows it could never pay for the $800-million fixed cost of
inventing the pill in the first place. That means it won’t spend
that $800 million in the first place, and so the pill will never
get invented.
Marginal cost pricing—which is efficient after the pill has
been invented—guarantees that the pill will never be invented in the first place.
To make matters worse, you need to wonder: once the
$800-million pill is invented, why won’t other firms come
along and make the same pill? After all, if it’s just an idea,
anyone can copy the idea and sell the pill for $10 or more. If
the pharmaceutical company expects that to happen, then once
again, the company is unlikely to invest the $800 million to
invent the pill in the first place. Whether the government forces
the company to set a price below average cost, or whether
competition from imitators does the same, we still end up in a
world where the pill never gets invented in the first place.
Solutions? The Founding Fathers of the United States used
one solution: give inventors artificial “property rights” to
their ideas for a limited period— enough time so that they can
charge a high enough price to cover the costs of invention.
That gives inventors a stronger incentive to invent. It’s not a
perfect solution—price is still above marginal cost, and so
too few pills get made—so economists are still looking for
better solutions. These include government subsidies for
research and government-sponsored research done at places
like the National Institutes of Health or at universities across
the country.
Chad spends some time on patents, trade secrets, government funding, and prizes as possible incentives for idea creation. A case study below, building on Chad’s footnote 9,
discusses Michael Kremer’s intriguing idea of patent buyouts
as another solution.
Notice that to teach this unit, you don’t need to cover
monopoly pricing at all. There are no downward-sloping
demand curves, no extra-steep marginal revenue curves,
nothing like that at all. Yes, you need P > MC to show inefficiency, but since P ≥ AC by the nonnegative profit condition,
all you really need to establish is that AC > MC. Chad did that
when he showed that the average cost falls everywhere for a
high-fixed-cost/fixed-marginal-cost product.
(Note: Merrill Goozner’s book The $800 Million Pill
[Berkeley, CA: University of California Press, 2004] provides
an unsympathetic account of the idea discovery process in
the pharmaceutical industry.)
EXPANDED CASE STUDY: WHAT HAPPENS
WHEN POPULATION STARTS FALLING?
Experts predict that this is the century when global population will probably start falling. Without immigration, it would
already be falling in some developed countries. This is good
news for those who think that there are too many humans,
but it is bad news for economic growth if the Romer model
is roughly true.
Why? Because in the very long run, an economy’s rate of
innovation depends on how many researchers there are—in
other words, to find gold, one simply must have people panning for gold. In a world of falling population, there are fewer
people around to pan for the gold of good ideas. Even sophisticated versions of the Romer model have this property (see
Jones’s Introduction to Economic Growth2 for a relatively
2. Charles I. Jones, Introduction to Economic Growth (New York: W.
W. Norton, 2013).
50 | Chapter 6
sophisticated example). A long-run decline in population
ultimately means fewer researchers, fewer new ideas, and—
eventually—no detectable change in GDP per capita
whatsoever.
How can this be? Even if there are only ten people left
in the world, and half of them are full-time researchers, won’t
those five researchers come up with valuable new ideas? Yes,
they will—but compared to the previous stock of knowledge—
the billions of ideas created by their predecessors during the
high-population centuries—their small contributions will be
puny and undetectable by comparison.
At least that’s what the Romer model says. There are a few
reasons why we needn’t worry any time soon: first, much of
the world’s population hasn’t had a chance to join the search
for new ideas. People in the world’s poorest countries could
very well become quite effective idea miners in the future if
new technologies make it easier for them to participate in
the search for knowledge. So, although in today’s world only
OECD residents are likely to become researchers, in the
future, that pool of possible researchers could expand. Thus,
even when global population starts falling, the number of
researchers could just possibly continue rising. Second, the
search for ideas could become so mechanized, so automated,
that the number of researchers could become quite unimportant: In other words, the Romer model’s “idea production function” might depend solely on growth in capital rather than on
growth in workers.
Both of these hopes rely on technological fixes to the
problem of technology creation—so they may pan out (pun
intended) or they may not. In any case, if the Romer model
is anywhere close to the truth, then discussions of long-term
population growth are quite incomplete without a discussion
of the impact of population growth on the growth of ideas.
(Note: The positive link between population growth and
innovation, which became clear with Romer’s endogenous
growth model, has an impor tant informal predecessor in the
work of the late Julian Simon, who argued that human beings
are, as he entitled his major work, The Ultimate Resource.)
REVIEW QUESTIONS
1. Ideas can be copied for free. Objects cannot. Ideas include
food recipes, ideas for inventions, the words in novels or
plays, musical scores, and philosophical concepts. Objects
include cookbooks, printed novels or plays, motorcycles, and
tubas.
2. Nonrivalry exists when one person’s use of a good leaves
just as much of that good for someone else. A nonrivalrous
good can’t be “used up,” since no matter how much it gets
used, there’s still just as much of it around for everyone else.
It leads to increasing returns because once one person pays
the cost of creating it, many people can use it without paying
any extra cost. As the scale grows larger, the average cost of
producing the nonrivalrous good always falls. The more it
gets used, the better.
The standard replication argument fails in this case: having two “idea factories” to produce the same good is inefficient. It’s more efficient to have one person pay the price of
invention once, and then replicate it repeatedly at the same
factory.
National defense is nonrivalrous. One can quibble with the
details, but it costs roughly as much to defend 100 people
from invasion as to defend 100 million people from invasion.
So you might as well just create one military force to defend
everyone.
3. The words themselves—when in the author’s mind—are
nonrivalrous. But it can be expensive to print a hardcover
book. The physical book is an object. The words in the book
are ideas—free to replicate. If the novel is sold at marginal
cost—the cost of just printing another book—then the author
won’t get paid for her effort of writing the book. That gives
her no financial incentive to write the book in the first place.
4. I’ll take equations 6.2 and 6.3 as the “two key production
functions.” In 6.2, Chad notes that “new workers can always
use the same stock of ideas.” That’s increasing returns to
scale in ideas. In 6.3, Chad notes that “it is the same stock of
ideas that gets used in both the production of output and the
production of ideas. Again this is because ideas are nonrivalrous.” So ideas get used twice in the same model: once to
create output and once to create new ideas.
5. Equation 6.7 calls this
. ( , the letter “ ,” and then ).
is how efficiently researchers can use the old stock of ideas
to create valuable new ideas. is the fraction of the workforce
devoted to creating ideas rather than creating goods. is
the size of the overall labor force. More efficient idea creation, a larger fraction of workers searching for ideas, or
more workers in the first place would increase the economy’s overall growth rate.
6. Growth accounting gives us a first look at why a par ticular economy is growing over time. Is it because the economy
added people? Machines? Ideas? How much of each? Growth
accounting taught economists that ideas were much more
impor tant than many wanted to believe— capital wasn’t the
driving force behind “capitalism,” after all—which eventually encouraged economists to build good models of where
ideas come from.
EXERCISES
1. (a) Nonrivalrous
(b) Rivalrous
(c) Rivalrous; the painting itself is a good, not an idea.
(d) Nonrivalrous
Growth and Ideas | 51
(e) Rivalrous; each fish I eat means less for others. If one decided that the number of fish was “close to infinite,” then I’d
be comfortable saying fish are nonrivalrous.
(c) Doubling A0: 188 and 1362
doubling : 88 and 4444 (Remember to change it in the technology growth and output equations!)
2. This is a worked exercise. Please see the text for the
solution.
doubling : 94 and 4747. The best deal so far.
3. Figure 6.2: It doubles every twenty years, so by the rule of
70, we’d guess the growth rate must be 3.5 percent per year.
Figure 6.3: Let’s round a little and say that it almost doubles between 2000 and 2020: that’s a 3.5 percent growth rate.
It really looks like a bit less—3 percent perhaps? After the
break, it doubles every ten years: a 7 percent growth rate.
Figure 6.4 looks like the same story: a bit less than
3.5 percent before the break, and 7 percent afterward.
4. (a) growth in technology = growth in output per
capita =
(b) The figure looks exactly like Figure 6.3: a straight line
with an upward kink in 2030.
(c) Perhaps computers make it easier to weed out the bad
ideas—for example, chemists can now try out new drugs on
a computer before they try them on laboratory animals. The
computer simulations, while not perfect, help weed out useless chemical combinations.
Also, government could change the law to allow new times
of experimentation. In some societies, certain kinds of medical tests involving stem cells or animals might be banned—
in such societies, z might be lower.
5. The planet with more knowledge is always twice as rich.
That’s all. It’s an upward shift. The graph below is on a ratio
scale, so constant growth rates show up as a straight line.
Per capita GDP
Earth
Mars
200
100
doubling : 94 and 4747. The same as doubling z! This is scale
effects at work: more people mining for idea-gold means finding more idea-gold than all of humanity can eventually use.
(d) This is a personal choice.
8. (a)
(b) Intellectual Property Products’ share of GDP has increased
on a trend over the last sixty years. In our textbook model,
this trend can be attributed to three factors: z, the technology
production coefficient—the United States has become more
productive at producing intellectual property; the percent of
the labor force engaged in the production of ideas—the United
States has more workers, given the size of the labor force,
producing intellectual property; and L, the size of the labor
force—the United States’ larger labor force causes more workers to be engaged in the production of intellectual property.
(c) We expect that the growth rate in real GDP and percapita output to have increased. However, we suspect that
long-run growth rates have not increased as intellectual
property’s share of GDP has increased. One possible explanation, as described in the next exercise, is that ideas run
into diminishing returns. The growth rate effects of new
ideas diminish. This result, like in the Solow model, causes
the growth rate to fall as the economy moves to a higher
level of output and per-capita output. For example, if
ΔAt + 1 = At(1/2)LAt, then, by dividing both sides of the equation by At, we will get gAt, = At(−1/2)LAt, and the growth rate
in ideas diminishes as new ideas are discovered.
Time
6. This is a worked exercise. Please see the text for the
solution.
9. (a) Ideas run into diminishing returns: you find the best
ideas first, then you find less useful ideas down the road.
(b) Growth rate of knowledge is the same as before:
7. (a) This economy grows at 2 percent per year:
(1/3000) × 0.06 × 1000 = 0.02
(b) Initial level of output per person: 94. After 100 years: 681.
.
(c) Growth rate of per-capita output is (1/2)
. We use the
growth-rate shortcut and notice that the exponent on At in
the production function is ½.
52 | Chapter 6
(d) yt = [A0(1 +
)t]1/2(1 − )
Per
capita 10
output
y
The only difference from equation 6.9 is the square root
term.
y'
10. (a) Growth rate of TFP: 0.02
1
(b) Growth rate of TFP: 0.0167
(c) Growth rate of TFP: 0.01
MORE EXERCISES (APPENDIX 6.9)
0.1
1. In the Solow-Romer model, the economy has a balance rate
of growth, where the capital stock, output, and total factor
productivity grow at constant rates. A change in the underlying parameters of the model, for example, a change in , đ,
, or can alter the growth rate temporarily, but, as in the
Solow model, due to diminishing returns to capital, the economy will transition back to a balanced rate of growth. The
further the economy is below its balanced-growth per-capita
output, the faster will be the economy’s intermediate term
growth rate.
2. Growth in the Solow-Romer model is faster than in the
Romer model, because the effects of changes in technology
are amplified by changes in the capital stock. Technological
change changes output, the change in output changes savings,
the change in savings changes investment, the change in
investment changes the capital stock, and the change in the
capital stock changes output (subject to diminishing returns).
3. A balanced rate of growth requires that g*Y/L = (3/2)(gA).
(a) A European economy: gA = 0.02 = gY/L − gK/L . So,
g*Y/L = gY/L = 0.03
(b) A Latin American economy: gA = 0.0167 = gY/L − gK/L . So
g*Y/L = 0.015 < gY/L = 0.0167.
(c) An Asian economy: gA = 0.01 = gY/L − gK/L . So, g*Y/L = 0.015
< gY/L = 0.06.
1
6
11
16
21
26
31
36
41
46
51
56
61
66
Time
4. (a)
(b) The immediate effect of the increase in the depreciation
rate is to reduce per-capita income. Given the rate of growth
of the total factor productivity coefficient, per-capita output
continues to grow at the same rate as before.
5. (a) gYt = (4/3)gAt. Given that the marginal product of capital is smaller, the amplification factor is smaller.
(b) yt = Yt/ = [s/gy + d)]1/3(At)4/3(1 − ). Given that the marginal product of capital is smaller, the amplification factor is
smaller.
6. (a) gYt = (1/(1 − α))*gAt. In the text α = 1/3, and (1/
(1 − α)) = 3/2.
(b) yt = Yt/ = [s/gy + d)][α/(1−α)(At)1/(1−α)(1− ). In the text,
/1 − α = (1/3)/(2/3) = 0.5, and 1/(1 − α) = 1/(2/3) = 1.5.
(c) (1/(1 − α)) shows the amplifying or multiplier effect of a
1-percentage-point increase in the total factor productivity
growth rate. A 1-percentage-point increase in the growth rate
today increases output by 1 percentage point today. Subsequently, the increase in the growth rate in output leads to
more savings and more investment and more capital and more
output. Due to diminishing returns to capital, the amplifying effect approaches zero over time.
CHAPTER 7
The Labor Market, Wages, and Unemployment
CHAPTER OVERVIEW
At first glance, you’ll think this is a conventional labor market chapter: it covers shifts in supply and demand, defines
“unemployment,” and notes that Europe and the United States
have different unemployment rates. Many of you will want
to just define the unemployment rate, mention a few key labor
market facts, and move on— and given time constraints, I
wouldn’t blame you if you did just that.
But there are a few extra topics here that many of you will
be interested in covering: job creation and destruction (7.2),
wage stickiness (7.3), the bathtub model (7.4), net present
value and the annuity formula (7.5), and a lengthy discussion
of the college wage premium (7.6). Most likely, your department won’t require students to take either a finance course
or a labor economics course for the economics degree, and
these are practical and impor tant topics.
To students and voters, “the economy” is often indistinguishable from “the job market.” The time you spend here
might not feel like the cutting edge of economic theory, but
it may be the part of the course your students think about
most ten years from now.
7.1 and 7.2 Introduction and U.S. Labor
Market Facts
The key fact to start off with is that real wages have grown
over the past few decades. Chad draws this out by recycling
the fact that the labor share has been stable across the decades:
if gross domestic product (GDP) per capita has grown about
2 percent per year, and if the wage share is a stable two-thirds
of GDP per capita, then wages must have grown about
2 percent per year on average.
(Note: Wages did not grow at two-thirds of 2 percent per
year: if real GDP per capita grows at 2 percent, then its two
subcomponents, wage income and capital income, must have
both grown at 2 percent annually: 2% × (2/3) + 2% × (1/3) = 2%,
for the income shares to be unchanged.)
The second fact Chad emphasizes in Figure 7.1 is that the
fraction of the population employed (the E-Pop, as it’s known)
has also risen over the past few decades, driven by the
increase in women working outside the home. Clearly, since
population itself has risen, the total number of people must
be much higher than in decades past. So, if we want to explain
the labor market’s good long-run per for mance, we have to
explain how wages and employment can both increase. Our
long-run growth model is poised to give us an answer—labor
demand increased because of more capital and technology—
but you can save that explanation for later. The sharp students will figure that out, so let them pat themselves on the
back for now.
After this, Chad defines the unemployment rate without a
lot of fuss. Students often gripe about the unemployment rate
as a measure of labor market slack, perhaps because their
Principles textbooks prime them to do so. They correctly
point out that some people— discouraged workers, as they are
officially known—give up looking for work and leave the
labor force. These folks don’t count as unemployed.
It’s worth noting that the U.S. government keeps track of
these people in their current population survey, and that in
general, throwing the “discouraged workers” into the unemployment rate doesn’t change the overall story that much.
Regardless of how we define things, the ups and downs fall
at about the same time, with peaks in the unemployment rate
occurring during or just after the official end of a recession.
Big shifts in the number of discouraged workers are worth
paying attention to, but in recent U.S. experience there just
53
54 | Chapter 7
haven’t been big shifts among discouraged workers unless
there was a similar shift among unemployed workers. (See
www.bls.gov/news.release/empsit.t15.htm for a comparison of
the U-3 unemployment rate and the U-6 unemployment rate
that counts discouraged workers.)
Even the E-Pop tells us the same overall business cycle
story as the unemployment rate in most cases, as you’ll see
if you compare the two: the E-Pop peaks a bit before the
recession and starts rising after the recovery. And the E-Pop
doesn’t raise any questions about unemployed versus discouraged workers. The fact that the E-Pop and the unemployment rate both tell us just about the same labor market story
gives us some confidence that our labor market measures are
pretty good, all things considered. These data can be found
at http://data.bls.gov/timeseries/ LNS12300000.
Notice that this has been the first time we’ve had any excuse
to talk about economic fluctuations since Chapter 2—and so
you may want to follow Chad’s approach of drawing attention
to the NBER recession dates, noting that recessions seem rarer
and perhaps milder than they used to be—well, that is before
the Great Recession. Planting these facts in the students’ minds
now will mean they have some stylized facts for your business
cycle model to explain in a few weeks.
THE DYNAMICS OF THE LABOR MARKET
Job creation and destruction: students seem to love this stuff;
a case study below builds upon this section. Emphasizing the
importance of churn will remind students that employment
relationships are much like personal relationships: they form,
break up, and then (usually) form again.
Also, Chad briefly mentions the perverse incentive effects
of unemployment benefits—and notes that the unemployed
are quite likely to get jobs, in normal times, a week or two
after their benefits are cut off. Mentioning this fact gives you
a chance to sound like someone who knows something about
the real world—a rare opportunity for a macroeconomist.
7.3 Supply and Demand
Yes, you can cover this in ten minutes. But don’t pass up the
opportunity to mention the economics of wage rigidity, and
take a look at the case study below that ties this in with the
Solow model.
Also, if you’re into definitions, 7.3.4 quickly covers the
classic unemployment = frictional + structural + cyclical equation. This comes in handy if you want to have a clear discussion of European versus American unemployment.
7.4 The Bathtub Model
Students who were taught the injection/leakage approach
to equilibrium in macroeconomics principles will quickly
grasp the bathtub model. In the bathtub model, the water
level in the bathtub is a metaphor for the level of unemployment. The faucet and drain represent job destruction and job
creation. If more water is leaving the bathtub (job creation)
than entering the bathtub (job destruction), then the level of
unemployment decreases. If the number of jobs created
equals the number of jobs destroyed, the water level in the
bathtub is unchanged; the change in unemployment is zero.
If the change in unemployment is zero, the economy must
be in Solow’s steady state, and the unemployment rate must
be at its natu ral level. This conclusion is reached by
ΔU1 + l = Et − Ut; where Et = job destruction (employed
people who lose their jobs), and Ut = job creation (unemployed people who find new jobs). Setting the change in
unemployment to zero, defining Et = L − U, where L is a
fixed labor force and solving for Ut / L gives a measure of
the natural unemployment rate, where Ut / L = / ( + ). The
impor tant implication is that the natural unemployment rate
changes only in response to the job creation and job destruction rates. Government policies intended to reduce job
destruction, for example, the imposition of firing costs, may
backfire by creating disincentives for job creation. Going to
the FRED database and using the average of separations-toemployment ratio as 0.01 and the average of new hires-tounemployment ratio as 0.2 as approximate measures of
and allows us to estimate the natural unemployment rate at
about 4.8 percent.
7.5 Labor Markets around the World
Here you can quickly compare Europe to the United States.
In 7.4, Chad lays out Blanchard’s hysteresis view, which
shows how bad shocks plus bad institutions can explain high
persistent rates of European unemployment. In the United
States, with its more flexible institutions, bad shocks don’t
necessarily mean persistently high unemployment.
This section shows that even if we ignore the ambiguous
unemployment rate measure and look directly at hours
worked per person, Europeans work much less than Americans. Chad mentions Ed Prescott’s preferred explanation:
high European tax rates. In a case study below, I go into some
more detail on this widely discussed explanation.
7.6 How Much Is Your Human Capital Worth?
In order to get students to pay attention to the economics
of human capital, Chad makes it quite personal. He gets students to calculate the net present value of their own future
wages, and he discusses the rising value of a college education. Once students understand net present value (NPV), you
can use this later when discussing the microfoundations of
investment and consumption, if you’re so inclined. You can
also discuss bond prices a bit when you get to monetary
policy— discounting comes up more often than you’d expect.
The Labor Market, Wages, and Unemployment | 55
(Note: In Excel, you can use the “NPV” command to calculate a net present value: just give an interest rate [in the
command itself] and a series of payments, and you’re done.
So, the formula “=NPV(0.05, A1:A50)” would calculate the
net present value of 50 payments located in cells A1 to A50,
discounted at 5 percent. After students have established the
intuition that a dollar today is worth more than a dollar in
the future, the Excel command may be more efficient than
teaching students the text’s annuity formula.
7.7 The Rising Return to Education
Since your students are probably juniors or seniors, you may
think it’s a little late to drive home this lesson if our goal is
to get students to earn a degree. However, at all but the best
schools, attrition rates are quite high, and we all know folks
who, like the title character in the film Tommy Boy, took
seven years to finish college. So, pointing out that a degree
pays for itself quite quickly (on average) could change the life
of one of your students.
The section notes that the college premium is rising and
points to skill-biased technological change and globalization
as explanations. On this point, I like the comment by Daniel
Pink that I saw in the February 2005 issue of Wired magazine: “Any job that can be reduced to a set of rules is at risk.
If a $500-a-month accountant in India doesn’t swipe your job,
Turbo Tax will.”1 That lets students know what kind of job
they shouldn’t be aiming for. And it lets them know what
kind of skill they should be trying to acquire in college: an
ability to come up with creative solutions to new problems.
SAMPLE LECTURE: SUPPLY AND DEMAND
FOR LABOR WHEN IMMIGRANTS ARRIVE
A case study back in Chapter 5 showed that in the Solow
model, a big increase in population has no impact on wages
in the long run. That’s because when new immigrants arrive,
the abundance of workers makes it easier to build new capital goods. That raises the capital-labor ratio right back up to
its old level in the long run.
How does that translate into a supply-and-demand model?
It’s quite simple:
1. The rise in immigrants boosts labor supply, so the supply
curve shifts right. That means more workers and lower
wages. Bad news for the native workers.
2. Since the workers are building extra capital goods, and
since capital makes labor more productive, the demand
for labor increases: firms want more of these capitalenhanced workers. (This contradicts the “common
1. Daniel H. Pink, “Revenge of the Right Brain,” Wired, Issue 13.02,
February 2005.
sense” intuition that machines reduce demand for
workers.)
3. This process continues until the wage is back at its old
level. Notice that unless we had the Solow model’s insights
about the steady-state capital-labor ratio, we would have
no idea whether the new steady state would land us above,
below, or equal to the old wage— one reason to spend
time on the Solow model.
But does anything like that happen in the real world? David
Card and Alan Krueger, in a classic study, showed that the
U.S. economy is amazingly efficient at absorbing new immigrants. The perennial problem with studying the effect of
immigrants on the economy is the same issue social scientists face everywhere: disentangling cause from effect. In
general, in the United States, immigrants—legal or illegal—
tend to be located in the most prosperous parts of the country. New York, Los Angeles, San Francisco, and Boston all
appear to attract immigrants from around the world. But
would wages be even higher without them? Would unemployment rates be lower without them?
Fully addressing this question would take a course in itself,
but Card and Krueger’s Mariel boatlift study gives an intriguing set of answers. During the Car ter administration, Cuban
dictator Fidel Castro, after years of forbidding Cubans from
leaving the country, decided to let anyone leave who could
literally make a boat and start paddling. Tens of thousands
of Cubans took this once-in-a-lifetime opportunity to flee.
The window of opportunity lasted only a few months: Castro
closed the flow of immigrants as abruptly as he opened it.
Most of the immigrants went to Florida, and most of that
group went to the Miami area. When tens of thousands of
workers with little education show up, our model would predict a large decline in wages—at least among low-skilled
workers. It would also predict a large increase in unemployment rates, as U.S. workers had to compete against eager,
poverty-stricken immigrants to find new jobs.
What changed in Florida in the weeks and months after
the Mariel boatlift? The short answer: nothing. Wages didn’t
budge, and the unemployment rate rose just slightly. The
number of workers rose, so the economy apparently absorbed
many of the immigrants.
The quantity of workers increased with little change in
wages. The only way that happens within our model is if the
demand for labor increased at the same time as the supply.
That could happen if capital (machines and equipment)
flowed quickly to the Miami area to employ the new workers, raising the demand for labor. It’s also possible that immigrants moved quickly to the parts of the country with the
best job prospects, taking the edge off Miami-area labor market pressures. Card and Krueger admit that they don’t know
which of these explanations (or some other) is most important. They emphasize the simple fact that when the labor supply increased by tens of thousands, wages quite clearly did
not fall.
56 | Chapter 7
This reminds us that when we think of the U.S. economy
as a whole, changes in supply are rarely separate from changes
in demand: that’s why the general equilibrium approach of
the production function and the Solow model come up again
and again when discussing the aggregate economy.
CASE STUDY: NOBEL PRIZE WINNER ED
PRESCOTT ON TAXES AND LABOR SUPPLY
“Why do Americans work so much more than Europeans?”2
That’s the title of a paper by Edward C. Prescott. He says the
reason is high taxes: wage taxes as well as sales-type taxes.
We know from the basic supply-and-demand model that wage
taxes are likely to cut the quantity of labor supplied—but why
should sales taxes hurt labor supply?
People don’t work for the pleasure of it. They work in order
to buy consumer goods, either now or in the future (or perhaps they work to let their descendants buy more consumer
goods). In Europe, taxes on consumer spending are quite
high—20 percent or more is a common rate—so this tax
wedge probably does have important macroeconomic effects.
Prescott shows that Europe’s tax rates started skyrocketing
during the same years—the early 1970s—when their hours
worked started falling. (Some students might be surprised to
learn that Europe’s tax rates used to be lower, not higher, than
in the United States.)
Many macroeconomists—including most of those whom
Chad discusses in the text— think that Prescott’s analysis
is incorrect. They emphasize that in Prescott’s view of the
world, workers are very sensitive to taxes, wages, and consumer goods prices when deciding how much to work. In
other words, Prescott thinks most people have a highly elastic labor supply. A lot turns on that belief; perhaps that’s why
Prescott spent much of his Nobel lecture explaining why he
believes in a high-wage elasticity of labor supply.
It’d take us too far afield to jump into a big discussion of
labor supply elasticities, but even if Prescott’s estimates are
a bit generous, we should keep in mind that as a general rule,
both wage taxes and consumption taxes will depress labor
supply.
Note this public finance comment: consumption taxes
increase the tax wedge between consumption and leisure.
Higher consumption taxes make leisure look like a (relatively)
better way to get utility compared to consumer goods. So,
higher consumption taxes means less work. If only government could find a way to tax leisure at the same time it taxes
consumer spending, then it could reduce or eliminate the distortion caused by consumption taxes.
2. Federal Reserve Bank of Minneapolis Quarterly Review 28, no. 1
(July 2004): 2–13. Available at www.minneapolisfed.org.
CASE STUDY: MONTHLY JOB CREATION
AND DESTRUCTION
In an average month during the last decade or so, the U.S.
economy created about 125,000 net new jobs. We all know
that number varies from month to month and from year to
year. But what we don’t often notice is how much churn hides
behind those monthly numbers.
Davis, Haltiwanger, and Schuh, in their now-classic book
Job Creation and Destruction (Cambridge, MA: MIT Press,
1998) show how much churn goes on in the United States.
My favorite statistic is that about 2.1 million (gross) new
jobs are created every month, and about 2 million jobs are
destroyed. The gap between those two— about 125,000
jobs—is the net job growth number that gets reported in the
news. When the creation and destruction numbers are so very
large, it’s easy to see how a modest 10 percent change in a
month’s creation or destruction numbers can lead to massive
changes in net job growth. A 10 percent drop in job creation
for one month gets you a 75,000-net job loss for the month,
while a 10 percent drop in job destruction get you a 325,000net job increase for the month.
Another notable fact from Davis, Haltiwanger, and Schuh’s
research is that recessions appear to be associated with bursts
of job destruction, accompanied by modest slowdowns in job
creation. Thus, the reason it’s so hard to find a job in a recession isn’t because firms aren’t hiring—it’s because there are
so many other unemployed workers out there hunting for the
same jobs you are. The number of layoffs are greater than
the number of hirings.
(Note: This stylized fact about “recessions as bursts of job
destruction” is disputed by University of Chicago’s Robert
Shimer in a series of papers.) Shimer notes that in a field with
few quits [like unionized manufacturing], the only way to get
rid of workers is to fire them, while in fields with lots of quits
[the rest of the economy, relatively speaking] you can get rid
of lots of workers just by slowing down the hiring process.
One simple way of resolving the dispute would be to note
that Davis, Haltiwanger, and Schuh’s work focuses largely
on manufacturing industries, which are often associated with
mass layoffs. Perhaps their results don’t generalize to the rest
of the economy.
Fortunately, the U.S. government, along with many state
governments and governments of foreign countries, is starting to pay attention to labor market churn. The U.S. survey
that keeps track of churn is appropriately called JOLTS: the
Job Opening and Labor Turnover Survey. Its data are widely
available on the Web. It gives a clear picture of job creation
and destruction for the U.S. economy as a whole. JOLTS
was created precisely because of the success of Davis, Haltiwanger, and Schuh’s research agenda—an example of academic macroeconomics impacting government statistical
methods.
The Labor Market, Wages, and Unemployment | 57
SAMPLE LECTURE: USING THE JOB OPENINGS
LABOR SURVEY TO CALCULATE THE FLOW
CONSISTENT UNEMPLOYMENT RATE AND
TREND UNEMPLOYMENT RATE
Chad provides a nice, simple, and easy example as to how to
find the “natural” unemployment rate. However, Chad’s measure of unemployment rate should not be confused with the
“flow consistent” unemployment rate (FC-U). For example,
see Sahin and Patterson (http://libertystreeteconomics.new
yorkfed.org/2012/03/the-bathtub-model-of-unemploymentthe-importance-of-labor-market-flow-dynamics.html#.V5JJn1fwjFJ). The flow consistent unemployment rate is the
unemployment rate that would prevail had the level of separations and hirings been equal given the monthly separations
and hiring rates. For example, like Chad, if: ΔU = Separations − Hirings; and Separations = (Separations/Employment)*Employment, and Hirings = (Hirings/Unemployment)
*Unemployment, and letting s = Separations/Employment
(= the separations rate) and f = Hirings/Unemployment
(= the hiring rate), the change in unemployment in any time
period t, can be written as
ΔUt = st * Et − ft * Ut.
So, if Et = 140 million, Ut = 10 million, st = 1%, and ft = 15%,
the change in unemployment is −1.4 million–1.5 million net
new jobs were created. The flow consistent unemployment
rate is based on the idea, given the temporally determined
separation and hiring rates, st, and ft, what unemployment
rate would prevail had the flows of separations and hirings
exactly balanced out, that is
FC-Ut = ft/(st + ft) = 0.01/(0.15 + 0.01) = 6.25%.
Sahin and Patterson use the flow consistent unemployment
rate to show, for example, that a negative gap between the
flow consistent unemployment rate and the actual unemployment rate acts as an indicator of turnarounds (future
decreases) in the actual unemployment rate.
The key difference between the presentation in the textbook and that of Sahin and Patterson is that both the separations and hiring rates have cyclical component, and,
therefore, the flow consistent unemployment rate likewise has
cyclical component. Figure 1, below, shows that both the
separation and hiring rates are quite cyclically volatile.
Given the cyclical variations in the separation and hiring
rates, a possible approach to reconsider the analysis of the
“natural” unemployment rate is to remove the cyclical components from the separation and hiring rates. For example,
we can write the separation rates as
st = + so Ỹt
Figure 1. Separation Rates and Hiring Rates
(Author’s Calculations: see https:// fred.stlouisfed.org /search
?st= JOLTS)
where and represent the trend separation and hiring rates,
Ỹ is the cyclical variation in output (measured as the difference between current output and potential output divided by
potential output, such that so Ỹ and fo Ỹ are the cyclical components of the separations and hiring rates). Following
Chad’s approach in the textbook (see equation 7.4) allows us
to write the natural unemployment rate, Un, as
Un = /( + ).
As a “rough” statistical illustration (see Tables 2–5 below),
the trend separations and hiring rates were estimated using
monthly data from the JOLTS series provided in FRED
DATABASE, for two different time periods: 2001, month 2
to 2007, month 12, and 2008, month 1 to 2016, month 1.
These results are summarized in Table 1. In the time period
prior to the Great Recession, the trend separation and hiring
rates were estimated as 0.036 and 0.687, generating a natural unemployment rate of 4.9 percent. Since 2008, around the
beginning of the Great Recession, the trend hiring and separation rates were estimated as 0.031 and 0.586, generating a
natural unemployment rate of around 5 percent. One of the
key differences between the two time periods is that the Ỹ
coefficient in the second time period is positive—separations
were positively related to the cyclical variation in output
Table 1. ESTIMATES OF THE NATURAL
UNEMPLOYMENT RATE
Time
2001,m2–2007,m12
2008,m1–2016,m1
and
ft = +
o
Ỹt,
(Author’s calculations.)
Un
0.036
0.031
0.687
0.586
4.9%
5.0%
58 | Chapter 7
Table 2. ESTIMATES OF THE TREND SEPARATION RATE: 2001 MONTH 2, TO 2007, MONTH 12.
PRAIS-WINSTEN AR(1) REGRESSION— ITERATED ESTIMATES
Source
SS
df
MS
Model
Residual
.000263997
.0001598
1
83
.000263997
1.9253e-06
Total
.000423797
84
5.0452e-06
st
Coef.
Std.
Ȳ
−.0330158
.0362625
.5995441
.0149005
.0004262
rho
Number of obs
F(1, 83)
Prob > F
R-squared
Adj R-squared
Root MSE
Err.
−2.22
85.09
=
=
=
=
=
=
85
137.12
0.0000
0.6229
0.6184
.00139
t
P>|t|
[95% Conf. Interval]
0.029
0.000
−.0626524
.0354149
−.0033792
.0371101
Durbin-Watson statistic (original) 0.793544
Durbin-Watson statistic (transformed) 2.329222
Table 3. ESTIMATES OF THE TREND HIRING RATE: 2001, MONTH 2, TO 2007, MONTH 12. PRAIS-WINSTEN AR(1)
REGRESSION— ITERATED ESTIMATES
=
=
=
=
=
=
Source
SS
df
MS
Model
Residual
.099050555
.076127147
1
83
.099050555
.000917195
Total
.175177702
84
.002085449
Coef.
Std.
Err.
t
P>|t|
[95% Conf. Interval]
.923109
.0375465
1.11
18.30
0.270
0.000
−.8114719
.6125872
2.860581
.761944
ft
Ȳ
rho
1.024555
.6872656
.9156587
Number of obs
F(1, 83)
Prob > F
R-squared
Adj R-squared
Root MSE
85
107.99
0.0000
0.5654
0.5602
.03029
Durbin-Watson statistic (original) 0.086066
Durbin-Watson statistic (transformed) 2.041092
Table 4. ESTIMATES OF THE TREND SEPARATION RATE: 2008, MONTH 1, TO 2016, MONTH 1.
PRAIS-WINSTEN AR(1) REGRESSION— ITERATED ESTIMATES
Source
SS
Model
Residual
.000225025
.000100898
1
94
.000225025
1.0734e-06
Total
.000325923
95
3.4308e-06
st
Coef.
Ȳ
.0763619
.0313902
.7711338
rho
df
MS
Number of obs
F(1, 94)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
Std.
Err.
t
P>|t|
.0210175
.0004676
3.63
67.13
0.000
0.000
.0346311
.0304617
Durbin-Watson statistic (original) 0.490562
Durbin-Watson statistic (transformed) 2.445775
96
209.64
0.0000
0.6904
0.6871
.00104
[95% Conf. Interval]
.1180926
.0323186
The Labor Market, Wages, and Unemployment | 59
Table 5. ESTIMATES OF THE TREND HIRING RATE: 2008 MONTH 1, TO 2016, MONTH 1. PRAIS-WINSTEN
AR(1) REGRESSION— ITERATED ESTIMATES
SS
df
MS
Model
Residual
.008734884
.038388885
1
94
.008734884
.000408392
Total
.047123769
95
.00049604
ft
Coef.
Std.
Err.
t
P>|t|
Ȳ
2.127632
.5867028
.9959058
.5672209
.2046729
3.75
2.87
0.000
0.005
1.001402
.18032
rho
Number of obs
F(1, 94)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
Source
96
21.39
0.0000
0.1854
0.1767
.02021
[95% Conf. Interval]
3.253862
.9930856
Durbin-Watson statistic (original) 0.082522
Durbin-Watson statistic (transformed) 2.538708
(a negative coefficient is expected). Perhaps this finding
reflects continued weakness in the job market during the
recovery from the Great Recession.
REVIEW QUESTIONS
1. The rise in the employment-to-population ratio is largely
driven by women entering the labor market. The civilian
employment-to-population ratio (for noninstitutionalized
civilians) fell from 62.8 percent in 2008 to 58.4 percent in
2013, a fall of 4.4 percentage points. For each percentage
point decline in this ratio, about 2.4 million jobs disappear.
So, in total, about 10.5 million jobs vanished.
2. The unemployment rate equals the number of people
employed divided by the “labor force.” The labor force is the
sum of the number of people employed plus the number of
people out of work yet still looking for work. Importantly,
people who are out of work but not looking are not included
anywhere in the unemployment rate.
3. Examples include the following: Labor supply might
increase because the population increases or because jobs
become easier and more fun (for example, you can talk on
your cell phone at work). Labor demand might increase
because domestic firms expand into foreign markets and need
more workers, or because firms discover new technology that
makes existing workers more profitable to keep around.
If labor supply increases, holding demand constant, then
the wage falls and the employment-population ratio rises. If
labor demand increases, holding supply constant, then the
wage and the employment-population ratio both rise.
4. Since this is a review question, I’ll answer informally.
It’s easier to discuss this in terms of the natural level of
unemployment, as in Chad’s discussion surrounding equation
7.1. Equation 7.1 makes clear that natural unemployment plus
cyclical unemployment equals total unemployment.
Frictional unemployment is a long-term issue, structural
unemployment is a medium-term issue, and cyclical unemployment is a short-term issue.
Frictional unemployment is caused by the fact that even in
the best of all possible worlds, employment relationships will
break up, and it will almost always take time to find a new
employment relationship. People will want to move, firms
will occasionally go out of business through bad management, some people will hate their jobs, and some firms will
hate a par ticular employee. It takes time to search for a new
job—and from the firm’s point of view, it takes time to look
at all the résumés, have meetings to decide what kind of person they’re looking for, meet all of the applicants, and check
up on their backgrounds.
Structural unemployment is unemployment caused by
medium-term shifts in the economy. In principle, it can be
positive or negative. If the auto industry is declining, then
there are going to be a lot of people with car-making skills
who might find it very tough to transition—their “friction”
in the labor market is big enough and noticeable enough that
we create a new category for it. That’s an example of positive frictional unemployment. Negative frictional unemployment would happen if a big new industry moved to town and
started hiring lots of workers—“friction” would be much
lower than usual. This wouldn’t last forever, since the new
industry (an auto assembly line in Ohio; a movie industry in
Vancouver, British Columbia; government hiring during a
time of war) would probably just need to grow quickly to a
certain level, and then would just start acting like a normal
industry—hiring and firing at a regular “frictional” rate.
Cyclical unemployment can be positive or negative, and it
reflects changes in unemployment caused by the temporary,
two-to-three year fluctuations in the overall economy we call
the “business cycle.” Cyclical unemployment is positive
60 | Chapter 7
(during a bad time) about as often as it is negative (during a
good time).
5. The unemployment rate is higher in Europe than in the
United States. Hours worked per person are much lower. This
may be because wage taxes and sales taxes are higher in
Europe and because labor markets are more regulated than
in the United States. In Europe, it is much harder to fire workers in most countries than it is in the United States. Therefore, European businesses need to be very sure about the
quality of a worker. By contrast, an American business can
take a chance on someone new, since it can fire the person if
it doesn’t work out. Thus, American firms tend to hire people
more quickly than European firms.
6. Finding out the value today of a share of stock that pays
$2 per year in dividends forever; finding out the value today
of a college education that raises my average wage by $20,000
per year for forty years; finding out the value today of a bond
that pays $10,000 in ten years.
7. The best answer is that the demand for college-educated
workers has increased rapidly. When wages and employment
both rise, that is a good sign of a rise in demand.
EXERCISES
1. From FRED DATABASE, in October 2009, the Civilian
Labor Force was 153.784 million persons. If the unemployment rate was 6 percent, 94 percent or 144.557 million people
would have been employed. Because the actual unemployment rate was 10 percent, the actual number of people working was about 138.4 million persons. Quite a difference!
2. (a)
grown. The stagflation events of the 1970s further caused
women to enter the labor force to maintain family living
standards.
(c) Since 2000, the trend for women has flattened out, where
about 55 percent of the female population is working. This
could be due to a lack of job opportunities for women, as the
employment growth stagnated in the first decade of the
twenty-first century.
3. A marginal tax cut increases labor supply and drives down
the wage— but it will increase the after-tax wage for the
worker. The employment-population ratio will also increase.
This is just a standard “rise in supply” story.
The effect on unemployment is quite ambiguous— I’m
inclined to say that if the economy is at the natural rate of
unemployment, it is likely to stay there— there are always
some people entering and leaving employment relationships.
It’s hard to imagine that a change in the tax rate would impact
that “job creation and destruction” process very much, after
a short transition period. So, the simplest answer is, “no effect
on unemployment.”
But in that short transition period, anything is possible,
and not just in theory—in practice as well. When news arrives
of the tax cut, many people who were completely out of the
labor force could start searching for work—so they would
count as unemployed until they find jobs. The people who
were already unemployed but searching will probably become
less picky, now that they get to take home more money each
week, so that will tend to push unemployment down. The net
effect could go either way in the very short run.
4. This is likely to raise labor demand, since firms will be
able to produce output more efficiently within the non-oilproducing country. The rise in labor demand will increase
wages and the employment-to-population ratio.
5. This is a worked exercise. Please see the textbook for the
solution.
6.
1%
a
b
5%
c
d
a
b
c
d
$49,505 $45,264 $10,100 $3,958 $47,619 $30,696 $2,100 $1,917
7. (a)
(b) During the post–World War II baby boom many women
left the labor force and reentered after their children had
1%
$2,296,693
2%
$1,895,037
4%
$1,357,577
5%
$1,175,754
The Labor Market, Wages, and Unemployment | 61
(b) When the interest rate is higher, I won’t be able to earn
as much if I save my salary in the bank, so the same money
buys me less lifetime consumption in a high-interest-rate
world.
Another way to put it is that if I try to borrow money from
a bank based on my future income, the bank will lend me
less money if it thinks future interest rates will be high. So,
the “present discounted value” of my future earnings can’t
get me a good bank loan when future interest rates are high.
(b) Present discounted value of spending four years in expensive college and then working (net of the present value of the
cost of tuition): $1,510,541. The discounted present value of
tuition beginning in year 0, and continuing through years 1,
2, and 3, is $76,572. The discounted present value of postcollege earnings beginning in year 4 and continuing to the
end of year 49 is $1,587,113 = 70,000{1 − [1 / (1 + 0.03)]}50 /
{1 − [1 / (1 + 0.03)]} − 70,000{1 − [1 / (1 + 0.03)]}4 / {1 − [1 /
(1 + 0.03)]}.
8. (a) w0 + w0 (1 + g) / (1 + R) + w0 (1 + g)2 / (1 + R)2 + . . . + w0
(1 + g)t / (1 + R)t
(c) If these numbers are close to the truth, the value of a college education is still massive, even if the student has to pay
his or her own tuition at private school.
(b) PDV = w0*[(1 + g) / (1 + R) + (1 + g)2 / (1 + R)2 + . . . + (1 + g)45
/ (1 + R)45]
(c) a = (1 + g)/(1 + R)
PDV = w0{1 − [(1 + g) / (1 + R)]45} / {1 − [(1 + g) / (1 + R)]}
It’s essentially equation 7.10 with “1 + g” on top of “1 + R.”
(d) 4 percent: 1,535.740
3 percent: 1,862,219
2 percent: 2,300,00
At a 2 percent growth rate, the effects of the growth rate and
the discount rate cancel each other out, and we’re just adding up forty-six years of payments worth $50,000 per year.
10. This is a worked exercise. Please see the textbook for the
solution.
11. (a) This equals a paid vacation that lasts twenty-six
weeks—but you can only get the paid vacation if you don’t
get a job. Many workers will choose to stay unemployed until
about the twentieth week or so, when they will start looking
for a real job.
(b) Workers would have a strong incentive to start looking
for work quite quickly. They might spend some money on a
quick vacation. After all, you don’t want to take a vacation
as soon as you start a new job—it looks bad. So vacation a
little for the first few weeks, and then start looking for work.
9. We’ll assume that school time is four years, and that work
time is still forty-five years, beginning in time zero, adding
up to a forty-nine-year noncollege work career.
12. For the year 2010:
Italy: $98 per hour
France: $116 per hour
Germany: $97 per hour
United Kingdom: $85 per hour
United States: $115 per hour
Japan: $73 per hour
South Korea: $53 per hour
(a) Going straight to work, no college: $1,060,066.28. With
$40,000 earned in time 0, applying the annuity formula:
PDV = w{1 − [1/(1 + R)]}50/{1 − [1/(1 + R)]}.
Clearly, France, the United States, Italy, and Germany are
more productive than the United Kingdom, Japan, and South
Korea on a per-hour basis.
(e) As the discount rate decreases the present value of the
future stream of income increases. At a lower discount rate,
the present value of human capital must be higher to generate a given future stream of income.
CHAPTER 8
Inflation
CHAPTER OVERVIEW
In this chapter, you get to cover one of the things that economists really, genuinely know: the cause of high, persistent
inflation. You also get to establish the classical dichotomy
between real and nominal variables—which sets the stage for
showing (apparent) breakdowns of the dichotomy at businesscycle frequencies. Throw in the Fisher equation and the link
between bad fiscal policy and hyperinflation, and you’ve got
a chance to spend two lectures covering some of the bestunderstood parts of macroeconomics. You can’t omit anything in this chapter.
Unlike the last chapter, this chapter has little “news you
can use,” aside from the Fisher equation—but it does have
lots of big ideas that have stood the test of time. Cobb-Douglas
could, just conceivably, fade away someday—but it’s hard
to imagine a future without the quantity theory of money
(QTM). (Aside: Clearly the policy significance of QTM has
diminished since the 1980s, as the connection between monetary aggregates and nominal GDP has broken down. If that
were not the case, Taylor’s rule would not have been developed. However, the relevance of QTM remains contingent
upon historical circumstances. These circumstances are outlined in this chapter.)
8.1 Introduction
Most of our students have no experience with inflation consistently above 3 percent per year. So, by letting them know
that the United States had a fairly recent decade of 7 percent
inflation, you’re doing them a favor.
In fact, for many students, the big-ticket item they buy most
often— consumer electronics—has been subject to outright
deflation during their lives. Therefore, inflation isn’t all that
62
relevant to them. This gives you a chance to emphasize that
their complacency and ignorance reflects what Thomas Sargent rightly called a “conquest” in the title of his book, The
Conquest of American Infl ation (Princeton, NJ: Princeton
University Press, 2001). I think there’s room for some gloating here: our profession won this battle—at least for the time
being, at least for the developed countries— and no one is
going to trumpet our victories but ourselves.
Chad mentions a few hyperinflations in the introduction
and has a case study about the Consumer Price Index (CPI)
that gives students practice (if they need it) with how to think
about purely nominal price changes. An expanded case study
below looks briefly at how the CPI is calculated and emphasizes how it can be an effective price index when it must keep
track of goods of constantly changing quality.
8.2 The Quantity Theory of Money
Here you go: this is the first or second most controversial
identity in macroeconomics (a rough tie with the definition
of gross domestic product [GDP]). Students have no idea what
they’re getting into when you put this up on the board: it looks
like a mere identity, and that’s how we sell it to them, but it
turns out to contain a theory of long-term inflation and a theory of short-term business cycles all in one. We only cover
the first part now and Chad drops some hints about the second part. You might want to create an air of mystery about
the equation: let students know there’s more to come so that
they won’t just forget this after the exam.
OTHER DEFINITIONS OF MONEY
In the previous section, Chad mentions the level of currency
(C). Here he lays out the monetary base, M1, and M2. Please
Inflation | 63
don’t make your students learn discontinued series like M3
and L— they already get the idea that lots of things have
money-like qualities. A case study lets students know that
digital cash is just cash, and below I discuss a perennial student question: Are credit cards money?
THE QUANTITY EQUATION
MtVt = PtYt. At this point, it’s an identity, not a theory. For any
M, P, and Y, there is a unique value of V. We could just as
easily have written potatoes × velocity of potatoes = PY, but
we chose the former because we have observed that money
gets used to buy nominal GDP much more often than potatoes are used to buy nominal GDP.
As you can tell, I’d be less aggressive than Chad at calling
this a theory at this point. It’s still just an identity, but we have
an underlying theory of price determination that explains
why this identity is worth paying attention to.
THE CLASSICAL DICHOTOMY, CONSTANT VELOCITY,
AND THE CENTRAL BANK: THE QUANTITY THEORY FOR
THE PRICE LEVEL
Now we have a theory: if V is (roughly) fixed, and if Y isn’t
impacted by changes in M, then changes in M must cause
changes in P. That’s because of our four original variables,
two (V and Y) are now pinned down—they’ve actually been
turned into parameters and aren’t really variables anymore.
(Note: Students sometimes have a clear distinction in their
minds between parameters and variables, perhaps from
chemistry and physics courses— and we macroeconomists
often blur these distinctions with our assertions that “everything is endogenous in general equilibrium.” Let’s not contribute to the blurriness this semester!)
I often make a big deal out of this in lecture: I circle the Y
and draw an arrow pointing to it, with words like these at the
arrow’s other end: “We just spent two months explaining this:
the number of green pieces of paper had nothing to do with our
story.” You may be so bold as to use the word “exogenous.”
Why do we assume velocity is constant? Well, as Chad
notes, in practice it roughly is when we’re looking at M2
velocity (it’s been more volatile for other money measures the
past three decades, presumably because of financial innovation). But more broadly, it does seem that people use their
money in regular cycles: on the income side, many people get
paid every two weeks or every month; on the outflow side,
they pay their mortgages and other bills every month. So,
there is a reason to think that most money gets turned over
on a regular basis, at least when we’re looking at a stable institutional environment.
Also, in actual human experience, big fast changes in the
quantity of money are (sadly) quite common, so it’s the biggest source of short- to medium-term variance on the lefthand side of the equation. Since our big goal in this chapter
is to understand big changes in inflation, making V a fixed
parameter is a shortcut that takes us where we want to go.
(Note: In recent decades in rich countries, big fast changes
in M aren’t that common anymore—so it’s worth it for policymakers to spend a little time studying changes in V.)
I know many of you will be sorely tempted to spend time on
the nuances of velocity—the impact of expected inflation and
nominal interest rates and institutional innovation on V. Chad
tries hard not to contribute to that temptation, and neither will
I. There are plenty of great theories to teach in this chapter,
and you’ve still got the entire theory of business cycles to
cover before the semester is over—please consider the opportunity cost of teaching a full-fledged model of velocity!
Equation 8.2 is boxed in the text—so your students will
surely use their highlighters on it: Pt = MtV / Yt. Only V lacks
a time subscript. So, although Yt is exogenous with respect
to changes in the money supply, it’s not a “fixed parameter.”
Perhaps you can call it a “fluctuating parameter”: anything
to let students know that M only changes P.
You may spend a few minutes explaining why Yt is considered exogenous. The theory that explains the exogenous nature
of output is called the classical dichotomy. In the classical
dichotomy, it is primarily changes in the money supply that
cause shocks to aggregate demand. A change in the money
supply simultaneously changes the aggregate price level and
the aggregate levels of factor prices, leaving the real wage rate,
the real rental price of capital, and factor employment
unchanged. With inputs into the production process unchanged,
production, Yt, remains unchanged. In the classical dichotomy,
the aggregate price level and nominal factor prices act as
aggregate demand shock absorbers—that is, output prices and
factor prices are fully flexible to ensure supply-side equilibrium at full employment. As mentioned in Chapter 1, this circumstance defines the long run in macroeconomics.
THE QUANTITY THEORY FOR INFLATION
Now you get another payoff from the time spent back in
Chapter 3 on growth rates: you can show that MV = PY converts easily into growth rates. Since velocity is assumed to be
zero, you can rearrange to get boxed equation 8.4: π = ḡM − ḡY.
I’d give this equation a workout with quite a few numerical examples. I like illustrating that the cliché about “too
much money chasing too few goods” is actually quite accurate: you can have high money growth and zero inflation as
long as the real economy is growing quickly. This helps
explain why central banks need to know how fast the economy is growing—partly so they can permit the right amount
of money growth. You can also show that zero money growth
will lead to deflation in a growing real economy—and in the
simplest classical model, that poses no economic problems
whatsoever.
Chad doesn’t create an aggregate supply/aggregate
demand (AS/AD) framework to teach this— and you don’t
64 | Chapter 8
need to, either. Remember: Students don’t know that AS/
AD is the way this is usually taught, so whatever way you
teach it to them will (probably) work just fine!
The cost of drawing a vertical AS curve and a hyperbolic
AD curve is five minutes of lecture—with minimal real payoff. Students are primed to believe that money growth
causes inflation—most have heard stories about wheelbarrows of money in Germany—so you can get away with minimal modeling. You can always tell them a Friedman-style
“helicopter drop” story if you like at this point.
Most importantly, Chad is saving AS/AD for an inflation/
output gap model later on—so no need to confuse students
by using the same jargon twice.
Chad’s charts in this section are great—note that the crosscountry money/inflation chart uses the ratio scale— and
these should be part of your lecture. Macroeconomists rarely
get relationships that are this precise.
8.3 Real and Nominal Interest Rates
This subsection is covered in a sample lecture to come.
8.4 Costs of Inflation
Chad uses three people to illustrate the costs of inflation. In
these three cases, the real value of a pension gets inflated
away; the real value of a bank’s mortgage repayments get
inflated away, so the bank collapses; and a variable-rate mortgage payment spikes after inflation, forcing a homeowner to
sell her home.
All three stories illustrate the redistributive costs of (surprise) inflation. A case study below works out the tax distortions caused by inflation. Chad closes the section with the
dollar-as-a-ruler analogy— and notes just how confusing it
would be if a foot had twelve inches in one year but eleven
or thirteen inches in another. That’s a source of confusion we
could probably live without.
8.5 The Fiscal Causes of High Inflation
Why do countries let high inflation happen? The answer
forces us to think about the link between fiscal and monetary policy. Chad blurs the line between nominal and real
here, and if you can at all get away with following him on
that, I’d recommend doing so. All you need to drive home is
that the printing press is just another way of raising funds by
government expenditures.
The key identity is
G = T + ΔB + ΔM.
Each year’s government purchases must be funded from somewhere: from taxes, from new borrowing, or from printing new
money. Governments that can’t raise taxes any more—perhaps
because voters would revolt, or perhaps because the government isn’t competent enough to run a good tax collection
system—must turn to the other two options. And if potential
lenders don’t trust you enough to lend money to you, then
you’re down to one option: printing more currency.
There are great political stories to tell about how governments get into those situations—is G high for political reasons? Is T low for political or bureaucratic reasons? Is ΔB low
because the country burned its bridges with creditors too often
in the past, or even better, because potential lenders know that
rock stars and Hollywood celebrities will pressure them to forgive the loans someday? In addition, you can build in current
concerns about austerity/stimulus/the budget deficit debate.
You can mention that with the recent budget deficits, M2 grew
8.6 percent in 2012, 6.7 percent in 2013, 6.2 percent in 2014,
and 5.9 percent in 2015 (FRED DATABASE).
You’ll probably want to put some meat on the bones along
these lines—and what you’ll end up doing is illustrating Sargent’s classic “Unpleasant Monetarist Arithmetic”: the inevitable link between fiscal and monetary policy.
8.6 The Great Inflation of the 1970s
This is our transition to the short-run model: Chad notes that
economists didn’t really begin to understand business-cycle
fluctuations in inflation and output until the work of Friedman, Phelps, and Lucas in the late 1960s and early 1970s.
We’ve finished our treatment of long-run inflation and output growth; from the next few chapters, we’ll be looking at
time spans that the mainstream media can handle, periods
of ten years or less.
SAMPLE LECTURE: REAL VERSUS NOMINAL
INTEREST RATES
How can you tell if it is expensive to borrow money? You
don’t just look at the rate posted at the bank. That tells you
how many dollars you must pay in interest if you borrow $100
for a year. (When interest is reported in dollar terms, we call
it the nominal interest rate.)
Instead, you compare the nominal interest rate against how
easy it’s going to be to get the nominal dollars to repay your
loan in the future. Are you planning to repay the loan by selling hamburgers? Then you need to have an idea of the future
price of hamburgers. I could give more examples but the point
is clear: nominal interest rates—the rates we see quoted by
banks and in newspapers— can’t be “high” or “low” except
in comparison to the future prices of goods and services. In
other words, we must adjust interest rates for inflation.
Inflation | 65
R = i − π.
EXPANDED CASE STUDY: HOW CAN THE
CONSUMER PRICE INDEX BE ACCURATE
IF THE QUALITY OF GOODS KEEPS
CHANGING OVER TIME?
R is the real interest rate (how much real buying power you
must give up a year from now if you borrow today); i is the
nominal interest rate (how many dollars you repay a year
from now), and π is, as always in macro, the inflation rate.
(Note: I start with this version of the Fisher equation because
it ties into the previous “adjusting for inflation” discussion
more directly.)
So, if the nominal interest rate for borrowing is 10 percent,
and inflation is 8 percent, then the real interest rate is only
2 percent. Thus, if you borrow $100 today, you must only
increase the real value of that $100 by $2 to justify borrowing the money.
That might be moving a little too fast, so here’s another
way to think about it: when you borrow $100 at 10 percent
interest today, you’re promising to repay $110 a year from
now. But getting $110 a year from now—by investing, by
washing some cars, by cleaning some houses—is going to be
easier than it would to get that same $110 today. Why?
Because of the 8 percent inflation: the price of the average
good or service is going to “float up” by 8 percent over the
course of the year. So, inflation makes it easier to pay back
loans, if the nominal interest rate stays fixed.
That’s part of the reason farmers in the Grange and Progressive movements of the late nineteenth and early twentieth centuries pushed for pro-inflation policies: they already
had loans from banks with a fixed nominal interest rate, and
they wanted the government to create inflation. Inflation
would push up the price of their products— corn, grain, and
vegetables—and then they could pay back their loans much
more easily.
What was the farmers’ preferred method for creating
inflation? They wanted the U.S. government to issue lots of
silver-backed money in addition to the standard U.S. policy
of issuing small amounts of gold-backed money. Presidential candidate William Jennings Bryan, a left-of-center candidate by the standards of the day, gave a famous pro-farmer
speech in which he declared, “You shall not crucify mankind upon a cross of gold.” (Bryan was also the prosecuting
attorney in the famous Scopes monkey trial; he was on the
antievolution side in that case, made famous in the play
Inherit the Wind.)
(Note: You’ll be tempted to talk a lot about expected versus unexpected inflation at this point, but I’d recommend
holding off until you’ve covered business cycles a bit. Expectations come up quite naturally when discussing business
cycles, and Chad brings up expectations quite often. When
you cover monetary policy thoroughly in Chapters 11 and 12,
you’ll have plenty of time (if you didn’t get bogged down in
two weeks of lectures about velocity) to discuss the relative
costs of surprise versus expected inflation.)
Out of all the measures of inflation available in the United
States, the one that gets the most attention is the Consumer
Price Index (CPI). It comes out every month, and it usually
gets reported in the news in two ways: including food and
energy prices, and excluding food and energy prices.
The stated reason for excluding food and energy prices
isn’t because those goods aren’t impor tant— it’s because
those prices tend to have sharp jumps up and down from
month to month, jumps that don’t seem to be strongly
associated with movements in the rest of the CPI (at least
these days).
To measure the CPI, the U.S. government sends its people
into actual grocery stores, electronics stores, and department
stores to measure the actual prices of a fixed set of goods.
For example, the government literally keeps track of the price
of Campbell’s cream of tomato soup in dozens of places
throughout the country—and it does the same for dozens of
other consumer goods. The prices are all averaged together,
with goods weighted according to estimates of how much the
average American buys of that good. For example, we don’t
buy a new TV every year, but we might buy one every eight
years: therefore, the government might include one-eighth of
a flat-screen TV in the CPI, while it might include fifty cans
of soup in the index.
But the color TV brings up an interesting problem: How
does the government keep track of new goods, or goods of
changing quality? And what happens when an old TV model
from the CPI basket is no longer made? The methods for taking account of quality increases are constantly evolving—
and genuinely improving, but the simplest method works as
follows.
In a month when both the up-to-date and the outdated
color TVs are for sale, the government agent writes down the
prices of both TVs. So, if the up-to-date model is $120 but
the outdated one is $100, the government agent counts the upto-date model as equal to 1.2 outdated models.
The main idea is that if both models are being sold in the
real world, then the up-to-date one must be providing the
usefulness of 1.2 outdated models. In other words, in order
to get the same usefulness as I get from one outdated model,
I only need to buy five-sixths of an updated model (since
5/6 = 1/1.2).
After a few months, we know that the outdated model will
stop showing up on store shelves, and there will only be the
up-to-date model, perhaps selling for $110 or even $90. So,
at the slot in the CPI basket once held by one outdated model,
we now include 5/6 of today’s price of the up-to-date model.
That’s a quick but accurate overview of how the CPI keeps
track of quality changes.
Irving Fisher figured this out in the early twentieth century,
and he put it into an equation (a variant of equation 8.5):
66 | Chapter 8
(Note: Consumer electronics have been one area where
rapid deflation is the norm, as your students will recognize.
You can use this to argue against the ideas that companies
create inflation because they are greedy, prices always tend
to go up, and the like. Why do prices of tech goods keep falling, despite their producers’ self-interest in charging higher
and higher prices?)
CASE STUDY: INFLATION, SAVINGS,
AND TAXES
Chad notes the tax distortions caused by inflation and
famously emphasized by Martin Feldstein. The U.S. tax code
(like other advanced-economy tax codes) taxes you on your
nominal interest. (That’s what shows up on the 1099-INT you
get at the end of each year, if you have a savings account.)
So, when inflation is high, nominal interest rates tend to be
high, and you earn a lot of nominal interest. That means you
pay a lot of tax when inflation is high—and in fact, you can
even wind up paying so much in tax that you earn a negative
real return after paying the tax.
Example: inflation is 10 percent, and the nominal interest
rate is 12 percent. That means your real interest rate is
2 percent. If you save $100 in the bank for the year, and if
the tax rate is 25 percent, then what is your real return after
taxes?
Interest for the year showing up on your 1099-INT: $12.
Tax you pay to government: 25 percent of $12 = $3
Nominal return after taxes: $112 (bank balance at end of
year) − $100 (amount you originally saved) − $3 (tax) = $9. A
9 percent return on your $100 investment. So, while the bank
told you that you’d earn 12 percent interest, after taxes you
really earned 9 percent interest. Let’s calculate the allimportant real return:
real interest rate = nominal interest rate − inflation
−1% = 9% − 10%
Congratulations! By deciding to save, your $100 has
shrunken its buying power by 1 percent during the course
of the year! That’s because the year’s 10 percent inflation
was larger than the 9 percent interest you earned after
tax.
All of these Fisher-equation calculations help us to keep
track of a simple fact: when the tax system makes you pay
interest on nominal returns, the government earns more real
tax revenue when inflation is higher. If inflation is high
enough, as in this example (which roughly matches the late1970s U.S. experience), the government may even take the
entire real return from the investor. This tends to discourage
saving when inflation is high.
CASE STUDY: THE FRIEDMAN RULE
I can rarely resist teaching the Friedman rule. It comes
through too clearly in too many rigorous models, and once
you’ve covered the Fisher equation, it’s a snap to teach Friedman. Maybe there’s an argument for waiting until you actually get to the monetary policy chapter before you cover this
(if you ever do), but you don’t need much apparatus to cover
this simple idea.
What is the cost of holding money in your pocket or in an
interest-free checking account? It’s the opportunity cost of the
foregone interest—the nominal interest rate, i. That’s kind of
a hassle, isn’t it? People spend a fair amount of time moving
money between bank accounts to avoid that kind of hassle.
Wouldn’t it be nice if money— currency in your pocket—just
paid interest so that you wouldn’t have to think about that?
As it turns out, the Confederate States of America did just
that during the U.S. Civil War: some Confederate money had
little “coupons” on the side that you could cut off and redeem
for more money. In short, the money paid interest.
But there’s an easier way for money to pay interest: the government could slow down money growth to actually create
deflation. If the government created deflation, then money
in your purse would actually be increasing in value—average
prices would fall every year, and $1 would buy more the longer it stayed in your purse! Money wouldn’t be paying nominal interest—but it would be paying real interest, and that’s
what matters.
But what level of deflation is the right one? Nobel laureate
Milton Friedman famously argued that the rate of deflation
should equal the economy’s average real interest rate. That
way, people wouldn’t have their decisions about how much
money to hold distorted by the difference between how much
money earns in your pocket versus in your savings account.
No more shifting money between savings and checking
accounts to earn the most interest—and you’d carry money
in your purse (or not) because it was convenient for you, and
you wouldn’t have to worry about the interest you were losing. As in much of economics, good monetary policy often
focuses on making sure that government isn’t a source of
problems. By setting the deflation rate equal to the real interest rate, government could eliminate one more governmentcreated distortion.
Friedman thought that the real interest rate was about
2 percent. So, he argued that the government should aim for an
inflation rate of negative 2 percent. Perhaps surprisingly, that
meant that the nominal interest rate would average 0 percent!
Let’s look at the Fisher equation to see if this is right:
R=i−π
2% = i − (–2%)
0% = i
Yes, it checks out: the Friedman rule, which argues that the
inflation rate should be the negative of the real interest rate,
Inflation | 67
means that the nominal interest rate should equal zero. If the
government did that, then currency would be earning real
interest.
CASE STUDY: ARE CREDIT CARDS MONEY?
Even though we’re supposed to tell students that credit cards
are not money, credit cards sure feel a lot like liquid wealth.
A credit card is, after all, a promise by a bank to create a loan
whenever the credit card holder desires, and loan creation is
how banks create money. Therefore, a credit card is the ability to create money by creating a loan obligation—it’s not
money itself.
At the moment you make the purchase at the grocery store,
you are borrowing money from your credit card issuer (a
bank) to make that purchase. A few days later, the credit card
issuer sends funds out of its bank reserves directly to the grocery store’s checking account—and since bank reserves don’t
show up in M1 but checking accounts do, then M1 increases
as soon as the funds arrive in the grocery store’s account.
If you pay off your credit card balance the next month,
money goes from your checking account (part of M1) into the
bank’s pile of reserves (not part of M1), so the money supply
falls back to its prepurchase level. The loan is now paid off,
and all that has happened is that you’ve moved money from
your checking account into the checking account at the grocery store—by way of a little bit of time travel we know as
credit cards.
The clearest way to state this is that by actually using
a credit card, you create money, and when you pay off that
credit card, you restore the amount of money back to its old
level.
CASE STUDY: THE GREAT DISINFLATION
AND NOMINAL INTEREST RATE
The Fisher equation tells us that as the rate of inflation changes,
so do nominal interest rates. One way to illustrate the Fisher
equation is to consider the relationship between the nominal
rate of interest on ten-year Constant Maturity Treasury Bonds
and the Core Personal Consumption Expenditure (Core PCE)
inflation rate. A case in point is the “great disinflation” that
followed the recession of 1982. Following the inflation experiences of the 1970s, inflation expectations remained temporarily high, and nominal interest rates remained high relative to
the inflation rate through the early 1980s. As actual inflation
experiences declined, so too did inflationary expectations, and
the price disinflation led, for the last three decades, to declines
in nominal interest rates. Also, with the increased confidence
that inflation was and is under control, we’ve seen further real
interest rates decline. The graph below illustrates the movements in the ten-year treasury bond yield and the Core PCE
inflation rate. We can see that, over time, the gap between the
nominal interest rate and the inflation rate has narrowed. This
conclusion is further evidenced in the table below, where the
averages of the annual yield, the annual inflation rate, and the
annual real interest rate are summarized over the last thirtyfive years. We have seen this (rough) measure of the real rate
of interest fall from an average of about 5.6 percent in the
1980s to 4.3 percent in the 1990s to 2.6 percent in the 2000s
and to about 1 percent from 2010–2015.
The Great Disinflation: A Look at the Relationship Between
the 10-Year Treasury Constant Maturity Rate and the Core
Personal Consumption Expenditure Inflation Rate
CASE STUDY: DOES MONEY GROWTH CAUSE
GDP GROWTH IN THE REAL WORLD?
The classical dichotomy tells us that in the long run, changes
in real variables cause real GDP growth: the number of ideas,
the number of machines, and the number of workers. Money
growth just doesn’t make the list. But when we look at the
real world, does this hold up?
“Some Monetary Facts,” by McCandless and Weber1 tells
the story: lots of countries have tried running the printing
press in the last few decades, and they just don’t grow that
fast. If the reason for poverty was not enough money, we
would’ve solved that problem long ago. For the world as a
whole, money growth is worthless as a predictor of real economic growth.
1. George T. McCandless Jr. and Warren E. Weber, “Some Monetary
Facts,” Federal Reserve Bank of Minneapolis Quarterly Review 19, no. 3
(Summer 1995): 2–11. Available at www.minneapolisfed.org.
AVERAGE TEN-YEAR CONSTANT MATURITY TREASURY
BOND YIELDS, AVERAGE CORE PCE INFLATION RATES,
AND AVERAGE REAL INTEREST RATES
Time Period
Average
10-Year
Constant
Maturity
Treasury
Bond Yield
Average
Core
PCE
Inflation
Rate
Average
Real
Interest
Rate
1980 to 1989
1990 to 1999
2000 to 2009
2011 to 2015
10.6%
6.7%
4.5%
2.5%
5.7%
2.4%
1.9%
1.5%
5.3%
4.3%
2.6%
1.0%
(Author’s Calculations: FRED DATABASE.)
68 | Chapter 8
REVIEW QUESTIONS
1. Inflation is a general increase in all prices in the economy,
including wages. Inflation eats away at the real buying power
of currency, so those hundred-dollar bills will lose buying
power over the years if there is inflation.
2. This summary is right. The quantity theory shows that you
can get inflation if the money supply rises, holding velocity
(V) and output (Y) constant. The quantity theory also shows
that you can get inflation if Y falls, holding money supply (M)
and V constant. More money or less output both cause inflation. Of course, in practice, big spikes in M are much more
common than big falls in real output.
3. Increases in and raise the price level; an increase in
reduces the price level.
4. We think the classical dichotomy holds in the long run
because prices (P) are flexible in the long run.
That means that the relative prices of wages, machines,
and output will adjust so that all capital and labor will be
used efficiently to create real output. The price of labor
adjusts so that all the workers who want to work get jobs, the
price of capital adjusts so that all the machines get rented,
and the price of output adjusts so that output gets sold. The
number of colored pieces of paper (money) won’t have an
impact on these decisions.
5. The nominal interest rate answers the question, “If I put
$100 in the bank today, how many $1 bills will I earn in interest in one year?” The real interest rate answers the question,
“If I put $100 in the bank today, how much more real buying
power will I have in one year?” The Fisher equation says
that the real interest rate is the nominal interest rate minus
inflation—it tells us that when inflation is high, we shouldn’t
get too excited about hearing that the bank is offering 10
percent or 20 percent annual interest.
6. The costs of inflation include the inflation tax—that’s the
real buying power we lose from holding money in the form
of non-interest-paying currency or checking accounts. Other
costs include the need to go to the bank more often when inflation is high, because you want to keep the maximum amount
possible in the bank rather than in your wallet—so you never
walk around town with $200 in cash. The cost of having to
think about price changes all the time is also important—just
imagine if someone asked, “How many inches would you like
there to be in a foot this year?” It’s mentally costly to convert
prices in our heads every few months—but people need to do
that when they live in a high-inflation society.
7. Government spending = change in money supply +
taxes + change in bonds. When the government doesn’t want
to raise taxes, and when it can’t borrow anymore because
people don’t trust it to repay, the only way to pay for extra
government spending is through increasing the money supply. Countries with hyperinflation are almost always trying
to pay for government spending.
8. No, it does not— the U.S. government raises only a tiny
amount of revenue from seigniorage (changes in M). The Federal Reserve just let inflation get out of control in the 1970s,
perhaps because it didn’t know how the economy really
worked. Later chapters will give a more thorough answer to
this question— a topic that is still much debated among
economists.
9. People who hold currency and other non-interest-paying
forms of money, like most checking accounts.
EXERCISES
1. From Table 8.1
Table 8.1 (2012 = 100)
(a)
(b)
(c)
(d)
(e)
(f)
Year
CPI
CPI2015/
CPIt
1900
1930
1950
1970
1980
1990
3.43
7.05
10.16
16.39
34.76
55.14
29.15
14.18
9.84
6.10
2.88
1.81
Current
dollar
prices
Constant
dollar prices
$1,000.00
$80,000.00
$0.05
$0.55
$2.25
$0.45
$29,154.52
$1,134,751.77
$0.49
$3.36
$6.47
$0.82
2. This is a worked exercise. Please see the textbook for the
solution.
3. (a)
(b) China has, in the recent past, had lower inflation than
India. China’s average (consumer price) inflation rate from
2011 to 2015 was about 2.8 percent, and India’s average (consumer price) inflation rate for the same time period is about
8.3 percent.
4. The price level is the key endogenous variable in the quantity theory: it is the only thing that responds to changes in
the money supply, velocity, or real output.
Inflation | 69
(a) The price level doubles.
(b) The price level rises by 10 percent.
(c) The price level falls by 2 percent.
(d) Nothing—the two increases in money and output just balance out.
10. (a)
5. (a) 2 percent annual inflation
(b) 7 percent annual inflation
(c) 97 percent annual inflation
(d) 0 percent inflation: stable prices
(e) 3 percent inflation
(f) 3 percent annual inflation; technological innovation might
make it easier for people to pay bills online, so they spend
their money faster.
(b) As Irving Fisher has taught us, every nominal rate of
interest contains an inflation premium. As the inflation rate
declines, so does the inflation premium.
6. This is a worked exercise. Please see the textbook for the
solution.
(c) The vertical distance between the ten-year yield and the
inflation rate is a measure of the real rate of interest.
7. (a) 4 percent nominal
(b) 5 percent real
(c) 4 percent inflation
(d) 13 percent nominal
(e) −4 percent real
(f) 9 percent inflation
11. (a) Real interest rates can be negative any time the nominal interest rate is less than inflation. This was true in the
United States during much of the 1970s.
8. (a) 9 percent nominal
(b) Bank A will be flooded with business.
(c) Bank B will be flooded with customers—no one will
invest in machines and they will save money at banks instead.
Of course, it’s tough to imagine how the bank will actually
come up with that 12 percent nominal interest if the nominal
return in the private sector is 9 percent.
9. There will be a 14 percent nominal return—6 percent
will go toward replacing the worn- out capital, while the
extra 8 percent will go to the investor who bought the
machine.
The Fisher equation is 3% real (net) return = 8% nominal
return − 5% inflation.
But of course, there’s a bit of fantasy involved in acting as if
businesspeople are required to “replace the worn-out capital.” So, you may understand the intuition better if you think
of the business as owning the capital beforehand and then
selling it someday, when the business shuts down or gets sold.
The worn-out capital just can’t sell for as much afterward.
That 6 percent depreciation is a real, live cost of doing business. Any company with worn-out capital just isn’t worth as
much as a company with fresh, intact capital. Therefore, it’s
quite reasonable to look only at the net, after-depreciation
returns.
(b) It’s essentially impossible for nominal interest rates to be
negative. If a bank offered −1 percent nominal interest for a
savings account, people would just hold their money in the
form of currency— colored pieces of paper—instead. Currency earns 0 percent nominal interest.
Aside: In the worst days of Japan’s deflation in the 1990s,
nominal interest rates on short-term government bonds were
briefly negative. Apparently, investors thought that the safety
of government bonds was well worth paying for. After all,
who wants to put millions of dollars of currency in a safe?
It’s easier to just hold a few government bonds. In addition,
since 2014, the European Central Bank has maintained its
benchmark interest rate (the Main Refinancing Operations
yield) at negative levels.
12. This is a matter of judgment, so I will leave most of this
to you. Constant inflation has the kinds of costs listed in
review question 6. But surprise inflation means that people
must change their behaviors and react to surprises. When
bread gets 15 percent more expensive, is that more because
of inflation or more because bread is just harder to make these
days? Will I get a cost of living increase big enough to cover
the spike in prices, or will business be able to trick me into
lower wages in the short run? Processing these changes is
mentally taxing. These adjustment costs are quite high.
13. In a hyperinflation, people often start using safer foreign
money or they use barter, both of which are difficult to do.
These practices occur because governments can’t or won’t
raise funds through taxes or borrowing.
70 | Chapter 8
14. Sargent has noticed that the government budget constraint
is the key driver of hyperinflation: governments get themselves in a fiscal bind and resort to the “printing press” to
make their troubles go away.
This is really a political conclusion made by Sargent, an
economist. He has concluded that since high, persistent inflation is socially costly, the only reason a government would create high, persistent inflation would be if it received some benefit
to offset those costs. And the only benefit around is the power
of the printing press to solve troublesome fiscal problems.
15. (a) $164,088 million in monetary base; currency equals
base minus reserves, so currency equals $137,469.
(b) The (GDP Implicit Price Deflator) inflation rate in 1981
was 9.34 percent. The inflation tax is $15,325.82 million—
about 0.48 percent of 1981 GDP.
(c) The only special thing I noticed about 1981 was that it was
lower than the years immediately surrounding it. The change
in the base was lower than any year since 1975, and it has
never been that low since. The government printed less money
in 1981, and that’s why inflation dropped rapidly the next year
(1982) in the United States.
16. (a) This gives us (change in M/M) × (M/PY), or money
growth times money per unit of output.
(b) I will use lowercase for growth rates and uppercase for
levels. As usual, I will assume velocity growth is zero.
(π + y) × M/PY
(c) i. In 1981, GDP inflation was 9.34 percent, so π +
y = 11.34 percent. The data show that M/PY = 1/V = 5.1 percent
(using the monetary base in 15(a) as our measure of M). The
product of these two is 0.58 percent of GDP.
This is more than 20 percent the amount from exercise 15(b).
I’d guess the reason is because inflation is “sticky,” as we’ll
see later. It took a year or two for inflation to fall to the lower
level predicted by the quantity theory. Remember, just to keep
it simple we completely ignored velocity shifts. So, our “inflation tax” equation gets us close to the truth—we may just
have to wait a couple of years for the nominal shocks to work
out to get the same answers.
ii. In 2005, GDP price inflation was 3.2 percent, so that
π + y = 5.2 percent, and assuming a constant velocity and
given that 1/V = 6%, the inflation tax in 2005 as a percent of
GDP was about 0.31 percent.
(d) All through this inflation tax discussion, we’ve been
(intentionally) ignoring the fact that the inflation tax creates,
well, inflation! As inflation rises, the buying power of the
government’s newly printed money falls dramatically. That
makes it harder for the government to create buying power
with the printing press.
To make our story complete, we’d have to go through
exercise 16’s formulas again, dividing through by the price
level. But that would take us too far afield—we’ll leave that
for an advanced course. For now, just keep in mind that all
hyperinflations are temporary— eventually, the government loses the ability to raise real buying power by printing money.
17. This is an essay response that I will leave to you to answer.
Suffice it to say that Friedman and Schwartz’s book is a classic, still read and respected by economists from a variety of
political and economic viewpoints.
CHAPTER 9
An Introduction to the Short Run
REVIEW AND PRELUDE
This might be a good time to review what has come before:
perhaps take a minute or two to remind students that the previous story was largely a supply-side model: each year, there’s a
fixed number of workers, machines, and ideas; markets work
well enough to make sure they all get used efficiently. In real
life, this might not be a good model of how things work at
every moment, but economists tend to think it’s a good explanation on average.
Now, for the next six chapters, demand is in charge. We’re
now entering an upside-down world, and the ultimate goal
will be to explain how things can be driven by demand in the
short run and supply in the long run. The last chapter in this
section, Chapter 15, synthesizes the analyses of the short run
and the long run.
CHAPTER OVERVIEW
In this short chapter, you get to explain what business cycles
are, why they matter, and what causes them. It sounds like
a lot to do in just a few pages— especially the causation
part. But if you treat this as the “How I would explain New
Keynesian theory to my grandmother over coffee” chapter,
you’ll probably capture just the right tone. This is the chapter for intuition and memorable oversimplifications. Details
come later.
9.1 and 9.2 Introduction and the Long Run,
the Short Run, and Shocks
Chad starts off with Keynes’s quip that “in the long run, we
are all dead.” Especially when disasters like the Great
Depression are possible, it’s important to keep in mind the
need to avoid the terrible storms of awful short-term performance. As a case study notes below, the Depression was sufficiently awful that it made the government-planned economies
of the Soviet Union look relatively attractive—a fate most of
the Western world avoided partly because of the academic
innovations of men like Keynes and the political entrepreneurship of men like Franklin D. Roosevelt.
Chad consistently uses the term “short-run output” rather
than “GDP gap.” Thus, you and your students will see the
words “positive short-run output” and “negative short-run
output” repeatedly in the text. A heavy emphasis on what
these terms mean will pay off; a sample lecture below gives
some examples of how you might do that. Essentially, both
professional macroeconomists and your students must be in
the habit of sorting actual gross domestic product (GDP) into
two bins: “potential GDP” and “short-run GDP.” We can
usually identify short-run GDP after the fact, because if we
see too much of it, inflation rises. That’s learning the hard
way, of course, and so a case study below focuses on how
former Federal Reserve chairman Alan Greenspan and the
editors of Business Week magazine did the job in real time.
MEASURING POTENTIAL OUTPUT AND
CYCLICAL FLUCTUATIONS
There are two ways to measure potential GDP:
1. Use the production function: find out the size of the
workforce, the capital stock, and the level of technology,
and estimate how much GDP would be produced if the
economy worked efficiently. This is what the Congressional Budget Office does when it measures “potential
GDP,” and yes, it takes a lot of hard work combined
with some intelligent guesswork.
71
72 | Chapter 9
2. Draw a straight trend line through the actual path of real
GDP.
Surprisingly, both methods get us much the same answer,
though in method 1, real-life recessions look bigger and
booms look smaller, since the CBO tends to assume that
boom times are “when things are going right,” not “when
things are booming unsustainably.”
Most macroeconomists these days tend to use method 2.
As mentioned above, there’s a third “hard way” to measure
potential: after the fact, by way of the Phillips curve. That is
discussed in Section 9.3.
Regardless of how you decide to measure potential output, you can define actual output as the sum of the long-run
trend and short-run fluctuations Yt = Yt – t + t, so Yt / t
= Ỹt + 1; where t is potential output, and Ỹ is short-run output
[Yt – t] / t). To ensure that we can compare short-term fluctuations across time, we measure short-term fluctuations as
a percentage of potential output—that is, for a given year,
the difference between current output and potential output
divided by potential output. Chad refers to this measure of
cyclical variation as Ỹt or short-run output.
This should give students a rough idea of how this all ties
together.
9.4 Okun’s Law: Output and Unemployment
Arthur Okun, as is well known, found a statistical relationship between output and unemployment. This statistical relationship, known as Okun’s law, has withstood the test of time.
Okun’s law means that even though we’ll spend our energies in Chapters 9–14 talking about fluctuations in short-run
output, that’s roughly the same as talking about fluctuations
in the unemployment rate. It’s a good thing to remind students about this every couple of lectures.
9.5 Filling in the Details
Yes, there’s more to be done: this chapter is, after all, the
“explaining it all to Grandma” chapter.
SAMPLE LECTURE: THE DIFFERENCE BETWEEN
THE LONG RUN AND THE SHORT RUN
9.3 The Short-Run Model
Here it is, in just a few sentences:
1. Shocks push actual GDP away from potential GDP in
the short run—so actual GDP and potential GDP are not
the same thing.
2. Monetary and fiscal policy impact actual GDP in
the short run— perhaps as shocks, or perhaps (if we’re
lucky) as stabilizers. So maybe monetary and fiscal policy can make things better, or maybe they make things
worse.
3. The (accelerationist) Phillips curve tells us that positive
GDP shocks raise the rate of inflation, and negative GDP
shocks reduce it.
That’s pretty much the model. But how can you present this
to students briefly yet clearly? Chad’s approach is to focus
squarely on point 3. He tells an intuitive story about the Phillips curve, shows that the data support his story, and moves
on. Since you get to spend Chapters 10 and 11 delving into
points 1 and 2 in some depth, I’d do the same.
The most I’d do is loosely tie together the Phillips curve
story of inflation with the money growth story of inflation
that you just finished covering. You may want to point out
that when the Federal Reserve prints more money, the shortrun effect is to push actual output above potential output,
which in turn creates inflation in the longer run.
So, the causal mechanism runs this way: Higher money
growth → Positive short-run output → Higher inflation.
Chad then launches into an explanation of the differences
between the short and long runs. If you can help your students understand the difference, you’ll make it a lot easier for
them to read the newspaper.
In fact, that might make for a good in-class exercise: write
up ten different fake (or real) economic news headlines, and
have student groups discuss whether they are most likely stories about changes in potential GDP or whether they are
likely about mere fluctuations around the trend. Relatively
clear examples might include the following:
“Breakthrough drug receives patent”;
“Unemployment up 0.3 percent in May”;
“Crisis in housing market”;
“Congress raises minimum wage by $3 per hour”;
“New, tougher car-safety regulations issued”; and
“New bank regulations boost lending to underserved
markets.”
Why emphasize long run versus short run? This lets students
know that most news stories are extremely unlikely to matter
in the long run. Point out Figure 9.2 and mention to students
some of the major headlines that appeared in newspapers
from the late 1940s through today: “Dewey Defeats Truman,”
“Korean War Ends,” “Man Lands on Moon,” and so on. Note
that none of those news stories, which may have been important in their own rights, appeared to do anything noticeable
to the long-term trend in GDP. Yes, the 1/2 percent to
1 percent changes in trend growth that apparently happened
in the early 1970s and the mid-1990s are impor tant— but
An Introduction to the Short Run | 73
those are really the only two major macroeconomic events
of the last fifty years as far as potential GDP growth goes (and
perhaps as far as the unemployment rate is concerned as
well).
Your students have all seen the film Jurassic Park, and
many of them either believe or want to believe Jeff Goldblum’s suggestion that a butterfly flapping its wings in the
Amazon can cause a hurricane halfway around the world.
Students are quite open to the belief that everything is interconnected and that what we decide today will impact the infinite future.
But time-series analysis appears to tell us that almost all
economic shocks have short-term impacts that die off within
a few quarters. Whether we use ocular econometrics or the
sophisticated tests in the time-series literature, we seem to
get the same story: 2 percent trend growth has been with us
a long time (+ or − 1 percent), and so our best bet is that it will
be with us for quite some time to come.
Of course, one skill worth developing is the ability to discern a big break in the trend—something that Alan Greenspan and the writers of Business Week did in the early 1990s.
A case study below looks into this a bit more.
CASE STUDY: SEEING THE NEW ECONOMY
In the mid to late 1990s, the long-term trend in potential GDP
growth shifted for the better. Why would we discuss this in
a chapter on business cycles? Because good economic policy demands that economists sort economic output into two
big categories: potential GDP and short-run GDP. If they do
a bad job, then bad economic policy is the result. In par ticular, if the Phillips curve is right, then when actual GDP is
above potential GDP, inflation rises. That means policy makers need to know what potential GDP really is.
When potential GDP (per capita) first started growing faster
in the mid-1990s, few economists believed it. Instead, they
concluded that what was growing wasn’t potential GDP—it
was just some extra short-run GDP, the kind of output that
drives inflation up.
Prominent economist and New York Times columnist Paul
Krugman mocked the idea that the economy’s “speed limit”
had really increased. But Alan Greenspan and the editors of
Business Week saw it clearly.
Krugman closed a 1997 essay in the prestigious Harvard
Business Review this way: “We would like to believe that
America can grow much faster if only the Fed would let it;
but all the evidence suggests that it cannot.”1
By contrast, Stephen Shepard, editor in chief at Business Week, put it this way at around the same time: “We have
1. Paul Krugman, “How Fast Can the U.S. Economy Grow?” Harvard
Business Review (July/August 1997), available at http://web.mit.edu
/ krugman /www/ howfast.html.
here the magic bullet— a way to return to the high-growth,
low-inflation conditions of the 1950s and 1960s. Forget
2 percent real growth. We’re talking 3 percent, or even
4 percent. Forget double-digit inflation and the natural rate
of unemployment.”2
As the data over the last decade have made clear, the Business Week view turned out to be closer to the truth. So why
did Krugman and other academic economists fail to see the
big change that was so obvious to Greenspan3 and the editors of Business Week? Perhaps it was because academics stay
a bit too far away from the day-to-day decision-making processes of business. Therefore, perhaps it’s worthwhile to
spend some time reading Business Week in between issues
of Econometrica.
EXPANDED CASE STUDY: THE GREAT
DEPRESSION AND THE INTELLECTUALS
After almost eighty years, it’s hard to realize just how important the Great Depression was at the time. To most intellectuals in the 1930s—whether professors, writers, or policy
professionals—it proved decisively that capitalism could not
sustain itself. The fact that the U.S. economy only fully recovered during World War II looked like further evidence that
massive government control of the economy was the only way
to keep everyone employed in useful jobs. Many U.S. intellectuals traveled to the Soviet Union, saw its massive industrialization (but rarely its terror, famines, and gulags), and
concluded that the way of the future was clear: a governmentrun economy was the only practical solution.
But after the end of World War II, something surprising
happened: tens of millions of soldiers returned to civilian
life—in the United States, in Japan, in England, and in
Germany— and in most cases, found private-sector jobs.
After a year or two of awful suffering, the war-torn countries
began to recover quickly, while the United States continued
its role as the world’s industrial leader, enjoying relatively low
unemployment rates. In the decades after the war, intellectuals slowly became convinced of the economic strengths
of mixed capitalistic systems, and most concluded that the
experiment with socialism/communism was an economic
disaster—not just a human rights disaster.
2. Stephen B. Shepard, “The New Economy: What It Really Means,”
Business Week (November 1997), available at http://www.businessweek
.com /1997/46/ b3553084.htm.
3. Alan Greenspan “Question: Is There a New Economy?” (September 4,
1998), available at http://www.federalreserve.gov/ BOARDDOCS/SPEE
CHES/1998/19980904.htm.
74 | Chapter 9
CASE STUDY: THE CAUSES OF
THE GREAT DEPRESSION
Randall Parker’s book Reflections on the Great Depression4
reports, according to Ben Bernanke, the current chair of the
Federal Reserve, that the Great Depression is “the Holy Grail
of macroeconomics.”5 As many know, Bernanke wrote his
PhD thesis, in part, on the Great Depression (see http://econ
-www.mit.edu/about /economic).
President Obama appointed Christina Romer as chair of
the Council of Economic Advisers. Romer, like Bernanke,
has written extensively on the Great Depression.6 Romer
(1993) describes the causes of the Great Depression in America. The Depression began with a series of aggregate demand
shocks, where the classical shock absorbers, flexible wages
and prices, were impeded by market rigidities, like sticky
prices. Moreover, Romer recognized the potential role of
price deflation in further destabilizing aggregate demand
either through price expectations effects or through increases
in real debt burden (when the shock absorbers become shock
enhancers). Romer concluded that domestic spending shocks
were impor tant in explaining the early years of the Great
Depression, while monetary shocks (an inelastic monetary
base thanks to the gold standard) and rising real interest rates
explained its latter years.
CASE STUDY: MILTON FRIEDMAN ON
THE GREAT INFLATION
John Taylor interviewed Milton Friedman about his life and
his work for the Quarterly Journal of Economics. Paul Samuelson and William Barnett republished the interview in
2007.7 Friedman, as in Chapter 8, ascribes inflation to political rather than economic problems. Essentially, the Kennedy administration took advantage of noninflationary
conditions (expectations) to stimulate the economy. The
effects of the economic stimulus gradually built up inflationary pressures. Moreover, after Richard Nixon was elected
president, Friedman’s former teacher, Arthur Burns, was
chair of the Federal Reserve. According to Friedman, during Burns’s term as chair, the money supply grew excessively,
with growth rates over 6 percent. Moreover, President Nixon
wanted a rapid increase in the money supply to improve his
4. Randall E. Parker, Reflections on the Great Depression (Northampton, MA: Edward Elgar Publishing, Ltd., 2002).
5. Ben S. Bernanke, Essays on the Great Depression (Princeton, NJ:
Princeton University Press, 2004), 5.
6. Christina D. Romer, “The Great Crash and the Onset of the Great
Depression,” Quarterly Journal of Economics (August 1990); Christina D.
Romer, “The Nation in Depression,” Journal of Economic Perspectives
(Spring 1993).
7. Paul A. Samuelson and William A. Barnett, Inside the Economist’s
Mind (Malden, MA: Wiley-Blackwell Publishing, 2007).
reelection chances in 1972. Nixon believed that the recession
of 1960 contributed to his defeat against Kennedy. In hindsight, many thought Burns misunderstood the level of potential GDP, and therefore the reason for the inflation was a
mistake of overestimating potential GDP: having an expansionary monetary policy at a time when potential GDP was
falling and therefore short-run output, Ỹt, was increasing.
Friedman disagreed with this conclusion. Friedman thought
the mistake was not in economics but in politics.
CASE STUDY: DATING BUSINESS CYCLES
The National Bureau of Economic Research (NBER) dates
business cycles (see http://www.nber.org/cycles/main.html).
The NBER identifies peaks, troughs, and the durations of
contractions and expansions. The NBER has identified business cycles ranging as far back as 1857, right up to date. The
NBER has identified the most recent recession as beginning
in January 2008 and ending in June 2009. The peak of the
previous cycle was December 2007 and that cycle began in
November 2001 and lasted seventy-one months. This last
recession was the longest of the post–World War II era—
lasting eighteen months.
In identifying the beginning of the contraction, the recession, the NBER identified the following conditions: (1) a
significant decline in economic activity across the country
lasting more than a few months; (2) that economic activity is
widely reflected in production and payroll employment; and
(3) that other monthly data, such as real personal income less
transfer payments, real manufacturing, and so on, can be useful indicators. An examination of these data series caused
the NBER to conclude that the Great Recession had begun
in January 2008.
Note that the NBER Business Cycle Dating Committee
does not use the standard two- consecutive- quarter decline
in GDP to define a recession. The committee defines a recession as a “period of falling economic activity spread across
the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales” (see http://www.nber.org).
The reasons for defining a recession in this way include the
following: (1) economic activity is not solely defined by real
GDP; (2) GDP is published quarterly and the committee is
looking for monthly indicators; (3) a recession is defined not
only according to the duration of the decline but also according to the depth of the decline; and (4) the statistical discrepancy between GDI and GDP makes the percent change in
production sometimes difficult to ascertain.
The NBER Business Cycle Dating Committee met in
April 2010 to consider whether the recession had ended. It
was not willing to declare the recession over, despite the
improvement in many indicators. Many indicators at that
point were too preliminary to be conclusive. When the com-
An Introduction to the Short Run | 75
mittee met again in September 2010 it was able to declare the
recession over as of June 2009. This declaration was based on
quarterly measures of GDP and GDI; monthly measures of
GDP and GDI provided by a private forecasting firm and the
independent research of committee members; and monthly
data of payrolls, employment, manufacturing, industrial production, and sales.
CASE STUDY: THE FLATTENING OUT OF
THE PHILLIPS CURVE
Chad, at the end of the chapter, exercise 4, asks a question
about the what happens if the Phillips Curve were to flatten
out. This happens to be a very apropos question, as empirical evidence suggests that the Phillips curve has indeed flattened out over time. Consider the following statistical
illustration. The change in the inflation rate is measured as
the change in the Core Personal Consumption Expenditure
inflation rate, and short-run output is measured, as described
in the text, as the cyclical variation in real GDP relative to
potential real GDP. Two time periods are considered: (a) 1950
to 1999; and (b) 2000 to 2015. In the first time period, for every
1 percentage point change in short-run output, the change in
the inflation rate is 0.186 percentage points. In the second, for
every 1 percentage point in short-run output, the change in the
inflation rate is about 0.082 percentage points. The empirical
evidence suggests that the Phillips curve has flattened out and
the inflation is, perhaps due to a myriad of factors—including
the weakening of unions and the outsourcing of labor as the
domestic labor market tightens—less sensitive to changes in
the cyclical variations in output.
These findings are further illustrated in Figures 1 and 2
below.
Figure 1. Phillips Curve Estimates 1950 to 1999
(Slope = 0.186)
Figure 2. Phillips Curve Estimates 2000 to 2015
(Slope = 0.082)
Table 1. PHILLIPS CURVE ESTIMATES OF THE SHORT- RUN PHILLIPS CURVE: 1950 TO 1999
(THE DEPENDENT VARIABLE IS THE CHANGE IN THE CORE PERSONAL CONSUMPTION EXPENDITURE PRICE
INDEX, AND THE INDEPENDENT VARIABLE IS “SHORT- RUN” OUTPUT).
Prais-Winsten AR(1) regression— iterated estimates
Number of obs
F(1, 48)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
50
7.23
0.0098
0.1309
0.1128
1.2651
Source
SS
df
MS
Model
Residual
11.5660868
76.8173425
1
48
11.5660868
1.6003613
Total
88.3834293
49
1.80374345
Coef.
Std.
Err.
t
P>|t|
[95% Conf. Interval]
.1861757
.0337255
−.1046613
.0692342
.1623274
2.69
0.21
0.010
0.836
.0469711
−.2926556
.3253804
.3601066
Δπ
Y
_cons
rho
Durbin-Watson statistic (original) 2.193797
Durbin-Watson statistic (transformed) 2.041349
(Data source: FRED Database and author’s calculations.
76 | Chapter 9
Table 2. PHILLIPS CURVE ESTIMATES OF THE SHORT- RUN PHILLIPS CURVE: 2000 TO 2015 (THE DEPENDENT
VARIABLE IS THE CHANGE IN THE CORE PERSONAL CONSUMPTION EXPENDITURE PRICE INDEX, AND THE
INDEPENDENT VARIABLE IS “SHORT- RUN” OUTPUT.)
Prais-Winsten AR(1) regression— iterated estimates
Number of obs
F(1, 14)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
16
5.77
0.0308
0.2918
0.2412
.29328
Source
SS
df
MS
Model
Residual
Total
.496099681
1.20419222
1.7002919
1
14
15
.496099681
.08601373
.113352793
Coef.
Std.
Err.
t
P>|t|
[95% Conf. Interval]
.0343293
.1118075
2.40
1.76
0.031
0.101
.0088163
−.0434217
.1560745
.4361848
Δπ
Y
_cons
rho
.0824454
.1963816
.0444605
Durbin-Watson statistic (original) 1.890987
Durbin-Watson statistic (transformed) 1.950175
(Data source: FRED Database and author’s calculations.)
REVIEW QUESTIONS
1. The short-run model is used to explain fluctuations in output around potential output. The long-run model explains the
level and growth in potential output. In order to understand
the size and sign of short-run output, long-run output must
be known.
2. One reason is that the size of the short-run output fluctuations tends to be constant in percentage terms: positive output shocks are in the 3 percent range, not in, say, the $300
billion range. In other words, expressing short-run output as
a percent of potential output allows for comparisons across
time. A $100 billion fluctuation in short-run output in 2013
is (relatively) much smaller than the same fluctuation in output in 1965.
recession periods, inflation is more of a random walk, just
based on this simple graph.)
6. Okun’s law is handy because typical voters care about
unemployment rates more than they care about the GDP
numbers. Our model focuses on short-run GDP, but we can
speak to the person on the street by running our model
through Okun’s law. Also, since unemployment rates tend to
fall a year or so after GDP starts to rise, one can use today’s
GDP growth to forecast changes in the unemployment rate
over the next year.
EXERCISES
1. (a)
3. If we look at Figure 9.3, we can see that Ỹ in the 1981–82
recession was almost −8 percent. In comparison, Ỹ, at its
worse in the 2007–09 recession was about −7 percent. However, the cumulative effects of these recessions have been
quite different. Following the 1981–82 recession, the recovery in Ỹ was quite sharp, and, as is well known, the current
recovery remains quite slow.
4. In 2010, some recent shocks had been high oil prices and
the subprime mortgage market collapse (pushing down stock
prices and tightening credit markets) and a fall in new home
buying.
5. We see the Phillips curve in Figure 9.5 because every time
the inflation rate crosses a gray NBER recession line, the rate
of inflation tends to fall. Therefore, when the economy drops
below potential GDP, inflation drops noticeably. (During non-
(b)
An Introduction to the Short Run | 77
(c) As Chad writes in the textbook, the slowdown in investment means a slowdown in the accumulation of capital goods
and decrease in the rate at which potential output grows.
2. This depends on the student’s choice.
3. This is a worked exercise. Please see the text for the
solution.
Change in inflation
4. Slope of the Phillips curve
three cases, all three years of lost output add up to 6 percent.
The real question is, do I want a quick, sharp recession or a
slow, draining one? The Reagan/Volcker recession was like
option 1, and by the time reelection came three years later,
people had almost forgotten about the recession. As a famous
TV ad said, in 1984 it was “Morning in America.” In 1991,
by contrast, George H. W. Bush had a much milder recession
that seemed to linger on until his reelection campaign, much
like option 3, and he lost. This is a tough question, one where
we can’t give a clear answer without a clearer understanding
of what the politician wants.
(c) Here, the answer seems clearer: if we care about low inflation, then we want option 1. That gets us to our goal quickly.
(d) The only way to lower inflation (a good thing, usually) is
to create a recession (a bad thing, almost always).
0%
6. (a) True output falls to a new, lower level—in other words,
policy makers accidentally create a recession.
0%
Short-run output
(a) In the steep (solid) economy, a boom causes a sharp rise
in inflation, while a bust causes a fast drop in inflation.
Changes in inflation happen more slowly in the flat (dashed)
economy.
(b) The slope might be different because people in the flat
(dashed) economy aren’t used to seeing inflation change—
maybe inflation has been stable for years, so they don’t think
about it much. Alternatively, government rules or strong
monopoly or union power could make it difficult to change
prices in the dashed economy.
(c) It seems to be flatter than in the late 1970s (and early
1980s). A casual look at Figure 9.7 shows that the big outliers in that picture are in the upper-right and lower-left corners. Those outliers tend to come from the 1970s and early
1980s. So, if we redrew the trend line but only used those
outliers as data, we’d have a somewhat steeper line than we
see in Figure 9.7. It’s not a major difference, but perhaps the
line grew flatter in the past two decades as Americans grew
used to low, stable inflation.
5. (a) The slope is +1/2. For each option, in year 1, for every
two-percentage-point decrease in Ỹ, the change in inflation
is −1 percentage point.
(b) If I only care about the cumulative lost output, as Chad
does in the text, then I can’t decide between the three. In all
(b) Inflation falls.
(c) If the central bank was too optimistic instead, then the
central bank would accidentally create a long-lasting boom,
which would push inflation up every year.
This is one leading explanation for what the U.S. Federal
Reserve did in the 1970s: the economy’s long-run productivity growth rate fell, but the Federal Reserve thought a shortterm recession was the true cause of the slow growth—so the
Fed stimulated the economy with low real interest rates. That
created a boom (positive short-run output). The Phillips curve
turned out to be right: the boom led to higher inflation for
most years in the 1970s.
7. (a) + (b)
Year
Actual
output
Yt
Potential
output Yt
Yt − Yt
Short- run
output Yt
Growth
rate of
actual
output
%ΔY
2018
2019
2020
2021
2022
2023
2024
18.00
18.60
19.00
18.90
19.00
20.00
20.90
18.00
18.45
18.91
19.38
19.87
20.37
20.87
0.00
0.15
0.09
−0.48
−0.87
−0.37
0.03
0.00%
0.81%
0.47%
−2.50%
−4.37%
−1.79%
0.12%
3.33%
2.15%
−0.53%
0.53%
5.26%
4.50%
(c) The economy is in recession in 2021–2023. Note that
under our definition of “recession,” any time output is below
potential, we’re in recession.
78 | Chapter 9
(d) So even though the economy grew between 2022 and
2023, it still receded compared to its true potential. In fact,
current output—the real value of goods and services— only
fell in 2021.
Just as professional athletes, corporations, and movie ticket
sales are judged according to prior expectations, the overall
economy is judged the same way. If you can’t meet the high
expectations, people conclude that you’re in trouble.
As this question and question 4 imply, in real life, creating
an accurate expectation of an economy’s potential output is
one of the hardest things about being a central banker.
8. (a) 4.5 percent, 5 percent, 5.5 percent, and 6 percent,
respectively
(b) −2 percent, −4 percent, and 2 percent, respectively
CHAPTER 10
The Great Recession: A First Look
REVIEW AND PRELUDE
This chapter makes the study of macroeconomics topical.
Leading news stories are brought into the classroom. How the
economy worked itself into the Great Recession and how government reacted to the Great Recession are reviewed. Students are introduced to the importance of balance-sheet
decisions in affecting spending flows and aggregate economic
activity. Business majors, particularly finance majors, will
probably pick up these concepts faster than economics
majors.
understand the causes and cures of the crisis and our future
economic risks.
10.2 Recent Shocks to the Macroeconomy
In this section, the role of housing prices, the global savings
glut, subprime lending, rising interest rates, the financial turmoil of 2007, and oil prices are all discussed as causes leading up to the Great Recession.
HOUSING PRICES
CHAPTER OVERVIEW
This chapter examines some of the major causes of the financial crisis that began in the summer of 2007. The importance of the effects of leverage in explaining systematic risk
or contagion is discussed. The depth and duration of the Great
Recession, which began in January 2008 and ended in
June 2009, is compared to previous recessions. The Great
Recession has international dimensions that are explored.
The Great Recession is the longest and deepest recession the
United States has experienced since the Great Depression.
Large and respectable investment companies made huge profits in the securitized mortgage markets. Many companies
literally “bet the bank” on these mortgages. When homeowners began to default, fears of chains of bankruptcies, a collapse of the fi nancial markets, and a repeat of the Great
Depression ensued. The public-sector responses to the crisis
were unprecedented, with multibillion dollar bailouts and
loan guarantees. The suddenness and depth of this crisis and
the government response have become an important research
topic in macroeconomics as macroeconomists attempt to
Here we see the familiar story of the inflation of housing
prices and the bursting of the bubble. In the decade leading
up to 2006, housing prices increased by a factor of 3, or about
10 percent per year. Housing price inflation was greater in
some markets (such as Boston, Los Angeles, New York City,
and San Francisco) than others. Housing prices peaked in
2006, then dropped by 36 percent between 2006 and 2012.
The question is, “What caused the rise and collapse of housing prices?”
THE GLOBAL SAVING GLUT
The global saving glut is tied to the international financial
crises of the 1990s. Some countries, like Mexico, Russia,
Brazil, and Argentina, switched from net borrowers to net
savers. With this saving glut, foreign demand for U.S. assets
increased and this increase in demand led to asset price inflation in the United States. Although not mentioned in the
text, some economists have argued that the saving glut can
be traced to the trade imbalance between the United States
and Asian countries, particularly China, and that these
79
80 | Chapter 10
countries had plenty of liquidity to invest in U.S. financial
markets. Still other economists, such as John Taylor, dispute whether such a glut existed in the first place. Robert
Shiller, in the second edition of Irrational Exuberance
(Princeton, NJ: Princeton University Press, 2005) emphasized other causes in explaining asset (housing) price inflation. See the case study on housing price inflation.
SUBPRIME LENDING AND THE RISE OF INTEREST RATES
Here Chad provides a Minksy-esque tale of the financial crisis (see the case study that follows: “Hyman Minksy and the
Financial Market Instability Hypothesis”). The worldwide
savings glut led to lower interest rates and lax lending standards that encouraged mortgage debt and the purchases of
new homes. The reduction in lending standards led to the rise
in subprime mortgages. By 2006, subprime mortgages represented about one-fifth of all new mortgages. Many of these
subprime mortgages had adjustable rates and included low
(below market) teaser rates. Following 9/11, the Fed reduced
one of its impor tant lending rates, the federal funds rate, to
historic lows. Between 2004 and 2006, the Fed increased the
federal funds rate from 1.25 percent to 5.25 percent in anticipation of higher-than- expected inflation. The increased
interest rates reduced home prices and increased the interest
payments on adjustable rate mortgages. Borrowers were
unable to refinance their homes, because many borrowers had
little or no equity to begin with and the decrease in housing
prices caused borrowers to be upside down in their mortgages
(the value of their homes was less than their mortgages).
Therefore, they were required to make higher interest payments they could not afford. The result was a wave of foreclosures and a glut of housing. The collapse in the housing
market violated the conventional wisdom that the U.S. housing market, in the aggregate, was immune from such a crisis.
The collapse of the conventional wisdom caused widespread
financial turmoil.
THE FINANCIAL TURMOIL OF 2007–2009
As is now well understood, the financial crisis is related to
the development of a financial innovation—the securitization
of mortgages, or mortgage-backed securities (collateralized
debt obligations). Many students will probably be unaware
that banks sell most or many of the mortgages they write to
the Federal National Mortgage Association (Fannie Mae)
and the Federal Home Loan Mortgage Corporation (Freddie
Mac) (or other investment companies) and that these companies pool (package) individual mortgages into marketable
securities. The underlying value of the securities is dependent
upon each household making good on its promise to pay its
mortgage. Fannie Mae and Freddie Mac cornered the prime
mortgage market. Other investment companies wanted a
piece of the profits and purchased and packaged subprime
mortgages into securities. Investors originally thought that
the mortgage-backed securities were relatively safe—the U.S.
housing market was almost good as gold—and that the higher
rates of interest charged offset the risk associated with the
subprime mortgages. Unfortunately, this conventional wisdom unraveled as households defaulted on their mortgages.
Banks and other financial institutions that were heavily
invested in these instruments became at risk of failing (see
the case study “CDOs, Leverage, and Capital Requirements”).
Lenders became concerned about the risk of defaults and
interest rates. An important measure of the expected default
risk is the spread between the London Interbank Offered Rate
(LIBOR) and the Treasury bill (T-bill) rate. LIBOR is a rate
of interest charged to banks on short-term loans, and the
Treasury bill rate is the rate of interest the U.S. Treasury pays
on short-term loans. There is no default risk in holding Treasury bills. Under normal circumstances, the default risk of
banks is expected to be small, and the spread between LIBOR
and T-bills is likely to be small (0.2 to 0.4 percentage points).
The news of defaults in the mortgage industry spread. No one
knew with perfect certainty which banks were in trouble.
Consequently, premiums increased. In October 2008, the
three-month LIBOR was 4.05 percent; the T-bill rate was
0.67 percent. The spread was 3.38 percentage points. As
reflected in the high-risk premium, the rise in uncertainty led
to a decline in lending, and the decline in lending caused the
decline in asset prices. The decline in asset prices led to further declines in asset prices, as businesses were forced to sell
assets to meet debt requirements. The S&P 500 peaked in the
third quarter of 2007 at 1,505.45 and by the second quarter of
2009 had fallen to 786.28 (about a 48 percent decline).
OIL PRICES
The Federal Reserve Bank of Dallas provides an estimate of
the relationship between the price of a barrel of oil and the
gross domestic product (GDP) growth rate. During normal
times a $10 increase in the price of a barrel of oil is likely to
reduce the GDP growth rate by 0.3 percentage point (see
Federal Reserve Bank of Dallas, “Do Rising Oil Prices
Threaten Economic Prosperity?” Southwest Economy, no. 6
[November–December 2000]). Oil prices rose from a low of
about $20 per barrel in 2002 to more than $140 per barrel in
2008, a sevenfold increase in prices. The rise in the price of
oil raised the price of other commodities, for example, corn
and wheat. Corn was in increased demand to produce ethanol, a substitute for gasoline, and land was diverted from
wheat production to corn production to produce more corn.
The rise in the price of oil has been attributed to increases in
world demand (particularly from developing countries like
India and China) and to speculative elements. For example,
oil futures were seen as a means to hedge a potential fall in
The Great Recession: A First Look | 81
the value of the dollar. If the value of the dollar fell, the value
of the oil futures increased in terms of dollars. With the Great
Recession, just as during the recessions between 1979 and
1982, the price of oil collapsed to $40 per barrel a few months
later. Of course, a “new chapter” in the oil-price story must be
written as increased production and the recent global slowdown in demand has caused Brent Crude prices to drop from
about $114 per barrel in June 2014 to around $45 in July 2016.
10.3 Macroeconomic Outcomes
The collapse in the housing market, the financial instability,
and the rising prices of oil combined to generate the deepest
recession in the post–World War II era. Many indicators evidenced the recession:
1. Employment fell—the economy lost 8.5 million jobs;
2. Short-term output fell below potential output by as much
as 7 percent; and
3. The unemployment rate increased from about 4.5 percent
in 2007 to over 10 percent in 2009, and remained above
7 percent in 2013.
Further evidence that this recession is different from past U.S.
recessions is apparent. First, compared to earlier recessions,
its eighteen-month duration is longer than the previous two
recessions in 2001 and 1991, which were each eight months
long. Second, declines in the major indicators were stronger.
Third, the sudden and steep decline in housing prices and
stock prices, the failures of major financial institutions, and
the international dimensions of the declines were reminiscent
of the Great Depression. Moreover, in the last two recessions,
the rate of growth in personal consumption expenditures
slowed, but in this recession consumers actually reduced their
consumption expenditures. As in past recessions, disinflation
occurred. However, in this recession, with oil and other commodity prices falling so dramatically, some deflation occurred.
Students should be made aware that during downturns and
upturns, the unemployment rate lags real GDP. Moreover, students might be interested in knowing that productivity (real
GDP divided by employment) moves countercyclically. When
employment initially decreased, productivity increased. In the
third quarter of 2008, when the economy was shedding jobs,
productivity grew at 8.4 percent. Finally, the international
linkages of the Great Recession are quite strong. For the rest of
the world in 2009, as shown in Table 10.3, while growth rates
slowed in India and China, real GDP fell in Japan, the United
Kingdom, the euro area, and Brazil. The United Kingdom, the
euro area, Italy, and Spain double dipped into recession in
2012. By 2015, most countries, except for Brazil, recovered,
but real GDP growth remains stagnant in Japan and the euro
area.
10.4 Some Fundamentals of Financial Economics
Given that the housing crises, the financial crises, and the
Great Recession are all interrelated, an understanding of the
role of balance-sheet decisions in these crises is useful.
As Chad writes, in many ways the Great Recession is a
balance-sheet crisis. To familiarize students with the balance
sheet, you can recognize that the balance sheet is simply a
set of records identifying the values of what the public owns
(assets) and what the public owes (liabilities). The difference
between what is owned and what is owed is net worth or
equity. Balance sheets are records of stock variables measured at a point in time, as opposed to income and expense
statements, which are records of flow variables (variables
measured through time). An important goal of investors is to
maximize the rate of return on equity. An easy device for
increasing the rate of return is leverage. Leverage is the ratio
of indebtedness to equity. For example, suppose an investor
has $1 and borrows $99 to purchase a stock at a price of $100
(ignore the interest expense). If the value of the stock rises
by $2, or 2 percent, the return on the equity position in the
stock is 200 percent ($2 gain divided by the investment of
$1). Given this lucrative return, an investor has a strong incentive to risk borrowed funds to maximize the rate of return
on equity. The difficulty arises, of course, if the value of the
stock does not increase. If the value of the stock decreases
by $2, the investor’s equity position in the stock is not sufficient to cover the losses. In this case, not all of the loan can
be repaid. The loan is in default, and the lender’s asset, the
investor’s IOU, decreases in value. The lender’s net worth and
ability to pay its loans diminishes. When asset values fall
below the value of liabilities, net worth becomes negative,
and bankruptcy ensues.
Banks have the same incentives as investors to use leverage and borrowed funds to increase the rate of return on
equity. However, banks are limited in their use of leverage.
The limit on the use of leverage by banks is referred to as
capital requirements. Capital requirements specify the ratio
of assets to equity. These capital requirements limit banks’
ability to borrow funds to purchase assets to increase the rate
of return on equity, and, in effect, reduce bank exposure to
risk. The Federal Deposit Insurance Corporation (FDIC)
insures most bank deposits. The capital requirements reduce
the FDIC’s exposure to risk. Given the capital requirements
on banks and given the securitization of mortgages, mortgage
lending moved away from regulated banking into less regulated financial institutions and the exposure to risk increased.
Such a risk becomes systemic when the potential failure of
one or a few institutions puts the whole system at risk. For
example, if American International Group, Inc.’s (AIG) subprime mortgage securities fail to perform and AIG can’t meet
its own debt obligations, then lenders to AIG potentially fail
(here we have the too-big-to-fail argument).
82 | Chapter 10
Any of us who has seen the movie It’s a Wonderful Life
(1946) knows of bank runs. Banks have a mismatch of assets
and liabilities. Banks borrow funds short term at low interest rates and lend long term at high interest rates. The liabilities are liquid but the assets are illiquid. Much of the evolution
in bank management and innovations in financial structures
in banking result from coping with this imbalance. Prior to
this evolution, after large withdrawals from depositors, banks
might have to sell assets to generate liquidity to pay depositors. Sometimes assets are sold at fire-sale prices, and the
liquidity crisis then turns into a solvency crisis as asset values fall below the values of liabilities. During the last financial crisis, a new type of bank run developed. Deposits are
insured by the FDIC, so the depositor run on the banks was
not as prevalent as in It’s a Wonderful Life. However, bank
stockholders, fearing a collapse in the value of their stocks,
sold their stocks. This became known as a stockholders’ run
on the banks. When stockholders sold their stocks, the market value of the stocks fell, the equity or net worth of the
banks declined, and banks failed to meet their capital requirements. Failure to meet capital requirements causes banks to
sell financial assets, which further depresses the value of
assets and further reduces asset prices.
CASE STUDY: HYMAN MINSKY AND THE
FINANCIAL INSTABILITY HYPOTHESIS
Hyman Minsky (1919–96) was a Keynesian economist who
endogenized variables that most economists consider exogenous in their analyses of the economy. Since the financial
crisis, renewed interest in Minsky’s financial instability
hypothesis (FIH) has emerged.1
In Minsky’s story of the business cycle, every economic
fluctuation is tied to a series of financial “events” (cycles of
financial booms and busts). For example, Steven Keen2
describes Minsky’s FIH as follows:
Suppose the economy just finished with a bust. Investors have
been unable to realize their investment plans, suffered losses,
and are now highly risk averse. This risk aversion limits
investment to only the most financially sound fi rms. As a
result, investment plans are realized and risk aversion on the
part of both lenders and borrowers declines.
The decline in risk aversion leads to an expansion debt. The
expansion in debt leads to asset price inflation—an increase
in the value of securities and capital gains. The capital gains
1. Stephen Mihm (2002), “Why Capitalism Fails,” Boston Globe (September 13, 2009). For a sample of Minsky’s works, see: Can “It” Happen
Again (M. E. Sharpe, 1982); “The Financial Instability Hypothesis,” Working Paper No. 74, Jerome Levy Economics Institute (1992); John Maynard
Keynes (New York: McGraw-Hill, 2008); and Stabilizing an Unstable
Economy (New York: McGraw-Hill, 2008).
2. Steven Keen, Debunking Economics (London: Zed Books, 2002).
re-enforces borrowing, external finance, and investment and
economic growth.
As such, investment plans continue to be validated. This
validation leads to a euphoric economy—where borrowers
and lenders have diminished perceptions of risk. Liquidity
becomes in short supply and interest rates start to rise as do
debt-to-equity ratios.
Some businesses get caught in a Ponzi scheme—where
debt service exceeds cash flow. As such borrowers are borrowing funds from others to make debt ser vice payments to
others—getting more and more in debt without adding capital goods to the businesses. As liquidity becomes more and
more short in supply, interest rates continue to rise and bankruptcies start to increase. Cash flows and asset prices become
out of line. Only two forces can get asset prices in line with
cash flows: 1) asset price deflation (collapse in the price of
financial assets); and 2) current price inflation (current price
inflation with low investment leads to stagflation). The economy is caught between a rock and a hard place— deflation and
stagnation, or inflation and stagnation.
CASE STUDY: ROBERT SHILLER’S IRRATIONAL
EXUBERANCE AND REAL ESTATE PRICES
Robert Shiller’s Irrational Exuberance3 is a modern-day
classic, linking economics and psychology and thereby
stretching the boundaries of economic thinking. Shiller, like
many behavioral economists, considers the conventions used
and the consequence of using conventions when decisions
must be made under conditions of uncertainty. In short,
Shiller debunks the efficient market hypothesis, shows the
limits to rational decision making, and shows the process by
which markets become unstable. In the second edition of the
book, published in 2005, prior to the crisis in the real estate
market, Shiller describes the forces that lead to booms
(bubbles) and busts in that market. Shiller, like Minsky, endogenizes variables that economists often consider exogenous.
For example, Shiller introduces the concept of price-feedback
loops to explain how an exogenous shift in demand can result
in further multiple shifts in markets, leading to bubbles or
busts in markets. For example, following an exogenous
increase in market demand for housing via a decrease in
interest rates, current prices increase. The increase in current
prices leads to an increase in expected future prices. The
increase in expected future price increases demands further
increases in current prices. The increase in housing prices
creates wealth effects, which further increases demand. The
boom behavior is reinforced by stories, such as new economy
stories (“This is a new set of circumstances, so the sky is the
limit”) or myths (such as the myth that real estate prices
always go up). The stories and conventions used in making
3. Robert Shiller, Irrational Exuberance, 2nd edition (Princeton, NJ:
Princeton University Press, 2005).
The Great Recession: A First Look | 83
decisions are fragile in that they are not based on a true
knowledge of the future. When they are proven wrong, behaviors suddenly shift (the animal spirits), and markets bust.
CASE STUDY: LEVERAGE AND PROFITABILITY
A common measure of profitability is the rate of return on
equity (ROE). The ROE is defined as profits/net worth. Multiplying and dividing ROE by assets and rearranging terms
yields ROE = (profit/assets) × (assets/equity). If we assume
that businesses can manage the profit-to-asset ratio (it’s
roughly fixed), then they can increase their ROE by increasing their asset-to-equity ratio. The asset-to-equity ratio can
be increased by using debt, or leverage, to acquire assets or
to reduce (buy back) equity. An impor tant asset for banks is
loans. Loans expose banks to risk, and therefore the FDIC
imposes capital requirements on banks. The capital requirements are related to the associated risk of assets. The greater
the risk of an asset, the greater is the capital requirement, the
greater is the equity-to-capital requirement, the smaller is the
asset-to-equity ratio, and the less profitable is the business.
Securitization of assets that result in high investment grades,
such as AAA, therefore results in lower capital requirements,
higher asset-to-capital ratios, and higher profits. The pressure
toward higher profitability allegedly created a moral hazard
in the securities-rating business whereby risk was underestimated in the pursuit of higher profits.
REVIEW QUESTIONS
1. From Figure 10.1: 42.5 percent (from peak in 2006 to
trough in 2012). From Figure 10.4: the stock market declined
from about 50 percent of its peak in 2007 to 2009. As of this
writing, stock prices have more than recovered.
to purchase a stock at a price of $100 (ignore the interest
expense), and the value of the stock rises by $2, that is,
2 percent, the return on the investor’s equity position in the
stock is 200 percent ($2 gain divided by the investment of $1).
The high profits validate investors’ expectations and encourage
more debt to purchase more stocks, creating asset price bubbles.
The difficulty arises, of course, if the value of the stock does
not increase—if the value of the stock decreases by $2, the
investor’s equity position in the stock is not sufficient to cover
the losses. In this case, not all of the loan can be repaid, the
loan is in default, and the lender’s asset, the investor’s IOU,
decreases in value. The lender’s net worth and ability to pay its
loans diminish. When asset values fall below the value of liabilities, net worth becomes negative, and bankruptcy ensues.
EXERCISES
1. This is a student choice question, so the answers as to how
the economy has evolved will be quite varied. Here are a
couple examples:
Real
CPI
Federal
Change in
inflation
deficit
GDP
Unemployment
employment
rate
as a
growth
Rate
(thousands)
(Figure
percent
Year
rate
(Figure 10.8)
(Figure 10.9)
10.10)
of GDP
2008
−0.3
5.8
−756
3.8
3.1
2009
−2.8
9.3
−5,941
−0.3
9.8
2010
2.5
9.6
−947
1.6
8.7
2011
1.6
8.9
1,158
3.1
8.5
2012
2.2
8.1
2,232
2.1
6.8
2013
1.5
7.4
2,208
1.5
4.1
2014
2.4
6.2
2,558
1.6
2.8
2015
2.4
5.3
2,894
0.1
2.5
(Source: Federal Reserve Bank of St. Louis, FRED Economic Data.)
2. (a)
2. It was the most severe recession in the post–World War II
era, lasting from January 2008 to June 2009 (eighteen
months). During the recession, the largest percent change in
real GDP relative to potential real GDP was about −7 percent.
The decline in employment was about 8.5 million jobs. The
unemployment rate increased by more than 5 percentage
points. See Exercise 1.
3. A balance sheet is a set of accounts depicting the value of
what is owned (assets) and what is owed (liabilities). The difference between the value of what is owned and owed is net
worth.
4. Leverage is the ratio of total liabilities to net worth. Leverage is important to understanding the asset price inflation and
deflation that led to the financial crisis. The pursuit of higher
profits causes investors to increase debt to purchase assets,
driving up asset prices. If an investor has $1 and borrows $99
(b) In the 1990s, the average price of Brent Crude—Europe
was $18.23. In 2015, the average price of oil was about $52.
(c) The price of oil fell from a recent height of over $111 in
2012. The oil market is influenced by a number of geopolitical and economic factors. The recent fall in oil prices can be
explained by OPEC countries increasing oil production, the
invention of fracking technologies in the United States, and
the global economic slowdown.
84 | Chapter 10
3. For comparison purposes, see the same data for 2013
below. Students should incorporate these data into their twoparagraph answers.
Inflation rate (HICP)
Monetary aggregate M3
GDP in prices of the previous year
(economic growth)
Unit labour costs
Population (in millions)
Unemployment rate
(as a % of labour force)
Labour productivity
Current account balance
(as a % of GDP)
US dollar / Euro exchange rate
Government deficit (−) / surplus
(+) (as a % of GDP)
Government debt (as a % of GDP)
Inflation rate (HICP)
Monetary aggregate M3
GDP in prices of the previous year
(economic growth)
Unit labour costs
Population (in millions)
Unemployment rate
(as a % of labour force)
Labour productivity
Current account balance
(as a % of GDP)
US dollar / Euro exchange rate
Government deficit (−) / surplus
(+) (as a % of GDP)
Government debt (as a % of GDP)
0.1
5.0
1.7
2016Jun
2016Jun
2016Q1
0.9
337
10.1
2016Q1
2014
2016May
0.3
2.34
2016Q1
2016Q1
1.0997
−1.9
26 Jul 2016
2016Q1
91.7
2016Q1
1.4
3.2
−1.1
2013May
2013Apr
2013Q1
1.7
332
12.2
2012Q4
2011
2013Apr
−0.3
1.32
2012Q4
2013Q1
1.3209
−3.1
10 Jun 2013
2012Q4
90.7
2012Q4
(Source: European Central Bank Statistical Data Warehouse, http://sdw.ecb
.europa.eu /.)
4. As of December 31, 2015 (thousands of dollars):
Citigroup, Inc.
Assets
$1,731,210,000
Equity
Equity/Assets
$221,857,000
12.8%
Goldman Sachs
$861,395,000
$86,728,000
10%
In 2013, for Citibank, for each $100 of assets, $12.80 is
financed by equity and $87.20 is financed by liabilities. For
Goldman Sachs, for each $100 of assets, $10 is financed by
equity and 90 is financed by liabilities.
5. (a) Bank B, assets = 1,500, liabilities = 1,400, equity = 100;
Bank C, assets = 800, liabilities = 700, equity = 100
(b) Bank B, 1,400/100 = 14/1; Bank C, 700/100 = 7/1
(c) Bank C, NW = −200
(d) Bank B’s net worth declines.
(e) The value of any financial asset is backed by a promise to
pay. In this case, Bank C fails to meet its promise to pay and
reduces the value of assets held by Bank B. Systematic risk
occurs when a failure of one business, like Bank C, causes
the failure of another business, like Bank B.
6. (a) A capital requirement sets the maximum asset-to-equity
ratio. Recall that the asset-to-equity ratio is sometimes called
rate of return on equity multiplier, because the ROE = (Profits/Equity)*Assets/Assets = (Profits/Assets)*(Assets/Equity).
(b) A higher capital requirement means that firms must maintain more equity relative to assets. With more equity on
hand, firms have a greater cushion against asset devaluations
and insolvencies.
7. This is an open-choice essay question. However, please
note that “Brexit” was discussed on July 12, 2016. There were
two questions: Will the United Kingdom’s per-capita income
be lower in a decade? Will the rest of the European Union’s
income be lower in a decade? A majority of respondents
believed that the Brexit vote will lower per-capita income for
both the United Kingdom and the rest of the European Union.
CHAPTER 11
The IS Curve
CHAPTER OVERVIEW
Here you get to derive a version of John Hicks’s famous IS
curve. This version builds on more orthodox microfoundations than those used by Hicks that include the permanentincome/life-cycle hypotheses and the user cost theory of
investment. You can keep this chapter simple if you like—
Sections 11.1 through 11.4 tell the main story—or you can go
further and present intuition-driven microfoundations for the
permanent-income hypothesis and Ricardian equivalence.
You’ll want to pay close attention to Chad’s simple definitions of demand for C, I, G, and NX in Section 11.2—they
clear out a lot of baggage that has accumulated in the IS curve
over the decades, and they let you focus on real economics
or, if you choose, on the social hydraulics, like the states of
confidence and expectations.
11.1 Introduction
Chad tells the big story of the IS curve first, and I recommend
you do the same: a rise in interest rates causes a fall in investment demand, which hurts real gross domestic product
(GDP). The rest of the chapter is about the details. Note that
Chad leaves out the multiplier completely in his first pass at
the topic—a reasonable choice that lets you focus on the most
volatile component of GDP: investment purchases.
This might be a good time to reiterate that when we talk
about the short run, we emphasize demand, while in the long
run we emphasize supply. Students often come away with a
topsy-turvy feeling when moving between the long run and
short run, and a minute or two of big-picture talk every few
lectures might pay dividends. I like to note that in the long
run, we tend to believe that everything will find its price—
wages will adjust until all the workers get jobs (minus natu-
ral unemployment), all the machines get rented, and all the
final goods and services get sold. So, in the long run, it’s reasonable to assume that the supply of K and L determines the
amount of Y.
But in the short run, things aren’t so simple. As students
will see later in the chapter, businesses probably aren’t perfectly rational when it comes to setting prices, and as Blanchard
and Kiyotaki famously demonstrated, pricing errors that have
no noticeable impact on a company’s profit can have a noticeable impact on overall GDP. So in the short run, prices don’t
perfectly adjust to set quantity supplied equal to quantity
demanded. Markets aren’t in equilibrium.
So, when prices are a little higher or a little lower than P*,
what happens? In Principles, students are usually taught that
the “short side of the market” rules the roost. That means that
Q can never be higher than Q*. This is not true in our model.
In the short run, we assume that firms produce whatever gets
ordered. It’s only over the longer haul—months or perhaps
years—that firms decide to adjust prices, and even then, they
may take a while to set prices exactly right.
So in the short run, demand runs the show. In the short run,
we assume that whatever consumers, businesses, the government, and foreigners demand actually gets produced. That’s
probably a reasonable assumption for short time periods, for
differences that only add up to a few percent of GDP.
11.2 Setting Up the Economy
Here, Chad sets up his simplified IS curve. Here’s what you
cannot forget: in his basic model, consumer spending depends
on potential GDP, not actual GDP. That means no multiplier
effects! This is roughly the same as if consumption depended
on permanent income—so he’s keeping the model quite
neoclassical to begin with. Since empirical consumption
85
86 | Chapter 11
multipliers are quite small, this rigor-driven simplification
is a quite reasonable choice.
In his notation, bars denote exogenous variables. Thus,
Ct = ā C
t
is a reminder that is potential GDP, which is taken as a
fixed parameter in the short run; ā C, the fraction of output
going to consumption, is also a parameter.
Note that he does not call ā C the marginal propensity to
consume. He also does not include autonomous consumption
at all. Overall, Chad’s simplification of consumption saves
you class time with little loss of economic understanding.
This gives you time to cover more topics that academics and
policy makers actually talk about—by contrast, few academics or policy makers talk about the multiplier in the detail
accorded it in most intermediate macroeconomics textbooks.
You’ll get to cover the multiplier later in the chapter, but for
now, you get to focus on deriving an investment-centered IS
curve.
The key microfoundation equation turns out to be the
investment equation. Chad sets it all out so that students can’t
help but be reminded of the links between the short-run and
long-run models. , the marginal product of capital from the
production function, comes back to us. And the focus is on
Rt, the real interest rate, not it, the nominal rate. Here’s the
equation:
It / t = āi − (Rt − ).
You’ll see that āi is the fraction of GDP devoted to investment when the real interest rate equals the marginal product
of capital. It is investment’s long-run, flexible-price fraction
of GDP. You may want to remind students that any time Rt is
away from , something unusual is going on in the economy. Eventually, they’ll see that Rt is almost always either
a little above or a little below , so that the “unusual” will
become quite usual.
Since you’ve probably already covered interest rates in the
inflation chapter, you should be able to cover the investment
equation quite quickly. The economic point to emphasize is
that Rt is a financial rate of return, determined (indirectly)
by the Federal Reserve, while is a physical concept—it’s
how much more output one extra dollar’s worth of capital
could produce. When Rt is higher than , firms are reluctant
to borrow money to buy more capital equipment.
11.3 Deriving the IS curve
Take a moment to look at Table 11.1, which lays out the definitions of C, I, G, EX, and IM. All but Investment are just
a fixed pa rameter times potential GDP—painfully simple.
(Don’t spend too much time on this section if you can help
it— there are a lot of good topics to cover later in this
chapter.)
If you just mentally divide the C, G, EX, and IM equations
by t, you’ll see that they all can be added together with the
investment equation to get a definition of GDP as a fraction
of potential GDP, t. Chad then subtracts one from both
sides to convert the ratio of Yt / t into a percentage, Ỹt (he
began referring to short-run output as Ỹt in the previous
chapter). The result is the IS curve, which looks suspiciously
like the investment equation:
Ỹt = ā − (Rt − )
So, everything here except for is a percentage would be
the interest semi-elasticity of output, if you’re inclined to
mention that kind of detail.
A point worth emphasizing is that ā should equal zero “on
average” (or strictly speaking, in steady state); the ā components reflect the long-run, flexible-price shares of C, I, G,
EX, and IM, and Chad subtracts one from their sum in
order to create ā.
You may want to emphasize that the components of ā sum
to 1 in the long run before you derive the IS curve. That way,
when you subtract the 1 from both sides at the end, many
students will foresee the zero sum themselves, before you
even point it out to them.
The fact that ā is zero on average emphasizes that this
really is a short-run model. It will be almost impossible for
students to come away from the IS curve thinking that monetary policy can impact long-run GDP—after all, you’ve
already made the point that Rt will hover above and below ,
and you’ve noted that any time moves, so that Rt − moves
away from zero, that’s really a “shock” that will eventually
go away.
Note: In the model, any shock to the individual C, I, G, EX,
or IM parameters that doesn’t go away quickly will eventually get absorbed by an opposite adjustment in one or more
of the other parameters.
Example: A permanent rise in āC (the consumption share)
would likely be accompanied by a rise in ā IM (the import
share) or a fall in āi (the long-run investment share). That’s
another way of saying that long-lasting consumption booms
tend to lead to either a rise in the trade deficit (possibly the
U.S. case) or a fall in investment. You may just want to store
this idea for later, as it will be useful in fiscal policy and trade
chapters, but keep it in mind for now.
Note: While this model does a formidable job linking
short-run and long-run relationships, one minor incongruity
does come up. I point this out because some instructors like
linking up short- and long-run stories: if people permanently
increase their savings rate in the Solow model (or permanently lower their rate of time preference in a Ramsey
model), then the steady-state real interest rate ( ) would fall.
But in this model of the IS curve, a permanent fall in has no
long-run relationship with the investment share, since Rt and
must equal each other in the long run. One possible way to
rectify this problem is that R is set in the loanable funds
The IS Curve | 87
market, and the increase in savings, in the long run, in tandem, reduces R and . This is explicitly a short-run model
of investment demand. If you do want to address permanent
changes in the investment share, you should treat them as
permanent shocks to āi rather than to .
11.4 Using the IS Curve
The first three subsections are typical: Is it “movement along”
the IS curve or a “shift of” the IS curve? Students have a
tough time with this, often because instructors are sloppy
in our language. (Am I the only one who forgets to say “rise
in quantity demanded” all the time?)
The section entitled “A Shock to Potential Output” deserves
a few comments of its own. Since everything in the model is
divided by potential GDP, changes in potential GDP have no
impact on the results.
That is, unless we explicitly state that the change in potential also changes something else in the model: Chad’s examples all focus on changes in the marginal product of capital.
The MPK might change due to technology or due to capital
destruction; in either case, it sets off a round of medium-run
adjustments within the full-blown IS-MP-Phillips curve
model.
This brings us back to the point in a previous aside: that in
this model, permanent changes in the MPK have no permanent effect on the investment share. Therefore, you might not
want to draw too much attention to questions that will point
out that difficulty. This is a short-run, or at most a mediumrun, model.
11.5 Microfoundations of the IS Curve
CONSUMPTION
This gives you a good intuitive explanation of PILCH: the
combined Permanent-Income/Life- Cycle Hypothesis. The
basic story requires no math: in a world where people can
borrow and save easily, people’s consumption spending this
year should be based on their average lifetime incomes.
For a youngish woman, this means that a one-year rise or
fall in her income should have only a tiny effect on this year’s
consumer spending. If she gets a one-time bonus, she should
save most of it; if she gets laid off for a month or two, she
should borrow money to keep her standard of living about
where it was before. The only time to make a massive change
to her consumer spending is when she gets news about changes
in her lifetime income: for example, she finds that her job
training will raise her wages much more than she thought; she
unexpectedly inherits a large sum of money (so she can spend
a little of it each year); or she gets bad medical news about her
long-term ability to work.
Later, I work out some lecture notes to illustrate the PILCH
in a zero-interest-rate world. It’s a powerful idea, and as Chad
notes when reviewing the empirical literature, there’s just
enough evidence of forward-looking consumers that it
deserves substantial attention.
Note: An obvious refutation of the PILCH is sitting in your
classroom: your students, few of whom are consuming as
much as they expect to a few years after they graduate.
Also, note that you get another chance here to use discounted present value, which you may have covered in the
labor market chapter.
MULTIPLIER EFFECTS
Here you get the multiplier you’ve been looking for— but
without the added burden of “autonomous consumption.”
Chad just flat out assumes that the consumption share of GDP
depends partly on short-run output (equation 11.15) and then
plugs that into the IS curve.
Out pops a familiar sight: the same old IS curve as before,
but with everything multiplied by 1/(1 − ). Chad doesn’t
give an explicit name to , so you can give it your own—and
you don’t have to use the cumbersome “marginal propensity
to consume.” He does call the 1/(1 − ) term the “multiplier.”
Chad notes in this section that he’ll keep using the
multiplier-free IS curve in the text, but he wants readers to
keep the (modest) multiplier effects in the back of their minds,
a good convention to follow.
INVESTMENT
Chad offers an explanation of why a firm’s investment level
might depend not just on profit opportunities but also on current cash flow—he uses the umbrella term “agency problems” to capture this effect.
This gives you a good reason to include short-run output
(a.k.a. short-term firm revenue) in the investment equation—
yielding another multiplier effect. Mercifully, he spares you
and the students the math on this matter—he just reminds you
that the same multiplier principle applies, although for a different reason. Agency problems create cash-flow constraints
for investment, which create multiplier effects.
GOVERNMENT PURCHASES AND NET EXPORTS
Automatic stabilizers might be reasonable, but discretionary
fiscal policy will probably come too late—it’s an example of
Friedman’s “fool in the shower” (the parable can be Googled).
Chad then covers Ricardian equivalence with intuition
alone. Several homework problems illustrate Ricardian
equivalence and show how it is closely linked to the PILCH.
Ricardian equivalence says that the timing of government
purchases should have a major impact on today’s economy,
but the timing of taxes should not. (That’s part of the reason
88 | Chapter 11
Chad could leave taxes out of his consumption equation:
David Ricardo told him he could.)
Chad appears to take the view that the world isn’t all that
Ricardian—in his hypothetical example, a rise in G coupled
with an equal rise in taxes results only in “raising output by
a small amount in the short run.” He says that “most economists accept” this characterization. A number of Ricardian
equivalence questions are included in the end-of-chapter
questions.
By and large, Chad defers the discussion of NX until
Chapter 19.
SAMPLE LECTURE: SPENDING OUT
OF PERMANENT INCOME IN A
ZERO-INTEREST-RATE WORLD
I find that students need a little practice to understand what
the PILCH (Permanent-Income/Life- Cycle Hypothesis)
really means.
To keep it simple, let’s consider a world where the interest
rate is zero, people can borrow and lend money for free
(though loans must be repaid), and where the average consumer wants to consume the same amount every period. That
will let us focus on the big idea: that today’s consumption
spending (and tomorrow’s as well) doesn’t depend on today’s
income—it depends on our average lifetime income.
1. First, think of a two-period life span: “young” and “old.”
When you’re young, you earn no money, but when you’re
old, you earn $10. How much will you consume each
period? Easy: $5 when young and $5 when old. You pay
for your youthful consumption by borrowing—which is
exactly what many of your students are doing with their
student loans.
2. a. Next, let’s add some more time, and some news that will
change our plans. Let’s make it a 10-year life span, and
let’s assume we make $10 per year in years 1–5, $20
per year in years 6–8, and $45 each in years 9 and 10.
How much do you consume each year now? Well,
total income is $200, so you consume 200/10 = $20 per
year. So when you’re young, you should borrow money—
you build up a debt of $50 in years 1 through 5—and
then in years 9 and 10, you pay back the $50. You’ll still
consume $20 each in years 9 and 10, so you’ll pay back
the loan at a rate of $25 a year.
b. Suppose now, before you start shopping in year 1, you
get news that you’ve been added to your rich uncle’s
will. He’s going to give you $1,000 when he passes
away. You don’t know exactly when he’ll die, but you’re
100 percent sure it’ll be in years 5 through 9. How does
that impact your lifetime consumption plan? Easy! The
news by itself added $1,000 to your lifetime income,
and since you’re going to spread it out evenly across
your life, you’re going to spend $100 more every year
starting in year 1 on consumer goods.
So now, you’ll consume $120 each year. How? By
borrowing $100 per year against your future inheritance. You’ll build up debt each year, and then, in the
year when you receive your inheritance, you’ll pay it
all back and keep consuming $100 per year.
One key lesson of the PILCH is that you don’t
change your consumer spending patterns when your
income changes—you change your spending patterns
when news about your present or future income arrives.
3. a. There are two final illustrations of the PILCH, one of
which we’ll apply to discussing tax cuts. Suppose your
annual after-tax income is $10 per year, and you’re going
to live for 10 years. One day, Congress tells you it’s going
to give you a $5 tax cut in year one, and this tax cut will
be permanent—perhaps Congress finds someone else to
pay for your tax cut. How does this change your spending pattern?
Let’s do a “before” and “after” analysis. Before the
tax cut, your lifetime income was a sum of $100 dollars, so you’ll obviously consume $10 per year. Afterward, your lifetime income rises to $105, so you’ll
consume $10.50 per year. In other words, you’ll only
consume fifty cents of your tax cut in the year it arrives,
and you’ll save the rest, slowly consuming it over the
years.
So when the government cuts big one-time checks,
rational consumers will save most of it, just like the
smart kid on Halloween who saves his candy stash, eating just a piece or two every week.
b. Now, let’s be more realistic in thinking about the onetime tax cut: you’re going to have to repay it later. So,
you get a $5 bill from the government this year, and
you’ll have to repay it in seven years. You get $15 in
income in year 1, and $5 in year 7. This case is absurdly
simple and counterintuitive: your lifetime income is
back at $100, so your consumer spending is back to $10
per year. A temporary tax cut that you must repay later
has no impact on consumer spending ever if the PILCH
is strictly true.
If we try to make this more realistic by making it
tough to borrow money, the story changes a bit— but
remember, in the United States, most adults own their
own homes, and most of the income is earned by people
with relatively easy access to credit, either through
home equity loans, credit cards, car loans, or family and
friends.
In practice, as Chad notes, people appear to be quite
a bit more impatient than the PILCH implies, spending
up to half of a big one-time payment right in the first
year. But there’s no serious evidence that people spend
The IS Curve | 89
80 to 90 percent of a big one-time payment immediately, so the average person does indeed engage in
some PILCH-like behavior.
EXPANDED CASE STUDY: WHY IS IT CALLED
THE “IS CURVE”?
Nobel Prize–winner John Hicks1 is the man who turned
Keynes’s General Theory into a workable economic model.
He converted Keynes’s prose into a simple model known as
IS/LM. Today, we tend to drop the LM part of the model—
the part that used to explain how monetary policy impacts
interest rates. Now, we just assume that the central bank has
the power to control the short-term real interest rate directly.
Keynes’s 1936 book created a sensation among economists
who wanted to understand why the Great Depression had
occurred, what could be done to end it, and what could be
done to prevent such economic tragedies from ever happening again. Unfortunately, few economists understood his
work. It’s just a hard book to trudge through—and this isn’t
just my opinion. Nobel Prize–winner Robert Lucas2 (who
eventually helped overturn much Keynesian thinking)
describes this conversation with his fellow University of Chicago colleague, Nobel Prize–winner Gary Becker:
“. . . I asked my colleague Gary Becker if he thought Hicks
had got the General Theory right with his IS-LM diagram.
Gary said, ‘Well, I don’t know, but I hope he did, because if
it wasn’t for Hicks I never would have made any sense out of
that damn book.’ That’s kind of the way I feel, too, so I’m hoping Hicks got it right.”
Hicks rejected the LM half of the IS/LM model, stating that
Keynes’s liquidity preference theory was based on uncertain
expectations.3 With uncertain expectations, the equilibrium
requirement of the model will not be fulfilled.
CASE STUDY: AGENCY PROBLEMS
AND THE DEATH OF CEOS
Chad notes that business investment is often sensitive to corporate revenues or corporate profits. He notes that a key part
of the reason, according to many economists, is “agency
problems.” In other words, banks and investors are reluctant
to trust firms with their money, since they believe that some
of the money will be wasted on pet projects, high salaries,
and various inefficiencies. Therefore, businesses often choose
1. John R Hicks, “IS-LM: An Explanation,” Journal of Post-Keynesian
Economics 3, no. 2 (1980): 139–54.
2. Robert Lucas, “My Keynesian Education: Keynote Address to the
2003 HOPE Conference,” History of Political Economy 36 (2004): 12–24.
3. See Steven Keen, Debunking Economics (New York: St. Martin’s
Press, 2001), 210.
to finance their investment with “retained earnings,” another
term for profits.
Are there good reasons for banks and investors to be concerned about agency problems? In par ticular, are there good
reasons to think that when a CEO has his or her hands firmly
on the reins of power, he or she is likely to be wasting valuable resources? If so, how big is this effect? This has been a
tough question for financial economists to solve, but in the
last two decades a few papers have taken a creative approach.
They have watched what happens to a stock’s price when a
CEO unexpectedly dies. If “good men are hard to find,” then
we might expect the share price to go down, but if the “dead
wood needs to be cleared,” then we might expect the share
price to go up.4
What happens? On average, the share price goes up. And
it appears to go up more if it’s a company founder who unexpectedly dies (tight hold on the reins of power?) or if the
board of directors is more independent (less chance of picking a crony?). The effects are on the order of 1 percent or
2 percent of the company’s stock price. So agency problems
appear to be real. That’s why the stock market gets excited
by the prospect of picking a new CEO: it apparently means
that, for a while at least, the CEO will find it difficult to use
the reins of power for her own private ends.5
CASE STUDY: THE EFFECTS OF TEMPORARY
TAX CUTS IN THE SHORT RUN
In 1992, heading into an election year, President George
H. W. Bush announced in his State of the Union Address
that he didn’t believe in the permanent-income hypothesis.
Of course, he didn’t state it in those words; instead, he
announced that he was going to reduce the amount of tax
that would be withheld in every American paycheck.
But tax rates hadn’t changed, so if the government withheld fewer tax dollars during the year, then in April 1993
when it came time to calculate the tax bill, workers would
find that they had smaller tax refunds than usual—or bigger
tax bills than usual. The president’s goal was to stimulate
consumer spending, among other things. However, there’s no
evidence that consumer spending was any higher as a result
of the temporary tax cut—it appears that consumers saved
the tax cut in anticipation of paying higher taxes in the future.
We all know how the story ended: President Bush lost his
reelection bid, due largely, it is widely believed, to a weak
economy. A temporary, short-term tax cut like this one
appears to have no impact on consumer spending.
4. Kenneth A. Borokhovich et al., “The Importance of Board Quality in
the Event of a CEO Death,” Financial Review 41, no. 3 (2006): 307–37.
5. Bruce Johnson et al., “An Analysis of the Stock Price Reaction to
Sudden Executive Deaths,” Journal of Accounting and Economics 7, nos.
1–3, (1985): 151–74.
90 | Chapter 11
In a 2001 NBER paper, “Consumer Response to Tax
Rebates,”6 Matt Shapiro and Joel Slemrod surveyed Americans and asked them what they were planning to do with the
$300 and $600 tax rebate checks that the government was
mailing out. Only 22 percent said they planned to spend most
of the money—further evidence that one-time tax changes
have only small effects on consumer spending.
CASE STUDY: MODIGLIANI’S “THE LIFE CYCLE
HYPOTHESIS AND THE RICARDIAN
EQUIVALENCE THEORY”
Franco Modigliani, though recognizing that households may
attempt to smooth their consumption over time, rejected the
Ricardian equivalence theorem.7 Modigliani recognized that
the burden of today’s deficit may result in future generations
paying higher taxes, rather than simply changing the timing
of tax payments made by the current generation. If current
taxpayers don’t care about their heirs or if they do not have
heirs, then the future tax burden does not adversely impact
life- cycle (or permanent) income, and therefore does not
adversely affect consumption.
CASE STUDY: PRIVATE SECTOR SHOCKS
AND THE GREAT RECESSION
The initial impact of private sector shocks during the Great
Recession can be reflected in changes in the personal savings
rate and gross domestic private investment’s share of potential (long-run) output. The change in personal savings rate
brought back into vogue Keynes’s “paradox of thrift.” The
paradox of thrift reflects the situation where an increase in the
savings rate reduces consumption, production, and incomes,
thereby frustrating an increase in the level of savings. In the
table below (source: FRED DATABASE and author’s calculations), the cyclical variation in output (short-run output), the
personal savings rate, and gross domestic private investment’s
share of long-run output are provided for the period of 1999 to
2015. Following the recession of 2001, as short-run output
was recovering, the personal savings rate decreased through
2007. During the Great Recession, in 2008 and 2009, the savings rate increased and short-run output decreased. In terms
of the IS curve, this increase in the savings rate is consistent
with a decrease in āC, shifting the IS curve to the left. In addition, following the recession of 2001, we see that investment’s
6. Matthew D. Shapiro and Joel Slemrod, “Consumer Response to Tax
Rebates,” working paper 8672, National Bureau of Economic Research,
Cambridge, MA (2001).
7. William Barnett and Robert Solow, “An Interview with Franco Modigliani,” Macrodynamics 4 (2000): 222–56, reprinted in Paul Samuelson
and William Barnett, eds., Inside the Economist’s Mind (Malden, MA:
Blackwell Publishing, 2007).
share of long-run output bottomed out in 2002 and recovered
through 2006. With the Great Recession, investment’s share
of long-run output fell from a high of 18.72 percent in 2005 to
a low of 12.14 percent in 2009. Since 2009, we have seen
investment’s share of long-run output recover, but, as of 2015,
it still remains below the post– Great Recession high. The fall
in investment’s share in our IS model is a consequence of two
factors: (a) the liquidity crisis, caused by the related financial
crisis, increasing R relative to —for example, the 10-year
Treasury constant maturity rate less the Federal Funds Rate
(see FRED DATABASE “Interest Rate Spreads” increase
from –0.39 percent in 2007 to 3.10 percent in 2009, reflected
as movement up and to the left along the IS schedule), and (b) a
decrease in expectations of future profitability/sales, reflected
as a decrease in ai-bar, reflected as a leftward shift in the IS
schedule.
Year
Ỹt
Personal Savings Rate
I/Y- bar
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
1.45%
2.04%
−0.64%
−2.22%
−2.38%
−1.21%
−0.30%
−0.08%
−0.58%
−2.73%
−6.80%
−5.46%
−4.90%
−3.87%
−3.85%
−3.06%
−2.19%
4.40%
4.20%
4.30%
5.00%
4.80%
4.60%
2.60%
3.30%
3.00%
4.90%
6.10%
5.60%
6.00%
7.60%
4.80%
4.80%
5.10%
18.76%
19.30%
17.48%
16.80%
16.98%
18.01%
18.72%
18.67%
17.67%
15.72%
12.14%
13.56%
14.12%
15.44%
15.90%
16.51%
17.06%
REVIEW QUESTIONS
1. First and foremost, the IS curve tells us how changes in
the real interest rate impact GDP. The “I” in “IS” reminds us
that “i”nvestment purchases are sensitive to interest rates. It
also helps us keep track of all of the components of GDP—
Consumer purchases, Investment, Government purchases,
and Net Exports. The IS curve reminds us that regardless of
the shocks that happen to C, I, G, or NX, interest rates still
have a powerful role to play in determining the level of shortrun output.
2. Because a fall in interest rates encourages businesses and
homebuyers to borrow more to purchase more investment
goods.
3. Movements along the IS curve: the central bank raises the
real interest rate or cuts the real interest rate.
Examples of shifts in the IS curve include the following:
shifts right when consumers become more optimistic or for-
The IS Curve | 91
eigners demand more U.S. goods; shifts left when government cuts purchases or when businesses become pessimistic
about the future.
4. If we want to be able to read the newspaper, it’s useful to
know that shifts in the curve (that is, changes in the ā term)
can be caused by many different factors—foreigners, government, businesses, and consumers all play a role in determining the level of short-run output. In setting the real interest
rate, the central bank must keep track of shocks in all of these
sectors of the economy.
5. First, variations in Rt, where R ≠ , through variations in
investment cause Ỹt ≠ 0. Second, consumption depends on
permanent income, and changes in short-run output have
little to no effect on consumption, making standard income
multipliers very close to 1. Third, temporary tax changes
have little effect on consumption.
6. Because John Hicks reminded us that in this model of the
economy, investment must always equal savings. Savings
is defined as the sum of government savings, private savings, and foreign savings (known as the trade deficit).
EXERCISES
1. (a) Short-run output falls by 0.5 percent.
(b) rises by 0.25 percent
(c) rises by 1 percent
(d) falls by 2 percent
(e) rises by 2 percent
2. This is a worked exercise. Please see the text for the
solution.
3. (a) This is an increase in āi: if the government is giving
temporary tax breaks for investment goods, then regardless
of the interest rate, firms want to buy more investment goods.
That’s an intercept shift, not a slope shift.
Overall, this shifts the IS curve to the right, boosting the
aggregate demand for goods and services in the short run.
(b) This is an increase in ā EX. Foreigners want to buy more
U.S.-produced goods; this shifts the IS curve to the right.
(c) An increase in ā IM. This raises imports—which, holding
everything else on the demand side equal, means the GDP
will fall. This shifts the IS curve to the left.
(d) A fall in āi. Remember, new homes are part of I, investment purchases. This shifts the IS curve to the left.
4. To keep things simple, let’s focus on the case where the
rise in government purchases is temporary. Also, in this
answer and in answers 5 and 6, I am using the simplest version of the IS model, that of Section 11.2, to answer the question: that means that short-run consumer spending depends
only on potential GDP, not on actual GDP.
In a world without Ricardian equivalence, where consumers
spend based on each year’s income, this is what happens: if
the hike in government purchases is financed with a tax
increase, then ā G rises while ā C falls. The government purchases more, but consumers (who have to pay the tax increase
out of this year’s pay) purchase less. The effects come close
to canceling each other out. The IS curve won’t shift very
much, but it will still shift slightly to the right.
If instead the new government purchases are financed by
new government borrowing, then that means that consumers
won’t have to pay higher taxes until they get to the future. That
means that consumers will have the same pay as before, so
their consumer spending will be the same as before. Now, āG
increases, but āC doesn’t change at all: the IS curve shifts to
the right. More government spending adds up to more overall
demand for goods and services. Note that this is the “common
sense” view of government spending.
In a world with Ricardian equivalence, where consumers
make today’s spending decisions based on their lifetime
incomes (present and future), this is what happens:
This answer turns out to be about the same as in the previous paragraph—IS shifts right—but for a different reason.
As before, ā G surely increases. But regardless of when the
government raises taxes—now or later— consumers know
that they have to foot the bill. This is the big story behind
Ricardian equivalence: how the government pays for its
spending doesn’t matter to rational consumers.
When a rational consumer knows he or she must pay off
some debt, he or she probably pays off a little of it every
month—not all at once. The rational consumer wants to keep
his or her consumption smooth from year to year, if possible—
he or she doesn’t want feast or famine. This is the basic story
behind the life-cycle hypothesis, and that’s also the basic
story behind Ricardian equivalence.
If the government decides to borrow to pay for the temporary boost in G, and if the government raises taxes slightly
over the next few decades to repay the debt, then it is doing
just what rational consumers would do themselves: paying a
small price each year to pay for a big one-time purchase.
If instead the government decides to raise taxes immediately to pay for the temporary boost in G, then even though
consumers have a temporarily higher tax bill, they still have
a choice about how much money to spend on consumer goods.
They can just borrow some money today to consume some
more today, and then repay the money slowly over the next
few years.
So, whether the government raises taxes a lot now or raises
taxes slightly in the future, the effect on consumer spending
92 | Chapter 11
is the same under Ricardian equivalence. (Hence the word
“equivalence.”) The effect on ā C should be small: ā C falls
slightly for years to come when government raises G temporarily. Overall, the IS curve shifts to the right.
5. I assume in this answer that this is a permanent increase
in government benefits— quite likely if we’re talking about a
popular middle-class program like Social Security. If Ricardian equivalence holds, then a rise in Social Security payments to the elderly has no net impact on the IS curve.
ā C would be pushed up since the elderly would have more
income, but ā C would also be pushed down by exactly the
same amount because workers would have to pay more in
taxes (either now or in the future) to pay for the higher Social
Security payments. So the elderly would have more to spend
on consumer goods, while the workers would have less to
spend on consumer goods, and the effects would cancel each
other out.
If Ricardian equivalence does not hold, so that consumers
make this year’s spending decisions based just on this year’s
income, then we need to know how the government is going
to pay for the extra Social Security payments.
If the government borrows money to pay for Social Security today but doesn’t raise taxes to pay for it until the distant
future, then elderly consumers will have more income and
spend more (pushing āC up), but workers will keep on spending just like before. So for the overall economy, the net
effect is a rise in ā C: the IS curve shifts to the right.
If instead the government permanently raises taxes just
high enough to pay for the extra benefits, then there is next
to no impact on ā C: the elderly consume some more, the
workers consume a little less, and the two forces balance out.
6. After an earthquake, potential GDP will fall. Think about
the supply side: you’ve got less capital stock, with the same
number of workers and ideas. That adds up to less output in
our production function. The production function reminds us
that when capital is scarce, the rental rate of capital (the marginal product of capital, ) will rise.
What will happen to short-run output, which is driven by
demand? Let’s ignore G and NX, and just assume that the
government and foreigners don’t change their behavior after
the earthquake (you can imagine that G would increase after
an earthquake, but that’s a political decision, outside the
scope of this model).
I: With a high marginal product of capital, the demand for
investment goods will increase. The easiest way to see this
is to look at equation 11.7, the investment demand curve. If
rises, the investment share of output will rise as well (two
negatives make a positive). It works just like an increase in
the intercept term: as the investment demand curve goes, so
goes the entire IS curve. This pushes the IS curve to the
right.
C: Consumption’s share of potential output, C/ , will stay
the same, so although consumer spending falls, it won’t fall
as a fraction of potential output. In other words, ā C is fixed.
Thus, the earthquake’s overall impact on short-run output
is positive.
Actual GDP is the sum of potential output and short-run
output, so the earthquake’s impact on actual GDP is ambiguous: falling potential output plus rising short-run output. In
practice, you might expect that if the earthquake is small,
then the country would want to rebuild quickly, and people
wouldn’t be so poor that they’d have to cut back on consumer
spending—so the overall effect might be positive. Chad’s
answer in the text is similar to this “small earthquake” case.
But a bad enough earthquake— destroying, say, half the
capital stock—would make the average person so poor that
consumer spending would plummet and even strong rebuilding efforts wouldn’t go that far. Then actual GDP would fall.
Just think of the case of Europe’s “earthquake” known as
World War II. Even a country like France, which lost relatively few soldiers during the war, had low GDP for a few
years. It took strong rebuilding efforts just to get GDP back
up to where it was before the war.
7. To work with Microsoft Word files, I found that downloading the graph as a “PowerPoint” works best. To get a good
look at the data, I decided to look at the graph two ways: (a)
as described in the question, choosing the “move up” option
and choosing to measure real government purchases on the
right-hand side of the graph.
a)
The IS Curve | 93
Subtract 1 from both sides and collect all the ās (minus one)
into one ā term:
Ỹ = + Ỹ + ā − (R − )
(1 + )Ỹ = ā − (R − )
Ỹ = [1/(1 − )][ā − (R − )]
A graph of the IS schedule will show that it is flatter: a change
in interest rates will now have a bigger impact on short-run
output. A cut in rates, for example, will spur investment purchases, which will give more income to workers, who will
then have more money to spend on consumer goods.
9. (a) This is almost the same as question 7, except that the
last line will look like this:
b) After the Great Recession, real government purchases
decreased as real GDP increased.
Ỹ = [1/(1 + ñ)][ā − (R − )]
Notice that plus sign in the multiplier term!
Here’s how it goes:
c) The data is open to interpretation. One interpretation is that
the decrease in real government purchases caused real GDP
to increases. A second interpretation is that the decrease in
real government purchases has dampened the increase in real
GDP during the economic recovery.
d) In order to understand which interpretation is correct, we
need a fully specified theory, where we can test, holding other
things constant, the effects of changes in government purchases and changes in the government budget stance on real
GDP. A cursory look at other recessions, like 1953 and 1969,
suggests that government purchases fell during the recession
and recovered as the economy recovered. In addition, the
increase in government purchases seems to play an important role in the post–2001 recovery.
Y/ = C/ + I/ + G/ + NX/
= āc + āi + (R − ) + . . . + ā IM + ñỸ
Subtract 1 from both sides and collect all the ās (minus one)
into one ā term:
Ỹ = + Ỹ + ā − (R − )
(1 + ) = ā − (R − )
Ỹ = [1/(1 − ñ)][ā − (R − )]
(b) So, this “multiplier” is actually a “reducer.” When interest
rates get cut, businesses want to buy more investment goods, but
some of those investment goods are manufactured in foreign
countries and then imported back to the home country. Those
imported investment goods don’t count in home country GDP.
Note: In the old days, they called imports “spending leakage.” When some of the extra investment spending (or extra
spending caused by a shock to ā) gets produced overseas, it’s
“leaking out” into the global economy.
10. (a) As always, start with the definition of GDP, and divide
both sides by .
Y/ = C/ + I/ + G/ + NX/
Plug in your definitions of the components of GDP:
= āc + c(R − ) + āi + (R − ) + . . .
Collect the ās and subtract one from both sides to yield the
final answer:
Ỹ = ā − ( + c)(R − )
8.
Y/ = C/ + I/ + G/ + NX/
= āc + Ỹ + āi + (R − ) + . . .
(b) Now, a cut in interest rates helps short-run output in two
ways: it spurs more investment-good demand and it spurs
more consumer-good demand. The IS curve is now flatter.
94 | Chapter 11
11. Parts (a) and (b) answered in text, as part of worked
exercise.
(c) I’ll cut my consumer spending by $1,000 each year forever. $10,000 × 0.10 = $1,000.
But how do I do that in real life? As soon as the news
arrives of the one-time tax, I go out and borrow $10,000 from
the bank at 10 percent interest. I use that money to pay the
tax. Now I have a $10,000 debt, and I’ll pay $1,000 in interest payments every year, forever, to the bank.
(d) I’ll put the money in the bank and spend only $1 million
each year—I’ll just spend each year’s interest on the $10
million.
(e) We’ve got to figure out the present value of the $10 million. That’s $10 million/(1.15), or $6.2 million right now. So
if I went to the bank and promised them that they could have
the $10 million when it arrived in five years, they would be
willing to pay me $6.2 million right now for that privilege.
Now the question reduces to this: if I get $6.2 million
today, how will that change my consumer spending? The
answer is that I will raise my consumer spending by $620,000
each year, starting right now.
What happens to my consumer spending in year five and
after? Nothing! I keep spending my $620,000 just as before.
The bank takes its $10 million—that was our agreement after
all—and it doesn’t impact my life at all.
CHAPTER 12
Monetary Policy and the Phillips Curve
CHAPTER OVERVIEW
We cover the IS-MP-Phillips curve model here. Figure 12.1
provides a great outline of the theory, and I’d start the lecture with that. But along the way, you have an excuse to
follow Chad’s lead and cover the basics of the term structure, oil shocks, the profession’s collective mistake of the
pre–Friedman-Phelps Phillips curve, and the tough love of
Paul Volcker.
You can skip the two microfoundations sections—on the
possible sources of sticky inflation (he avoids the term “sticky
prices”) and on how the money market determines interest
rates—if necessary. My guess is that most macroeconomists
would find the first topic more interesting, while most students would find the second topic more interesting. Students,
even those who rarely get engaged, really are curious about
how the Federal Reserve (the Fed) has the power to control
interest rates. It looks like a superpower.
12.1 Introduction
Again, Figure 12.1 is a great road map. This is what it tells
you: the Federal Reserve sets a nominal rate, which determines the real rate, which determines a point on the IS
curve, which determines short-run output, which determines
a change in inflation through the Phillips curve. That’s what
we’re doing here.
This chapter ends up presenting our positive theory of
monetary business cycles; the next chapter presents the normative theory of optimal monetary policy.
12.2 The MP Curve: Monetary Policy
and Interest Rates
The Monetary–Policy (MP) curve is a straight horizontal line
that tells us what the real short-term interest rate is. The Federal Reserve chooses a nominal rate (always it), and since
inflation is sticky in the short run (which Chad says is six
months or so), that tells us what the real rate is (always
denoted Rt).
Chad uses an arbitrage argument to explain how the Fed
can set one par ticular rate (he lays out a money supply story
at the end of the chapter). He notes that as long as the central
bank is willing to lend or borrow an unlimited amount of
money at the target federal funds rate, then no other bank can
afford to lend or borrow at any other rate. Banks lending at
higher rates would get no business, and banks lending at
lower rates would have infinite business.
But is this what the Fed really does? Does it really borrow
and lend money to banks at the fed funds rate? Yes, Chad’s
story is accurate in its broad outline, although we rarely teach
it to students this way— and indeed, monetary economists
rarely think of it this way themselves. This is one of Chad’s
innovations, and it is worth emphasizing.
We have tended to think of the Federal Reserve’s open market operations (OMOs) this way: “The Fed increases the money
supply by buying bonds,” or “The Fed reduces the money supply by selling bonds.” That is true, of course, but there’s another
equally accurate way to look at it.
What is the Fed almost always doing when it buys and sells
bonds? (I’ll talk in terms of interest rates instead of bond
prices so it translates more easily into lecture-speak.) It is
making short-term agreements to lend money (when it buys
bonds) or borrow money (when it sells bonds) at (or very near)
the going fed funds rate.
95
96 | Chapter 12
So, Chad’s summary is close to a complete story: the Fed
freely borrows and lends to banks at the target fed funds rate.
The bonds are just collateral in a loan deal—and we don’t
need to tell our students about the collateral, now, do we? Go
ahead and leave the previous paragraph’s parentheses out of
your lecture notes. You can strip the story down to its basics,
take comfort that you’re telling students the truth, and be
done with the question of how the Fed controls interest rates
in two or three minutes. Yes, it will feel awkward the first
time, but you’ll soon appreciate the opportunity this gives you
to emphasize the law of one price.
Here’s a technical point: on a daily basis, almost all of the
Fed’s transactions are temporary—these are known as repurchase (RP) agreements when the Fed temporarily buys a
bond or as a reverse when the Fed temporarily sells a bond.
The average RP or reverse is a one-day, overnight transaction. Many others only last a few days.
FROM NOMINAL TO REAL INTEREST RATES
If you covered Chapter 8 on inflation, you can just lightly
review the Fisher equation. It’s a good chance to mention
“inflation stickiness” at this point: it’s the reason that control
of nominal rates turns into control of the real rate.
THE IS/MP DIAGRAM
Again, the MP curve is just a horizontal line telling us the
Fed’s monetary policy decision. Lay it over the Investment–
Savings (IS) curve, and you’ve determined short-run output.
The next subsection applies the model to a bursting housing
bubble: starting at potential gross domestic product (GDP),
IS shifts left (ā goes from zero to negative), so if the Fed
wants to keep GDP at potential, it needs to cut the nominal
rate.
Chad uses Friedman’s famous expression “long and variable lags” to explain why the Fed can’t perfectly counteract
IS shocks. Feel free to repeat that phrase dozens of times.
12.3 The Phillips Curve
Here is possibly the most argued-about idea in late-twentiethcentury macroeconomics. I’d recommend reading the introduction to this section once or twice; Chad’s New Keynesian
Phillips curve is fully conventional, but it’s worth familiarizing yourself with his thought process.
Chad starts off with equation 12.3, a Phillips curve that
could have come straight out of Lucas’s “Expectations and
the Neutrality of Money.” Inflation over the coming twelve
months depends on the average firm’s expected inflation plus
some function of demand conditions.
Chad explicitly notes that equation 12.3 is the average of
all firm pricing decisions—and he walks students through a
tale of how a firm might go about setting prices from year
to year. So, anecdotal microfoundations are surely there. You
can beef it up if you like in lecture, but as it stands, it gives
students a sense that inflation depends on the average choices
of firms—it’s not an external event imposed by government.
Next, Chad takes the conventional shortcut of assuming
that expected inflation equals last year’s inflation— and he
labels this “adaptive expectations.” In Chapter 13, he introduces rational expectations and shows how more rational
expectations impact monetary policy.
Finally, Chad writes the Phillips curve (PC) in changes:
change in inflation equals some function of short-run output.
When output is above potential, the economy faces inflation
pressures. Why? Because businesses are operating at higherthan-average capacity, which they’re only willing to do if
they earn a premium price.
A sample lecture that follows shows how to use the Phillips curve to find out whether an economy is above or below
potential.
PRICE SHOCKS AND THE PHILLIPS CURVE
Oil shocks remain topical, and so Chad uses them as the
archetypical price shock, ō. A one-time oil price shock pushes
PC up for one year. After the oil shock goes away—that is,
if oil stays at the new, higher price—then next year, PC goes
back to its old level.
So, a one-time price spike raises inflation persistently in
this model, but it only raises the change in inflation exactly
once.
(Note: Casual observation suggests that oil price shocks,
even in 2008, haven’t persistently changed inflation for at least
one decade, perhaps two. But that may reflect better monetary
policy, creating what Bernanke refers to as well-grounded
inflation expectations. A world of bad policy may [rationally]
be more adaptive in its expectations formation.)
COST-PUSH AND DEMAND-PULL INFLATION
The short-run output term in PC is “demand-pull,” while ō
is “cost-push.” Both are covered in this model.
12.4 Using the Short-Run Model
Regarding the 1970s and Volcker, Chad goes in reverse order,
since Volcker’s story is much simpler to tell. The Volcker
story tells itself; you’ll just want to spend a moment looking
at Figure 12.12, Chad’s time-series method of storytelling. It’s
a useful tool to which you may find yourself coming back.
Chad explains the 1970s as driven by the Federal Reserve’s
belief that potential output was higher than it actually
was. Thus, when the economy grew more slowly than usual in
the 1970s, Fed officials thought the economy was below poten-
Monetary Policy and the Phillips Curve | 97
tial. They didn’t have our Phillips curve around then, so
they didn’t know that rising inflation was a sign that GDP
was above potential. They saw high unemployment rates
and slow economic growth and figured they needed to keep
real interest rates low to push the economy back up to what
they thought was potential.
12.5 Microfoundations: Understanding
Sticky Inflation
You may not need to spend time on the rest if you like; the text
does a solid job making the key points on sticky inflation, and
the next unit on the link between money and interest rates
might take quite a bit of time if you want to cover it clearly.
All told, there’s an argument for heading to Chapter 13.
That said, I love teaching both of these topics—they are
at the heart of macro- and monetary economics, respectively.
Here’s a list of the explanations Chad provides for sticky
inflation (he italicizes them in the text):
Imperfect information
Costly computation
Contracts
Bargaining costs
Social norms
Money illusion
With all of these reasons for sticky inflation (prices), we can
expect that in the short run relative prices change and the
classical dichotomy doesn’t hold.
12.6 Microfoundations: How Central Banks
Control the Interest Rate
This is your basic money demand story. Chad gives the simple
case of inelastic money supply and shows how that determines
rates; then he shows that the Federal Reserve can peg the rate
by supplying money, perfectly inelastically, at the target rate.
The key economic idea here is that the nominal interest
rate is the opportunity cost of holding money—it reflects
interest foregone if you hold your wealth in the form of checking accounts or currency (or if banks hold it in the form of
reserves).
In this section, the basic tools of monetary policy are
quickly reviewed: (1) the federal funds rate, (2) the reserve
requirement ratio, (3) the discount rate, and (4) open market
operations. As mentioned throughout the chapter, the federal
funds rate is influenced by the demand for and supply of bank
reserves. Here you will have to mention that bank deposits
are subject to a reserve requirement ratio, the percentage of
deposits that must be kept in the form of cash in vaults and/
or deposits in other banks. In the normal course of business,
banks engage in a number of activities that affect total
reserves relative to required reserves. Deposits and debt
repayment increase reserves. Withdrawals and loans (investments) reduce reserves. Banks with deficient reserves can
borrow funds (buy reserves) from other banks. Banks with
excess reserves can loan funds (sell reserves) to other banks.
The demand for and supply of reserves, federal funds, determines the federal funds rates. The Fed can target the federal
funds rate by influencing the demand for and supply of bank
reserves. Lowering the reserve requirement ratio allows
banks to hold less in reserves, increasing the supply of
reserves and lowering the federal funds rate. Lowering the
discount rate, the rate of interest the Fed charges banks on
its loans, reduces the demand for federal funds and lowers
the federal funds rate. Finally, open market operations, the
purchase and sale of government securities by the Fed, influence the total volume of reserves in the banking system and
can be used to alter the federal funds rate. An open market
purchase of securities causes bank deposits and reserves to
increase and can lower the federal funds rate. An open market sale of securities has the opposite effect—bank deposits
and reserves decrease and the federal funds rate increases.
Chad concludes by showing that the purchase and sale of
government securities can have direct effects on interest
rates. For example, as a consequence of government sale of
securities, the price of securities decreases and the yield on
the security, approximated as the contractual interest payment divided by the price, will increase.
12.7 Inside the Federal Reserve
This section provides a quick overview of how the Federal
Reserve interacts with the banking and financial systems.
Students will likely have had some variation of this discussion in Principles, and I recommend you don’t spend much
time on this.
The policy tools (the federal funds rate, reserve requirements, the discount rate, and open market operations) of the
Federal Reserve are reviewed.
Chad begins the discussion by stressing that conventional
tools used by the Fed include the federal funds rate, reserve
requirements, and the discount rate.
The Fed requires banks to maintain reserves, cash on hand
or deposits in other banks (including the Federal Reserve
Bank), as a fraction of deposits. Chad doesn’t mention it, but
the main purpose of the reserve requirement is to control the
volume of bank lending. To maintain reserves, banks with
deficit reserves can borrow reserves, on an overnight basis,
from other banks with surplus reserves—these transactions
take place in what is commonly known as the federal funds
market. The price of the reserves is the federal funds rate—
the interest rate on overnight loans of reserves. The Federal
Reserve can change the reserve requirement (a tool seldom
used) and therefore change the volume of bank lending.
98 | Chapter 12
Typically, the Fed does not pay banks interest on their reserves,
but it did begin paying a modest amount in 2008, following the
financial crisis. The discount rate is the rate of interest the Federal Reserve charges banks for reserves on overnight loans.
When it was created by the Federal Reserve Act of 1913, the
Federal Reserve was charged with being a lender of last resort
to the banking system—that is, when the banking system was
short of reserves, the Federal Reserve would supply reserves to
the banking system. During the financial crisis of 2007, discounting became very impor tant, as the Federal Reserve
provided the banking and financial systems with trillions of
dollars of liquidity.
The final tool used by the Federal Reserve is open market
operations—in which the Federal Reserve purchases and sells
government bonds to affect the levels of bank reserves and
bank lending, the price of bonds, and nominal interest rates.
When the Fed sells government bonds, it takes money
(liquidity) from the public, the banking system included, and
supplies the public with bonds. The sale of bonds has three
effects. First, the supply of bonds increases, reducing their
price and increasing their yield. Here you can give the standard example of a bond sold at par of $100 paying interest of
$3; the yield is 3 percent, but if the price of the bond falls,
say, to $97, the yield rises to $3/$97 = 3.1 percent. Second, the
withdrawal of liquidity from the banking system creates
shortages of reserves and simultaneously drives up the federal
funds rate. Third, the decline of reserves in the banking system slows down bank lending and reduces the money supply.
The opposite is (all) true when the Federal Reserve engages in
an open market purchase of securities.
negative price shock or because the real world is just more
complicated than our simple model. But on average, the Phillips curve is a good description of the U.S. experience. So,
you wouldn’t want to make too much out of one year of falling inflation, but if you had two or three years of falling inflation, then your friend’s story of economic weakness would
look plausible.
How would you know if he or she was wrong about the
economy being weak? If he or she was wrong, you’d see three
or four years of no change in inflation—inflation would stay at
its same rate year after year. In practice, there might be some
small wiggles—a year up, a year back down, perhaps—but if
real GDP is equal to potential, we wouldn’t expect to see
year after year of falling inflation.
And of course, if inflation has been rising year after year,
then that’s good evidence that actual GDP has been above
potential—or, as Chad likes to say, short-run output has been
positive.
Notice that if we do this, we’re reading the Phillips curve
from left to right. Normally, we’d plug in a number for shortrun output and find out what the change in inflation is going
to be. Now, we’re going to plug in the change in inflation to
find out the likely level of short-run output. This is a handy
tool that you can use in real life.
That means that just by reading the newspaper and checking out some basic numbers on past inflation, you can know
whether U.S. GDP is probably above, below, or about equal
to its potential.
A FEW EXAMPLES:
Assume the Phillips curve works like this:
SAMPLE LECTURE: USING THE PHILLIPS CURVE
TO LEARN ABOUT THE ECONOMY’S POTENTIAL
Suppose your friend tells you that the U.S. economy is performing far below its potential: too many people are unemployed, too many factories are closed, and too many people
are on welfare. He or she says things have been this way for
years. How can you figure out whether he or she is right or
wrong?
You could try to estimate potential GDP in a couple different ways—by carefully estimating the long-run average
trend in GDP per person, or by carefully measuring the size
of the capital stock, labor supply, and the level of technology.
But of course, those methods would be extremely difficult for
a student to do. Is there an easier way?
According to the Phillips curve, yes there is. All you have
to do is see if inflation has been falling for the last few years.
Inflation tends to fall when actual GDP is below potential
GDP. If inflation has fallen, that’s a sign that output may well
be below potential.
Of course, the Phillips curve isn’t a perfect relationship in
real life: every so often, inflation falls all by itself, due to a
change in inflation = 0.5 × short-run output
1. Inflation over the last three years has been 6 percent in
year 1, 4 percent in year 2, and 2 percent in year 3 (that’s
this year). Has short-run output probably been positive,
negative, or zero during this time?
2. Inflation over the last three years has been 10 percent
in year 1, 14 percent in year 2, and 18 percent in year
3 (that’s this year). Has short-run output probably been
positive, negative, or zero during this time?
3. Inflation over the last three years has been 0 percent in
year 1, 1 percent in year 2, and 2 percent in year 3 (that’s
this year). Has short-run output probably been positive,
negative, or zero during this time?
EXPANDED CASE STUDY: THE TERM
STRUCTURE OF INTEREST RATES
Chad notes correctly that long-run rates are a rough average
of short-term rates. That’s how the Federal Reserve can move
Monetary Policy and the Phillips Curve | 99
the one-year and five-year interest rates in the same direction as the one-night federal funds rate. How strong is this
relationship? Not as strong as one might hope. Glenn Rudebusch’s widely cited 1995 Journal of Monetary Economics
piece, “Federal Reserve Interest Rate Targeting, Rational
Expectations, and the Term Structure,”1 found that changes
in the fed funds rate were an excellent predictor of changes
in interest rates of up to ninety days. Timothy Cook and
Thomas Hahn, in a widely cited 1989 piece in the same journal, “The Effect of Federal Funds Rate Target Changes on
Market Interest Rates in the 1970s,”2 found a clear, correctly
signed effect on rates of up to twenty years. Other researchers
since then have found broadly similar results, especially for
bonds of ten years or less. It appears that the federal funds
rate is the one rate to rule them all.
they had some idea that inflation might rise if society tried
to keep short-run output so high.
But without the rigorous models of Lucas and Sargent
invented in the 1970s, and without the basic insights of Friedman and Phelps’s “natu ral rate hypothesis,” Solow and
Samuelson, giants in the field of economics, could do no
better than say that inflation might rise or fall after a few
years of very high unemployment:
EXPANDED CASE STUDY: A BRIEF HISTORY
OF THE PHILLIPS CURVE
This case study illustrates how difficult it is for even great
minds to see the complex world clearly when they have the
wrong model in mind. If they had our Phillips curve—the
one with the change in inflation—they would have clearly
understood that an economy can’t be away from potential
GDP for very long without noticing a big change in the inflation rate.
In a 1960 article3 in the American Economic Review, future
Nobelists Robert Solow (author of our Solow model) and Paul
Samuelson (inventor of models of money demand, interest
rates, social security, and much else) argued that it might be
possible to keep unemployment low while keeping inflation
at the same rate forever. They weren’t sure about it, but they
argued that it was a possibility. In short, they thought the
Phillips curve might look like this:
level of inflation = 3% + v × short-run output
They said the following: “price stability . . . is seen to
involve about 5 percent unemployment . . . [while] 3 percent
unemployment . . . is seen to involve a price rise of about
4 percent per annum.” They thought it was possible—not
certain, but possible— that society could have a 2 percent
drop in the unemployment rate (4 percent more output by
Okun’s law) just by putting up with 4 percent inflation.
Could this situation last forever, then? Would the level of
inflation stay unchanged at 4 percent even if the unemployment rate stayed at 3 percent, a level not seen in the United
States in decades? Solow and Samuelson recognize that
something would probably change in the medium or long run:
“It would be wrong, though, to think that . . . price and unemployment behavior will maintain its same [relationship] in
the longer run.” Reading the paper today, one can see that
1. Glenn D. Rudebusch, “Federal Reserve Interest Rate Targeting, Rational Expectations, and the Term Structure,” Journal of Monetary Economics 35 (April 1995): 245−74.
2. Timothy Cook and Thomas Hahn, “The Effect of Changes in the
Federal Funds Rate Target on Market Interest Rates in the 1970s,” Journal
of Monetary Economics 24 (July 1988): 331−51.
3. Paul A. Samuelson and Robert M. Solow, “Analytical Aspects of AntiInflation Policy,” American Economic Review 50 (May 1960): 177−94.
[I]t is conceivable that after they had produced a [high
unemployment] economy . . . prices might continue to rise
even though unemployment was considerable. Nevertheless, it might be that . . . wage and other expectations
[would] shift the [Phillips] curve . . . in the longer run—so
that over a de cade, the economy might enjoy higher
employment with price stability than our present day estimate would indicate.
CASE STUDY: ALAN BLINDER’S STICKY
PRICE INTERVIEWS
Alan Blinder, a Princeton economist who has served as
vice chair of the Federal Reserve, wanted to find new evidence about why prices are sticky. His solution was to do
something that economists rarely do: he went and talked to
businesspeople. He had graduate students interview hundreds of business leaders, and among other things they
were asked about twelve different possible explanations for
sticky prices. So, which theories did the businesspeople
believe?
The top four theories—the only ones that received a greater
than 50 percent vote—were:
• Coordination failure: a standard oligopoly story; no one
wants to be the first to raise prices, for fear that others
won’t follow
• Cost-based pricing: firms only think it’s right to change
prices when actual costs change, not when demand
changes
• Nonprice competition: consistent with real business
cycles and other flexible price theories; fi rms might
fi nd it easier or cheaper to change quality rather
than price, freeing up society’s resources to be used
elsewhere
• Implicit contracts: the “invisible handshake”—an understanding that it’s wrong to change nominal prices
100 | Chapter 12
SAMPLE LECTURE: THE MP CURVE
AND THE LM CURVE
Chad provides a nice “case study” on the IS/LM model, and
shows that the MP part of the model is easily deduced from
the Liquidity–Money (LM) curve (that most of us older economists were taught). In addition, following the financial crises and musings of Paul Krugman (see: http://krugman.blogs.
nytimes.com/2011/10/09/is-lmentary/), the IS/LM model has
received both positive and negative commentary. For those
who are interested, Chad’s short-run model can be easily used
to “crank” out the LM curve (following Chad’s approach of
deriving the IS curve that likewise emphasizes short-run output [measured as the cyclical variation in output around
potential output]. To derive Chad’s version of the LM curve,
the LM curve needs to be slightly redefined: the LM curve is
now defined as depicting the equilibrium rate of interest in
the money market for different levels of short-run output. To
derive the LM curve, demand for the money in the money
market must be dependent on short-run output. To illustrate,
suppose that real money demand depends on the following:
(a) potential output; (b) the variation in current output from
potential output; and (c) the difference between the current
real rate of interest and the long-run (marginal product of
capital) real rate of interest; that is,
Md/P = m0 t + m1(Yt − t) − m2(Rt − ) t,
where Md = money demand; m0, m1, and m2 > 0, increases in
the real rate of interest relative to the long-run rate of interest reduce real money demand, and increases in potential
output and increases in current output relative to potential
output increase real money demand. Dividing both sides of
the money demand function by potential output, , yields
money demand relative to nominal potential output; that is,
Md/P = m0 + m1(Ỹt) − m2(Rt − ),
where Ỹ is short-run output.
Setting money demand equal to money supply yields the
LM curve, with the current real rate of interest as dependent
on short-run output, the long-run rate of interest, and the
ratio of the money supply to nominal potential output. For
example,
Md/P =
s
short-run equilibrium rate of interest in the money market.
In addition, an increase in the money supply decreases the
equilibrium rate of interest in the money market.
To crank out the MP curve, recall that Rt = , and that as
Ỹ changes, the change in demand for money (relative to
nominal potential output), m1ΔỸ, must equal the change in
the supply of money (relative to nominal potential output).
Going through this exercise makes me doubly appreciate
Chad’s ability to focus on the essentials. However, some students may be curious about the formal process of relating
Chad’s MP curve to the traditional LM curve (so here it is).
REVIEW QUESTIONS
1. The Fed’s only actual choice is to set the nominal interest
rate.
Since the inflation rate is given, this determines the real
interest rate (real = nominal − inflation). The Fisher equation
shows us this relationship, and the real rate is the horizontal
(so far) line known as the MP curve. (More realistic versions
of the MP curve will occur later—they slope upward.)
The real interest rate determines short-run output, Ỹ. The
IS curve shows us this relationship.
If output is above potential (positive short-run output), then
inflation rises in the future. If output is below potential (negative short-run output), then inflation falls in the future. This
is the Phillips curve.
2. The major story is that people are not perfectly rational
agents—and they don’t have perfect knowledge about how to
set exactly the profit-maximizing price.
So, when a typical business is deciding on price increases,
the owners are likely to ask themselves, “What have we done
recently?” If they use that as a starting point for discussions
about price changes, that gives inertia, all by itself. If things
have been especially busy (positive short-run output), they
might raise prices more than last year. If things have been
especially slow (negative short-run output), they might raise
prices a little less than last year or even cut prices. As long
as “last year’s price increase” is the starting point for discussions at the typical business, then inflation inertia will exist.
3. By raising or lowering the nominal interest rate; that’s the
only impor tant tool it has.
/P ,
so that
Ms/P = m0 + m1(Ỹt) − m2(Rt − ).
Solving for Rt yields the LM schedule:
Rt = (1/m2)[m0 + m1Ỹ + m2 −
s
/P ].
The resulting LM schedule pulls out the familiar relationships. An increase in current output, an increase in nominal
potential output, and an increase in the long-run rate of
interest all increase the demand for money and increase the
4. Friedman’s statement means that the Fed can’t use interest rate changes to perfectly offset all shocks to the economy:
if a bad shock hits today—like a collapse in home building—
then an interest rate cut today might increase short-run GDP
six months from now, or it might increase it eighteen months
from now. It’s hard for experts to know how long it takes for
the “medicine” to get “into the system.”
A number of lessons flow from this: first, you definitely
can’t use monetary policy to respond to purely short-term
Monetary Policy and the Phillips Curve | 101
(lasting less than six months) shocks to GDP. The medicine
won’t get there in time to cure the problem. Therefore, you
must live with some short-run GDP fluctuations.
Second, it tells us that good policy must be both forwardlooking and cautious: the central bank must set the interest
rate today based on what interest rates it thinks the economy
will need six to eighteen months from today. Since the future
is always hazy, running a central bank is much like driving
into a fog. And the first rule of driving in fog is “slow down.”
That probably means to slow down your rate cuts as well as
your rate increases. Alan Blinder formalized this line of
thinking—a sort of “precautionary principle”—in his short,
nontechnical book, Central Banking in Theory and Practice
(Cambridge, MA: MIT Press, 1999).
Overall, Friedman’s statement is a counsel of humility for
economic policy makers. The fluctuations you will always
have with you.
(Note: This chapter isn’t discussing the role of the Fed as
providing short-term liquidity to solve short-term financial
problems—as in the days after 9/11, around Y2K, or at the
end of each quarter, when firms are dressing up their balance
sheets. Then, there appears to be a role for the Fed in solving purely short-run problems in financial markets by making sure that borrowers and lenders can coordinate with each
other.)
EXERCISES
5. The Phillips curve tells us that the level of short-run output impacts the inflation rate: booms raise inflation above
what people expected, and busts do the opposite.
Reading from left to right, actual inflation (π) depends
on people’s inflation expectations (π e) and on “demand
conditions,” that is, how much ( ) a short-run boom or bust
(Ỹ) causes firms to speed up or slow down their price
increases.
3. (a) This boom means that the IS curve shifts to the right.
At the same old nominal interest rate, this creates a rise in
short-run output.
6. Volcker raised the real interest rate—and since inflation
started off high, this meant that the nominal rate was the
highest ever seen in the United States. The high real rate
caused a deep recession (negative short-term output) in the
early 1980s. As our model predicts, the recession caused
firms to slow down their price increases, and so inflation fell
quickly.
7. Because the demand for money shifts around too much, a
fixed (vertical) money supply combined with a constantly
shaking money demand curve would mean that interest rates
would change constantly and unpredictably. This would probably be bad for the economy.
Money demand appears to shift due to technological
changes that make it easier or harder to hold money: ATMs,
credit cards, electronic transfers between banks— these all
probably have some impact on our desire to hold our wealth
in the form of money rather than in the form of houses, stocks,
bonds, or other assets.
1. First, let’s address the question of how a nominal rate
impacts a real rate: every nominal interest rate has a corresponding real interest rate. Just find out what the expected
inflation is over the relevant time period (that is, next year’s
inflation for a one-year bond, inflation over the next decade for
a ten-year mortgage, and so on), and use the Fisher equation
to find out the corresponding real rate.
Second, let’s address the question of how the Fed can indirectly influence long-term rates when it only has direct control over short-term rates: as Chad shows in the case study,
the long-term rate tends to be a rough average of short-term
rates, and when the Fed changes short-term rates, it tends
to either keep them at the new level for a while or it tends to
keep making even more moves in the same direction. So, the
Fed has a form of inertia when it changes the short-term rate.
People in financial markets know this, so when the short-term
rate changes today, many long-term rates tend to move in the
same direction—not days or weeks later, but on the very
same day.
2. The MP curve shifts down, and so it crosses the IS curve
down and to the right of its old location. This stimulates
investment spending, which increases short-run GDP.
(b) A central bank that cared about keeping short-run output
right where it was before the consumption boom would
immediately raise the nominal interest rate. This would raise
the real interest rate (since inflation expectations don’t change
in the short run), which would hurt investment purchases.
While consumers would probably consume a bit more of
GDP (due to their optimism, presumably), businesses would
consume a bit less (due to the Fed’s decision to raise the interest rate).
In IS/MP, this means IS shifts right and then MP shifts up
just enough so that short-run output is the same as before the
consumption boom.
4. This is a worked exercise. Please see the text for the
solution.
5. This is an appropriate goal because any time output moves
away from potential, one of two bad things happens: if you let
output fall below potential, then you have unused resources—
unemployed workers and machines. This is unlikely to be
popular. If you let output rise above potential, people might
be happier today (or they might complain that they are overworked), but in the next year or so, inflation will rise, which
will make people unhappy. To make matters worse, the only
102 | Chapter 12
reliable way to get rid of the higher inflation is by creating a
recession, which will, again, make citizens unhappy. In the
short-run model, “free lunches” are hard to come by—so it’s
best to stick close to potential output.
6. Assume that in all cases, Ỹ starts off at zero before the news
arrives.
(a) This means IS shifts left. The Fed should respond by
cutting rates (pushing MP down) to put Ỹ back to zero.
(b) The IS curve shifts right. The Fed should respond by raising the nominal interest rate (raising MP) until the corresponding real interest rate again equals the marginal product
of capital. This is the same as raising MP until Ỹ equals zero
again.
(c) IS shifts to the right. The Fed should raise MP until Ỹ is
back to zero.
(d) IS shifts left. This means fewer consumer goods will be
made in the United States. The Fed should cut MP until Ỹ is
back to zero.
(e) Same as (b). This raises the marginal product of capital
(capital is scarce, so it’s worth more). This shifts the IS
curve to the right. That means you need to raise the MP
curve if you want to head back to your (now lower) potential
GDP.
This isn’t as cruel as it sounds. As you may recall, in a
Solow “long-run” world, the economy will naturally start
accumulating capital immediately after an earthquake. The
goal of the monetary policy maker is to make sure that investment isn’t so high that it creates inflation.
(f) The IS curve shifts left. The Fed should shift MP down,
cutting interest rates.
7. Step 1: When inflation is sticky, a rise in the nominal rate
is the same as a rise in the real rate. This comes from the
Fisher equation.
Step 2: A rise in the real rate deters firms from buying new
investment goods and deters homebuyers from buying
new homes: This hurts short-run output.
Step 3: When short-run output is negative, firms are less
aggressive about raising prices, so inflation falls.
8. (a) First, let’s make the simple assumption that “absence
of any monetary policy action” means that the Fed keeps the
real interest rate constant. Then we’ll see what happens if the
Fed instead keeps the nominal interest rate constant.
The Phillips curve shifts upward for one period, and then
shifts back down. Meanwhile, the level of inflation permanently rises. So if it was 6 percent before, it might persistently
be 8 percent afterward.
If the central bank instead keeps the nominal interest rate
constant after the oil shock, then things get interesting. Now,
the rise in inflation will turn a constant nominal rate into a
cut in the real rate: the MP curve moves down. The central
bank has just unwittingly created a boom! With positive
short-run output, inflation will rise persistently, year after
year, as long as the central bank keeps the nominal interest
rate constant.
Remember: a constant nominal rate plus a rise in inflation
equals a cut in the real rate. And the real rate is what matters
for business decisions.
(b) I’d temporarily raise the real rate enough to create a recession that would push inflation down to its old level. Note that
this means a big increase in the nominal rate. For example,
if I need to raise real rates by 1 percent, and the oil price
shock raised inflation by 3 percent, then I need to raise the
nominal rate by 1 percent + 3 percent = 4 percent. I am not
likely to be a popular central banker if I do this. You can see
why U.S. central bankers in the 1970s were reluctant to undo
the effects of the oil price shocks.
Surprisingly, Volcker, who finally did raise rates high
enough, has had a very successful career since then as an
adviser to banks. So, in the United States at least, some forms
of political bravery are rewarded.
In graphs, the Phillips curve rises due to the oil shock for
one period and then goes back—here, nothing is changed. On
the IS/MP side, raise MP for one period to create a recession,
then put MP back to its old level.
9. I’ll just discuss the Phillips curve, since that’s the only clear
direct impact. I’ll also assume that the immigration is a onetime wave. We’ll assume that wages are a driving force
behind firms’ price changes. The Phillips curve drops down
for one period, and then goes back up to its old level. This
will push down the inflation rate one time, but the effect will
last. So, inflation might go from 4 percent to 2 percent, but it
would stay at 2 percent persistently.
If we want to look at IS/MP, then this story is the opposite
of the previous question: the issue for the MP curve is whether
a “do-nothing Fed” does nothing to the nominal rate or the
real rate. But the overall story is that if the Fed wants lower
inflation, one way to get that is to increase potential GDP—
whether by increasing the labor supply, the capital stock, or
the number of ideas. We saw this was true back in Chapter 8,
and it’s still true in the short-run model.
10. Assume we start with zero short-run output.
(a) If the Fed keeps the nominal rate unchanged, then a
rightward shift in the IS curve causes the following:
• IS/MP immediate effect: IS shifts right but MP stays
fixed. This yields positive short-run output.
• Phillips curve immediate effect: positive short-run output raises inflation.
Monetary Policy and the Phillips Curve | 103
• IS/MP next period effect: a fixed nominal rate plus positive inflation equals a lower real rate. The Fed has just
strengthened the boom, this time by accidentally pushing MP down. (This is the same as in the answer to 8(a).)
• Phillips curve next period effect: the boom is even bigger now, so inflation rises even faster than last year. If
inflation was 2 percent beforehand, it might have been
4 percent the first year but is now 8 percent this year!
• Further effects: you can see where this is headed—an
even lower real rate, since inflation is even higher. There’s
a bigger boom, which causes higher inflation, which cuts
the real rate again, and so on—all from a one-time boom
in consumer spending that the Fed just let pass on by.
• Summary: in this case, the IS curve only shifts once, and
it only shifts at the very beginning (rightward), due to
the consumption boom. The Phillips curve never shifts.
MP, by contrast, keeps falling every period, as higher
inflation accidentally reduces the real interest rate every
period.
(b) Assuming the goal is stable prices and production, as in
3(b) earlier, if the central bank raises the real rate of interest
in response to the autonomous increase in consumption, so
that short-run output is unchanged, the rate of inflation is
unchanged and the economy remains in its initial position on
the Phillips curve.
11. With a bigger , it’s easier to kill inflation. A small
recession now cuts inflation more than before. This would
make Volcker’s life easier.
Things that might make this happen include anything that
makes it easier for businesses to change prices in response
to demand shocks. For example, computer inventory tracking might make it easier for a company to know how much
is being sold each week; weaker unions might make it easier
to cut wages during a recession; more trust between unions
and firms might convince unions to take a temporary wage
cut in order to save jobs (there’s some evidence that Scandinavian unions and firms cooperate this way); decentralized
firms might sell directly to the consumer (there’s some evidence that goods that pass through many hands on their way
to the consumer have stickier prices).
12. This is a worked exercise. Please see the text for the
solution.
13. Inflation was stable in the late 1990s, so it appears that
short-run output was close to zero. If the new economy boom
was largely due to positive short-run output, then we would
have seen inflation rise quite a bit by now by way of the Phillips curve.
Greenspan was right, and his critics within the economics
profession were wrong. Since this is essentially an essay question, I’ll refrain from writing a full essay.
14. E-commerce has made it much easier to keep money outside of checking accounts, probably reducing the amount of
wealth that people hold in the form of M1. I can now make
many of each month’s purchases using credit cards and keep
my money in the form of savings accounts most days. At the
end of the month, when bills arrive, I can quickly move
money from savings into checking (no impact on M2, but
increasing M1), and then pay my bills. Of course, I need no
currency for these transactions, so e-commerce puts downward pressure on the demand for currency (part of every definition of money). In a world of unpredictable financial
innovation, shifts in money demand are quite likely. This is a
good argument for targeting the nominal interest rate rather
than a fixed money supply.
CHAPTER 13
Stabilization Policy and the AS/AD
Framework
CHAPTER OVERVIEW
This is the third simple dynamic general equilibrium model
we’ve covered this semester—first Solow, then Romer, and
now the New Keynesian model with a Taylor rule. Of course,
what makes this one different is that to complete the model,
we need to make assumptions about how the government
behaves. And fortunately, thanks to John Taylor, we now have
a useful shorthand for that: his monetary policy rule.
This chapter contains an impor tant invisible-hand result:
a monetary policy rule that only focuses on keeping inflation close to its target will also stabilize short-run output, as
if by an invisible hand. Students might have thought that in
order to stabilize short-run output, the Federal Reserve (the
Fed) would have to pay attention to, well, short-run output.
But no!
This should be the fun chapter on business cycles. You’ve
done the hard work of explaining the IS and Phillips curves,
and you’ve run through the examples of Volcker and the
1970s to give a sense of the dynamics. Now you can show
how a policy rule can automate much of the work of stabilizing the economy; you can talk about rules versus discretion and time consistency; and you can show how rational
expectations can really become a normative goal of good
economic policy.
Students will find some parts of this chapter difficult, especially those parts that involve dynamics (the use of interdependent shift factors), where changes in current inflation
cause changes in expected future inflation rates. Those
changes in expected future inflation rates can cause the AS
schedule to be unstable with respect to cyclical variations in
output.
104
13.1 and 13.2 Introduction and Monetary Policy
Rules and Aggregate Demand
Here, we introduce a simple Taylor rule (Chad just calls it a
“simple monetary policy rule,” but I’ll call it a Taylor rule).
It says that when inflation is above the target, the Fed should
raise the real rate above the marginal product of capital.
That’s it.
Rt − =
(πt − )
is just a parameter (1/2 in Taylor’s rule) that shows how
strongly the Fed reacts to inflation. A bigger means a bigger reaction.
Note that Chad has set this up so that it plugs into his
Investments–Savings (IS) curve easily; together, they give us
what we now call the aggregate demand curve:
<t = ā − ( × )(πt − )
Ỹt = ā − ( × )( t − )
You really should keep and separate in your equations:
that gives you a chance to show how short-run output
depends on both the market side of the economy (for example, how sensitive investment is to the real rate) and on government policy (for example, how strongly the Fed reacts to
changes in inflation).
In Figures 13.2 and 13.3, Chad plots this in inflation/
short-run-output space and shows an inverse relationship
between the inflation rate and the level of short-run output.
Note that the y-axis is the level of inflation, not the change in
inflation; that’s a change from last chapter’s Phillips curve.
Figure 13.3 is quite interesting—it shows that a higher generates a flatter aggregate demand (AD) curve.
I often emphasize that is a measure of how “mean” or
“uncaring” or “brutal” the central bank is. It shows how
Stabilization Policy and the AS/AD Framework | 105
SHIFTS OF THE AD CURVE
These are shifts of ā, the IS curve’s intercept; on average,
when output equals potential output, ā must equal zero.
Recall, ā shifts are defined to be temporary; an ā shift is
the sum of shifts to the C, I, G, and NX intercepts. Any shock
to one element of ā (such as the steady-state shares of consumption, investment, and so on) would be absorbed into
some other component of gross domestic product (GDP) in
the long run.
For example, either a shock to the consumption share is
temporary or, in the long run, it crowds out the investment
share or some element of net exports.
Here is another example: Chad’s model implies that a permanent rise in government purchases does not cause a permanent rise in the IS curve. In the long run, there’s crowding out
and IS shifts back. This means that any truly permanent
inflationary impact of higher G must come not through the
rise in G itself but either because of extremely sticky inflation expectations or because the government chooses to
accommodate the new, higher rate of inflation.
(Note: This story is just what would occur in a fully specified New Keynesian model. One key to any New Keynesian
model is that in the limit, you get to a neoclassical outcome.
And in any neoclassical model, a rise in one spending share
will cause a fall in another.)
(Let’s leave discussion of how permanent increases in G
impact the interest rate until Chapter 17.)
13.3 The Aggregate Supply Curve
practice. But when it comes to graphs, Chad makes a distinction. When Chad draws the Phillips curve using the level of
inflation on the y-axis, he calls that the AS curve. This lets
him plot it on the same inflation/short-run output space as the
AD curve.
By contrast, when he wants to think about how the Phillips curve interacts with aggregate demand, he wants to make
the history of inflation as clear as possible, so he keeps inflation in levels, and calls it aggregate supply. This distinction
is now conventional.
(Note: AS crosses the zero-short-run-output line at last
year’s inflation rate [plus or minus a price shock].)
How do you make this clear to students? With one equation (13.2) with arrows drawn to two separate graphs (AS and
PC): that’s the diagram I’d draw on the chalkboard.
As I emphasize below, the AS curve is the dynamic curve
in this model: it moves every year that short-run output isn’t
zero. One thing you might do on the chalkboard is draw
something like the chart below, to clarify AS’s simple
behavior.
Often the AS schedule is simply drawn for a given level of
inflation expectations. For positive fluctuations in output, the
actual inflation rate is greater than the expected inflation rate,
prices increase relative to costs, and profits increase as production expands. For negative fluctuations in output, the
reverse is true. Chad introduces dynamics by allowing the
expected inflation rate to vary in response to changes in last
period’s inflation. For example, following a positive aggregate demand shock, the actual inflation rate rises relative to
the expected inflation rate. The new, higher inflation rate then
becomes next period’s expected inflation rate. This higher
expected inflation rate, given the demand conditions, pushes
up the rate of increase in business prices, the inflation rate. As
such, the AS schedule successively shifts until the expected
inflation rate, last period’s rate of inflation, converges with the
actual inflation rate.
AS
If AD crosses AS
on this side, AS
shifts down/right
next year.
Inflation
willing the central bank is to push the economy into recession over something as apparently unimportant as purely
nominal inflation. This helps generate some drama and passion in a subject that often sounds dry— dry, that is, until it
happens in the real world.
I often prod students with questions like, “Why would the
Fed be so cruel as to start a recession just because inflation
is 2 percent above the target? Can’t we just live with a little
inflation?” This helps motivate a discussion and some policy
applications that fit in with conventional topics of noneconomic, real-world discussions: caring about the long run,
self-control, and how one sometimes needs to be cruel to be
kind. These themes recur throughout the chapter and can
culminate in Chad’s discussion of time consistency.
If AD crosses AS
on this side, AS
shifts up/left
next year.
The Phillips curve does double duty. This equation
πt = πt−1 + Ỹt + ō
is Chad’s adaptive expectations Phillips curve. It is also
Chad’s aggregate supply (AS) curve. When discussing the
equation itself, the terms are interchangeable— and in my
experience, that roughly follows standard macroeconomic
0%
Short-run output
(Note: When drawing the Phillips curve in the previous
chapter, a permanent rise in the oil price led to a one-time
106 | Chapter 13
rise in the PC; the PC went back to its old position the next
year. That’s because the PC was drawn as the change in
inflation.)
With the AS curve, a permanent rise in the oil price would
cause a persistent rise in the AS curve—we can’t really say
the AS shift is permanent, because the current model
makes us acutely aware that demand forces are always
moving AS.
13.4 The AS/AD Framework
Two equations with two endogenous variables— short-run
output and inflation. One piece of history—lagged inflation
(a.k.a. your state variable). A few relatively deep parameters.
That’s the model.
THE STEADY STATE
You can’t remind students enough that output heads to zero
in the long run. You can drive home that point by starting
off with the model’s steady state. Chad solves it numerically before he shows the graph— a good choice, since
it gives you a chance to explain why the steady state is
what it is.
In steady state (a.k.a. the long run, loosely speaking),
there are no aggregate supply shocks (ō equals zero),
and there are no aggregate demand shocks (ā equals zero).
Also, in steady state, inflation is steady at some rate, so
πt = πt−1 = some fixed number Chad calls π*. That’s all you
need to assume.
A little substitution between equations 13.3 and 13.4 (AD
and AS) shows that Ỹ will equal zero, and π* will equal not
zero, but rather , the target inflation from the policy rule.
I’d emphasize this outcome a couple of times— does not
head to zero: it heads to instead. That means the central
bank’s choice of matters quite a lot. This is a point to which
you can refer often.
THE AS/AD GRAPH
How you plot this the first time matters, so I’d follow Chad’s
lead and have them intersect at and zero short-run output.
When it comes time to review what AS and AD mean, the
point I’d make is that on the AD curve, inflation causes
short-run output (through the monetary policy rule), while
on the AS curve, short-run output causes a rise in inflation
(through the Phillips curve).
This is quite a contrast with the micro supply and demand
story, where price determines quantity on both sides of the
market. You’ll have to destroy some of students’ micro intuition to make this point stick—so you may want to repeat it
repeatedly throughout the chapter.
13.5 Macroeconomic Events in the
AS/AD Framework
After you’ve covered this section, your students should be
able to read the newspaper. That said, the big question that
may float around in their minds is one of timing. I try to
emphasize that in real life, output effects happen months
before inflation effects— and I make that point repeatedly.
Chad tells three stories that should encompass the only stories worth telling:
1. Zero shocks to the AD curve
2. One shock to the AD curve
3. Two shocks to the AD curve
Why no more than two AD shocks? In this model, the AD
curve is the static curve, while the AS curve is the dynamic
curve. So, every time AD shifts, it sets off a long round of
responses from the AS curve. For that reason, if you shift
AD around too often, students will just lose track of what’s
going on.
The three stories Chad tells are about a price shock (zero
AD shocks), a Federal Reserve decision to shoot for lower
inflation (one negative shock to AD), and a positive IS shock
that goes away eventually (two AD shocks: one positive, one
negative).
EVENT #1: AN INFLATION SHOCK
The first story is crucial because it shows the Taylor rule’s
invisible hand at work: if an inflation shock hits the economy,
eventually things return to zero short-run output and the target rate of inflation.
Longer version: an oil price shock hits the economy, pushing up inflation. As a result, the Fed chooses to raise the real
cost of borrowing, hurting the economy and making businesses think twice about raising prices. With more people
out of work and more products going unsold, businesses
choose to slow down their price hikes.
In year one, when the shock hits, the slope of the AS curve
itself summarizes this effect: note that for a given ō shock,
inflation rises by less than ō; that’s because the Fed is instantly
raising rates as soon as it gets news of the oil shock, and that
instantly (okay, within a year or less) starts putting downward
pressure on inflation.
In year two, a new dynamic takes place: AS shifts downward (in fact, if you’re interested, it shifts so that it intersects
potential output at year one’s post-shock inflation rate. A
numerical example is worked out in the end-of-chapter exercise 15).
Once inflation starts moving back toward normal, the Fed
can choose to relent a little—but not too much; it’s not trying to create a boom. It’s still putting the brakes on the econ-
Stabilization Policy and the AS/AD Framework | 107
omy, but it’s no longer slamming the brakes down to the floor.
This cools off the price hikes a bit more, bringing inflation
slowly back toward its target. Once inflation is back at the
target level, the Fed sets the real rate back equal to the marginal product of capital—and all is right with the world.
Notice that in this story, the Fed never says, “Goodness,
we created a recession: now we must do everything possible
to push the economy back to potential!” The only thing the
Fed cares about is inflation. In fact, the Fed actually wants
output to be below potential, since that’s its only tool for
bringing inflation downward. It is a cruel model of Fed behavior—but it nevertheless returns the economy right back to
potential GDP and target inflation as if by an invisible hand.
EVENT #2: DISINFLATION
This is one big permanent negative AD shock, where the
shock is a fall in the target rate of inflation. It’s basically a
dressed-up version of the Volcker disinflation story from the
previous chapter; it’ll give students a chance to see the same
story told with two different models.
Note two things: the central bank’s choice to disinflate
equals a choice to cause a short-term recession, since that’s
our only tool for bringing inflation down. Also, after the initial shock, inflation keeps falling—just as it does anytime
short-run output is negative.
EVENT #3: A POSITIVE AD SHOCK
This is the two-AD-shock story: a boom caused by a rise
in G, a wave of consumer optimism, high foreign demand,
something like that—anything that increases ā, the IS curve’s
intercept. But since ā shocks are temporary—long-term
shares of C, I, G, and NX must sum to one, after all—then
AD will shift back to its old position at some point.
The net result? A counterclockwise inflation-output loop.
The boom causes high output and higher inflation, pushing
output back to potential at a new, higher inflation rate. Then
the ā shock dissolves, creating a recession that pulls inflation
back down, ultimately landing us back at potential output and
target inflation.
This is a typical boom-bust cycle. The period between 1995
and 2004 would be one recent example of a small inflationoutput loop; the period between 1975 and 1984 would be the
biggest loop in postwar U.S. history. Chad presents data later
in the chapter—see Figure 13.18.
FURTHER THOUGHTS ON AGGREGATE DEMAND SHOCKS
Timing: this is a good place to talk about that. When an AD
shock hits the economy, the effects on output might take
months to show up, while the effects on inflation could take
a solid year to eighteen months to show up. Thus, a central
bank must react today to problems it might be facing in the
future.
It’s like driving a car on the freeway: you have to steer right
now to avoid that tire tread 150 feet up ahead. Forwardlooking behavior is thus key to good central bank policy. So,
if the Fed sees a bad AD shock coming and it wants to counteract it, it must cut interest rates before the bad shock really
hits with full force. Thus, central bankers need to be good
forecasters—they need a clean windshield.
Of course, what most of us would do if we were running
the central bank would be to aggressively cut rates whenever
there is a hint of bad news, while letting good AD news just
pile up in our inbox without a reply. After all, if something
bad might happen, shouldn’t we help people out by cutting
rates? And that good news, the news that might lead to
inflation—that’s just speculation, isn’t it? Thus, the suffering
of unemployment feels salient, while the cost of high inflation feels distant and intangible. We’ll see later what happens
if real-world policy makers behave just like you or I would.
Aside: I’ve heard more than one politician complain that
the Fed was raising rates when there was no sign of inflation—
why would he or she or do that?
Second aside: Shifts in the marginal product of capital are
hidden by the model. How must the Fed respond to productivity shocks that change the marginal product of capital? The
lessons of the IS curve are still true. A rise in capital’s productivity means that the Fed has to raise the real interest rate.
But the AS/AD model doesn’t let us tell that story.
Chad hid this problem away when he chose a monetary
policy rule that assumes that the Fed knows the marginal
product of capital. That means that there are no variables in
the AS/AD model that let us talk about policy errors that
grow out of mistaken Fed assumptions about MPK.
Result: Discussions about shifts in MPK are best left to the
side in the AS/AD framework.
13.6 Empirical Evidence
As an instructor, you always face the dilemma of whether to
show theory together with evidence—so students feel that it’s
relevant—versus showing the evidence afterward—pulling
the rabbit out of the hat. Both methods are probably equally
(in)effective . . . just mixing it up from chapter to chapter is
probably a good idea. Here, Chad presents the evidence afterward: he shows that our simple Taylor rule isn’t an awful
predictor, excluding recent recessions, of actual Fed behavior since 1960 (Figure 13.16) and that inflation-output loops
are for real (Figure 13.18).
The big story on the Taylor rule: Actual rates were too low
in the 1970s— even though they were high by current standards. In a case study below, we discuss an application of this
idea, now known as the Taylor principle.
108 | Chapter 13
13.7 Modern Monetary Policy
1. Governments can make commitments;
2. Prices are flexible; and
MORE SOPHISTICATED MONETARY POLICY RULES
What happens if the Federal Reserve wants to react to more
than just inflation? What if it wants to care about output as
well? When a normal human being asks that question, what
he or she is usually asking is, “If there’s a recession, can’t the
Fed ease up a bit on interest rates?” The short answer to that
is indeed it can. An end-of-chapter exercise works this out,
but the short version is that this makes the AD curve steeper
than before.
What this means in practice is that the Fed responds less
to inflation. If inflation goes up, the Fed wants to hurt the
economy (typical policy rule effect), but once the Fed sees
the economy is weakening, it relents a bit. The net result is
that inflation must be incredibly high before the Fed creates
a big recession.
On the flip side, under this output-sensitive policy rule, the
Fed dislikes economic booms so much that it raises rates
at the first sign of positive short-run output. Again, this is a
steeper AD curve—and a policy that keeps output close to
potential, even at the cost of wide swings in inflation.
This detail assumes that the monetary policy rule reacts
instantaneously to shifts in GDP; responding to lagged
GDP is more realistic, but it complicates the math beyond
the intermediate level. The policy implications are the same
either way.
RULES VERSUS DISCRETION AND THE PARADOX
OF POLICY AND RATIONAL EXPECTATIONS
Here we begin to move toward rational expectations. Adaptive expectations fit the data quite well in some ways, but
we know that workers and businesses don’t just expect this
year’s inflation to be the same as last year’s. People read
newspapers, they read forecasts, and they try to understand
what the Federal Reserve or Congress might do over the next
couple of years. They don’t get the answer exactly right, of
course, but they try to be forward-looking. After all, as we
saw before, when talking about consumption, we saw that
people do an okay job basing their consumption on their
future expected incomes—so they do try to anticipate the
future and take that into account when they make their decisions today. That forward-looking behavior matters for
monetary policy. As I mention below, I’d cover the next
section, “Managing Expectations,” before I cover time
consistency. A sample lecture on time consistency is also to
come.
MANAGING EXPECTATIONS IN THE AS/AD MODEL
I’d teach this before I teach about time consistency. This section shows how good policy is easy if
3. People are rational.
Of course, there’d be no point teaching this if it was just pie
in the sky. In practice, all three elements are partially true.
So, if the economy is stuck with high inflation, and it wants
to reduce inflation, it’s good to know that if half the economy is flexible and rational, then, if the government
announces a believable low inflation policy, AS will budge
more than our simple adaptive model suggests. Credible
announcements can probably cut the cost of disinflation.
The government should try to help citizens form accurate expectations of the future—and it should keep in mind
that a reputation for honesty is easy to lose.
After you’ve made these points, you can teach time consistency. This gives you a chance to show that government’s
ability to make and keep commitments is a big problem—
but a problem that the rich countries seem to have solved in
the last two decades.
In 2007, Fed Chairman Bernanke gave a speech that
touched on managing expectations; it received some media
attention at the time. The title is “Inflation Expectations and
Inflation Forecasting,” available at http://www.federalreserve
.gov/newsevents/speech / bernanke20070710a.htm. After
reading this chapter, students should be able to understand
the speech.
So, how does one keep a good reputation as an inflation
fighter? One way is by showing that you’re willing to risk a
recession rather than let inflation rise—and that you’re not
going to bail out the economy with low rates every time some
bad news comes along. If businesses know that the Fed chairman is willing to take a Marsellus Wallace attitude toward the
U.S. economy, they are unlikely to raise prices very quickly.
INFLATION TARGETING
I don’t have much to add to this—inflation targeting may help
the public focus its expectations, but it has to be backed up
with (expected) action as discussed in the section on time
consistency. Delegation to a “conservative central banker” or
building a reputation might work to solve the problem—but
those are the hard parts. Inflation targeting per se? That’s a
decision to publish a memo.
13.8 Conclusions
How should a central bank behave? Should it try to follow a
policy rule like our Taylor rule? Or should it just “see what
happens and make the best choice every day?”
As the time consistency story makes clear, the “best choice
every day” is to try to create a little boom today and reap the
Stabilization Policy and the AS/AD Framework | 109
high inflation down the road. But citizens figure that out and
push inflation up, yielding no boom and high inflation. So,
the second option isn’t going to work. Some kind of rule—
explicit or implicit—is necessary, as far as we can tell.
We apparently need a central bank to do more or less what
the Taylor rule says: kill the economy when inflation rears
its head. In the United States, elected politicians don’t make
those decisions; it’s delegated to the Federal Reserve Board.
Board members, who vote on interest-rate decisions, make
decisions that are painful and unpopular.
In fact, their job isn’t that bad—it’s worse! One impor tant
point that our model doesn’t really emphasize is that the Fed
is often adjusting real interest rates not based on what inflation is now but on what it thinks inflation will be a year or
two from now. Therefore, if the board believes inflation is
likely to rise a year from now, it often chooses to raise the
real rate today in order to cut off much of those inflationary
pressures. “Preemptive strikes” against future threats of inflation are an impor tant part of the monetary policy maker’s
strategy.
That’s probably why we don’t see retired Federal Reserve
chairmen running for Congress after they retire (that, plus
the fact that they can easily increase their salaries by a
factor of ten by going to work in the private sector). It’s surprising that democracies have been willing to pay the high
short-run cost of fighting inflation—it provides some evidence that democracies can pay a short-term price in order
to gain a long-term benefit. This theme of delayed gratification will come up again in the next chapter, when we talk
about fiscal policy.
SAMPLE LECTURE: TIME CONSISTENCY
Our first application of forward-looking expectations is with
time consistency. It’s an idea that helped Kydland and Prescott
win their Nobel Prize in 2004. There are plenty of good timeconsistency parables. Kydland and Prescott’s original one
about living in a flood zone is still salient: forward-looking
homebuyers will choose to live in a flood zone even if the
government says it won’t bail them out after a disaster,
because homebuyers know that politicians will bail them out
regardless of prior “promises.”
Another example is intellectual property. Governments
might “promise” to enforce drug patents, but if a medicine
is both extremely expensive and the best way to save lives,
the government might well break the patent. As a result, drug
companies will be reluctant to spend money investing in lifesaving medicines and will instead choose to invest in drugs
that are unlikely to come under government- or mediagenerated demands to break the patent—so more research
will be done on indigestion, hair loss, and acne. Fewer dollars will go into fields where the government’s promise might
be broken.
Capital income taxation is another famous example: companies will invest more if they know taxes on profits will be
low, but they know that even if government “promises” low
taxes today, once the businesses are profitable, the government will likely break the promise. As a result, businesses
invest less than they would otherwise.
A final example is that punishing criminals is too expensive to be worth the trouble. Is the government really going
to spend thousands of dollars to prosecute me just because
I stole $100 from a cash register? Of course not—that would
be irrational. If a lot of would-be criminals conclude that the
government won’t prosecute, you wind up with a lot of criminals. If the government could find some way to promise to
prosecute everyone it catches, then very few people would
commit crimes, and it might not have to spend that much
money on law enforcement. But making such a commitment
would be, well, somewhat irrational—after all, once a guy
does rob a cash register, are you really going to spend that
much money just to prosecute one guy?
Of course, we’re here to apply this to the question of monetary policy. It’s probably best to set up this story the way
Chad implicitly does: price-setters choose their prices first,
then the central bank decides whether to boost aggregate
demand.
The key insight is that when government keeps its “discretion” to make the “best possible decision,” the government’s
best possible decision is always the same: try to boost AD a
little and try to create a boom. And by now students should
recognize that a boom means higher inflation.
What should forward-looking businesses do when setting
prices in this kind of world? Well, if the Federal Reserve creates a boom, they don’t want to keep prices low—they want
to raise prices. And if the Fed doesn’t create a boom, raising
prices is just too dangerous. So, the average business is going
to choose high prices if the Fed chooses high AD and will
choose low prices if the Fed chooses low AD. Now that we’re
assuming that businesses are forward looking, it doesn’t take
years for AS to adjust: it adjusts right now, when they set their
prices.
Consider the following diagram, which just breaks the
model into two steps (business move and Fed move) and two
choices (low or high). The business decision of “low or high”
is about prices, while the central bank’s decision is about AD.
Step 1
Businesses set prices
(low or high)
Step 2
Central bank decides whether
to boost AD
(low or high)
With just a little reflection, businesses will conclude that no
matter what expectations they have—low or high—the central bank is always going to choose high AD. If businesses
set their prices low, then the Fed can create a boom economy.
110 | Chapter 13
If businesses set their prices high, then the Fed has little
choice. It has to boost AD in order to prevent a recession or
worse. So the Fed’s best choice is clear: high AD no matter
what the businesses do.
Businesses now know what they have to do: choose high
prices, in anticipation of the Fed’s high-AD policy. Net result?
Let’s look at the payoff matrix:
EXTENDED CASE STUDY: REAL
BUSINESS CYCLES
The final answer is that firms set prices high, the Fed boosts
the economy, and they wind up with high prices and no boom
whatsoever.
(Note: This is easy to illustrate using the AS/AD model.
But you should only try to illustrate it after you’ve shown that
high inflation/no boom is the equilibrium outcome. If you try
to do the whole story in AS/AD format, you’ll wind up with
a hopeless mess of lines on the board [low AS and low AD]
versus high AS and high AD: those are the only two options
I’d draw.)
Why can’t society get down to the low inflation, no-boom
scenario? Because such a policy is not time consistent. The
government would like to be able to sign a contract before
businesses form their beliefs; it would like to make some kind
of commitment, so that it can keep AD low. But because it’s
the government, it can’t sign a contract: it has discretion every
day, every moment, whether to make or break its promises.
The Fed wishes it could keep the promise it feels like making, but it knows it will break the promise when the time
comes. Its wishes beforehand don’t match up with its decisions afterward.
How do governments fix this problem in practice? There’s
a massive literature on this. The major solutions fall into three
categories: the government can try to build a reputation for
honesty, it can delegate its decisions to someone else who
doesn’t care as much about short-run booms and busts (as the
United States tries to do by having the Fed vote on interest
rates, not Congress), or it can create a real monetary policy
rule that it has to stick to, by law (like an inflation target or a
money growth target or a Taylor rule).
Alesina and Summers1 found a lot of evidence for the second method. In countries where interest rate decisions are
kept away from politics, inflation tends to be much lower,
while economic fluctuations are about the same size no matter
what. A politics-free monetary policy appears to be a free
lunch: something citizens should buy as often as possible.
What is the root cause of most business cycle fluctuations?
Do shifts in aggregate demand really push us away from the
optimal level of output? That’s the New Keynesian view
we’ve been discussing for the last four chapters.
The leading alternative view, known as real business cycles
(RBC), says that most economic fluctuations are caused by
changes in the level of technology. Some years, workers are
more productive, so they choose to work more hours, and
other years, when workers are less productive, they choose
to work fewer hours. That’s the basic RBC model.
Robinson Crusoe, alone on his island, provides a simple
example. When the weather is good, he works more and saves
coconuts and bananas for the future. When the weather is
bad, he stays inside, works very little, and consumes his
stored-up coconuts and bananas. According to U.S. government estimates, productivity really is usually higher during
booms than during recessions, and real wages apparently do
slightly rise with the overall economy.
How does this matter for government policy? If the RBC
model is roughly true, then there’s little point in trying to
“cure” economic fluctuations—after all, when the weather is
bad, it’s rational to work less. A government policy that tried
to get people to work more in bad weather would only make
matters worse.
Are real business cycles a major part of the story? Let’s
look at the answers given by two experts: one who largely
supports the RBC worldview and one who largely favors the
New Keynesian worldview of this textbook. In a 1999 interview with Bennett McCallum in Macroeconomic Dynamics,2
Nobel Prize–winner Robert Lucas stated his belief that since
World War II about 80 percent of business fluctuations fit into
the RBC framework. At the same time, he believed that the
Great Depression was largely caused by the monetary forces
we’ve studied here: a bad monetary policy rule that led to
high real interest rates.
Lucas believes that since the end of World War II, monetary policy has been much better—and now that AD shocks
are much smaller, whatever shocks are left are likely to be
due to changes in potential output, not what we’ve been calling short-run output. A similar phenomenon has happened
in medicine: most human beings once died of infectious diseases, but now, thanks to public health improvements and
antibiotics, we can die of cancer and heart disease instead.
But even though few humans die of infectious diseases, we
still want our doctors to know how to treat infectious diseases. Therefore, even if Lucas is right, it makes good sense
to spend our energies learning about good monetary policy.
1. Alberto Alesina and Lawrence H. Summers, “Central Bank Independence and Macroeconomic Per for mance: Some Comparative Evidence,”
Journal of Money, Credit, and Banking 25 (May 1993): 151–62.
2. Bennett McCallum, “An Interview with Robert E. Lucas, Jr,” Macroeconomic Dynamics 3 (1999): 278–91.
Businesses: Low
Businesses: High
Fed: Low
Fed: High
Low inflation, no
boom
Depression
Economic boom
High inflation, no
boom
Stabilization Policy and the AS/AD Framework | 111
Now let’s ask what a New Keynesian thinks about RBC.
In a 2004 paper in the Review of Economics and Statistics,3
Peter Ireland of Boston College estimated a rich New Keynesian model of the U.S. economy— essentially, a model that
combines elements of the Solow framework and the AS/AD
model, plus a heaping dose of rational expectations. He
included what one might think of as three “Keynesian”
shocks— shocks to people’s patience, shocks to the price
level, and shocks to the monetary policy rule. He also added
one RBC-style shock, a conventional “technology shock.”
What Ireland found when matching his model up to U.S.
post–World War II data is quite interesting. Before 1980,
about 10–25 percent of fluctuations could be attributed to
RBC-style technology shocks. But since 1980, 40–50 percent
of fluctuations appear to be due to RBC-style technology
shocks.
Ireland’s explanation for the big post-1980 change is similar to our story about infectious disease: since 1980, there are
fewer policy shocks. The Fed is behaving in a more predictable way to stabilize GDP around potential. That means that
a larger portion of the fluctuations that we’re left with are the
fluctuations that we don’t (yet) know how to fix—indeed,
many believe that we are better off not fixing them at all.
While RBC supporter Lucas and New Keynesian supporter Ireland disagree on many things, they agree that RBC
appears to matter more than it used to—and much of the reason is due to the good monetary policy that the United States
has enjoyed in recent decades.
EXTENDED CASE STUDY: RECENT OIL SHOCKS
AND THE MACROECONOMY
Since World War II, every recession except for one has
been preceded by a large, sustained increase in the real
price of oil. James Hamilton of the University of California, San Diego, is the best-known researcher in this area—it
grew out of his dissertation—and many macroeconomists
have wrestled with this robust relationship.
Are oil shocks a leading cause of U.S. recessions? That
would fit nicely into our model: a price shock forces the Fed
to fight inflation by hiking real interest rates, which causes a
recession. Plus, even in a “long-run” production function
framework, if you’ve got less oil to use, you just physically
can’t produce as much output: less gasoline, fewer plastics.
So an oil price shock is clearly bad news for the economy.
Between 2001 and 2008, oil prices more than doubled in
nominal terms, yet were these price increases the consequence of supply shocks and a cause of recession? Hamilton
speculates (on his blog, Econbrowser) that perhaps the recent
increases in oil prices are driven not by supply shocks—
3. Peter N. Ireland, “Technology Shocks in the New Keynesian Model,”
Review of Economics and Statistics 86 (November 2004): 923–36.
political turmoil in oil-producing states, the usual source of
shocks— but instead by a demand shock—particularly the
growth of demand in India and China. See: http://econbrowser
.com /archives/2011/01/oil_shocks_and_2.
Indeed, India and China are using enormous amounts
of raw materials as they build their economies. And if the
Chinese and Indians are using those raw materials to make
goods and services for the U.S. economy, then that kind of
oil shock is one that is less likely to cause trouble for the
United States.
A 2005 Federal Reserve Bank of San Francisco Economic
Letter entitled, “Why Hasn’t the Jump in Oil Prices Led to
a Recession?”4 discusses different views on this issue—
including an impor tant paper in the area coauthored by Ben
Bernanke.
Of course, we did see oil prices increase significantly by
over 40 percent in the first half of 2008. The NBER reported
that the Great Recession began in December 2007. During
2007, the price of a barrel of oil increased from over $50 to
over $90 by the end of the year—price increases that don’t
seem justified by rising world demand. Perhaps rising oil
prices and the financial crisis combined for a perfect storm
leading to the Great Recession.
CASE STUDY: TYING AS/AD TO MONEY GROWTH
AND INFLATION
This model says that high inflation comes from high aggregate demand, but in Chapter 8 we saw quite clearly, with lots
of evidence from around the world, that high inflation is
caused by high money growth. Are these two different
stories?
No, they are not. Any time you see “high aggregate
demand” in the AD model, you know that the central bank
is lending a lot of money to private banks, who can then lend
it out to consumers and businesses. This increases the money
supply, which in general creates inflation. And the reverse is
similarly true: low AD → low central bank lending → low
private bank lending → less private sector money for consumers and businesses.
CASE STUDY: THE TAYLOR PRINCIPLE
After you’ve covered Figure 13.16—actual and predicted fed
funds rates—it’s a good time to state the Taylor principle.
That’s the idea that when inflation rises by 1 percent, a central bank must raise the short-term nominal rate by more than
1 percent. Translating our abstract policy rule into nominal
interest rates will also help students read the news.
4. John Fernald and Bharat Trehan, “Why Hasn’t the Jump in Oil Prices
Led to a Recession?,” NFBSF Economic Letter (November 18, 2005).
112 | Chapter 13
Illustrating the Taylor principle with a few numerical
examples is the best way to make the point. If the nominal
rate is currently 4 percent with 2 percent inflation, and then
the Federal reserve gets news that inflation will soon rise by
1 percent, what must the Fed do? The Taylor principle says
the Fed must raise the nominal rate by more than 1 percent.
Let’s say it raises the rate from 4 percent to 5.5 percent. That’s
a big rate hike! Voters will complain; the central bank will
be unpopular. Nobody is happy— and all because the Fed
believes that inflation will rise otherwise.
Let’s look at what happens if the central bank chooses to
ignore the Taylor principle—let’s say that when news of
higher inflation rises, the central bank decides to be “tough”
but not “brutal.” So, when news arrives that inflation is heading up to 3 percent, it raises the fed funds rate to 4. Five
percent—that sounds tough, right?
But let’s compare the real cost of borrowing before and
after in these two cases:
Real before
Real after
Taylor principle
“Tough, not brutal”
4% − 2% = 2%
5.5% − 3% = 2.5%
4% − 2% = 2%
4.5% − 3% = 1.5%
Notice what happened in the two cases: under the Taylor
principle, when inflation rises the Fed raises the nominal
interest enough to raise the real interest rate—thus cooling
off the economy. Under the “tough, not brutal” policy, when
inflation rises, the Fed raises the nominal rate—so it “feels
tough”—but it ends up cutting the real rate! It has just made
the boom even bigger! This will increase inflation even more,
according to the Phillips curve.
(Note: If you really want to make the point painfully clear,
you can show that the “tough, not brutal” rule implies an AD
curve with a positive slope. It’s just a slightly negative slope
on the policy rule’s parameter. Under such a rule, if you start
from the steady state, any positive price shock leads to
explosive inflation—which may just be what happened in
the 1970s.)
REVIEW QUESTIONS
1. Thinking of policy in terms of a rule is helpful because it
helps the private sector to form accurate expectations about
the future. If the central bank can reduce uncertainty by following a rule, then private businesses and workers will be
better able to plan for the future, which may improve economic stability.
Also, following a rule is good for helping policy makers to
think clearly. When you use a rule, you can run economic
simulations where you compare your favorite rule against
other policy rules. That way, you can find out which rule is
best. Rules are easy to compare to one another, while discretion is hard to compare to anything.
Finally, it’s good to remember that even if you use pure
discretion, you are still following a rule—you just may not
know what the rule is yourself. The time consistency literature shows that if you have pure discretion, then what you
really follow is the rule called, “Do what’s best for the economy this year.” As you’ll see, you just wind up with high
inflation and an average economy.
2. AD slopes downward because of the link running from
the Taylor rule to the IS curve. If inflation is high, the Fed
will be “tough” and hurt short-run output with higher real
rates. If inflation is low then the Fed will be “kind” and
help spur short-run output with lower real rates. The AS
curve slopes upward because it’s just the Phillips curve:
positive short-run output causes fi rms to raise prices more
aggressively.
It’s like a standard supply-and-demand model because a
quantity measure is on the x-axis while a price-related measure is on the y-axis. It’s unlike a supply-and-demand model
because the only reason AD slopes downward is because of
a government policy decision to hurt short-run output when
inflation is high. In markets, a high price for an individual
good generally causes consumers to substitute over into buying other, cheaper goods. In brief, AD is about government
policy.
3. AD shocks: government spending shocks, investment
optimism, consumer optimism, foreign recession
AS shocks: oil price shocks, union wage hikes, cheap
imports
4. The AS curve is our fundamental source of dynamics,
as discussed above. The economy takes several periods to
return to steady state because of sticky inflation—it takes a
while before inflation finally gets to the level where the Fed
chooses to set short-run output equal to zero.
5. They are counterclockwise because the cycle is boombust, not bust-boom. The boom might be caused by some
kind of good news—any shock to ā will do. Then inflation
rises, and the economy heads back to steady state. But now,
either the ā shock dissolves or the Fed chooses to tighten
monetary policy, and so a recession occurs. This pushes
inflation down, and eventually the Fed relents and sets the
real interest rate equal to the marginal product of capital.
6. Businesses set prices (and workers negotiate for wages)
based on what they think average inflation will be in the
future. If they believe inflation will be high, they demand
higher prices, and so the inflation expectations become
self-fulfilling.
If the Fed can convince businesses that it will not tolerate
inflation, then businesses know that their competitors are
Stabilization Policy and the AS/AD Framework | 113
unlikely to raise prices, and so each business itself will choose
not to raise prices. This is a much easier way to keep inflation
low compared to causing recessions. If the Fed can manage
inflation expectations, it can avoid much of the ugly work of
monetary policy . . . but it can only avoid that work if everyone
believes that it will hurt the economy rather than risk inflation.
In 2015, the inflation rate was approximately 1.4 percent.
If the target inflation rate was 2 percent, and the was
2 percent, and = .5, the predicted federal funds rate was
3.1 percent. The actual federal funds rate was 0.13 percent.
Apparently, our monetary policy rule doesn’t account for
continued hangover of the Great Recession and continued
threats of global stagnation.
EXERCISES
3. This is an increase in the AS curve—it shifts down and to
the right. This creates a temporary boom, and a fall in inflation. If no other shocks happen, this works as the opposite
of the oil shock story, example 1. AS slowly drifts back up
to its target rate, and the boom ends.
1. (a) 10 percent inflation → 6 percent real, 16 percent
nominal
5 percent inflation → 3.5 percent real, 8.5 percent
nominal
2 percent inflation → 2 percent real, 4 percent nominal
1 percent inflation → 1.5 percent real, 2.5 percent
nominal
(b) 20 percent nominal, 10 percent real
10 percent nominal, 5 percent real
4 percent nominal, 2 percent real
2 percent nominal, 1 percent real
This rule implies a central bank that is tougher on
inflation. This implies a flatter AD curve.
2. (a) The 2015 inflation rate, measured as the percent change
in the Core PCE (chained) price index, was 1.38 percent.
(b) The 2015 inflation rate, measured as the percent change
in the PCE (chained, including food and energy) price
index, was 0.35 percent.
(c) Decreases in the price of energy, especially oil and gasoline, have caused the PCE inflation rate to be less than the
Core PCE inflation rate.
(d) From equation 13.5, the federal funds rate is
it = Rt + πt = + πt + (πt − )
4. (a) The change in the price of oil causes a supply shock. A
decrease in the price of oil, as in question 3 above, causes
an increase in the AS curve—it shifts down and to the right.
(b) In response to an increase in the price of oil, the macroeconomy evolves as follows. First, assume the economy
starts in the long-run steady state. Next, assume a one-time
increase in the price of oil. The increase in the price of oil
shifts the AS curve up and to the left, and the immediate
response is an increase in the inflation rate and a reduction
in short-run output. In Chad’s model, the current period’s
expected inflation rate is based on last period’s actual
inflation. With no further increases in the price of oil,
the oil shock has dissipated, but inflationary expectations
remain higher than what they were in the steady state; as
such, the AS schedule shifts down and to the right, but not
all the way back to the steady state, because of the higher
inflationary expectations. The result is a decrease in the
inflation rate in the second period. The decline in the inflation rate in the second period reduces inflationary expectations in the third period, which further shifts the AS curve
down and to the right. Eventually, through reductions in
inflationary expectations, the AS curve shifts back into its
steady-state position. During this adjustment, the economy
will experience disinflation and an increase in short-run
output.
The opposite holds for a one-time decrease in the price of
oil. First assume the economy is in the steady state. A onetime decrease in the price of oil shifts the AS curve down and
to the right. The immediate effect of the oil price reduction is
a lowering of the inflation rate and increase in short-run output. In the second period, the price of oil increases, but
inflationary expectations are reduced. The consequence of
these events causes the AS curve to shift up and to the left,
where the leftward shift is dampened by the decline in inflationary expectations. The result is an increase in the inflation rate and a reduction in short-run output. The increase in
the rate of inflation in the second period causes the
expected inflation rate to increase in the third period. This
increase in the expected inflation rate further shifts the AS
curve up and to the right. Through lagged adjustments in the
114 | Chapter 13
5. The big story is that this is a clockwise inflation-output
loop—the opposite of textbook case 3.
This is a fall in AD, which pushes the economy into recession and pushes inflation down. AS slowly shifts down, bringing the economy back to potential output.
Eventually, either European or Japanese economies
recover, pushing AD back up to its old level. Alternatively,
other sectors of the economy pick up the slack, as domestic
consumers or businesses increase their demand for goods;
that’s another way to get AD back up. The final result is that
output and inflation end up back at their preshock levels.
6. This works like an AD boom that lasts. Now that the central bank implements the new ', it’s cutting the real rate.
After all, ' is now higher than πt, the current inflation rate.
This shifts AD outward. Higher AD means a move along
the fixed AS curve for the first year—so demand pressures
push inflation up a bit, but not quite high enough to be in
steady state. Over the next few years, AD stays in its same
(new) position, and AS slowly creeps upward: the boom creates more inflationary pressures, so firms raise prices more
each year. Eventually, the economy winds up back at zero
short-run output, with ' equal to πt. The central bank then
ends the boom: we are now in a new steady state.
7. (a) AS slopes upward because positive short-run output
creates pressures for price hikes on the demand side. With
positive short-run output, firms are selling more than they
want to at current prices. Therefore, they raise prices more
than the previous year. If the average firm does this, then
overall inflation increases.
(b) A steeper AS would mean that output would fluctuate
less, but inflation would fluctuate more under AD shocks.
(c) A steeper AS would mean that both output and inflation
would fluctuate less for a given oil price shock. (Note that
the oil price shock is a y-intercept shock.)
(d) A steeper AS curve would occur if inflation were less
sticky. So, anything that might make businesses more
rational and forward-looking when setting prices might
make inflation less sticky and more flexible. Weaker unions,
computerized price setting, customers being more willing to
tolerate price changes, more firms in each industry (so no
one firm can set a price)— any of these features could make
inflation more flexible.
8. (a) When inflation rises, the central bank chooses to
raise real interest rates and slow down the economy.
(b) Note that ā is an x-intercept. Under a steeper AD curve,
a shock to ā has a bigger effect on output and inflation.
Worse on both counts!
(c) Under a steeper AD curve, a shock to ō creates a smaller
swing in output, but a bigger swing in inflation.
(d) A Fed that doesn’t care much about inflation causes AD
to be steeper. Also, if investment responds only weakly to
shifts in interest rates, or if the consumption and investment
multipliers get smaller, then AD gets steeper.
9. This is a worked exercise. Please see the text for the
solution.
10. Rt − = (1/b) (ā). Inserting this into the IS curve,
Ỹt = ā − (R − ), yields
Ỹt = ā − (b/b)ā = 0.
Every time ā shifts one way, the Fed instantly counteracts it
by changing the real interest rate. A positive AD shock
causes a hike in rates; a negative AD shock causes a fall in
rates.
11. (a) The IS curve has a negative slope, as usual. But the
MP curve has a positive slope!
(b) Output fluctuates less now, compared to the fixed interest rate rule from beforehand. This is another version of
what we just saw in question 8. There, we also saw that output fluctuates less when the Fed cares about stabilizing real
output.
(c) If there’s a positive IS shock, then the real rate gets hiked.
The higher rate “crowds out” investment spending because
when borrowing is expensive, firms are reluctant to go into
debt to take on new projects.
12. (a) The function being graphed is it = ( + ) + (1 + m) πt.
The slope is greater than one. As noted in the manual, this
concept is known as the Taylor principle. In the graph below,
= = 2 percent, m = 0.5.
12
10
Nominal interest rate
expected inflation rate, the AS curve moves back into its
original steady-state position.
8
6
4
2
0
0
5
10
Inflation rate
15
20
Stabilization Policy and the AS/AD Framework | 115
(b) It would mean that higher inflation would cause a cut
in the real interest rates. That appears to be what often happened in the 1970s: the Fed responded too weakly when
inflation rose, and it (perhaps accidentally) cut real rates.
When setting policy, it’s impor tant to remember that as a
rule, real rates impact spending, while nominal rates do not.
13. This is a worked exercise. Please see text for the
solution.
Time
0
1
2
3
4
5
6
7
8
9
Inflation
Short- run output
2.00
3.77
3.57
3.40
3.24
3.10
2.97
2.86
2.76
2.67
0.00
−0.44
−0.39
−0.35
−0.31
−0.27
−0.24
−0.22
−0.19
−0.17
14. As this is an essay, there is no set answer.
15. The main idea behind this question is that the Fed can
only temporarily reduce the unemployment rate, at a cost of
persistently higher inflation. It’s like paying for a nice party
with your 20-percent-interest-rate credit card, and making
minimum payments for years: Can that really be worth it?
The only way, in this simple model, to keep unemployment permanently low would be to keep increasing inflation
forever. But, of course, we know from looking around the
world that countries with hyperinflation are poor, not rich.
So, our New Keynesian model isn’t really useful for understanding persistently increasing inflation. For that, you have
to go back to Chapter 8.
16. (a) Take πt–1 as , the steady state value. Now, you have
a system of two equations and two unknowns (Ỹt and π t).
Let us keep ā equal to zero, since there’s no AD shock. This
quickly simplifies to
πt = + ō/(1 + vmb)
and
Ỹ1 = ā − bm(ō/(1 + vmb))
so not all of the oil shock gets passed through immediately.
That’s because when inflation starts to rise, the Fed tightens
up on the economy, reducing the demand pressures and
cooling the willingness of businesses to raise prices.
(b) Plugging the AD curve into the AS curve yields a firstorder difference equation that can be easily solved, such as
(for ā = 0):
πt = (πt − 1)/(1 + vmb) + × vmb/(1 + vmb),
which is a simple first-order difference equation. Here are the
first ten years, just to be safe.
(c) You’ll see that even after ten years, inflation is still twothirds of a percentage point above target. This is a slowly
converging economy: steep IS curve, modest monetary policy
rule reaction, and sluggish inflation. All add up to supply
shocks lasting a long time.
17. Again, here are ten years, assuming ā stays at 2 percent
the whole time:
Time
0
1
2
3
4
5
6
7
8
9
Inflation
Short- run output
3.00
3.80
4.44
4.95
5.36
5.69
5.95
6.16
6.33
6.46
0.00
1.60
1.28
1.02
0.82
0.66
0.52
0.42
0.34
0.27
You can see by looking at the parameter values that the
new steady-state inflation rate will be 7 percent: 3 percent +
ā/(bm) = 3 percent + 2 percent/0.5.
A long-lasting 2 percent ā shock doesn’t give a 2 percent
boom, even in the first year. Why? Because even in the first
year, inflation rises, which forces the Fed to immediately
start cooling off the economy with higher real rates.
CHAPTER 14
The Great Recession and
the Short-Run Model
CHAPTER OVERVIEW
Students will find this chapter useful in applying what they
have learned so far in understanding the Great Recession.
This chapter introduces financial considerations, particularly
financial frictions, into the short-run model. Financial frictions generate liquidity shortages and insolvencies and are
reflected in risk premiums. Financial frictions, as reflected
in additions to the real rate of interest, are used, in part, to
explain the Great Recession. The roles of asset price bubbles
and price deflation are used to understand the Great Recession. The Federal Reserve’s (the Fed’s) balance sheet is introduced as a tool for understanding the Federal Reserve’s
reaction to the financial crisis. Other public responses to the
crisis, including the Troubled Asset Relief Program, budget
deficits, and financial reform are discussed. Finally, Chad
introduces the concept of secular stagnation and discusses
whether the United States and Europe, like Japan, have
entered into an era of secular stagnation.
14.1 Introduction
This chapter considers the policy difficulties encountered in
stimulating the economy during a severe economic downturn. This chapter is impor tant for understanding the limits
to monetary policy, the connection between a key monetary
policy tool, such as the federal funds rate, and the long-term
rate of interest, and how the economy can fall into a deflationary spiral and a liquidity trap. Previously, in developing
the IS/MP and AS/AD models, the long-term interest rate
danced to the tune of the federal funds rate. In this chapter,
long-term interest can change due to changes in the federal
funds rate and changes in financial frictions. During a severe
financial crisis, as the Federal Reserve lowers the federal
116
funds rate, risk premiums increase, causing long-term interest rates to remain high relative to the federal funds rate. During such severe economic downturns, monetary policy takes
an unconventional path. For example, the central bank might
attempt to purchase long-term securities to drive up prices and
decrease yields.
14.2 Financial Considerations in the
Short-Run Model
The increase in financial frictions is illustrated as the difference between the BAA corporate bond rate and the ten-year
treasury yield—the “normal” spread is about two percentage
points. Typically, during economic downturns financial frictions increase. During the Great Recession, financial frictions
increased dramatically and BAA/ten-year treasury yield
increased to around 6 percentage points. To incorporate
financial frictions into the IS/MP model, the real rate of interest, R, is simply defined as the real federal funds rate, Rff,
plus the effects of the financial frictions, . During normal
times, is assumed to be zero.
FINANCIAL FRICTIONS IN THE IS/MP FRAMEWORK
Following a collapse of housing prices, negative wealth
effects result in lower consumption, a reduction in ā, pushing the IS curve to the left. Under normal circumstances, the
Federal Reserve reduces the federal funds rate, and other
interest rates follow suit, shifting down the MP schedule to
counteract the adverse demand shock. However, during a
severe downturn, financial frictions increase, and as the federal funds rate decreases, the long-term rates increase, in
effect shifting the MP schedule upward, causing further
declines in short-run output.
The Great Recession and the Short-Run Model | 117
FINANCIAL FRICTIONS IN THE AS/AD FRAMEWORK
In the AS/AD framework, financial frictions are introduced
as an AD shock. As financial frictions rise, the real rate of
interest increases, and, given the sensitivity of output to the
rate of interest R, shifts the AD schedule to the left (while
the slope of the demand schedule still depends of the strength
of the Fed’s reactions to inflation). Given the leftward shift
in the AD schedule, the economy slides down the AS schedule, as the decrease in short-run output reduces the inflation
rate. If the economy was initially in its steady state, with a
low inflation rate, inflationary expectations fall. The decline
in inflationary expectations causes the AS schedule to shift
down and to the right, further lowering the actual rate of
inflation. The decrease in inflationary expectations potentially sets off a process whereby inflation turns negative and
deflation takes hold of the economy.
THE DANGERS OF DEFLATION
To illustrate the dangers of deflation, recall the Fisher equation: it = Rt + πt. In response to a severe economic crisis, it is
reduced to zero, and Rt = −πt. The real rate of interest becomes
the negative of the rate of inflation. In times of deflation, the
inflation rate is negative and the real rate of interest is positive.
If the inflation rate is –5 percent, the real interest rate is
5 percent. The high real rate of interest chokes off investment.
Firms and households choose not to borrow. In this case monetary policy gets “trapped” inside the banks, and the Federal
Reserve cannot stimulate the economy. During the downturn,
as the deflation rate increases, real interest rates increase, acting procyclically, further reducing short-run output. Deflation
acts in the same way as an increase in financial frictions:
increasing real rates of interest. The emergence of deflation
can lead to a deflationary spiral. As deflation increases real
rates of interest, the increase in real rates of interest causes
further decreases in short-run output, which in turn generates
more deflation. This deflationary spiral becomes one of the
key reasons for a fiscal stimulus. Chad includes a case study,
“Is There a Zero Bound . . . ,” and cites recent evidence from
Japan and Europe, where central banks pay negative interest
rates on bank deposits. He concludes that the lower bound may
not be not be precisely zero, but it is certainly close to zero.
14.3 Policy Responses to the Financial Crisis
THE TAYLOR RULE AND MONETARY POLICY
To set up a benchmark for assessing monetary policy over the
last decade, the actual federal funds rate is compared to the
federal funds rate predicted by Taylor’s rule:
it = πt + rt + .5(πt − ) + .5Ỹt
= πt + 2% + .5(πt − 2%) + .5Ỹt.
Three conclusions are reached: (1) the actual federal funds
rate is less than predicted, suggesting an expansionary monetary policy, but, due to financial frictions, the low federal funds
rate did not translate into low borrowing rates for the private
sector; (2) the federal funds rate was below the predicted level
from 2001 to around 2006—which may have contributed to
the asset price bubbles (as mentioned in one of the case studies
in the text, asset bubbles are mostly likely related to other
factors, such as relaxed lending conditions—including lowered capital requirements); and (3) the recent low federal
funds rate can be attributed to the Federal Reserve’s concern over deflation, as short-run output remains significantly
below potential output.
THE MONEY SUPPLY
During the year prior to and during the early years of the Great
Depression, the Fed increased interest rates and curtailed the
amount of money in circulation. As is now generally accepted,
and as explained by Friedman and Schwartz, this tight monetary policy played a significant role in creating the Great
Depression. The question that then comes up is whether the
Fed is repeating the mistakes of the past. The rates of growth
in various measures of the money supply, currency in circulation, M1 and M2, is considered. These measures of the
money supply exhibited rapid growth as the Great Recession
developed.
THE FED’S BALANCE SHEET
Given the limits of interest-rate policies during a severe
downturn, new policies were devised in an attempt to stabilize the economy. Institutions in crisis were able to switch
so-called troubled or toxic assets, like mortgage-backed
securities, for treasury securities. Under normal circumstances, the Fed engages in open market operations to engineer changes in bank reserves and affect changes in the
federal funds rate. During the financial crisis, the Fed,
through three “quantitative easing” programs, increased purchases of commercial paper, other loans, and mortgagebacked securities while more than quadrupling its assets. The
Fed has typically financed these purchases by crediting
banks’ deposits and by borrowing from the Treasury. In addition, the Fed now pays 0.5 percent interest on bank (required
and excess) reserves. This interest rate can be used to better
control the lending activities of banks that impact the money
supply. Evidence indicates that the first quantitative easing
program, QE1, where the Fed purchased $1 trillion dollars
in mortgage-backed securities in 2008 and 2009, was crucial
to avoiding a second Great Depression. Evidence on the
effectiveness of the subsequent quantitative easing programs
is subject to debate. The most optimistic prediction is that the
second and third “quantitative easing” programs (which
involved purchases of around $2.1 trillion dollars) had the
118 | Chapter 14
same effect as lowering the federal funds rate by about a
quarter of a percentage point and reducing the unemployment
rate by about 1.25 percentage points.
THE TROUBLED ASSET RELIEF PROGRAM (TARP)
In 2008, Congress passed TARP. TARP provided a $700
billion fund to purchase and insure assets held by financial
institutions to ensure the flow of credit. Some of these funds
were eventually used to purchase equity positions in troubled
corporations, including automakers, to prevent insolvencies
and bankruptcies.
FISCAL STIMULUS
In 2009, President Obama signed into law the American
Recovery and Reinvestment Act. This act included more than
$250 billion in tax cuts and more than $500 billion of new
government spending (on such things as unemployment benefits, infrastructure, education, health, and grants-in-aid to
states). The consequence of the stimulus was a sharp increase
in the government budget deficit to almost 10 percent of gross
domestic product (GDP). The reaction of the growth in the
budget deficits has been mixed. Some economists have
argued that the limits of monetary policy stimulus had been
reached (with the federal funds rate close to zero) and that a
fiscal policy stimulus was necessary. Others have argued, for
example, pointing to the Ricardian equivalence theorem, that
the deficit would do little to stimulate the economy while
undermining the financial security of the United States.
THE EUROPEAN DEBT CRISIS
As the financial crisis went global, several countries in
Europe, including Greece, Ireland, Italy, and Spain encountered severe problems in their banking sectors, which led to
significant increases in interest rates; this in turn limited
the ability of these countries to service their national debts.
When a country cannot ser vice its national debt, this problem is referred to as a sovereign debt crisis. Chad discusses
this problem further in Chapter 20.
FINANCIAL REFORM
Given the events that have led up to the financial crisis, an
important question arises as to what can be done to prevent
it from happening again. Bailing out failed institutions, as is
often discussed, creates a moral hazard and an incentive to
take excessive risks, because the bailout in effect privatizes
the profits and socializes the risk. Chad uses a nice expression to characterize this situation: “heads I win, tails the
economy loses.” In moving the debate forward, guidelines for
regulation are discussed: (1) enhanced capital requirements;
(2) having a systemic (risk) regulator; (3) linking executive
compensation to performance; (4) requiring convertible debt
(debt that converts to equity); (5) requiring “living wills,” a
set of instructions for reorga nizing failed banks. Many of
these features have been incorporated into the financial
reforms approved in July 2010. See the case study later in this
chapter.
In thinking about the future of financial reform, I often use
a metaphor to consider the long-term success of financial regulations. I live on the edge of a wildlife sanctuary. On my
morning walk, I notice that beavers have built a dam, and the
water levels are rising, threatening homes. The Department
of Environmental Protection approves a drain pipe to go
under the dam, where both ends of the drainpipe are encased
in a steel mesh to keep the beavers out. Within a short time,
however, the beavers simply expand the dam around the area
where the pipe drains and the water backs up again. Installing the drainpipe doesn’t change the nature of the beaver. The
threat remains. Are financial institutions like the beavers?
Will putting in financial regulations remove the systemic
risk?
14.4 The Aftermath of the Great Recession
Chad summarizes the aftermath of the Great Recession—
lackluster macroeconomic performance characterized by a
slow job recovery and below-expected GDP growth (in other
words, real GDP growth typically below 2.5 percent. For
example, from 2010 to 2015, the U.S. GDP growth rates were
2.5 percent, 1.6 percent, 2.2 percent, 1.7 percent, 2.4 percent,
and 2.5 percent, respectively. Two possible causes of the slow
recovery are discussed. The first is secular stagnation. Secular stagnation is an old idea that comes out of the original
writings of Keynes. It is caused by an increase in savings and
a reduction in investment, requiring negative real rates of
interest to equilibrate the loanable funds market. The resulting decline in investment leads to low capital accumulation
and slow growth. The second cause is due to a productivity
slowdown. The productivity slowdown is evidenced in Bureau
of Labor Statistics’ estimates of multifactor productivity (see
http://www.bls.gov/mfp/mprdload.htm). The causes of the
productivity slowdown are not yet fully understood (a good
thesis project for an honors student), but possible explanations
for the productivity slowdown include R&D spending (which
does not exhibit much of a slowdown) and credit constraints
that have limited investment opportunities.
14.5 Conclusion
The Great Recession is different from other recessions that
have occurred during the post–World War II era. Typically,
The Great Recession and the Short-Run Model | 119
recessions are related to the Federal Reserve’s attempts to disinflate the economy (as described by Rudi Dornbusch—see
page 400, footnote 14, of the text). The Great Recession, like
the Great Depression, was caused by a balance sheet crisis,
in which asset values collapsed. The effects of the Great
Recession linger, as reflected in slow real GDP growth, the
continuing threat of deflation, high unemployment, and an
economy that appears to be stuck below potential GDP.
SAMPLE LECTURE: SHOCK ABSORBERS
VERSUS SHOCK ENHANCERS
The Great Depression led to a great debate about the nature
of capitalist/market economies. In par ticular, the question of
how well these economies absorb aggregate demand shocks
was debated. A number of models were developed to consider
this issue following Keynes’s publication of the General Theory in 1936. Initially, Keynes argued that if aggregate
demand were shocked away from aggregate supply (at potential output), then the economy had no mechanism to get
back to full employment. Price deflation would generate
wage deflation and aggregate demand would get stuck below
full employment. A. C. Pigou, Keynes’s colleague and former teacher, responded with the Pigou effect: price deflation
increases the supply of real money balances and has a direct
effect on aggregate demand, stimulating the economy back
to full employment. With a strong Pigou effect, a mild amount
of deflation could act as a shock absorber, stimulating the
economy.
After Hicks’s publication of the IS/LM model, the Pigou effect
became refined within the Keynesian framework. In this
model, as with Pigou’s, the price level determines the quantity of real money balances, and therefore the equilibrium rate
of interest for any given level of output. If the level of output
is below potential output, then price and wage deflation occur.
The wage deflation restores the equilibrium real wage rate and
employment. The price deflation increases the supply of real
money balances, reducing the interest rate and moving aggregate demand to full employment. This story became known
as the neoclassical synthesis that reduced Keynes to a special
case, a short-run story.
Within the neoclassical synthesis, price and wage deflation continue to serve the role of shock absorber, and the
debate in economics about the nature of economic stability
has been reduced to “How long does it take for the economy
to adjust from an out-of-full-employment situation to a fullemployment situation?” The answer to this question could be
addressed by examining the slope of the aggregate demand
schedule. If the aggregate demand schedule was steep (flat),
as graphed, then substantial (little) price deflation was necessary to absorb the aggregate demand shock. The slope of the
aggregate demand schedule, as in Chad’s approach, can be
traced to the slopes of the IS and LM (MP) schedules. For
example, the IS/LM-AD slope story goes like this: a decrease
in the price level increases the supply of real money balances,
which, in turn, depending on the interest elasticity of money
demand, reduces the real interest rate. The more inelastic the
money demand, the greater the decrease in the rate of interest.
Given this decrease in the rate of interest, aggregate demand
increases; the size of the increase depends on the interest elasticity of investment (or in the old models, the interest elasticity
of various autonomous expenditures). If the AD schedule has a
flat slope as graphed (because money demand is interest
inelastic and autonomous expenditures were interest elastic),
then a slight amount of price deflation could be sufficient to
absorb adverse aggregate demand shocks. Given that this
price deflation was a once-and-for-all event, it acted as a shock
absorber and built the case for laissez-faire.
Many Keynesians objected to the neoclassical synthesis
and the conclusion that price deflation can act as a shock
absorber. A central feature of Keynes’s analysis was that decisions had to be made in an environment of true uncertainty.
To cope with uncertainty, economic agents agree to contracts.
The terms of contracts are expressed in nominal terms. As
Chad points out, price deflation therefore increases the real
costs of borrowing. The real rise in the real costs of borrowing is not just felt in terms of rising real rates of interest but
also in terms of adverse wealth effects. With price and wage
deflation, the ability of existing debtors to service their debts
diminishes. Bankruptcies arise and balance sheet crises
ensue. These adverse wealth effects in response to deflation
destabilize aggregate demand. Rather than price deflation
restoring aggregate demand back to full employment, it
causes aggregate demand to shift below full employment.
Price deflation is not a shock absorber at all—it is a shock
enhancer. The conclusion is that some macroeconomic policy intervention is necessary to prevent the shock enhancers
from taking hold.
CASE STUDY: THE PROVISIONS OF THE WALL
STREET REFORM AND CONSUMER
PROTECTION ACT
On July 21, 2010, President Obama signed the Wall Street
Reform and Consumer Protection Act, popularly known as
Dodd-Frank, into law. The actual bill passed reflects the
guidelines that Chad outlines in this chapter. The legislation
includes (1) protections for consumers who shop for mortgages, credit cards, and other financial products; (2) provisions to end too-big-to-fail bailouts by imposing new capital
and leverage requirements; (3) a warning system to identify
systemic risk; (4) provisions to promote transparency and
accountability for exotic instruments; (5) provisions to monitor credit-rating agencies; and (6) provisions to strengthen
existing regulations.
A complete summary is available at https://www.congress
.gov/ bill/111th-congress/ house-bill/4173.
120 | Chapter 14
CASE STUDY: OPEN MARKET OPERATIONS
VERSUS DISCOUNTING
Students are typically told that of the three main tools of monetary policy, open market operations is the strongest and discounting is the weakest. The story typically revolves around
the notion that banking and the nonbanking public can do
nothing to offset the effects of an open market purchase or
sale of securities, and inevitably the Federal Reserve will
change bank reserves and the federal funds rate to suit its policy goals. On the other hand, if the discount rate is changed,
then banks may or may not change their reserves, and, therefore, the money supply may or may not change. Robert Shiller
and George Akerlof show that although this assumption may
hold for normal times, it doesn’t hold for the extraordinary
circumstances of current times.1 Open market operations have
a limited effect, as Chad points out, because the Fed can only
drive interest rates to zero. Discounting, providing liquidity
to banks and other financial institutions, has proven to be an
effective strategy for limiting the liquidity and solvency crisis.
Through discounting the Fed has become the banker of last
resort and has limited systemic risk.
CASE STUDY: THE FED CHAIR TAKES HIS
CASE TO THE PEOPLE
On November 3, 2010, the Federal Reserve announced its
plans to purchase an additional $600 billion of longer-term
treasury securities. Ben Bernanke, chair of the Fed at the time,
took his case to the people with an op-ed piece.2 Bernanke
wrote that the United States had faced the worst financial crisis since the 1930s, that the Fed’s purchase of securities helped
stop the “economic free fall” and helped turn the economy
around, that stagnation continued, and that “the risk of very
low inflation can morph into deflation.” He went on to write
that short-term interest rates “are about as low as they can go,”
and that the Fed planned on purchasing longer-term securities.
Interestingly enough, the day after this announcement, the
Dow Jones Industrial hit its record high for the year to date.
CASE STUDY: THE FEDERAL RESERVE CHAIR
AND THE STOCK MARKET
In February 2010, chair of the Fed Ben Bernanke testified
before Congress. Following one sentence of his testimony, the
Dow rose by 1 percent within a few minutes. Below is a piece
of the transcript as reported on National Public Radio’s “Morn1. George A. Akerlof and Robert J. Shiller, Animal Spirits: How Human
Psychology Drives the Economy, and Why It Matters for Global Capitalism (Princeton, NJ: Princeton University Press, 2009).
2. Ben S. Bernanke, “What the Fed Did and Why: Supporting the Recovery and Sustaining Price Stability,” Washington Post (November 4, 2010).
ing Edition” on February 26, 2010. NPR’s Steven Inskeep and
Adam Davidson discuss the following quote from the Fed chair:
Mr. BERNANKE: The FOMC continues to anticipate that
economic conditions are likely to warrant exceptionally low
levels of the federal funds rate for an extended period.
INSKEEP: What makes you think that sentence was worth
billions of dollars this week?
DAVIDSON: I actually have proof it was worth many billions
of dollars, because you can actually watch the Dow Jones
Industrial Average for the moments before and after he said
that sentence. And right before he said that sentence, the Dow
was in a really—it was dropping and there wasn’t a lot of trading going on. Clearly, everyone interested in stocks and
bonds was listening for that sentence. The second he finishes
that sentence, boom, it shoots up one percent.
A transcript and audio of the “Morning Edition” segment are
available at http://www.npr.org /templates/story/story.php
?storyId=124105175.
REVIEW QUESTIONS
1. Financial frictions are a cause of disruptions to financial
markets. Financial frictions result in shortages of liquidity
and insolvencies. Financial frictions are evidenced in rising
spreads in yields between risky securities (such as corporate
bonds) and relatively safe securities (such as government
securities). For example, the difference in yields between a
ten-year BAA corporate bond and a ten-year treasury security
reflects the potential risk that the corporate bond issuer will
not meet its promised payments. If the yields on the two
bonds were the same, investors would choose the government
bond, because it has no risk of default. To induce investors to
hold the corporate bond, the yield will have to rise to encourage them to take the added risk to purchase the bonds. In the
IS/MP diagram, financial frictions affect the real rate of interest. As financial frictions increase, the real rate of interest
rises, in effect shifting up the MP schedule, reducing shortrun output. In the AS/AD model, a rise in financial frictions,
through rising interest rates, adversely shocks aggregate
demand, shifting the aggregate demand schedule to the left
and down. The economy slides down the AS schedule to a
new lower level of short-run output and inflation.
2. The AS/AD framework is predicated on the notion that the
central bank will follow a predicable pattern—like raising
and lowering interest rates in response to changes in actual
inflation relative to target inflation. If the central bank is not
following a predictable pattern, the slope of the AD schedule
is not well known and tracing out policy effects is difficult.
This problem is not encountered in the IS/MP model.
3. Deflation is a negative rate of inflation—when the price
level is actually decreasing. Deflation poses a problem for the
economy, because deflation increases real rates of interest. For
The Great Recession and the Short-Run Model | 121
example, if the nominal rate of interest is zero, the real rate of
interest is the negative of the inflation rate. With zero nominal
interest rates, further deflation increases real interest rates,
discourages spending, and leads to short-run declines in output. Short-run declines in output generate further deflation
and further increases in the real rate of interest. Real interest
rates might become so high as to choke off borrowing. With
borrowing choked off, banks are trapped holding liquidity.
(c) If the financial crisis were severe, the Federal Reserve
might come up against the zero boundary. The Fed can’t
lower the federal funds rate below zero. In this case it might
attempt to influence long-term rates by purchasing long-term
securities (quantitative easing). Purchasing long-term treasury securities, for example, will increase the securities’
prices and reduce yields and interest rates, thereby driving
down other long-term rates.
4. The low federal funds rate relative to that predicted by
Taylor’s rule suggests that monetary policy is intended to
offset the adverse effects of financial frictions.
(d) Expansionary fiscal policy could also be considered.
5. The Fed’s balance sheet in normal times largely consists of
loans to banks and treasury securities. During the financial
crisis, the Fed expanded the size and changed the composition
of its balance sheet. In 2007, the Fed had about $900 billion in
assets. In 2013, the Fed had over $3 trillion in assets. Since
2007, the Fed has changed the composition of its assets to
include mortgage-backed securities issued by Fannie Mae and
Freddie Mac, Fannie Mae and Freddie Mac debt, and other
assets formerly held by Bear Stearns and AIG. The Fed decided to increase its holdings of mortgaged-backed securities
and these other assets as a means to provide the financial system with liquidity and solvency and reduce financial frictions.
3. (a) In the textbook, following Taylor’s rule
= 2%, and = 2%.
6. Capital requirements set the minimum equity-to-asset
ratio and, therefore, limit financial institutions’ exposure to
the risk of insolvency. For example, a financial institution
with a 2 percent equity-to-asset ratio will become insolvent
following a 3 percent market devaluation in its assets, whereas
a firm with 10 percent equity to asset ratio remains solvent
following the 3 percent market devaluation.
7. Fiscal stimulus could be justified when monetary policy
ceases to be effective in increasing short-run output during a
recession. This occurs during a liquidity trap, as described in
question 3 above.
EXERCISES
1. (a) In the IS/MP diagram, with the economy initially at
potential GDP, the real rate of interest equal to the marginal
product of capital, and a stable inflation rate, a mild financial
crisis that increases financial frictions and raises the interest
rate from zero to 2 percent shifts the MP schedule up and
causes a movement along the IS schedule to the left, depending
on the size of b, a measure of the sensitivity of investment (and
real output) to changes in the real interest rate. To illustrate, you
can assume that the MP schedule is horizontal at the real federal funds rate. The result is a reduction in short-run output, Ỹ.
(b) The typical Federal Reserve response is to lower the federal funds rate and shift the MP schedule down toward the
horizontal axis.
2. This is a worked exercise. Please see text for solution.
= = 1/2,
(b) The Core CPE inflation rate in 2015 was 1.3 percent. The
Core PCE inflation rate is the rate of inflation all consumer
“goods” measure by the Bureau of Economic Analysis and
reported in the National Income and Product Accounts of the
United States. Since 2010, the Core PCE inflation rate has
averaged around 1.5 percent.
(c) The short-run measure of output, Ỹt, equals the difference between actual and potential output divided by potential output. Annual measures of Ỹt are provided from 2001
to 2015. Short-run output has been negative during this
period. In 2009, the actual output was almost 7 percent
below potential. See the table that follows.
(d) Using Taylor’s rule, it = π t + rt + .5(π t − ) + .5Ỹt = it = π t +
2% + .5(πt − 2%) + .5Ỹt generates the following predictions of
the federal funds rate:
Year
Y
π
Federal
Funds
Rate
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
–0.64
–2.22
–2.38
–1.21
–0.30
–0.08
–0.58
–2.73
–6.80
–5.46
–4.90
–3.87
–3.85
–3.06
–2.19
1.8
1.7
1.5
1.9
2.2
2.2
2.2
2.1
1.2
1.3
1.5
1.9
1.5
1.5
1.3
3.88
1.67
1.13
1.35
3.22
4.97
5.02
1.92
0.16
0.18
0.1
0.14
0.11
0.09
0.13
Predicted
Federal
Funds
Rate
3.38
2.44
2.06
3.25
4.15
4.26
4.01
2.79
–0.60
0.22
0.80
1.91
1.32
1.72
1.85
The predicted federal funds rates are higher than the actual
federal funds rate in all years except 2001, 2006, and 2007.
After 9/11, the Federal Reserve maintained the federal funds
122 | Chapter 14
rate below the level predicted by Taylor’s rule. Notice that in
2009 the predicted federal funds rate is negative, a testimony
of just how severe the situation was. Since 2009, the predicted
federal funds rate has been greater than the actual federal
funds rate—a sign that the Fed is still concerned about financial frictions and the sluggish recovery, and that the Fed perceives Taylor’s rule as specified above to be the incorrect
monetary rule.
4. This is the student’s choice.
5. Students can find the FOMC minutes and press releases
at https://www.federalreserve.gov/newsevents/press/mone
tary/2016monetary.htm.
The June 28, 2016, press release is as follows (the
“actions” are highlighted below):
Information received since the Federal Open Market Committee met in June indicates that the labor market strengthened and that economic activity has been expanding at a
moderate rate. Job gains were strong in June following weak
growth in May. On balance, payrolls and other labor market
indicators point to some increase in labor utilization in recent
months. Household spending has been growing strongly but
business fixed investment has been soft. Inflation has continued to run below the Committee’s 2 percent longer-run
objective, partly reflecting earlier declines in energy prices
and in prices of non-energy imports. Market-based measures
of inflation compensation remain low; most survey-based
measures of longer-term inflation expectations are little
changed, on balance, in recent months.
Consistent with its statutory mandate, the Committee
seeks to foster maximum employment and price stability.
The Committee currently expects that, with gradual adjustments in the stance of monetary policy, economic activity
will expand at a moderate pace and labor market indicators
will strengthen. Inflation is expected to remain low in the
near term, in part because of earlier declines in energy
prices, but to rise to 2 percent over the medium term as the
transitory effects of past declines in energy and import prices
dissipate and the labor market strengthens further. Nearterm risks to the economic outlook have diminished. The
Committee continues to closely monitor inflation indicators
and global economic and financial developments.
Against this backdrop, the Committee decided to maintain the target range for the federal funds rate at 1/4 to
1/2 percent. The stance of monetary policy remains accommodative, thereby supporting further improvement in labor
market conditions and a return to 2 percent inflation.
In determining the timing and size of future adjustments
to the target range for the federal funds rate, the Committee
will assess realized and expected economic conditions relative to its objectives of maximum employment and 2 percent
inflation. This assessment will take into account a wide range
of information, including measures of labor market conditions, indicators of inflation pressures and inflation expectations, and readings on financial and international
developments. In light of the current shortfall of inflation from
2 percent, the Committee will carefully monitor actual and
expected progress toward its inflation goal. The Committee
expects that economic conditions will evolve in a manner that
will warrant only gradual increases in the federal funds rate;
the federal funds rate is likely to remain, for some time, below
levels that are expected to prevail in the longer run. However,
the actual path of the federal funds rate will depend on the
economic outlook as informed by incoming data.
The Committee is maintaining its existing policy of reinvesting principal payments from its holdings of agency debt
and agency mortgage-backed securities in agency
mortgage-backed securities and of rolling over maturing
Treasury securities at auction, and it anticipates doing so
until normalization of the level of the federal funds rate is
well under way. This policy, by keeping the Committee’s
holdings of longer-term securities at sizable levels, should
help maintain accommodative financial conditions.
Voting for the FOMC monetary policy action were:
Janet L. Yellen, Chair; William C. Dudley, Vice Chairman;
Lael Brainard; James Bullard; Stanley Fischer; Loretta J.
Mester; Jerome H. Powell; Eric Rosengren; and Daniel K.
Tarullo. Voting against the action was Esther L. George,
who preferred at this meeting to raise the target range for the
federal funds rate to 1/2 to 3/4 percent.
6. This is the student’s choice. Economic indicators can be
found at European Central Bank Statistical Data Warehouse, http://sdw.ecb.europa.eu/.
Inflation rate (HICP)
0.1
Monetary aggregate M3
GDP in prices of the previous year
(economic growth)
Unit labour costs
Population (in millions)
Unemployment rate
(as a % of labour force)
Labour productivity
Current account balance
(as a % of GDP)
US dollar / Euro exchange rate
Government deficit (–) / surplus
(+) (as a % of GDP)
Government debt (as a % of GDP)
5.0
1.7
2016Jun
2016Q1
0.9
337
10.1
2016Q1
2014
2016May
0.3
2.34
2016Jun
2016Q1
2016Q1
1.0997
–1.9
26 Jul 2016
2016Q1
91.7
2016Q1
CHAPTER 15
DSGE Models: The Frontier of Business
Cycle Research
CHAPTER OVERVIEW
This chapter provides a synthesis of the long-run and shortrun models discussed in the previous two sections. The
chapter is divided into three main parts: the historical
development of dynamic stochastic general equilibrium
(DSGE) models; an illustration of a stylized DSGE (essentially an extension to neoclassical labor market analysis); and
an introduction to the impulse response functions (illustrations as to how macroeconomic variables react over time to
real and nominal shocks). Much of the heavy lifting in this
chapter is related to the labor market analysis. Some novel
extensions to the neoclassical labor market model are introduced through the DSGE models, and these extensions give
new (read different) explanations for economic fluctuations
that were not likely taught in Principles. The section on the
impulse response functions will require some hand-waving
class time, but Chad provides some excellent end-of-chapter
exercises that enable students to qualitatively map out the reaction of variables to various shocks. As in all good learning
exercises, the reactions of the variables clearly depend on the
underlying assumptions of the model. Therefore, you will have
another opportunity to allow students to make connections
between core assumptions and macroeconomic behaviors.
15.1 Introduction
Here Chad defines DSGE models: dynamic because the
behaviors of variables over time are analyzed; stochastic
because the role of random shocks in affecting changes in
variables is considered; general equilibrium because the
interrelationships between markets, output, labor, capital, and
financial are emphasized. Chad points out that DSGE models
are ultimately quantitative— that is, the quantitative behav-
iors of variables are studied. As illustrated throughout the
chapter, DSGE models are based on microfoundations. The
behavior of the economy is traced to behaviors of individual
decision-making units: households, businesses, and government, for example.
15.2 A Brief History of DSGE Models
In this section, Chad explains that the DSGE models can be
traced to the writings of Nobel Prize–winning economists
Finn Kydland and Edward Prescott on real business cycle
models. Kydland and Prescott show that fluctuations in the
total factor productivity (TFP) coefficient cause macroeconomic fluctuations that resemble what we normally think of
as business cycle fluctuations. Chad points out that we are
used to thinking in terms of positive TFP shocks but not negative TFP shocks. However, as explained back in Chapter 6,
institutional arrangements, including taxes and regulations,
affect TFP, and therefore much of an economy’s fluctuations
can be described in terms of temporary and persistent changes
in TFP.
FROM REAL BUSINESS CYCLES TO DSGE
As real business cycle models were extended and refined to
explain public-, foreign-, and monetary-sector events and the
effects of both nominal and real shocks for different degrees
of price and wage stickiness, the real-business-cycle models
evolved into DSGE models.
In coming full circle back to Chapter 1 (where we said that
models include endogenous variables, exogenous variables,
and parameters), the components of DSGE models are
explained to include endogenous variables, shocks, and
features. The endogenous variables include a list with which
123
124 | Chapter 15
students are already familiar: GDP, consumption, interest
rates, prices, wage rates, and inflation rates. The shocks are
shifts in the exogenous variables that cause fluctuations in
the endogenous variables. The list of shocks already studied
in the course is mentioned: shocks to TFP, fiscal and monetary policy shifts, changes in energy prices, and financial frictions. Added to this list is uncertainty (specifically policy
uncertainty), discussed in a case study below. Shocks can be
modeled as temporary or permanent. Features describe the
conditions that govern economic behaviors, and include nominal price and wage rigidities, adjustment costs (to capital, for
example), heterogeneity (of people and firms—the more different people and firms are the more varied the reactions
to shocks), and (in)complete markets (if markets are
incomplete—for example, if economic agents can’t ensure
their consumption—then shocks have a relatively larger effect
on the economy).
approaches, households make income (work) and leisure
choices to maximize utility. Chad, to simplify, modifies this
approach by treating savings exogenously. With savings exogenous, households choose a level of consumption and work
(and leisure) to maximize utility. As illustrated in the appendix, labor supply is positively related to the ratio of the real
wage rate to per capita consumption. The real wage rate is
an incentive to work and encourages hours worked. Per capita consumption, as discussed in the next section, captures
wealth effects on labor supply. The greater is per capita consumption relative to the real wage rate, the greater is wealth
and the smaller is the incentive to work. In this section, Chad
mentions that if the ratio of the real wage rate to per-capita
consumption is stable as the real wage rate grows, then labor
supply is likely to be stable. A shift parameter is included in
the labor supply function to capture the overall magnitude
of the labor force.
MATHEMATICS AND DSGE MODELS
EQUILIBRIUM IN THE LABOR MARKET
Given that DSGE models are microfounded, built from the
bottom up and based on the interrelated economic decisions
of many individuals and given that the variables in these
models evolve over time, mathematical complexity is inescapable. To cut through the complexity, in the next section
Chad revisits the labor market analysis of Chapter 7 and
introduces students to impulse response functions in a nontechnical way.
Chad illustrates the standard equilibrium in the labor market. He stresses that to derive this solution per-capita consumption is treated exogenously. Chad mentions that in
more complicated DSGE models, consumption is endogenized, and that current consumption depends on lifetime
consumption. As Chad points out, a key complexity in solving DSGE models is the “forward-looking consumption
problem.”
15.3 A Stylized Approach to DSGE
15.4 Using the Stylized DSGE Model
Chad’s novel approach for illustrating a DSGE model appears
to be similar at first glance to the sort of neoclassical labormarket analysis that you might see in other intermediate macroeconomics textbooks. As in Chad’s case, these texts use
the labor market as a lens for understanding the economy.
However, upon closer inspection, you can see that Chad has
introduced some novel approaches to his labor-market study
that provide different (new) explanations for various types of
economic fluctuations.
To develop the labor market, Chad reviews the labor
demand analysis back in Chapter 4. Businesses demand labor
to maximize profits. So labor is demanded up to the point
where the marginal product of labor equals the real wage rate.
Given the Cobb-Douglas production function, the marginal
product of labor is precisely defined, and the slope and the
shift factors of the labor demand schedule are precisely
known. The role of shifts in the TFP coefficient is highlighted. Increases in TFP increase the profitability of
employing labor and increased labor demand.
The labor supply schedule is microfounded in the utility
maximization decisions of households. In microeconomic
This section lays out the causal stories as to how the economy reacts to various shocks (such as changes to TFP, business taxes, government purchases, and monetary policy)
under different circumstances (features of the economy). The
main feature discussed is the presence or absence of sticky
wages and/or prices. Most of your time teaching this chapter
will be spent covering these issues. Having students do the
calisthenics to understand the connection between core
assumptions and conclusions continues to build the intellectual fortitude of your students.
A NEGATIVE TFP SHOCK
In this example, the negative TFP shock is temporary. The
decrease in TFP temporarily reduces the marginal product
of labor, shifting the labor demand schedule down and to the
left. Assuming no rigidities, the labor market equilibrates at
a lower real wage rate and lower level of employment. What
is interesting is that this TFP shock looks a lot like what happens during a recession: the real wage rate and employment
fall.
DSGE Models: The Frontier of Business Cycle Research | 125
A RISE IN TAXES PAID BY FIRMS
LESSONS FROM THE LABOR MARKET IN THE DSGE MODEL
A rise in business taxes has the same effects as a negative
TFP shock. The increase in business taxes reduces the marginal (benefit) product from labor employing labor and shifts
the labor demand schedule down and to the right.
To sum up, the simplified labor market model illustrates how
both real and nominal shocks affect employment and real
wage rates. Over business cycles, real wage rates and employment (and output) typically move in the same direction.
These procyclical movements can be explained by real shocks
or by nominal shocks when sticky prices are present. So
DSGE models have both elements of real business cycle models (shocks to TFP) and new Keynesian models (sticky prices
and monetary shocks).
A RISE IN GOVERNMENT PURCHASES
Here, Chad assumes that the rise in government purchases
has no aggregate demand effect and therefore no effect on
the aggregate price level. Chad begins the story by assuming
that the increase in government purchases is financed by a
rise in future (lump sum) taxes. The rise in the tax burden
reduces permanent income and reduces consumption (a
negative wealth effect) of all goods, including leisure, and
therefore increases labor supply. The increase in labor supply causes the equilibrium real wage rate to decrease as
employment increases. Chad concludes from this example
that increases in government purchases cannot be the driving force behind the economy, because a growing economy is
not based on lower per-capita consumption and falling real
wage rates.
15.5 Quantitative DSGE Models
An impor tant feature of DSGE models is that they are
quantitative— that is, they are used to make numerical predictions as to how various shocks affect impor tant macroeconomic variables. In this section, Chad gives some
examples to illustrate the “quantitative richness” of the
DSGE models— specifically, using impulse response functions, a variant of the Smets-Wouters model used in macroeconomic forecasting.
INTRODUCING MONETARY POLICY AND UNEMPLOYMENT:
STICKY WAGES
Chad provides a variant of the nominal sticky wage story
with which most of us are familiar. What is different in
Chad’s approach is that he sets the story up in the first case
with a sticky nominal wage that causes the real wage rate to
be above the equilibrium level. In other words, the economy is initially operating with an excess supply of labor. If
monetary policy is expansionary, and the price level rises,
the real wage rate falls. The decline in the real wage rate
stimulates an increase in the amount of labor demanded
and the level of employment. Chad points out that this situation does not fit the typical boom. During economic
expansions, the real wage and the level of employment both
typically rise.
IMPULSE RESPONSE FUNCTIONS
Impulse response functions show how endogenous variables over time react to stochastic shocks. Chad illustrates
impulse response functions for a number of cases. In this
section, he focuses on a temporary one-percentage-point
increase in the federal funds rate. Chad explains that the
Smets-Wouters model verifies Milton Friedman’s “long
and variable lags” conclusion. The maximum effect of the
shock is that after three or four quarters, the adverse effects
continue for five years. Similar effects are illustrated for
consumption, employment, and inflation, and the results are
qualitatively consistent with the predictions of the AD/AS
model.
A TOTAL FACTOR PRODUCTIVITY SHOCK
MONETARY POLICY AND STICKY PRICES
With prices perfectly rigid, the supply of output in the economy is assumed to be perfectly price elastic. When supply is
perfectly price elastic, businesses supply the output demanded
by hiring the inputs that are necessary to produce it. In the
labor market example, this requirement translates into a labor
demand schedule that is perfectly price inelastic (vertical).
With an expansionary monetary policy, through a lower federal funds rate that stimulates investment, aggregate demand
increases, businesses demand more labor, and real wage rates
increase.
Again, the qualitative results of the AD/AS model are
quantified. A permanent increase in TFP increases the
output growth rate (which declines via transition dynamics). An interesting result of the shock is that employment
initially falls, but subsequently recovers, following the
increase in TFP. The reason for the decline is the assumption of sticky prices. Following the increase in TFP, with
sticky prices, aggregate demand remains constant and less
labor is needed to satisfy it. Over time, as prices adjust,
aggregate demand increases, increasing the demand for
labor.
126 | Chapter 15
A SHOCK TO GOVERNMENT PURCHASES
A temporary one-percentage-point increase in government
purchases financed by a future tax increase is used to quantify the story Chad told in Section 15.4. The increase in future
taxes reduces permanent income and per-capita consumption
(a negative wealth effect) and increases labor supply and output, with little effect on inflation.
Assuming our representative agent is rational, the agent consumes leisure up to the point where the marginal benefit of
leisure equals the marginal cost of leisure. The marginal cost
of leisure is the real wage rate, w. The marginal benefit of
leisure is MRSleis,c, and MRS = |MUleis/MUc |. Substituting for
L (where L = T − leis) into Chad’s utility function generates
U = log(c) − (1/2)(1/ )(T − leis)2;
MUc = 1/c; and
A FINANCIAL FRICTION SHOCK
Here Chad discusses the effects of an increase in the wedge
between the borrowing rate of interest and the federal funds
rate. The results illustrated here are similar to the effects of
a restrictive monetary policy but with larger negative effects
on consumption.
MUleis = (1/ )L.
So, the marginal benefit of an hour of leisure is
MRS = (1/ )L/(1/c),
and the utility maximization condition is
(1/ )L/(1/c) = w.
Solving for L yields the labor supply schedule; that is,
15.6 Conclusion
To conclude, an explanation of shocks and frictions is necessary to explain cyclical fluctuations. How shocks affect the
economy depends in part on the significance of frictions/features (price, wage, and financial) in the economy. Macroeconomists over the last fifty years have increasingly relied
on models, such as the DSGE models, that incorporate
Solow’s production and transition dynamics. These models
are microfounded, incorporate frictions/features to make
quantitative predictions about economic fluctuations. The
recent financial crisis and the Great Recession continue to
pose challenges for macroeconomics that will likely result in
further changes to DSGE models.
APPENDIX: DERIVING THE LABOR
SUPPLY CURVE
This little appendix is used to illustrate the microfoundations
of the labor supply schedule. Chad uses a simple hypothetical utility function, in which a representative agent maximizes utility from consuming one good (output) and a bad
(labor) subject to a constraint that consumption, c, plus savings, (assumed to be constant), equals labor income, wL,
where w = the real wage rate and L = labor supply. In other
words,
Max U = U (c, L), subject to wL = c + .
By recognizing that time not worked is, in effect, leisure
(leis), where leis = T − L and T is the effective time available
in the day for work and leisure, the utility maximization problem can be rewritten as
Max U = U(c, leis), subject to w(T − leis) = c + .
L = (w/c).
SAMPLE LECTURE: THE ECONOMICS OF IDEAS
AND COMPLEXITY IN THE DSGE MODEL
In Chapter 6, we were introduced to the economics of ideas.
The economics of ideas imposes two challenges for economists: (1) the reconceptualization of markets as being other
than perfectly competitive; and (2) the endogenous character, with respect to changes in the level of employment, of the
total factor productivity coefficient, and therefore economic
growth. Let’s consider the implications of these challenges
for Chad’s stylized DSGE labor market model in reverse
order. We will see that the presence of endogenous growth
complicates our findings and that the presence of imperfect
competition introduces heterogeneity and bifurcation into the
labor market.
To begin, let’s review the effects of a positive TFP shock
in the stylized labor market model, assuming no price and
wage rigidities. The positive TFP shock increases the demand
for labor, the equilibrium real wage rate, and the level of
employment, generating Pareto-optimal improvements. If we
modify the stylized model by making the TFP endogenous
with respect to changes in the level of employment, the model
becomes dynamic and a virtuous cycle is stimulated. The reason, of course, is that the initial increase in employment
stimulates further increases in the TFP coefficient, which
result in further increases in the real wage rate and in employment. In other words, the initial increase in the TFP coefficient generates a set of dynamic feedback effects (or in the
context of the labor demand/labor supply diagram, a set of
interdependent labor demand shift factors) that generate a virtuous cycle of growth. As described toward the end of Chapter 6, diminishing returns can be introduced in the production
DSGE Models: The Frontier of Business Cycle Research | 127
1. I am borrowing from Michal Kalecki, Theory of Economic Dynamics (Cambridge: Cambridge University Press, 1965).
SAMPLE LECTURE: THE EXPECTATIONS DEBATE
AND THE IMPULSE RESPONSE FUNCTION2
In order for students to get a better handle on the impulse
response function (IRF), revisiting an old topic in microeconomics, the cobweb theorem, might be useful. The cobweb
theorem was developed by Nicholas Kaldor. Kaldor introduced a simple tweak to the supply and demand model to
explain why market prices might not simply (and timelessly)
adjust to equilibrium. In doing so, Kaldor developed an IRF
for a market price. Eventually, Kaldor’s IRF opened up a
debate about market stability and the nature of expectations—
leading to growth and development of rational expectations.
As many of us well know, Kaldor’s tweak to the simple
market-supply-and-demand model was to assume that quantity supplied depended on expected prices rather than on
current prices. If we assume that expected prices at time t
are simply last period’s prices, we derive the cobweb theory
of prices. To illustrate, let Qd = a − b(Pt) and Qs = h + x(Pt–1).
We assume that any disequilibrium in the current period is
resolved through a price adjustment so that Qd = Qs. Solving
for Pt generates the first-order difference equation: Pt =
[(a − h)/b] − (x/b)(Pt–1). Consider the IRF for three different
cases: (1) when b = x, the slope of the demand schedule
equals the slope of the supply schedule; (2) when b < x; and
(3) when x > b. The equilibrium price is when Qd = Qs at
Pt = Pt–1, or P* = (a − h)/(b + x). To simplify, let h = 0. For
each case, assume that Pt–1 > Pt. Each of the cases is illustrated below:
Case 1. x = b = 1, h = 0, a = 10, P* = 5
Price
of ideas (restricting the exponent on labor to be between zero
and one in the idea production function), and if so, the
dynamic process of adjustments is dampened until the TFP
and labor demand settle down at a new higher level.
The economics of ideas also implies that although positive
TFP shocks can generate virtuous cycles, negative TFP
shocks can generate vicious cycles. If employment and real
wage rates fall following a negative TFP shock, the decline
in employment reduces the TFP coefficient and sets in motion
a negative dynamic feedback loop.
If imperfect competition is a prerequisite in the production
of ideas, sticky prices and rigid real wage rates might result.
Suppose, for example, that as a result of imperfect competition businesses are able to administer prices as markups over
unit prime costs of production.1 Suppose that prime cost is
defined as labor costs, WL, plus materials costs, M. Further
suppose that M = jWL, so that unit prime costs equals
(WL + M)/Y. Rearranging terms yields unit prime costs as
W(1 + j)/(Y/L). If prices are administered as a markup, m, over
unit prime costs, then P = m[W (1 + j)/(Y/L)]. If nominal wage
rates change, holding other things constant, prices change
pari passu, and the real wage rate is constant—the result is
real wage rigidity. In the price-markup function, solving for
the real wage rate, W/P, yields W/P = {1/[m(1 + j)]}(Y/L).
Now let’s consider what happens following a positive TFP
shock, assuming that prices are rigid. The TFP shock
increases Y/L, and given the price rigidity assumption, one
or two adjustments (or a combination of the two) must result.
First, the nominal wage rate could increase, so that the benefits of the shock are passed onto wage earners. Second, business markups could increase, holding real wage rates
constant, and the benefits of the shock would be passed on
to business owners. Third, some combination of higher real
wage rates and price-cost markups could result. If real wage
rates are rigid, the second case prevails. This second case
accounts for the decline in employment following a positive
TFP shock, as explained in Section 15.5 (less labor is needed
to produce the level output that satisfies aggregate demand).
The presence of ideas, of course, also introduces heterogeneity into the labor market. For example, suppose the economy has two major industries—an industry based on
research and development (R&D) and an industry where
R&D is not impor tant. If the R&D industry is monopolistic,
and the non-R&D industry is highly competitive, then the
labor market is bifurcated. If prices and real wages are rigid
in the R&D-dominated industry, non-R&D workers are
crowded out of it into the more highly competitive industry,
creating rising real wage gaps between the bifurcated labor
markets.
Time
Pt
Pt−1
0
1
2
3
4
5
6
7
8
9
6
4
6
4
6
4
6
4
6
4
4
6
4
6
4
6
4
6
4
6
8
6
4
2
0
Pt
0
2
4
6
Time
8
10
12
2. Deirdre McCloskey’s presentation at the European Association for
Evolutionary Political Economy in Antwerp, Belgium, in 1996 inspired
this section.
128 | Chapter 15
Price
Case 2. x = 0.75 b = 1, h = 0, a = 10, P* = 5.714
Time
Pt
P t−1
0
1
2
3
4
5
6
7
8
9
6.00
5.50
5.88
5.59
5.80
5.65
5.77
5.68
5.74
5.69
5.50
5.88
5.59
5.80
5.65
5.77
5.68
5.74
5.69
5.73
price, subject to random errors. In other words, markets are
stable but subject to stochastic shocks. But if Muth is correct
about the rationality of agents, how do we explain the financial crisis? David Colander, citing Axel Leijonhufvud, argues
that for given corridors, some decision-making rules work
really well, but when the economy leaves those corridors, the
rules break down. More of Colander’s views are discussed
below in a case study.3
CASE STUDY: PUBLIC POLICY UNCERTAINTY
IN A DSGE MODEL
5.90
5.80
5.70
5.60
5.50
5.40
Pt
2
0
4
6
Time
8
10
12
Price
Case 3. x = 1, b = 0.75, h = 0, a = 10, P* = 5.714
Time
Pt
P t−1
0
1
2
3
4
5
6
7
8
9
6.00
2.00
7.33
0.22
9.70
−2.94
13.92
−8.56
21.41
−18.55
2.00
7.33
0.22
9.70
−2.94
13.92
−8.56
21.41
−18.55
34.73
40.00
30.00
20.00
10.00
0.00
–10.00
–20.00
–30.00
Pt
0
2
4
6
8
Time
10
12
As can be seen in our three cases, our assumptions about
expectations and the features of the model generate quite different IRF than predicted by the basic supply-and-demand
model.
What’s interesting about Kaldor’s cobweb theorem is that
John Muth critiqued it by pointing out what is now known to
be an obvious flaw—namely, that sellers fail to see and understand the pricing patterns. If sellers are smart and use rational expectations and understand the features of the model (in
this case the model’s parameters), then following any disruption to equilibrium, the market returns to the equilibrium
As a student of economics, I was first introduced to the debate
about the role of uncertainty in the economy through the
writings of John Maynard Keynes and Milton Friedman.
Keynes and the Keynesians advocated the expansion of
government to smooth out the business cycle and to push the
trend to potential output. Friedman and the monetarists
thought that expansion of the government, among other
things, was a destabilizing force. One of my earliest exposures to the econometrics of this issue was the Saint Louis
model, where the cumulative effects of government spending on GDP were essentially zero.
In the latest iteration of this debate comes the question of
the effects of policy uncertainty on the economy. Chad, in
introducing DSGE, defines the components of the models.
Recall that models have endogenous variables, “features,”
and shocks. Policy uncertainty, in this case, reflects a shock
that impacts the endogenous variables, such as output and
employment, given the features of the economy (such as price
stickiness). Chad cites a study by Baker, Bloom, and Davis
(BBD) that considers the effects of policy uncertainty as an
example of a stochastic shock.4 As Chad mentions, an
increase in policy uncertainty is expected to delay investment
decisions and slow economic growth.
BBD consider the effects of policy uncertainty by constructing an economic policy uncertainty (EPU) index, and
then use this index to test for its statistical significance in
explaining changes in major economic variables. The EPU
index has three major components: (1) a measure of the frequency of mention of economic uncertainty in major newspapers; (2) the number of federal tax code provisions set to
expire in a given year; (3) a measure of the disagreement
between professional forecasters regarding the forecasts over
future government expenditures (fiscal policy proxy) and
inflation (monetary policy proxy). The various measures are
aggregated into an index, compared against other “uncer3. David Colander, Macroeconomics, 8th ed. (McGraw-Hill Irwin, 2010).
4. See Scott R. Baker, Nicholas Bloom, and Steven J. Davis, “Measuring
Economic Policy Uncertainty,” available at http://www.policyuncertainty
.com /. EPU index numbers are available at the FRED database, http://
research.stlouisfed.org/fred2/series/ USEPUINDXD?cid=33201.
DSGE Models: The Frontier of Business Cycle Research | 129
tainty” measures, and then used to consider the effect of
changes in the EPU index of various economic variables. At
the micro level, BBD show that increases in uncertainty have
substantial adverse effects on business investment and
employment of government contractors; moreover, the greater
the exposure of businesses to government contracts, the
greater is the adverse effect of the increase in the EPU index.
While this result is not surprising, the macro findings are significant. BBD show that increases in the EPU index between
2008 and 2011 are impor tant in explaining a slow recovery
from the Great Recession; both industrial production and
employment were dampened. BBD conclude their paper with
a bit of hedge. They recognize that the cause and effect of
the uncertainty is hard to “distinguish.” To what extent would
policy uncertainty be present if the Great Recession hadn’t
happened in the first place?
CASE STUDY: USING DSGE MODELS TO INFORM
PUBLIC POLICY DECISIONS—DAVID
COLANDER’S TESTIMONY TO CONGRESS
On July 20, 2010, David Colander, the Christian A. Johnson
Distinguished Professor of Economics at Middlebury College, provided testimony to the House Science and Technology Committee on the state of macroeconomic science and
research and its applicability to public policy prescriptions.5
Colander, who describes himself as the court jester of the
economics profession (because he says what everyone knows
but will not repeat in polite company), expresses concerns
about the applicability of DSGE models to making public
policy decisions. Colander explains that the DSGE models are
the direct result of “pure scientific research” in economics.
Pure scientific research often searches for solutions, and the
solutions to DSGE models therefore require simplifications—
abstractions from complexities. These abstractions from complexities, while generating solutions, make the conclusions
of DSGE models sensitive to initial assumptions: changes
to initial assumptions can generate quite different results.
The complexities in the macroeconomy that are difficult to
model are those same microfoundations inherent in DSGE
models. According to Colander, the complexities are reflected
in the (microfounded) interactions between a “full range of
agents” with “full inter-agent feedback effects.” With this
complexity, forward-looking models, like the DSGE models,
are unsolvable, and we should be very careful in drawing
policy prescriptions from such models. Colander, recognizing the policy limitations of DSGE models, quotes Keynes:
“Economics is a science of thinking in terms of models
5. Professor Colander’s testimony is available at http://www2.econ
.iastate.edu /classes /econ502 /tesfatsion /Colander.StateOfMacro.Congres
sionalTestimony. July2010.pdf.
joined to the art of choosing models which are relevant to
the contemporary world.” 6
REVIEW QUESTIONS
1. D = dynamic, S = stochastic, and GE = general equilibrium.
DSGE models quantitatively predict the time path of endogenous variables and therefore are dynamic. DSGE models are
stochastic because random shocks, given the “features” of the
economy, are the primary source of economic fluctuations.
DSGE models are general equilibrium because the effects of
random shocks affect equilibriums across markets—labor,
capital, output, and financial.
2. Real Business Cycle (RBC) models preceded DSGE models. RBC models emphasized the effects of real shocks, for
example, TFP shocks, in explaining economic fluctuations.
DSGE models incorporate the insights derived from RBC
models but also incorporate the effects of nominal shocks,
due to shifts in monetary policy or changes in financial frictions. In short, RBC models are a special case within DSGE
models.
3. Both TFP shocks and monetary policy shocks under sticky
prices lead to movements in macro variables that resemble
business cycles— that is, the real wage rate, output, and
employment move in the same direction over the business
cycle.
4. Agents at the micro level make decisions to save, consume,
invest, work, or enjoy leisure based on current and expected
future circumstances.
5. We assume that per-capita consumption is relatively fixed.
With this assumption, the aggregate amount of labor supplied
varies positively with the real wage rate.
6. Nominal rigidities play an important role in explaining the
effects of nominal shocks. For example, if the nominal wage
rate is fixed and the real wage rate is above the equilibrium
level, a monetary policy expansion reduces the real wage rate
and stimulates production and employment. If the price level
is fixed, output is perfectly price elastic. Aggregate demand
determines the level of output, and the demand for labor is
perfectly price inelastic as businesses demand whatever labor
is necessary to generate the amount of output demanded.
7. The impulse response function shows how a (macroeconomic) variable evolves over time in response to a stochastic
shock. This reaction depends on the economy’s features
6. John Maynard Keynes to Roy Harrod, July 4, 1938. Available at
http://economia.unipv.it / harrod /edition /editionstuff/rfh.346.htm.
130 | Chapter 15
(including nominal rigidities, adjustment costs, heterogeneity of agents, and information asymmetries).
EXERCISES
1. This is a worked exercise. Please see the textbook for the
solution.
2. (a) A positive temporary TFP shock, for example, favorable weather conditions, increases the marginal product of
labor and the demand for labor. With no rigidities, assuming
“normal”-shaped labor demand and labor supply schedules,
the equilibrium real wage rate and employment increase.
(b) If prices are sticky, then aggregate demand is unchanged.
Given that aggregate supply is now higher due to the positive TFP shock, aggregate demand is now met by employing
less labor. The perfectly inelastic labor demand schedule
shifts to the left. The result is a decrease in the equilibrium
real wage rate and employment.
3. (a) A permanent positive TFP shock increases the marginal
product of labor and shifts the labor demand schedule to the
right.
(b) The permanent positive TFP shock increases permanent
income, increases per-capita consumption and leisure, and
reduces labor supply.
(c) Labor demand shifts to the right; labor supply shifts to
the left. Without knowing the relative sizes of the shifts, we
cannot make a prediction about the effect of the TFP change
on employment. Given the resulting excess demand for labor,
the real wage rate unambiguously increases for “normal”shaped labor demand and labor supply schedules.
4. (a) A large temporary decline in government purchases
financed by an expected decline in future lump sum taxes
will increase permanent income and per-capita consumption
of goods and leisure and will reduce labor supply. The reduction in labor supply reduces the equilibrium level of employment and increases the equilibrium real wage rate.
(b) If prices are sticky, labor demand is perfectly price inelastic. The decline in government spending, if financed by a
reduction in future taxes, increases current consumption and
reduces labor supply. The reduction in labor supply increases
the equilibrium real wage rate as employment is unchanged.
(c) The impulse response function in Figure 15.12 shows the
effects of an increase in government purchases financed by
a future increase in taxes. In Figure 15.12, the increase in
government purchases financed by future taxes stimulates the
economy in the short term by reducing permanent income
and increasing labor supply. The increase in employment generates higher levels of output, with lower levels of consumption. In this case, we have just the opposite effect. The
decrease in government purchases temporarily causes a
reduction in output, by reducing employment (via the wealth
effect of a lower future tax burden), but increases current and
future consumption.
5. (a) A decline in the value-added tax is the opposite of the
example given in the textbook (the increase in the sales or
excise tax). Assuming that the tax rate is t and that businesses
bear the legal tax incidence, the after-tax marginal product
of labor is (1–t)(2/3)(Y/L). The temporary reduction in the tax
rate, t, increases that after-tax marginal product of labor and
the demand for labor and increases the equilibrium real wage
rate and employment.
(b) If the decline in the value-added tax were permanent, then
labor demand would increase and labor supply decrease. The
decrease in labor supply, as in previous cases, is the result of
an increase in permanent income (increasing consumption of
output and leisure). The effects on employment depend on the
relative sizes of opposing shifts in labor demand and labor
supply. The real wage rate increases as a result of the excess
demand for labor.
6. (a) The decline in the labor income tax rate has no effect
on the labor demand schedule.
(b) The temporary decline might result in a modest increase
in permanent income, and, if so, the labor supply schedule
would shift modestly to the left.
(c) If the labor supply schedule does shift to the left, the equilibrium real wage rate increases, and the equilibrium level
of employment decreases.
7. (a) With the inflation rate on the vertical axis, and Ỹ on
the horizontal axis, an increase in financial frictions increases
the spread between the real rate of interest, R, and marginal
product of capital, r, and reduces aggregate demand (shifts
the AD schedule down and to the left). The leftward shift
in the AD schedule is immediately followed by a decrease in
the inflation rate and a reduction in short-run output. Over
time, the expected inflation rate declines, shifting the AS
down and to the right.
(b) A graph of the impulse response function for output shows
a recession (caused by the increase in financial frictions) and
a recovery (caused by a decline in the expected inflation rate).
(c) A graph of the impulse response function for inflation
shows a disinflation (initially caused by the increase in financial frictions and subsequently caused by a reduction in
DSGE Models: The Frontier of Business Cycle Research | 131
inflation expectations) to a new lower level of inflation (as
the economy recovers).
(d) The results described above are similar to the SmetsWouters model shown in Figure 15.13, as both output and
inflation stabilize over time.
8. (a) With the inflation rate on the vertical axis, and Ỹ on
the horizontal axis, a temporary increase in government purchases shifts the AD schedule up and to the right. The rightward shift of the AD schedule is immediately followed by
an increase in the inflation rate and in short-run output. Over
time, the expected inflation rate increases, shifting the AS
curve up and to the left, and the economy returns to long-run
output at a higher rate of inflation. However, if the central
bank maintains its prefiscal stimulus inflation target, the central bank increases the interest rate, causing a further leftward shift in the aggregate demand schedule, causing
short-run output and inflation to decrease. The decrease in
the inflation rate eventually reduces expected inflation, causing the aggregate supply schedule to shift to the right, and
the economy returns to long-run output at the target inflation
rate. This adjustment process is described in section 13.6 of
the textbook (inflation-output loops).
(b) A graph of the impulse response function for output shows
a temporary expansion (caused by the increase in government
purchases) and a contraction (caused by an increase in the
expected inflation rate and/or the central bank’s monetary
policy rule).
(c) A graph of the impulse response function for inflation
shows an acceleration of inflation (initially caused by the
increase in government purchases and subsequently caused by
an increase in inflation expectations). Assuming the central
bank maintains its inflation target, the real interest rate will
increase to stabilize the inflation rate at the central bank’s target level.
(d) The results described above are similar to the SmetsWouters model shown in Figure 15.13. As in the previous
problem, inflation and output stabilize over time with respect
to the shock.
(e) In the AD/AS model, the increase in aggregate demand
increases short-run output, and through Okun’s law the increase
in short-run output reduces unemployment. In the DSGE
model, Okun’s law is explained by variations in employment.
For example, the increase in government purchases financed by
an increase in future taxes reduces permanent income and
reduces consumption of output and leisure and increases
labor supply and employment. These results are shown in Figure 15.12; as short-run output expands, employment increases,
and as short-run output contracts, so does employment.
CHAPTER 16
Consumption
CHAPTER OVERVIEW
This chapter is the first of the last six chapters providing
applications and microfoundations. The combination of rigor
and intuition makes this chapter pleasing to teach. The intertemporal utility maximization model is developed. From
this model, the growth rate in consumption is related to the
real rate of interest. Given that the long-run growth rate is
determined by deep parameters in the Solow-Romer models,
the determinants of the long-run interest rate are pinned
down. In addition, through the permanent income hypothesis, consumption is related to wealth. Exceptions to the
permanent-income hypothesis, like borrowing constraints
and precautionary savings, are discussed. Borrowing constraints and precautionary savings increase the sensitivity
of current consumption to changes in current income. The
chapter concludes by examining the empirical evidence on
consumption.
16.1 Introduction
In the United States, personal consumption is the largest
component of gross domestic product (GDP); it is over twothirds of GDP and amounts to over $12 trillion. In this chapter, the neoclassical theory of consumption is considered. In
the neoclassical approach, a representative consumer chooses
a consumption pattern over his or her lifetime to maximize
utility, subject to a lifetime budget constraint. The microfoundations of utility maximization are related to aggregate
consumption behavior, and its empirical relevance for
understanding aggregate consumption behavior is discussed.
In the Solow-Romer–type growth models, aggregate consumption expenditures were a constant fraction of potential
132
income. This assumption is consistent with the microfoundations subject to certain exceptions, such as borrowing constraints and precautionary savings.
Many students who have had microeconomic theory will
find much of this chapter a review of material previously covered. But the clarity of explanation provided in the chapter,
the applications to macroeconomics, and the assessments of
the model add value to the students.
In the sample lecture below, the macroeconomic theory
of consumption is placed in a historical context of debate
between policy activism and laissez-faire.
16.2 The Neoclassical Consumption Model
In this model the consumer maximizes utility subject to an
intertemporal budget constraint (IBC). Utility depends on the
level of consumption in each time period.
To simplify the presentation, the time periods are assumed
to be two: today and the future. So U = U(ctoday,cfuture).
THE INTERTEMPORAL BUDGET CONSTRAINT (IBC)
The IBC shows that lifetime consumption must equal lifetime income. To illustrate, consumption today and consumption in the future are defined. Consumption today is
defined as income, y, today plus financial wealth, , today
less savings (where savings is financial wealth in the future),
and consumption in the future is defined as income in the
future plus financial wealth plus interest earnings on that
wealth.
(Note: In the growth chapters, y is per-capita output—
students will notice that y is now the income of a representative consumer.)
Consumption | 133
Given these definitions, the IBC is written in present-value
terms, where the present value of lifetime consumption equals
the present value of resources (income and wealth). The present value of resources is wealth, and wealth is equal to
financial wealth plus human wealth, where human wealth is
the present value of lifetime labor income.
loses utility equal to u'(ctoday), but given the IBC, the consumer’s dollar is now worth 1 + R in the future and the
consumer’s utility from future consumption increases by
β × u'(cfuture) × (1 + R).
If you are interested in deriving this result using the sort
of methods used in a microtheory course, please see review
question 5.
UTILITY
At this point an additive utility function is introduced
whereby
U = U(ctoday) + β × U(cfuture).
Consumption in each time period exhibits diminishing marginal utility. The “patience” coefficient, β, is introduced and
explained. The coefficient illustrates the weight the consumer
places on future consumption relative to current consumption. If β = 1, the consumer places equal weight on future
and present consumption. If β < 1, the consumer places a
greater weight on current consumption. As β decreases, the
consumer is less patient, and, therefore, current consumption,
as shown below, rises relative to future consumption.
CHOOSING CONSUMPTION TO MAXIMIZE UTILITY
This section illustrates the solution to the intertemporal utility maximization problem. To maximize utility, the consumer
must choose the levels of consumption today and in the future
that cause the change in the level of utility to be zero. If the
consumer chooses a consumption pattern for today and in the
future that causes utility to increase, then utility is not maximized. When utility is maximized,
ΔU = 0 = u'(ctoday) × Δctoday + β × u'(cfuture) × Δc ffuture,
where u' equals the respective marginal utilities. By dividing both sides by Δctoday, the utility maximization condition
is written as
ΔU = 0 = u'(ctoday) + β × u'(cfuture) × (Δcfuture)/Δctoday.
From the budget constraint where ctoday + cfuture/(1 + R) = ,
solve for cfuture and show that cfuture = X × (1 + R) – ctoday
× (1 + R) and that Δcfuture/Δctoday = −(1 + R). That is, if a dollar
of consumption is given up today, that dollar plus interest, R,
can be consumed in the future. Substitution of Δcfuture/
Δctoday = − (1 + R) into the ΔU = 0 expression yields the firstorder condition for utility maximization:
ΔU = 0 = u'(ctoday) − β × u'(cfuture) × (1 + R),
or by adding to both sides u'(cfuture) × (1 + R), the Euler equation is derived:
u'(ctoday) = β × u'(cfuture) × (1 + R).
To understand this expression, suppose the consumer
gives up a dollar of consumption today; the consumer
SOLVING THE EULER EQUATION: LOG UTILITY
The Euler equation can be nicely linked to the long-run
growth model by assuming that the utility functions are (natural) logarithmic; that is, U(c) = log c. In this case the marginal
utility is simply 1/c. Substituting this result in the Euler equation and solving for cfuture/ctoday yields
cfuture/ctoday = β(1 + R),
where cfuture/ctoday is 1 plus the growth rate in consumption. If
the economy has a long-run growth rate of 2 percent and the
savings rate is fixed, consumption grows at 2 percent over
time. If β = 1, then the real rate of interest is also 2 percent.
SOLVING FOR CTODAY AND CFUTURE: LOG UTILITY AND B = 1
From the expression above, expressions for ctoday and cfuture
are easily found (see exercise 5 below). Solving for cfuture in
the utility maximizing condition, and plugging this solution
into intertemporal budget constraint and solving for ctoday, and
plugging the solution for Ctoday back into intertemporal budget constraint and solving for cfuture yields
ctoday = (1/(1 + β)) × ;
cfuture = (β/(1 + β)) × (1 + R).
If β = 1, then these expressions reduce to
ctoday = (1/2) × ;
cfuture = (1/2) × (1 + R).
In a two-period model, half of the wealth is consumed in
period 1 and the remaining half is consumed in the next
period. In other words, the marginal propensity to consume
wealth in the current period is one divided by remaining life
expectancy.
THE EFFECT OF A RISE IN R ON CONSUMPTION
Typically, students at this point will be aware of the income
and substitution effects. That is, as R increases, current consumption becomes more expensive in terms of foregone future
consumption, so consumption in the future will be substituted
for consumption today— the substitution effect— and as R
increases, future income out of savings increases, increasing the level of income, making current consumption more
affordable—the income effect. In the log utility approach, the
income and substitution effects cancel each other out. The
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Chapter 16
effect of R on consumption is on the value of wealth. An
increase in R reduces present value of wealth and reduces
current consumption. This is the wealth effect of an interestrate change.
no impact on consumption today. See exercise 6(a). For persons who have borrowing constraints, the changes in current
taxes can affect changes in current consumption. If tax cuts
are progressive and low-income persons have severe budget
constraints, significant changes in current consumption can
result in response to tax changes.
16.3 Lessons from the Neoclassical Model
BORROWING CONSTRAINTS
THE PERMANENT-INCOME HYPOTHESIS
In the permanent-income hypothesis, consumption depends
on the level of permanent income. The level of permanent
income is related to the present value of wealth (the discounted future stream of income). For example, with a zero
discount rate and β = 1, and income today = $10,000 and
income in the future = $50,000, the consumer’s wealth is
$60,000, and annual permanent income is $30,000; $30,000
will be consumed each period.
As in the microeconomic study of risk and insurance,
when diminishing marginal utility is assumed, the consumer
receives more utility from smoothing consumption out than
from varying consumption between years of low income and
high income.
Consider the following example. Suppose consumption
equals income case:
Consumption
Utility
0
$10,000
$20,000
$30,000
$40,000
$50,000
0
100
180
240
280
300
If $10,000 of income is consumed today, and $50,000 of
income is consumed in the future, total utility is 380. If
$30,000 of income is consumed in each period, then total
utility is 480. The consumer has more satisfaction smoothing out consumption relative to income. This result follows
from the assumption of diminishing marginal utility. The
gain in utility derived from a $20,000 gain in consumption
is less than the loss of utility derived from a $20,000 loss in
income.
The implications of this result are impor tant (as stressed
before): (1) consumption doesn’t change as much as income
and may not change at all if the income change is anticipated;
and (2) the marginal propensity to consume (MPC) out of
wealth is one divided by life expectancy.
RICARDIAN EQUIVALENCE
Once again, tax changes simply upset the timing of taxes
and therefore the timing of disposable income during the
taxpayer’s lifetime. Tax reductions today will have little to
With borrowing constraints, persons are not able to borrow
against future income to smooth out consumption. In this
case, significant changes in consumption can result even if
the future income is anticipated.
CONSUMPTION AS A RANDOM WALK
If borrowing constraints are not present, consumers can borrow from their future incomes to smooth out consumption.
As a result, variations in consumption must be the result of
surprising or random events. In this case, consumption follows a random walk.
PRECAUTIONARY SAVING
During times of uncertainty, people save as a precaution
against an uncertain stream of income. If people are worried
about the certainty of their future incomes, they are likely to
reduce consumption and increase savings today. If and when
people realize more optimistic income levels, consumption
will increase income.
16.4 Empirical Evidence on Consumption
EVIDENCE FROM INDIVIDUAL HOUSEHOLDS
The Euler equation and the permanent-income hypothesis
apply to households with above-average wealth. For lowincome/low-wealth households, consumption tracks income
well. Given these results, the heterogeneity of households
requires some modified description of aggregate household
behavior. Behavioral economics offers the potential for
rethinking consumption and savings behavior.
AGGREGATE EVIDENCE
The aggregate evidence indicates that wealth effects are
impor tant in explaining consumption and savings behavior.
As housing and financial wealth increased, consumption and
indebtedness increased relative to income. During the Great
Recession, wealth decreased, and consumption and indebtedness fell relative to income. These wealth effects provide
evidence to support the Euler equation and the permanentincome hypothesis.
Consumption | 135
SAMPLE LECTURE: THE DEBATE ABOUT
CONSUMPTION, ECONOMIC STABILITY,
THE TREND, AND POTENTIAL OUTPUT
With the publication of Keynes’s General Theory in 1936,
consumption theory was placed front and center in terms of
understanding macroeconomic failures. As is well known,
Keynes and others attributed the Great Depression to an inadequate level of effective demand. In The General Theory,
Keynes introduced economists to the term “marginal propensity to consume.” From the MPC, the multiplier effect was
derived. With an MPC between zero and 1, say closer to 1
than zero, the effects of shifts in autonomous expenditures
on incomes and employment were magnified. The greater
these multiplier effects were, the greater the instability in the
economy. Moreover, Keynes identified the cause of the business cycle as an imbalance between savings and investment
(leakages and injections). With Keynes’s absolute-income
hypothesis, where
c = autonomous consumption + MPC × Y,
as the economy grew, the consumption rate fell, the savings
rate increased, leakages increased relative to injections, and
effective demand potentially blocked the economy from
reaching full employment. This underconsumption tendency
prevented the economy from reaching full employment and
caused the trend level of production to fall below the potential level of production, causing the economy to operate with
persistent unemployment.
Milton Friedman, understanding that empirical work on
consumption showed Keynes’s absolute-income hypothesis to
be too simplistic, countered with the permanent-income
hypothesis. With the permanent-income hypothesis, the marginal propensity to consume out of current income is close
to zero, and the multiplier effect is practically nonexistent.
Moreover, as the economy grows, the ratio of consumption
to income is likely to remain steady. Underconsumption (and
underemployment), secular stagnation—as described in
Chapter 14, in Friedman’s view—is not a central feature of
capitalist/market economies.
CASE STUDY: HOUSING WEALTH EFFECTS
VERSUS OTHER WEALTH EFFECTS
In the textbook, all wealth effects are typically treated equally
in terms of the size of the impact of the wealth effect on consumption. For example, using the Euler equation, if remaining
life expectancy is forty years, a dollar increase in wealth
(regardless of the type of wealth) increases consumption in
the current year by $0.025 (= $1/40). Recent evidence suggests
that a dollar increase in housing wealth has a much stronger
effect on consumption. For example, Case, Quigley, and
Shiller provide tentative evidence that a 10 percent increase in
housing wealth causes a 0.4 percent increase in consumption,
whereas a similar increase in financial wealth has no effect.1
REVIEW QUESTIONS
1. The neoclassical consumption model is based on the
assumption that a representative consumer maximizes utility derived from lifetime consumption subject to a lifetime
(intertemporal) budget constraint. Given the consumer’s preferences, the rate of interest, current income, future income,
and financial wealth, the consumer maximizes utility by
smoothing consumption over his or her lifetime. This process of utility maximization reduces the sensitivity of current
consumption to anticipated changes in income.
2. The intertemporal budget constraint (IBC) is based on
the notion that the value of lifetime consumption must
equal the value of lifetime income received plus financial
wealth. The IBC in the current period can be written as the
present value of lifetime consumption, equaling the present
value of lifetime income plus financial wealth.
3. The lifetime utility function shows the relationship between
utility and the consumer’s level of consumption in different
time periods. For example, in the two-period model, the utility function is written as U = U(ctoday,cfuture). Diminishing
returns to consumption in any given period are assumed. For
example, as the individual increases consumption today, his
or her tastes become sated, and he or she values consumption
today less relative to future consumption.
4. Given the consumer’s preferences, the rate of interest,
current income, future income, and fi nancial wealth, the
consumer maximizes utility by smoothing consumption
over the lifetime. This process of utility maximization
reduces the sensitivity of current consumption to anticipated
changes in income. The consequence is that consumption is
relatively stable and the Keynesian multiplier effects are relatively small (close to zero).
5. The Euler equation is derived as a consequence of
the first-order utility maximization condition, where
Δcfuture/Δctoday|IBC = MRSCtoday, C future = 1 + R. If U = log ctoday
+ β × log cfuture, then ΔU = 0 = MUCtoday × Δctoday + MU Cfuture
× Δcfuture = (1/ctoday) × Δctoday + β × (1/cfuture) × Δcfuture, then
MRSCtoday, cfuture = cfuture/β × ctoday. Given that utility is maximized when cfuture/(β × ctoday) = (1 + R), the ratio of future
consumption relative to current consumption is given as
cfuture/ctoday = β × (1 + R), where cfuture/ctoday = 1 + the growth
rate in consumption. As such, the Euler equation can be
1. Karl E. Case, John M. Quigley, and Robert J. Shiller, “Comparing
Wealth Effects: The Stock Market vs. the Housing Market,” Advances in
Macroeconomics 5, no. 1 (2005): 1–32.
136 |
Chapter 16
interpreted as the optimal growth pattern of consumption,
given R and β.
(d) If stock market and housing wealth increase, households
increase consumption and reduce savings relative to disposable income.
6. For a given savings rate, the growth rate in output determines the growth rate in consumption. Given β, the patience
coefficient, the real rate of interest, R, is determined. A
decrease in the patience coefficient, given cfuture/ctoday,
increases R.
4. (a) Using the Euler equation, cfuture/ctoday = β(1 + R); where
cfuture/ctoday, = 1 + consumption growth rate, so the consumption growth rate = 5 percent.
(b) −0.25 percent
(c) R = 7.4 percent
7. The MPC is the amount consumed out of an additional
dollar of income. If changes in income are anticipated, then
they are already reflected in past and current levels of consumption, and therefore changes in current income have little
effect on current consumption. If households face borrowing
constraints or if they save for precautionary reasons (due to
uncertainty about future income streams), consumers may
react strongly to changes in current income. Suppose, for
example, you expect a $10,000 bonus next year. In our twoperiod model, you would spend half the bonus this year on
goods and interest ($4,762 on goods and $238 on interest if
the interest rate was 5 percent) and the other half next year.
But if you were denied access to credit this year, you would
spend the whole bonus next year (an MPC of 100 percent). A
similar story is true if you were unsure of receiving the
bonus next year, and if you actually did receive it in the second period.
5. (a) ctoday = (1/(1 + β)) × ; cfuture = (β/(1 + β)) × (1 + R)
(b) If β = 1, then ctoday = (1/2) , and cfuture = (1/2) × (1 + R).
(c) If β < 1, Ctoday increases and cfuture decreases; because
less utility is derived from future consumption, the rational consumer substitutes current consumption for future
consumption.
8. In recent decades as housing wealth and financial wealth
increased, the personal savings rate decreased. The decrease
in the savings rate means that households are spending more
relative to their incomes. In order to spend more relative to
income, indebtedness increased.
EXERCISES
1. This is a worked exercise. See text for solution.
2. (a) human wealth = $109,524; total wealth = $159,524
(b) ctoday = $79,762; cfuture = $83,750; Stoday = $20,238
(c) ΔStoday = $10,000
(d) Δctoday = $4,761
(e) Δ = −$434; Δctoday = −$217; ΔStoday = $217
These effects are smaller in exercise 1 because the college
professor’s future income is $10,000 as compared to the student’s future income of $100,000. The college professor is
saving in the current period, and the student is dissaving in
the current period.
(f) No, because the college professor is saving in the current
period. The professor’s consumption is not constrained by
borrowing constraints.
3. (a) ctoday = $70,000; cfuture = $70,000; Stoday = −$20,000
(b) Δ = $10,000; Δctoday = $5,000; ΔStoday = −$5,000
(c) Δ = $20,000; Δctoday = $10,000; ΔStoday = −$10,000
6. (a) Let the change in current taxes = – Txtoday. The change
in future taxes = Txtoday(1 + R). The before-tax intertemporal budget constraint (ignoring nonhuman wealth) is
= ytoday + yfuture/(1 + R). The after-tax intertemporal budget
constraint is = ytoday – Txtoday + (yfuture – Txfuture)/(1 + R). The
before-tax and after-tax wealth is unaffected by the tax
reduction today. So, the timing of consumption is unaffected
by the tax reduction today.
(b) If some individuals had their current borrowings constrained, the tax cut increases consumption today.
7. (a) For β = 1, the consumption function is c = (1/T) × ,
where T is the number of periods (or remaining life expectancy). Assuming T is the same for rich and poor, an increase
in the wealth of the rich relative to the poor will increase
the consumption of the rich relative to the poor.
(b) If unanticipated positive income shocks are present in
the economy, the consumption function can be written as
c = (1/T) + MPC × Yunanticipated, and assuming that the MPC
of the poor is greater than the MPC of the rich, the consumption of the poor increases relative to the rich.
8. (a) Recent data provided by FRED is as follows:
Year
Savings
Rate
Household
Debt-to- GDP Ratio
2007
2008
2009
2010
2011
2012
2013
2014
2015
3.00%
4.90%
6.10%
5.60%
6.00%
7.60%
5.00%
5.60%
5.80%
96.95%
98.20%
97.65%
92.61%
87.88%
84.07%
82.05%
80.68%
79.89%
(b) These results are more or less anticipated. As wealth
decreases (increases), current consumption declines (increases)
relative to current income. The savings rate increases and the
debt-to-GDP ratio falls.
CHAPTER 17
Investment
CHAPTER OVERVIEW
This chapter teases out the neoclassical theory of investment
in an intuitive but rigorous way. Chad uses an arbitrage equation to intuitively develop the user cost theory of investment.
The result is a parsimonious but power ful model used to
explain capital investment decisions. The arbitrage approach
is applied to understanding equity prices (the price of corporate stocks), asset price bubbles, and informationally efficient
markets. The arbitrage equation is likewise applied to housing
prices. The chapter concludes with a brief review of inventory
investment theories.
and (2) investment, as illustrated in the Solow and Romer
models, explains changes in the capital stock (objects and
ideas), and, therefore, is a major cause of economic growth.
This chapter focuses on the microfoundations of investment decisions. The user cost theory of investment is developed using an arbitrage equation and is used to identify the
national savings rate. The arbitrage equation is also used to
explain stock prices and housing prices and to understand
price bubbles. The theory of inventory investment is also
reviewed.
17.2 How Do Firms Make Investment Decisions?
17.1 Introduction
This chapter focuses on the determinants of real investment
expenditures. In the introduction, investment and capital (in
economic terminology) are distinguished from financial
investment and financial capital. Economists refer to investment as the acquisition of capital goods. Capital goods are
goods used in making other goods. Investment in capital
goods, as defined in the national income and product
accounts, includes nonresidential fixed investment like equipment, structures, and intellectual property products, like
software; residential fixed investment; purchases of homes;
and inventory investment, the change in the stock of inventories. Financial investment refers to purchases of financial
assets. Financial assets are claims on the ownership of assets
backed by promises to pay. Financial assets are a store of
wealth— a means of bridging current income to future
consumption.
Investment in capital goods receives par ticular attention for two reasons: (1) investment share of output is
highly volatile compared to other components of output;
Investment decisions, as illustrated in Chapter 4, are guided
by business decisions to maximize profits. If MPK > R, then
the actual capital stock is less than desired and firms will
undertake investment to add capital (and vice versa). In this
chapter, the user costs of investment are expanded beyond the
real rate of interest to include a depreciation rate, đ, a capital gains rate, ΔpK /pK, where pK is the price of capital, and a
corporate tax rate, τ.
REASONING WITH AN ARBITRAGE EQUATION
A simple example is used to illustrate the user cost theory of
investment. In this example, an investor is considering an
investment of a sum of money in a bank account or in pizza
ovens. Differences in the risk associated with different investments are assumed away to simplify the discussion. Ultimately, the goal of the investment is to maximize the return
on an investment portfolio that consists of financial capital
(the bank account) and physical capital (the pizza oven). If
the prospective return on the pizza oven is greater than the
return on the bank account, the investor can make a higher
137
138 | Chapter 17
return from investing in pizza ovens, so at this point the return
on the portfolio is not maximized. If the prospective return on
the bank account is higher than the return on the pizza oven,
the investor will invest more in the bank account. Again at this
point, the overall return on the portfolio is not maximized.
When is the return on the portfolio maximized? The return
is maximized when the returns across assets are equalized.
If the returns are not equalized, a reallocation of the portfolio can generate higher returns.
The potential return on the bank account is the real interest
rate, R, times the price of a unit of capital, pK , had that amount
been invested in a savings account. The return on a unit of
capital is the MPK plus the appreciation of the capital, ΔpK.
Chad modifies the definition of the return in the next section.
To simplify your presentation, you should start with the modification, and define the return as the MPK including depreciation, đ × pK, plus appreciation, the capital gains, ΔpK, from the
resale of the asset at the end of the period. This generates the
arbitrage equation R × pK = MPK − đ × pK + ΔpK.
THE USER COST OF CAPITAL
Chad normalizes the price of capital, sets pK = 1, divides both
sides of the arbitrage equation by pK, rearranges terms, and
finds the familiar first-order condition for the desired capital
stock, where MPK = R + đ − ΔpK /pK, where the right-hand
side is the familiar user costs of capital. An investor chooses
the desired capital stock so as to maximize the return on its
portfolio by investing in physical capital up to the point where
the MPK equals the user costs, uc. Variations in the user
costs, given the MPK schedule, are then used to explain variations in the desired capital stock, investment.
EXAMPLE: INVESTMENT AND THE CORPORATE
INCOME TAX
As is well known, business income is taxed. The corporation
income tax rate in the United States is 35 percent. The effect
of the corporation income tax rate is to reduce the return on
capital. The return on capital is (1 − τ) × MPK. As such, the
arbitrage equation is now written as
R = MPK(1 − τ) − đ + Δpk /pk
and the first-order condition is given as
In the case study that follows in this section, the effects of
the corporation income tax rate on the estimated user costs
are considered for OCED countries. Assuming that each
country has the same user cost as the United States, variations in the user costs due to varying corporate income tax
rates are considered. For example, the user cost in France is
equal to the user cost in the United States times (1 − τUS)/
(1 − τFR). This example shows that wide variations in corporate tax rates do not result in large variations in user costs
across countries.
FROM DESIRED CAPITAL TO INVESTMENT
Given the user cost of capital and given the MPK as determined by the Cobb-Douglas production function, the desired
stock of capital is derived. From Chapter 5, the desired capital stock in time, t + 1, is Kt+1 = Kt − đ × Kt + It. Solving for It
yields an expression for the desired level of investment in
time t; that is, It = Kt+1 − Kt + đKt. Investment in time period t
is equal to the desired change in the capital stock plus depreciation. Given the existence of adjustment costs, several
periods of adjustment might be necessary to bring the actual
capital stock in line with the adjusted level of the capital
stock.
To connect investment to the desired capital stock, recall
from the Cobb-Douglas production function that
MPK = (1/3) × (Y/K) = uc, and, therefore, Y/K = 3 × uc. Also
recall that ΔKt+1 = It − đ × Kt and dividing both by Kt yields
ΔKt+1/Kt = (It/Kt) − đ, and multiplying and dividing (It/Kt) by
Yt and rearranging terms yields ΔKt+1/Kt = (It/Yt) × (Yt/Kt) − đ,
or ΔKt+1/Kt = gK = (It/Yt) × 3 × uc − đ, and solving for It/Yt =
(gK + đ)/(3 × uc).
As a result, the investment rate depends on the desired
growth rate in the capital stock, gK; the deprecation rate, đ;
and user cost, uc. Chad emphasizes that a higher user cost
lowers the investment rate, I/Y.
At the end of this section, Chad has a nice discussion as to
how the long-run growth model, for a closed economy, is now
completely specified. The long-run growth rates are given in
Chapters 5 and 6. Given the savings rate, the long-run growth
rate determines R, and given R (and the other user cost components), K is chosen, and the capital-to-output ratio and the
investment rate are determined.
MPK = [R + đ − ΔpK/pK]/(1 − τ)
where the right-hand side becomes the effective user cost
when corporation tax rates are nonzero. The introduction of
the corporation income tax rate, for any given user cost,
requires an increase in the MPK to equalize the after-tax MPK
to the user cost. The increase in the MPK is achieved through
a reduction in the desired capital stock and a decrease in
investment. In effect, the corporation income tax rate has
increased the user cost of capital.
17.3 The Stock Market and
Financial Investment
In this section, the arbitrage equation is used to derive an
expression for the price of a stock. Then the relationship
between price earnings ratios and price bubbles is explored.
The efficient market hypothesis is discussed, and Tobin’s q
theory of investment is reviewed.
Investment | 139
THE ARBITRAGE EQUATION AND THE PRICE OF A STOCK
Students who have had finance courses will recognize the
conclusions derived in this section as akin to Gordon’s dividend growth model (but with much less math). To simplify,
the zero-risk assumption is introduced. The condition for
maximizing the return on an investment portfolio is that the
returns across assets are equalized. In a two-asset model consisting of a savings account and a stock investment, that
condition is satisfied when R × ps = dividend + Δps, where ps
is dollars invested in a savings account or a stock. The return
on the savings account is R × ps; the return on the stock is the
dividend plus the capital gains, Δps. To express these returns
in percentages, divide both sides by the price of the stock,
ps, which yields R = (dividend)/ps + Δps/ps. If the returns on
the stock are greater than the returns on the savings account,
investors bid up the price of the stock today, lowering the dividend yield and the capital gains.
The arbitrage equation can then be used to solve for the
price of the stock. To do so, subtract Δps/ps from both sides
of the arbitrage equation, so that dividend/ps = R − Δps/ps, and
that ps /dividend = 1/(R − Δps /ps); multiplying both sides by
dividends yields the expression for the price of the stock:
ps = dividend/(R − Δps/ps). As Chad points out, when a constant flow is discounted, it is discounted by R; when the flow
is growing, it is discounted R minus its growth rate (in this
case R − Δps/ps).
PRICE-EARNINGS RATIOS AND BUBBLES?
The price-earnings ratio is the stock price relative to earnings per share. If the price-earnings ratio is increasing, investors are bidding up the price of the stock in anticipation of
higher future earnings. An expression for the price-earnings
ratio can be derived by dividing both sides of the ps equation by earnings. That is, ps/earnings = (dividend/earnings)/
(R − Δps /ps). If the dividend-earnings ratio and the interest
rate R are constant, then growth in the price-earnings ratio
must be attributed to anticipated capital gains. If the anticipated capital gains are not anchored in “rational expectations,” price bubbles emerge.
including the notion that investors can’t beat the market
averages—index mutual funds (with low management fees),
on average, outperform managed mutual funds (with high
management fees).
17.4 Components of Physical Investment
Here we are reminded that investment consists of not just
nonresidential fixed investment as discussed in the context
of the user cost theory but also residential construction and
inventory investment.
RESIDENTIAL INVESTMENT
The arbitrage equation is used to explain housing investment. If a return on an investment portfolio is maximized,
then returns across investments are equalized. Assume a
two-asset model: a savings account and a house. The investor has a choice of investing a down payment into a savings
account or in a home. The return on the savings account is
R × (down payment). The return on the home equals rent less
depreciation, đ*Phouse, plus capital gains, DPhouse, less the net
interest paid on the mortgage (where the mortgage is defined
as the difference between the price of the house and the
down payment). The net interest paid on the mortgage is the
interest payment minus the tax deductibility of the interest
payment; i.e.: R(1 − τ)(Phouse − down payment), where τ is the
investor’s tax rate. The arbitrage equation is R* down payment = Rent − đ*Phouse + ΔPhouse − R(1 − τ)(Phouse − down payment). By solving for Rent in the arbitrage equation, by
multiplying and dividing that solution by Phouse, and by defining = down payment/Phouse, and solving for Phouse, yields
Phouse = Rent/(Rτ + R(1 − τ) + đ − ΔPhouse/Phouse)). Increases in
the rental values of homes, increases in leverage (decreases
in ), increases in the tax deductibility of mortgage interest,
and increases in the expected price of homes result in higher
housing prices. Bubbles in housing prices can be related to
relaxed lending rules, increases in leverage, and increases in
expected capital gains.
INVENTORY INVESTMENT
EFFICIENT MARKETS
Financial markets are defined as informationally efficient if
prices fully reflect relevant and available information. In this
case, if an earnings report was accurately anticipated, the price
of the stock does not vary with the publication of the report,
since that information was already incorporated into the price
at an earlier date. If an earnings report was not anticipated,
the market quickly responds to the new information and the
price changes.
As a result of unanticipated information, stock prices follow a random walk. A number of implications arise from this,
Changes in inventories can be planned or unplanned. In this
section, planned changes in inventories are discussed. Three
motives for holding inventories are considered: (1) production smoothing: given an increase in demand, firms might
find it expensive to increase production to satisfy the increase
in demand, and therefore prefer to run down inventories; this
motive suggests that firms increase production of inventories
during bad times and that inventory investment is countercyclical; (2) the pipeline theory: in this case, inventories are
held as part of a production process; as demand increases
for finished goods, businesses hold more inventories of
140 | Chapter 17
intermediate goods to complete production; inventory
investment is procyclical; and (3) stock-out avoidance: firms
hold inventories for transaction purposes to ensure that customers’ needs are satisfied; inventory investment is again
procyclical. Given the confluence of these three motives,
inventory investment is expected to be procyclical, that is,
to rise and fall with short-run output.
SAMPLE LECTURE
Recall that the investment schedule was impor tant in developing the IS schedule and the short model. The investment
schedule was given as It/ = ai − (R − ), where R = the real
rate of interest and = MPK. If we assume that investment is
also related to cyclical variations in output, the investment
schedule can be rewritten as It/ = ai − (R − ) + c × (Ỹ),
where Ỹ = (Y − )/ , and where = potential output. Interestingly enough, Chad’s little textbook model of investment
performs remarkably well in explaining the behavior of
investment during the last decade and the Great Recession.
Using the Federal Reserve of Saint Louis’s FRED database,
data was gathered for nonresidential fixed investment, I,
potential output, , the interest rate spread between the tenyear treasury note constant maturity and the federal funds
rate, and the cyclical variation in output, Ỹ. The interest-rate
spread was used as a proxy for the difference between R and
, assuming that the changes in the risk premium over the
business cycle changed R relative to . For I/ , the augmented DF test failed to reject the null hypothesis. The data
were first differenced to generate a stationary series for I/ .
The constant was dropped from the equation as a result of
using first differenced data.
The Prais-Winsten technique was used to correct for serial
correlation. To estimate the investment schedule, contemporaneous values and one-quarter lagged values of the spread
and Ỹ were included in the regression equation. Statistically
significant estimates with the expected signs (although the
contemporaneous spread is only significant at the 90 percent
level) were derived. The estimates show that − b = − 0.11 (for
every one percentage point increase in the interest rate
spread, investment relative to potential output fell by 0.11 of
one percentage point), and that c = 0.34 (for every one percentage point increase in Ỹ, investment relative potential
output increased by 0.34 of one percentage point). This
simple model explains cyclical fluctuations in investment
well. In Figure 1, the actual changes in I/ are compared to
predicted changes in I/ .
0.5
0
–0.5
–1
2001q3
2004q3
2007q3
2010q3
I/PGDP, Δ
Linear prediction
Figure 1. Comparison of Actual Changes in I/ to Predicted
Changes I/
ESTIMATES OF THE INVESTMENT EQUATION: 2000, FIRST QUARTER, TO 2013, THIRD QUARTER
Prais-Winsten AR(1) regression— iterated estimates
Source
SS
df
MS
Model
Residual
Total
1.63105093
1.20448579
2.83553672
4
51
55
.407762733
.023617368
.051555213
ΔI/
Δspread
t
t−1
ΔỸ
t
t−1
rho
Coef. Std. Err.
2013q3
time
t
Number of obs
F(4, 51)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
=
=
=
=
=
=
55
17.27
0.0000
0.5752
0.5419
.15368
[95% Conf. Interval]
−.0790975
−.0475655
.0438255
.0438608
−1.80
−1.08
0.077
0.283
−.1670808
−.1356197
.0088858
.0404888
.1905966
.1532528
.3600193
.0336559
.0337695
5.66
4.54
0.000
0.000
.1230295
.0854577
.2581637
.2210479
Durbin-Watson statistic (original)
1.281909
Durbin-Watson statistic (transformed) 2.043467
(Source: Federal Reserve of St. Louis, FRED database. http://research.stlouisfed.org /fred2 /.)
Investment | 141
CASE STUDY: TOBIN’S q, PHYSICAL CAPITAL,
AND THE STOCK MARKET: MARGINAL q VERSUS
AVERAGE q
Tobin’s q theory of investment is based on the notion that the
stock market can provide a good estimate of expected profitability. If the present value of the future stream of income
generated by an additional investment is greater than the
costs of that additional investment, pK × ΔK, then the firm will
undertake the investment, as it increases net worth. That
expected increase in net worth is capitalized as an increase
in the market value of the shares. Additional investment
should be undertaken up to the point at which the present
value of the additional stream of income generated by the
investment is just equal to the cost of the additional capital,
or where marginal q (the ratio of the present value of the additional stream of income generated by the investment to the
cost of the additional capital) equals 1. If the optimal level
of investment is where marginal q is equal to 1, then the average q, the ratio of the stock market value of the firm to the
replacement cost of capital, is likely to be greater than 1. The
greater is average q relative to 1, the greater is the likelihood
that marginal q is greater than 1, and the greater is the likelihood additional investments can increase the net worth of
the firm.
CASE STUDY: THE EFFICIENT MARKET
HYPOTHESIS: WHEN THE RULE BECOMES
THE EXCEPTION
Most finance textbooks consider the efficient market hypothesis as the rule, subject to some exceptions, when explaining
stock price valuations. Shiller predicted the stock price and
housing price bubbles and essentially concludes that the
exceptions are the rules and the efficient market hypothesis
is the exception.1 As an example, Shiller examines the priceearnings ratio for the S&P composite index. Shiller shows
that high price-earnings ratios are correlated with lower
future stock prices—just the opposite of what the efficientmarket hypothesis predicts.
CASE STUDY: THEORIES OF INVESTMENT
The New England Economic Review published two studies
in 2001 that are must-reads for serious students interested in
the study of the determinants of investment spending.
The first study, by Richard Kopcke and Richard Brauman,
“The Performance of Traditional Macroeconomic Models of
1. Robert Shiller, Irrational Exuberance, 2nd ed. (New York: Doubleday, 2005), 175–203.
Businesses’ Investment Spending,”2 compares the out-ofsample predictions of various models, including accelerator
and cash-flow models. The major conclusions support our
findings above that cost-of-capital models that include an output measure perform well. They conclude that such models
outperform accelerator and cash-flow models. The second
study, by Geoffrey Tootell and others,3 shows that estimating disaggregated investment equations are useful in sorting
out industry-specific determinants of investment.
REVIEW QUESTIONS
1. Physical investment is the acquisition of capital goods.
Capital goods (equipment, structures, and software) are
goods used in making other goods. Financial investment is
acquisition of financial assets (capital). Financial assets represent a store of wealth that connects present income flows to
future consumption.
2. The arbitrage equation states that profit seekers will maximize profits when the returns are equalized across assets.
In the text, a two-asset model was used. If the return on a
savings account is greater than a return on an investment
in physical capital, resources will be reallocated away from
physical capital into the savings account. The reduction in
the investment in physical capital raises the MPK, until the
two returns are equalized. At that point, profits are
maximized.
3. A capital gain is the increase in the value of the asset. A
capital gain is realized at the time of the sale of the asset. The
capital gain adds to the return of an asset. The greater the
return on the asset relative to the return on the bank account,
the greater the investment in the asset.
4. The user cost of capital is the cost of using an additional
unit of capital. User costs reflect borrowing costs, R, depreciation, đ, and (inversely) capital gains. If the user cost is
less than MPK, the firm can increase profits by hiring additional units of capital (undertaking investment in excess of
depreciation).
5. Tobin’s q is a measure of the market value of the company’s stock relative to the value of capital. When the market value of the stock equals the value of the capital, q = 1,
and the present value of the future stream of earnings of the
2. Richard W. Kopcke and Richard S. Brauman, “The Per for mance of
Traditional Macroeconomic Models of Businesses’ Investment Spending,”
New England Economic Review, Issue 2 (2001): 3–39. Available at www
.bostonfed.org /economic/neer/neer2001/.
3. Geoffrey M. B. Tootell, Richard W. Kopcke, and Robert K. Triest,
“Investment and Employment by Manufacturing Plants,” New England
Economic Review, Issue 2 (2001): 41–58. Available at www.bostonfed.org
/economic/neer/neer2001/.
142 | Chapter 17
company equals the value of the capital, the firm has the
desired stock of capital. If, for example, q > 1, then investors believe that the present value of future earnings is
greater than the value of the stock, and the firm could invest
in more capital to raise profits.
6. In understanding the stock prices, a simple two-asset
model with the arbitrage equation can be used (assuming
equal risk across assets). To maximize profits on an investment portfolio, the return on the savings account should
equal the return on the stock investment. The return on the
stock investment is the dividend and the capital gains generated by the stock. In this case the arbitrage equation is
R × ps = dividend + Δps, where ps = price of the stock. Divide
both sides by ps so that R = dividend /ps + Δps /ps, where dividend/ps = dividend return, and Δps /ps = capital gains return.
7. From the arbitrage equation, R × ps = dividend + Δps, so
R = (dividend + Δps)/ps, and R − Δps /ps = dividend /ps, and
ps = dividend/(R − Δps /ps).
8. From the expression for the stock price derived in question 7, ps /earnings = (dividend/earnings)/(R − Δps /ps).
Bubbles in the market occur when ps /earnings are no longer
anchored to the right-hand-side variables dividend/earnings,
R, and when expected Δps /ps is greater than actual Δps /ps.
9. If the stock market is informationally efficient, then all
known and relevant information about the earnings of a stock
is reflected in the stock price. When expectations about
future events, like an earnings report, are realized, those
events are already reflected in the value of the stock, and the
stock price does not fluctuate with publication of the report.
When unexpected events affect the earnings of a stock, then
the stock price fluctuates. If those unexpected events are random, then the stock price follows a random walk.
10. The arbitrage equation equates the return on the down payment to purchase a house (had that payment been deposited
in a savings account) to the return on owning a house; that
is, R * down payment = Rent − đ * Phouse + ΔPhouse − R(1 − τ)
(Phouse − down payment). By solving for Rent in the arbitrage
equation, by multiplying and dividing that solution by Phouse,
and by defining = down payment/Phouse, and solving for
Phouse, yields Phouse = Rent/(Rτ + R(1 − τ) + đ − ΔPhouse/Phouse)).
Leverage is 1 minus . The greater the leverage, the smaller
is and the greater is the housing price.
EXERCISES
1. This is a worked exercise. Please see the text for
solution.
2. (a) uc = 0.1467
(b) Δuc = 0.0267
(c) With τ = 0, Δuc = ΔR = 0.02. Given the tax rate of
25 percent, an increase in the interest rate of 2 percentage
points causes the after-tax MPK to rise by 2 percentage points.
For the after-tax MPK to rise by 2 percentage points, the pretax MPK must increase by 0.0267. The increase in the interest
rate increases the user costs of capital more than the increase
in the interest rate because of the tax wedge between the
pretax and after-tax MPK. The increase in the user costs
lowers the investment rate.
3. (a) If τ = 0.20, uc = 0.125. If τ = 0.30, uc = 0.143.
(b) If uc = 0.10, τ = 0, I/Y = 0.30, gk = 0, I/Y = .30 = (đ)/
(3 × .10), đ = .09.
If τ = .20, I/Y = .09/(3 × .125) = .24. If τ = .30, I/Y = .09/
(3 × .143) = .21.
(c) The investment rate is given as I/Y = (gK + đ)/(3 × uc). As
illustrated in Table 17.1, variations in corporate tax rates
result in relatively smaller variations in user costs; therefore,
variations in tax rates likely explain some of the variation in
investment rates but not the large variations in investment
rates. The change in the investment rate as a function of the
change in the tax rate is Δ(I/Y) = − [(gK + đ)/3] × [R + đ −
(ΔpK/pK)] × Δτ. If Δτ = .10 and = Δ(I/Y) = –1/3 × Δτ = −0.033.
4. (a) When the investment tax credit is present and ΔpK = 0,
and pK normalized, pK = 1, the arbitrage equation is written
as R × (1 − ITC) = MPK × (1 − τ) − đ × (1 − ITC).
(b) uc = (R − đ) × (1 − ITC)/(1 − τ)
(c) If ITC = τ, then the effective tax rate on the MPK equals
zero. The tax on MPK is rebated through the ITC.
5. (a)
(b) What is being added and subtracted can be seen in the
header of the graph presented in 5(a). The result is a ratio of
the sum of gross private domestic and government investment less the respective investments in intellectual property
products to GDP (a rough measure of the ratio of private and
government investment in physical capital relative to GDP).
(c) The ratio derived above shows that investment in physical capital relative to GDP has been declining on a long-run
trend since late 1970s, and that this ratio has significantly
declined since its last cyclical peak around 2006. These data
provide evidence of the secular stagnation mentioned in
Chapter 14.
Investment | 143
6. (a) The increase in the TFP pa rameter, Ā, increases the
MPK. The increase in MPK causes MPK to be greater than
uc, causing an increase in the desired capital stock.
(b) With MPK > uc, investment increases.
(c) The investment rate is given as I/Y = (gK + đ)/3 × uc. In
the long run, as in the Solow model, gK = 0. Given no change
in đ and uc, the investment rate is unchanged.
7. This is a worked exercise. Please see the text for the
solution.
8. (a)
Growth rate of
condo prices
Down payment
rate, x̄
(percent)
Price of condo
0.00%
2.00%
5.00%
10.00%
5.00%
5.00%
5.00%
20.00%
20.00%
20.00%
20.00%
100.00%
10.00%
5.00%
$7,462.69
$8,771.93
$11,904.76
$29,411.76
$10,000.00
$12,195.12
$12,345.68
(b) Condo prices are sensitive to expected capital gain. With
no capital gain, the condo’s price is about $7,463. If condo
prices are expected to increase by 10 percent per year, holding
the down payment constant, the condo’s price rises to about
$29,412.
(c) Condo prices are likewise sensitive to the down payment
rate. If condo prices grow at 5 percent and the down payment is 20 percent, the condo’s price is about $11,905, but if
the down payment rises to 100% percent, the condo’s price
is $10,000. The use of leverage, the decrease in the down
payment, increases the return on the condo relative to the
bank account and increases the demand for the condo.
9. (a) R × pi = prof
(b) pi = prof/R
(c) The price of an idea is equal to the present value of the
future stream of income, the profit, generated by that idea, if
the profit is generated in perpetuity.
CHAPTER 18
The Government and the Macroeconomy
CHAPTER OVERVIEW
It’s best if you cover this chapter after you cover Chapter 8
on inflation (due to the link between hyperinflation and the
government budget) and Chapter 11 on the Investment–
Saving (IS) curve (forward-looking behavior and Ricardian
equivalence). Also, this chapter makes extensive use of net
present value, which was covered in Chapter 7 (valuing human
capital) and used again in exercises at the end of Chapter 11
(permanent income).
That said, the chapter omits business-cycle concerns completely, and aside from a clear, thorough discussion of the
government budget constraint (in a two-period world, mercifully), there is no formal modeling. It should be quite simple
to teach—students can just read most of it on their own. But
it still covers the key facts that will be important in your students’ lives: the long-term fiscal imbalances facing the rich
countries and rising health care spending.
The big thing for you to drill home will probably be the
government budget constraint. Interestingly, Chad sets up his
budget constraint so that you can easily answer the question
posed by the title of Barro’s classic article on Ricardian
equivalence: “Are Government Bonds Net Wealth?”1
18.2 and 18.3 U.S. and International Government
Spending, Revenue, and Debt
This covers the basic facts that every voter or international
businessperson should know. You may want to point out that
of all the spending items on Table 18.1 (the U.S. budget), only
1. Robert J. Barro, “Are Government Bonds Net Wealth?” Journal of
Political Economy 82 (1974): 1095–1117.
144
two items— National Defense and Other— are typically
counted as part of G. The rest are transfers of income.
(Note: Medicare is a bit ambiguous on that count— the
government regulates the private-sector purchases so heavily
that doctors receiving Medicare payments appear like government contractors in some ways. But Medicare is still officially counted as part of transfers.)
We also see charts on the size of the U.S. deficit and the
debt/gross domestic product (GDP) ratio since the Depression. I often emphasize that the experience of World War II
is quite solid evidence that temporary deficits are unlikely to
cause short-term to medium-term trouble for a country like
the United States. During World War II, the federal government deficit was over 25 percent of GDP, and the debt/GDP
ratio was greater than 1, yet the post–World War II period
from 1946 until the late 1960s was considered a golden age
of the U.S. economy.
Students are concerned about the current fiscal situation. With the Great Recession and the Economic Stimulus
Act we have seen significant increases in federal government deficits and debt, as reflected in the table below.
However, even with sharp increases in deficits and debt,
our situation is not anywhere near the levels reached during World War II—where federal government debt was
more than 100 percent of GDP.
The Government and the Macroeconomy | 145
The Federal Government Budget Deficit and Outstanding
Debt
Year
GDP
Fed
Govt
Deficit
2007
2008
2009
2010
2011
2012
2013
2014
2015
14477.6
14718.6
14418.7
14964.4
15517.9
16155.3
16691.5
17393.1
18036.7
353.9
780.6
1475.7
1508.7
1397.1
1193.4
698.3
681.4
602.3
%
of GDP
Fed Govt
Outstanding
Debt
%
of GDP
2.44%
5.30%
10.23%
10.08%
9.00%
7.39%
4.18%
3.92%
3.34%
5971.89
6684.55
8388.51
9950.55
11160.83
12449.71
13320.1
14148.92
14638.04
41.25%
45.42%
58.18%
66.49%
71.92%
77.06%
79.80%
81.35%
81.16%
(Source: FRED Database and author’s calculations. The budget deficit is
defined as the negative of net lending.)
The discussion of other developed countries demonstrates
that some countries have bigger governments and bigger
debts than the United States, while the Norwegian government is a net lender, holding large amounts of financial assets.
18.4 The Government Budget Constraint
Chad uses the government’s budget constraint in a two-period
framework to give students a solid understanding of what deficits and debt really mean. Later, in a sample lecture, I start with
a one-period budget constraint to develop the intuition.
18.5 How Much Can the Government Borrow?
Subsections 18.5.1 through 18.5.4 give largely nontechnical
answers to these four questions:
1. Can we grow our way out of debt? Answer: Sometimes.
2. How high can the debt/GDP ratio go before a government
turns to hyperinflation (seigniorage) to repay the debt?
Answer: Higher for the U.S. government than for less
stable governments.
3. When some later generation runs those primary surpluses,
won’t their taxes be high? Answer: Yes, under current projections of high future medical costs. That’s one more reason to focus on facilitating long-term economic growth.
4. And finally, does government borrowing “crowd out”
investment purchases? Answer: Income accounting identity shows that “I” can be financed by private, public, or
foreign saving. A deficit (fall in public saving) could
crowd out “I” in principle, but in U.S. practice, it looks
like private saving and foreign saving (trade deficits) have
made up much of the difference. This is a matter of serious debate, all the same.
Chad’s discussion is a great cocktail-party summary of these
issues—actually, it’s quite a bit more rigorous than that. And
while it may not look all that rigorous to you or me, it’s vastly
better than anything your students will see on a TV news
show for the rest of their lives. This is your chance to make
some impor tant points.
I have little to add to his discussions of these topics, so I’ll
let them stand on their own.
18.6 The Fiscal Problem of the
Twenty-First Century
Here Chad— quite appropriately— becomes more speculative. Drawing on his Quarterly Journal of Economics piece2
with Robert Hall, he shows that government health care
spending is the real long-term fiscal problem. At the same
time, drawing on Nobel Prize–winner Robert Fogel’s work,
he notes that in the twenty-first century, people in rich countries have apparently freely chosen to spend more on health
care.
As we’ve gotten richer, we’ve spent about the same fraction of our incomes on food—but we’ve spent much more on
health care. Here’s a shocking example: Brink Lindsey notes
in his book, The Age of Abundance3, that in 1900, the average American spent nearly twice as much on funeral expenses
as on medicine. Why? Because there just wasn’t that much
health care to purchase. The major fiscal problem of the
twenty-first century is largely caused by the fact that goods
that used to have an infinite cost—goods that didn’t exist—
are now just extremely expensive. Further, medical innovation is proceeding so rapidly that more goods are going
through that process.
As Alan Greenspan, then Federal Reserve chair, put it in
a speech, “Rapidly advancing medical technologies, essentially inelastic demand for medical services for the elderly,
and a subsidized third-party payment system have created
virtually unconstrained demand.”4 Many popular and policy
discussions focus on the third-party payment (insurance or
government provision) as the reason for exploding costs. But
that’s only a part of the puzzle. Really, we just want to buy
most anything that might make us healthier.
There’s also a Baumol cost disease factor, as well. Baumol
noted that if technology enhances manufacturing productivity but leaves service-sector productivity unchanged, then the
relative cost of providing services will increase.
2. Robert E. Hall and Charles I. Jones, “The Value of Life and the Rise
in Health Care Spending,” Quarterly Journal of Economics (February 2007): 39–72.
3. Brink Lindsey, The Age of Abundance (New York: Harper Collins,
2008).
4. Alan Greenspan, “Aging Global Population” (testimony before Special Committee on Aging, U.S. Senate, February 27, 2003).
146 | Chapter 18
Here is an example: the typical medical doctor treating
eight patients a day could in principle be working in a medical laboratory helping to invent a new medicine that could
be treating 8,000 people a day. So, having a doctor sit in an
office is an expensive way to use a highly trained resource.
But it’s unlikely that the cost of disease is the majority of
the problem—the treatments themselves, whether using electronic equipment, patented phar maceuticals, or in-person
cases, are generally quite expensive for all but the most routine cases. We’re back where we started: the major “problem”
is that we keep finding new ways to help people.
(Note: That rapid rate of innovation is a matter of slope.
Questions of whether the medical care system should be a
“single payer” system or a largely private system are likely
to be arguments about the long-run level of health care spending. And, of course, in the long run, issues of slope are vastly
more impor tant than issues about level; Chad makes this
point with Figure 18.8.)
SAMPLE LECTURE: THE ONE-PERIOD
BUDGET CONSTRAINT
Chad starts in the usual place with equation 18.1:
Gt + Trt + iBt = Tt + ΔBt+1 + ΔMt+1
The left side is spending: government purchases, transfers,
and interest on the outstanding debt (like making an interestonly payment on your mortgage). The right side is revenue:
taxes, borrowing (or new bonds), and seigniorage. We can
ignore seigniorage for now (it’s a minor source of revenue in
rich countries, and it would be a disaster if it became an
impor tant source), and to keep it simple we’ll just ignore
transfers or simply think of G as “government spending,” purchases plus transfers.
That gives us a simpler version:
Gt + iBt = Tt + ΔBt +1
And from this, surprisingly, we can get a complete theory
of the government’s dynamic budget constraint. Note that
ΔBt = Bt+1 − Bt. This gets us
Gt + iBt = Tt + Bt+1 − Bt,
which reorganizes to
Bt+1 = (1 + i)Bt + Gt − Tt.
Chad emphasizes that the last two terms, G and T, are the
“primary deficit,” a measure that the media ignores but which
is very important in macroeconomics. The measure to which
the media pays attention is “total deficit,” G + iB − T. That’s
primary deficit plus interest payments. It’s less impor tant
macroeconomically, as we’ll soon see.
(Aside: That’s because, in an infinite-horizon steady
state, the government must run a nonnegative primary defi-
cit. It can always run a total deficit in steady state, as long
as interest on the debt doesn’t grow faster than the overall
economy. I’m omitting some minor details, but this is the
big idea that Chad is trying to illustrate with his two-period
framework.)
Before we take Chad’s plunge into the two-period framework, let’s just think about a world that will only last for one
more period. We’ve accumulated some debts in the past, but
we’ve got to pay them off before the world ends. We’ll number the periods, using our previous budget constraint as a
model. The world exists in period 1 (now), but it won’t exist
in period 2. We write
B2 = (1 + i)B1 + G1 − T1.
If this is a one-period model, how much debt can exist in
period 2? The answer, of course, is zero. No one will lend to
a government that won’t exist in the future. So B2 must equal
zero. Let’s put taxes on one side and all the spending
items— G and debt repayment—on the other:
T1 = (1 + i)B1 + G1.
If the government is going to meet its obligations, then revenues must equal costs—and the costs include paying off the
outstanding debt (B1), making the final interest payment on
that debt (iB1), and paying for government purchases. “Revenues equal costs” sums this up well— and it reminds students that paying off the debt is a real cost.
Chad writes this another way as well, to make another
point:
T1 − G1 = (1 + i)B1.
The big story is that the primary surplus must be big
enough to pay off your bondholders. “Profits” must be
big enough to make your “debt payments.” This is a simple,
one-period version of the answer to Barro’s question, “Are
government bonds net wealth?” The answer, of course, is
yes. Government bonds have value because investors believe
that the U.S. government will create big enough (primary)
surpluses—profits, really—to repay the debt.
(Aside: In an infinite-horizon world, the government
doesn’t pay off its bondholders all at once: it amortizes the
debt. It just keeps making interest payments forever—so
the reason the debt/GDP ratio can’t rise indefinitely is that the
interest payments [as a fraction of the economy] can’t rise
indefinitely.)
Emphasizing that primary surpluses are the government’s
“profits” helps students use concepts with which they’re
already familiar. Any business must have some profits if it’s
going to pay down its debt. When you stretch this out to two
or three periods, the only change is that the government can
run temporary primary deficits, but on average you still must
make a profit, or people won’t lend to you anymore. Eventually, the government must make enough of a primary surplus
to at least make its interest payments.
The Government and the Macroeconomy | 147
(Illustration: If you’re borrowing money with one credit
card to make a minimum payment on the other, you know
you’re in financial trouble. At some point, you must consume
less in order to at least make the minimum credit card payment. You must pay down your credit card with your current income, not by borrowing. The same is true for the
government.)
Of course, one implication is that if we do see investors
gladly lending money to the U.S. government, then it means
that those self-interested, forward-looking agents think
there’s a very good chance that they’ll get repaid. If they
thought the chance of repayment was 1 in 10 or 1 in 100,
interest rates would be in the double or triple digits. They’re
currently nowhere close to those high levels.
Chad works through all of this in two periods in 18.3, and
many students can follow that just fine. With math-averse students, I’d run through this one-period model first.
EXPANDED CASE STUDY: FINANCING THE
SOCIAL SECURITY PROGRAM: A GLANCE
AROUND THE WORLD
In the United States, our Social Security system is a
government-run guaranteed pension program. The amount
you receive is roughly related to how much you made during
your lifetime, and Congress controls the payment amounts.
Of course, since the elderly vote at higher rates than other
citizens, it is unlikely that Social Security benefits will ever
be cut—and suggesting to do so would be political suicide
for any politician.
Do other countries run things the same way?5 Western
European countries tend to have systems similar to our own.
But the world’s newly industrializing countries have generally gone in a different direction. Poland, Sweden, Mexico,
and Singapore, just to name a few examples, require workers to save a fraction of their wages in a private investment
account. The workers have some control over where the
money is invested, and they can invest it in safe government
bonds, in riskier private stocks, or in some combination of
the two. Typically, the government regulates these accounts
so that workers can’t make choices that are too risky. In Australia, China, and Hong Kong, it is the employers who must
set aside money in private accounts for employees, but otherwise the system is much the same. In all these countries,
workers typically have a basic, low-paying governmentguaranteed pension in addition to the private plan (a “Social
Security lite”). This ensures that retirees don’t starve.
In all, dozens of countries have some sort of governmentmandated system of private retirement accounts.
5. This section draws on “Social Security Around the World,” Washington Post Online, available at http://www.washingtonpost.com /wp-srv
/ business/daily/graphics/pensions_041105.html.
CASE STUDY: DO DEFICITS RAISE
INTEREST RATES?
A key fiscal policy question is whether deficits hurt the overall economy. The channel we’ll focus on here is whether longlasting deficits raise interest rates—since if deficits do raise
rates, then domestic investment is quite likely to be hurt.
Much of the recent debate grew out of the return of deficit
spending in the early 2000s. The four papers below span the
spectrum on the issue: assuming that the deficit persistently
rises by 1 percent, Gale and Orszag6 argue that long-term
rates should rise by about 1 percent, while Laubach7 and Dai
and Phillipon8 argue for an effect about one-third that size.
Engen and Hubbard9 focus on the debt rather than the deficit
and argue that a persistent 1 percent rise in the debt would
have almost no effect on interest rates: a mere 0- to 0.03-percent
rise. All four papers are data driven, using sophisticated
econometrics to address the question. Perhaps the best guess
would be the median: one-third of the large Gale/Orszag
number.
At the level of raw data, what happened to long-term rates
as markets became aware that deficits were coming back in
the early 2000s? Between the summer of 2000 (before the
election of George W. Bush) and 2003 (when the news of high
deficits must have sunk into the financial markets), long-term
interest rates fell about 1.5 percent for corporate bonds, mortgages, and treasuries alike. Of course, the rise in the deficit
wasn’t the only thing happening to the U.S. economy at this
time. Perhaps some other factor explains why interest rates
didn’t appear to rise as a result of the Bush deficits. Or perhaps this is an area where economists need to rethink their
assumptions.
CASE STUDY: DO EXPENSIVE DRUGS
SAVE MONEY OR COST MONEY?
One ongoing health care debate concerns the cost of drugs.
New patented drugs are often very expensive. As economists,
one question we should ask is, “Expensive compared to what?”
Frank Lichtenberg of Columbia Business School has been
asking that question. In a 1996 National Bureau of Economic
6. William G. Gale and Peter R. Orszag, “The Economic Effects of
Long-Term Fiscal Discipline” (working paper, Brookings Institution,
Washington, DC, 2002).
7. Thomas Laubach, “New Evidence on the Interest Rate Effects of
Budget Deficits and Debt” (working paper, Board of Governors of the Federal Reserve System, Washington, DC, 2003).
8. Qiang Dai and Thomas Phillipon “Fiscal Policy and the Term Structure of Interest Rates” (working paper, National Bureau of Economic
Research, New York, 2005).
9. Eric Engen and Glenn Hubbard, “Federal Government Debt and
Interest Rates” (working paper, National Bureau of Economic Research,
Cambridge, MA, 2004).
148 | Chapter 18
Research (NBER) study, “The Effect of Pharmaceutical Utilization and Innovation on Hospitalization and Mortality,”10
he finds that “a $1 increase in pharmaceutical expenditure is
associated with a $3.65 reduction in hospital care expenditure,” and that “an increase of 100 prescriptions is associated
with 1.48 fewer hospital admissions, 16.3 fewer hospital days,
and 3.36 fewer inpatient surgical procedures.”
So, one impor tant trade- off for us to keep in mind is
drugs versus hospitals. Of course, this does nothing to
settle the question of what intellectual property rights are
appropriate for phar maceuticals— that’s another question
entirely.
The NBER’s health care and health economics working
groups publish excellent nontechnical summaries of these
kinds of findings in their free online NBER Reporter.
REVIEW QUESTIONS
1. This will depend on the year in which you answer. The
Economic Report of the President is one readily available
source of data. Most economists don’t find the current U.S.
debt-to-GDP ratio to be a major problem—it’s the future
large, primary deficits adding onto that debt that are the longterm problem.
2. Flow version: at a given point in time, the government
spends its money on purchases, transfers, or interest payments. It gets that money from taxes, new borrowing, or by
printing currency.
Intertemporal version: the government’s future debt is
equal to its old debt, the interest it must pay on the old debt,
and the government’s primary deficit. (I’m inclined to use
the term “primary deficit” a lot, since it’s an unfamiliar idea
to students.)
3. This depends on how trustworthy the government is. No
magic number exists.
4. Private saving (Y − C − T), public saving (T − G), or foreign saving (− NX). Crowding-out savings, national and/or
foreign, are diverted from investment to finance the government borrowings.
5. The fiscal problem of the twenty-first century is summarized in Figure 18.6. Entitlement programs, for example,
Social Security, Medicare, and Medicaid, are growing
faster than GDP, increasing federal government spending’s
percentage of GDP relative to federal government revenue’s
percentage of GDP. These programs’ share of GDP is
expected to rise to about 14 percent in 2030 and 21.1 percent
10. Frank R. Lichtenberg, “The Effect of Phar maceutical Utilization
and Innovation on Hospitalization and Mortality,” National Bureau of
Economic Research, Working Paper No. 5418 (January 1996).
in 2075. Possible solutions for Social Security focus on revenue enhancements, for example, raising Social Security
contributions, and reduced benefits by increasing the retirement age. Solutions for Medicare/Medicaid are quite difficult, since technological changes drive a significant increase
in health care costs (new medicines, MRIs and CTs, and
the like). Preferences drive many technological changes.
Increasingly, health care will be more managed (or rationed,
depending on your perspective) in an attempt to control
costs. The problem is deciding what mix of government
and market best achieves the simultaneous goals of efficiency and equity.
EXERCISES
1. This depends on current data. The data below are derived
from the 2013 ERP and my calculations.
Billions
of $’s
% of GDP
Per Capita
Revenue
Personal
Corporate
SSOASDI
Other
3,249.9
1,540.8
343.8
1,065.3
300
18.02%
8.54%
1.91%
5.91%
1.66%
10,031
4,756
1,061
3,288
926
Spending
National Defense
International Affairs
Health
Medicare
Income Security
Social Security
Net Interest
Other
Deficit
3,688.3
589.6
48.6
482.2
546.2
508.8
887.8
223.2
402
438.4
20.45%
3.27%
0.27%
2.67%
3.03%
2.82%
4.92%
1.24%
2.23%
2.43%
11,384
1,820
150
1,488
1,686
1,570
2,740
689
1,241
1,353
As a sign of the economic recovery, we can see (in comparison to Table 18.1) spending’s share and the deficit’s
share of GDP falling and revenue’s share of GDP rising.
2. The business’s long-run profits (primary surpluses) must
be big enough to pay off the investors’ (the government) debt.
This applies to primary budget balance, not total budget balance. From today’s point of view, the only reason to run primary surpluses in the future is to pay off today’s existing
debt. Yes, once we get to the future, there may be times where
we run a deficit or two, but the big picture, which shouldn’t be
lost, is that if we have a pile of debt today, then we know that
in the long run, we must run surpluses (on average, in net
present value terms) to pay off that debt.
3. The simplest way to answer this question meaningfully
without resorting to econometrics is to look at the years
immediately before the 1980s and the 2000s and see what
changed thereafter. Tax receipts were about 18 percent in
the late 1970s, dropping to 17.4 percent at their lowest in the
The Government and the Macroeconomy | 149
early 1980s. Therefore, tax changes apparently weren’t the
problem. Spending increased from about 20.5 percent to
about 22.5 percent of GDP over the same period—so clearly,
spending hikes were the bigger change. The two biggest
increases in spending were defense and interest on the debt.
The opposite was true in the 2000s. Taxes fell from
19.5 percent of GDP in the late 1990s to perhaps 17 percent
between 2002 and 2006. Government spending also rose,
but not by as much: it went from perhaps 19 percent to perhaps 20 percent of GDP. So, the tax loss was much larger.
The fall in taxes was mostly on the personal income side, and
the biggest spending increase was in defense—but the defense
increase was about one-third the size of the tax loss in
impact.
(Aside: the plummeting tax revenues of the early Bush
years surprised economists of all political backgrounds—
his tax cuts were expected to cause revenue decreases, but
not by that large an amount. The explanation appears to
turn partly on the collapse in the stock market: capital gains
taxes brought in much revenue in the later Clinton years.
That’s not the whole story, but it’s the least ambiguous part
of the story.)
1985: 2% primary deficit, 5.1% total deficit
1999: 3.8% primary surplus, 1.3% total surplus
2006: .01% primary deficit, 1.8% total deficit
2010: 7.65% primary deficit, 9% total deficit
2015: 1.2% primary deficit, 2.43% total deficit
(c) Under the examples in (a):
1. Private savings rise this year, and government savings
fall this year. No future impact. This is pure accounting
identity.
2. Private savings rise this year, and government savings
fall this year. Next year, private savings fall and government
savings rise. Consumers save the tax cut, because they
know they won’t be getting $105 billion a year from now.
The government side is accounting identity.
3. Private savings rise this year, and government savings
fall this year. In two years, private savings fall and government savings rise. Consumers save the tax cut, because they
know they must pay $110.25 billion a year from now. The
government side is accounting identity.
7. Because people trust the Belgians, Italians, and Japanese
to do whatever is necessary to pay off their debt—partly
because their private economies are rich enough that the
government can raise taxes without impoverishing the
people if necessary, and partly because investors trust the governments of those countries to make unpopular decisions if
needed. Investors may be wrong—perhaps the Argentines
would have paid everyone off— but that’s what they likely
believed.
6. (a)
1. The government can immediately cut spending by $100
billion.
2. It can also cut spending by $105 billion a year from now.
3. It can raise taxes by $110.25 billion two years from now.
8. If the government borrows the money, then public saving
falls as an identity. The question is, will consumers save that
tax cut (good for investment) or will they spend it on consumer goods (bad for investment)? The balance of evidence,
according to Chad, is that private saving rises by about 50
cents for every dollar of government deficit. So, private savings are unlikely to be enough to make this work.
Perhaps, just perhaps, the tax cuts will be structured in
such a way that they give strong incentives to investment. In
that case, private savings could, in principle, be even greater
than 100 cents on the dollar. But there is no substantial evidence in favor of that hypothesis, unless the tax incentive is
a one-time-only offer. But discussing that further would take
us far afield.
Perhaps foreigners will make up the difference, as well;
again, an investment tax incentive might bring in quite a lot
of investment from overseas. Particularly for a small economy, that could possibly have a big effect. That may be why
small European economies often have low tax rates on investment: so they can draw in savings from foreign countries. Big
economies like the United States might be able to meet their
savings needs domestically.
(b) To keep this simple, let’s assume that all government
spending is pure transfers. Otherwise, we get into the question
of whether cuts in G raise lifetime income.
Under the PIH, rational consumers do not change their consumption behavior at all: consumer spending depends on lifetime Y. If so, then these changes are a “tax shift” to the future.
9. (a) Health care. It is a problem for all the rich countries—
the spending slope is large and positive.
(b) Social Security eventually hits a peak in a few
decades—we know this because it’s a “defined benefit” program, where we know (roughly) how much we must pay to
how many people. With health care, we have essentially
(Source: Economic Report of the President, 2013, 2015)
4. (a) B2 = (1 + i)B1 + G1 − T1
B3 = (1 + i)B2 + G 2 − T2
B4 = (1 + i)B3 + G 3 − T3
(b) B4 = 0
(c) 0 = (1 + i)[(1 + i)B2 + G 2 − T2] + G 3 − T3
(d) 0 = (1 + i){(1 + i)[(1 + i)B1 + G1 − T1] + G 2 − T2} + G 3 − T3
(e) This indicates that in the long run (or at the end of time,
however I prefer to think about it), accumulated debt and
interest must be paid off.
5. This is a worked exercise. Please see text for solution.
150 | Chapter 18
promised to buy elderly people whatever health care services are invented in the future—we have written a blank
check.
(c) Given that entitlement spending is projected to grow much
faster than real GDP, finding ways to accelerate the growth rate
to match entitlement-spending growth is unlikely. The solution,
therefore, will be to rethink, rationalize, and ration the entitlement system. This process will result in redistributions of
incomes and tax burdens and is bound to be controversial (as
evidenced by the reaction to the Health Care and Education
Reconciliation Act of 2010).
(d) These are intractable problems, but must be solved. The
purpose of this question is to get your students thinking
about these public issues, if they haven’t already done so. If
you are looking for answers, you might consider the free-
market response to health care, in which markets allocate
and ration health care. You can then consider market failures
that will likely occur: (1) problems of asymmetric information, where healthy young people self-select out of the health
care system, driving up the cost of health care per person; (2)
problems with equity—should we not provide health care for
the uninsured or for those with insufficient incomes?; and (3)
the problem of technology and costs, whereby expensive technologies are highly income elastic, making “standard” health
care less affordable for those who have lower incomes. Consideration of these three problems typically causes people to
consider some sort of public policy response, like the Health
Care and Education Reconciliation Act of 2010. In short,
there are many answers to this question. Our best minds will
work on these issues for years to come.
CHAPTER 19
International Trade
CHAPTER OVERVIEW
This chapter covers the real side of international trade;
exchange rates are in the next chapter. The intuition you
built up in previous chapters about intertemporal budget
constraints— covering the permanent-income hypothesis and
perhaps the government budget constraint—pays off again
when you talk about the trade deficit and its possible link to
the budget deficit. Chad also discusses the cost of labor market churn.
If you just want to cover the intertemporal issues, you
could omit the middle of the chapter: Sections 19.5 through
19.7. Those sections cover static two-country production
and the costs of globalization and are over one-third of the
chapter.
Alternatively, if you like to get vigorous classroom debate
going, few things work as well as telling students that Greg
Mankiw was pretty much right when he said that outsourcing is just another way to reap the benefits of comparative
advantage. If you want to focus on the static trade issues, then
omit Sections 19.4 and 19.8, two large sections.
There’s a strong case for covering this material if your
department doesn’t require economics majors to take an
international trade course; in that case, this will likely be their
only relatively sophisticated exposure to a crucial policy area.
home to roost, apparently), and trade still looks like a good
idea prima facie. Your students probably don’t know these
facts, and they are impor tant.
19.3 A Basic Reason for Trade
Begin with Principles-level verbal coverage of the gains
from specialization and exchange: since your students have
probably forgotten this simple story, it’s definitely worth five
minutes to run through the numbers. Chad’s examples focus
on a theme that comes back in the next section on intertemporal trade: that a nation’s endowment may not be its preferred consumption bundle. Through simple exchange
(without production), societies can get a better mix of consumer goods.
There’s a broader principle here, one that comes up in the
LeBron James anecdote: most people and most countries are
especially skilled at producing many different things, but we
often like purchasing much the same things. In other words,
individuals and countries may be more different on the production side than on the consumption side. That’s a reason
for specialization and exchange.
19.4 Trade across Time
19.1 and 19.2 Introduction and Some Basic Facts
about Trade
The first two sections contain no surprises. The United States
isn’t that integrated into the world economy by European
standards; trade deficits have been with the United States for
a while now (the long-forecasted chickens have not yet come
Relying mostly on intuition and an illustrative example, Chad
shows that the present discounted value of the trade balance
must equal zero. That means that the trade deficits the United
States is running today must be repaid someday through trade
surpluses: the Chinese and Japanese aren’t taking our dollar
bills because they like the engravings of Washington and
Jefferson.
151
152 | Chapter 19
19.5 Trade with Production
This is a simple North-South economy, used to illustrate that
absolute advantage doesn’t eliminate gains from trade. Again,
this is a relatively routine example, the kind that many students worked through in Principles and then promptly forgot.
Paul Samuelson famously noted that comparative advantage
was one of the few ideas in economics that was both important and not obvious.
One way to enliven this arithmetic-heavy discussion is
to make students come up with examples of absolute versus
comparative advantage, both in their personal lives and in the
realm of international trade.
tion in the data between the two deficits, and that mild correlation is enough to dampen swings in investment. So, when
the U.S. government begins to “crowd out” domestic investment, foreigners often take a good look at those U.S. investment opportunities.
(Aside: In recent years, the Chinese government has been
famous for buying up U.S. Treasury bonds—so, one way to
tell this story to your students would be that when the United
States runs a deficit, foreign businesses and governments
choose to invest in safe U.S. treasuries, leaving the privatesector investment opportunities to U.S. savers.)
19.9 Conclusion
19.6 Trade in Inputs
Here you get to cover something new: migration and capital
flows. It’s the same Principles-style story as before, but Chad
slowly walks you through the welfare benefits of migration—a net positive if compensation or interpersonal welfare
comparisons are possible. Chad ties this back into Chapter 4’s
idea that most productivity differences across countries are
due to TFP, not capital. A case study below expands on this
topic.
19.7 The Costs of Trade
Chad’s case study on outsourcing is quite detailed, and any
class discussion on this topic is likely to arouse strong views.
Some questions you might discuss include the following.
Chad starts the chapter by noting that free trade is like a
machine for turning corn into automobiles. If such a machine
actually existed, would the government be obligated to
replace the jobs of the automobile workers?
In other words, is losing a job to a foreigner ethically (or
politically) different from losing a job to a machine? Or losing a job because your boss ran things poorly? Or losing a
job because your company’s product isn’t popular?
19.8 The Trade Deficit and Foreign Debt
Here we get the promised second look at the savings equation, and we find out that foreigners are apparently financing
a lot of U.S. investment. They are helping us build up our
capital stock, which raises the wages of U.S. workers.
Chad looks at the data on the twin deficits in Figure 19.5.
The simple story would predict that when the budget deficit
gets bigger, foreigners step in to meet the United States’
“required” level of investment. This story appears to broadly
fit the facts in Chad’s view. There is a mild positive correla-
You’ve taught the students so that they now have more formal knowledge than almost any politician on the topic of
international trade and foreign debt.
SAMPLE LECTURE: ARE TRADE DEFICITS BAD?
Are trade deficits bad? Compared to a hypothetical world
where the United States got to keep these Japanese and Chinese goods and never had to pay for them, yes—of course,
having to repay a debt is always an undesirable thing. But is
having this debt worse for the United States than living in a
world where trade is always balanced? This puts us in the
world of “that depends.”
And what “depends” is no great economic mystery: it
depends on the same things that would matter to any of us
when deciding whether to borrow a lot of money today. Will
today’s debt help me be more productive in the future?
Will today’s debt help me smooth out a temporary drop in my
income? Will today’s debt help me consume now, when I’m
poor, and do I have good reasons to believe that I’ll be very
rich in the future, so that it’ll be easy to repay? If any of these
answers is a solid “yes,” then (omitting the math) borrowing
could easily make sense.
But if you’re borrowing to throw a party for your friends,
that’s probably a bad idea. In general, consumers in the United
States appear to behave relatively rationally when it comes
to saving for retirement—the majority of Americans are saving enough—so it doesn’t look as though Americans on the
whole are making big mistakes when it comes to watching
out for the long run.
A January 27, 2007, New York Times article by Damon
Darlin, “A Contrarian View: Save Less and Still Retire with
Enough,” is an accessible literature review on the topic. Darlin interviews some economists who find that savings rates
are high enough—if anything, they may be too high for many
people. The most widely discussed paper on the topic is
Scholz et al., in the August 2006 Journal of Political Econ-
International Trade | 153
A strange thing happened in the Fall 2004 issue of the Journal of Economic Perspectives. Bhagwati, Panagariya, and
Srinivasan wrote a pro-outsourcing article that Chad cites.2
But one of the great supporters of the law of comparative
advantage, Nobel laureate Paul Samuelson, wrote a paper that
was widely interpreted as being antioutsourcing. This came
as a shock to many people. What did Samuelson argue? Did
he recant his past faith in free trade?
Samuelson noted that the gains from trade are larger when
countries are more different. Think of the simple productionand-exchange story we teach in Principles: if North and
South both have straight production functions as denoted in
the graph immediately below, there are clear gains from
trade. South is quite likely to specialize in apples and to trade
with North to get some bananas. Any price with a slope
between the slopes of North or South will yield a win-win
situation.
But now suppose that South has technological progress that
makes it better at producing bananas. For example, it might
send students to North to study how North produces so many
more bananas than South. As a result of this investment in
technology, South’s production possibilities for bananas
expand— and just to keep things simple, let’s assume that
South becomes a poorer carbon copy of North.
Now that there’s been technological progress in the poor
country, what has happened to the gains from trade? Shock1. John Karl Scholz, Ananth Seshadri, and Surachai Khitatrakun, “Are
Americans Saving ‘Optimally’ for Retirement?” Journal of Political
Economy 114 (2006): 607–43.
2. Jagdish Bhagwati, Arvind Panagariya, and T. N. Srinivasan, “The
Muddles over Outsourcing,” Journal of Economic Perspectives 18 (Fall
2004): 93–114.
Production Possibilities
Frontiers with large
gains from trade
Apples
EXTENDED CASE STUDY: PAUL SAMUELSON
AND THE “MUDDLE OVER OUTSOURCING”
ingly, the gains have completely vanished! Global output is
clearly going to be higher than before, but North is just as
clearly worse off than before. Free trade was great for North
when South was “diverse,” but now that South is just a poor
imitation of North, South reaps all the gains from its technological improvement.
So, if “globalization” is largely about Western ways of
doing business spreading like wildfire around the world, then
even though this will increase global gross domestic product
(GDP), it may mean that the rich countries will lose some of
the gains from trade. Samuelson’s story makes it clear that
diversity is key to reaping the gains from trade.
North
South
Bananas
Production Possibilities
Frontiers with no
gains from trade
Apples
omy, “Are Americans Saving ‘Optimally’ for Retirement?”1
They compare actual U.S. data to a life-cycle model of how
people should behave, and find that most (although not all)
Americans appear to be doing fine.
Here is the key to their results: official U.S. savings rates
omit capital gains— but capital gains in home prices and
stock prices form a key part of many people’s wealth. People
quite wisely count the value of their home as a part of their
balance sheet. This goes back to a theme raised in this manual back in Chapter 2 that capital gains are indeed income in
many respects.
So, if Americans are making reasonable choices about C
versus I, then perhaps they’re making reasonable choices
about the proper sign of NX. It’s not proof, but it should probably raise our confidence in the savings choices of Americans, whether talking about private saving or foreign saving.
North
South
Bananas
CASE STUDY: LUTZ HENDRICKS AND
IMMIGRANT PRODUCTIVITY
Back in Chapter 4, we saw that most differences in living
standards are due not to differences in the size of the capital
stock but to differences in productivity— often known as
“total factor productivity,” or TFP. This implies that (as long
as TFP is country specific, not worker specific) the free flow
of workers from low-TFP countries to high-TFP countries
154 | Chapter 19
will raise wages by much more than the free flow of capital.
Getting workers to the high-TFP places is more useful than
getting capital to the low-TFP workers.
Lutz Hendricks’s 2002 American Economic Review piece,
“How Impor tant Is Human Capital for Development? Evidence from Immigrant Earnings,”3 does a careful job documenting this fact. He starts by pointing out something that
seems obvious upon reflection: workers from poor countries
who come to the United States earn vastly more than they
could back home. He also shows that immigrants coming
from the richest countries do indeed tend to earn more than
immigrants coming from poorer countries— but the wage
differences are about 50 percent.
So, what immigrants “bring with them” to the United
States doesn’t seem to matter much when it comes to determining how much they can earn in the United States. What
makes poor immigrants so vastly unproductive in their home
countries is something located back in the home countries,
not something located inside the immigrants themselves.
That’s the key reason why immigration increases global GDP.
5. The deficit and the United States’ debtor status would be
problems if Americans behaved recklessly in accumulating
this debt. There are good and bad reasons for accumulating
any debt, and in many real-world, personal examples, borrowing money can be the best (or the same thing, the “least
bad”) solution. Since Americans seem to be prudent savers
on average, it’s reasonable to believe that the United States is
being prudent in accumulating this debt.
EXERCISES
1. Most fast-growing countries run trade deficits to pay for
their investment, but China isn’t doing that. For some reason,
the people and government of China have massively high savings rates and choose to invest some of their savings overseas.
High savings rates are a feature of all East Asian economies.
2. (a)
REVIEW QUESTIONS
1. This is an essay question; it is students’ choice.
2. When a person buys more than he or she earns in income,
he or she must borrow (or sell assets) to pay for those purchases. This is what a nation does when it runs a trade deficit.
Domestic citizens may literally pay for goods with currency
that is held overseas unused, but more likely foreigners just
use their U.S. dollars to invest in U.S. assets.
3. Most countries trade for the same reason that individuals
trade: because they are “best” at just a few things, but want
to consume many things. Even a big country like the United
States, which could make everything itself, finds that it’s
more efficient to specialize in a few things and trade for the
rest. The benefits of trade are more diverse products as well
as lower-cost products. The costs are the dislocated workers,
plus the fact that voters appear to intrinsically dislike receiving products from foreigners.
4. Yes, unless they have identical slopes to their production
functions (very unlikely). They trade because the gains from
trade are based on each country’s relative strengths, not its
absolute strengths. Even if LeBron James were the best lawnmower in the world, one hour spent mowing his own lawn
cannot be a good use of his time—he could make one more
commercial and earn enough money to pay an army of
workers to mow his lawn every day for the rest of his life.
3. Lutz Hendrick, “How Impor tant Is Human Capital for Development?
Evidence from Immigrant Earnings,” American Economic Review 92
(March 2002): 198–219.
(b) China has experienced more or less sustained growth
in its external balance since the 1980s. Germany’s external
balance has grown on a long-run trend since the 1980s, and
we can see that China’s external balance is more marked by
cyclical fluctuations than Germany’s external balance.
3. After the devastation of World War II, much of western
Europe was poor, but it was likely to recover quickly. Thus,
Americans were glad to export consumer goods as well as
machines and equipment to Europe on credit, sure that
they would be repaid soon.
Of course, the U.S. government also rebuilt much of western Europe through relief aid (note, however, that the Marshall Plan only started in 1947, and only really started
spending money in 1948), which also counted as exports. So,
both private and public institutions shipped exports to Europe
in the early postwar years. When net exports are positive,
you’re running a trade surplus. Recall:
Y = C + I + G + EX − IM
I = Private savings + Public savings + Foreign savings.
International Trade | 155
In the language of the first equation, the postwar world
was one where EX > IM. In the language of the second equation, we’d say that much of the “private savings” in the
United States was used to finance the trade surplus—in
other words, holding private savings (roughly) constant,
investment purchases and foreign savings fell by (roughly)
equal amounts.
How could investment purchases fall if the United States
exported machines and equipment to Europe? Let’s go
back to the definition of investment purchases: “I” is purchases of capital equipment for use within the United States,
regardless of where the capital equipment is manufactured.
Therefore, if Boeing, a U.S. company, buys a wrench made
in China, it shows up as “I” in the U.S. national income
identity. But if Lufthansa, a German airline, buys a Boeing
plane, that doesn’t show up as “I” in the U.S. national income
identity. It shows up as EX.
In the second equation, a simple story runs like this: U.S.
savers financed the trade surplus by shipping U.S.-made
investment goods overseas. “I” fell, but “EX” rose. That gave
us a big trade surplus.
There are many stories one can tell of the postwar recovery using these two identities, so clearly there’s more than
one way to answer this question correctly.
4. This is a worked exercise. Please see the text for the
solution.
5. The key assumption is that people spend half their
incomes on apples and half on computers.
(a) Autarky
Wage, w
Price of computer, p
Consumption of apples
(per person)
Consumption of
computers (per person)
Fraction producing
apples
Fraction producing
computers
Total production of
apples
Total production of
computers
North
South
160 apples
8 apples
80 apples
100 apples
50 apples
50 apples
10 computers
1 computer
50%
50%
50%
50%
8,000 apples
20,000 apples
1,000 computers
400 computers
Only the left column changes. The key here is figuring out
the new price of computers. Price of computer = slope of the
production possibilities frontier = 160 apples/20 computers
= 8 apples per computer.
(b) Trade
North
Fraction
producing
apples
Fraction
producing
computers
Total production
of apples
Total production
of computers
Wage, w
Price of
computers, p
Consumption
of apples
(per person)
Consumption
of computers
(per person)
South
0%
100%
100%
0%
0 apples
40,000 apples
2,000 computers
0 computers
400 apples
(40K/100 people)
20 apples (that’s
40K/2K)
200 apples
100 apples
(40K/400 people)
20 apples (that’s
40K/2K)
50 apples
10 computers
2.5 computers
(c) Both countries get more computers compared to the lowcomputer-productivity world seen in Table 19.4. Both countries benefit from the improvement in technology.
6. (a) Autarky
Wage, w
Price of computers, p
Consumption of
apples (per person)
Consumption of
computers
(per person)
Fraction producing
apples
Fraction producing
computers
Total production of
apples
Total production of
computers
North
South
160 apples
10 apples
80 apples
160 apples
80 apples
80 apples
8 computers
1 computer
50%
50%
50%
50%
8,000 apples
32,000 apples
800 computers
400 computers
156 | Chapter 19
(b) Trade
North
Fraction producing
apples
Fraction producing
computers
Total production of
apples
Total production of
computers
Wage, w
Price of computers, p
Consumption of apples
(per person)
Consumption of
computers
(per person)
South
0%
100%
100%
0%
0 apples
64,000 apples
1,600
computers
640 apples
40 (that’s
64K/1.6K)
320 apples
0 computers
160 apples
40 (that’s
64K/1.6K)
80 apples
8 computers
2 computers
(c) Now, the rise in apple productivity means that workers in
North and South both get more apples. Probably the most
surprising thing is seeing the price of computers skyrocket—
but that’s only natural.
After all, whenever you’re getting relatively better at one
thing, that means you’re getting relatively worse at something else. Every time a quarterback gets better at throwing
long passes relative to short passes, that’s the same as saying he’s getting relatively worse at throwing short passes—
compared to long ones.
This is sometimes known as the Baumol effect, and it
helps explain, for example, why medical innovation can
make doctor visits more expensive. When doctors get relatively more productive at inventing new drugs, it means
they’re getting relatively less productive at meeting with
patients. The opportunity cost of making computers is very
high in our model economy, as is the opportunity cost of
having a doctor meeting patients rather than sitting in a lab
testing new drugs.
More broadly, the Baumol effect explains why many services have become more expensive in recent decades in the
rich countries. It’s because the other major sector, manufacturing, has become so much more productive. Services in
the U.S. economy are like computers in this economy: they
only became relatively more expensive.
7. This Samuelson article is discussed in a case study for this
chapter and is illustrated with Principles-level production
possibility frontiers.
(a) No, North loses its comparative advantage. There will
be no reason for it to trade, since in both countries, the price
of a computer is ten apples.
(b) This means that North gets no gains from trade. It’s the
same as if North was back in the world of autarky.
(c) If the world were really like this—where all countries
have the same opportunity costs in production (and a few
other omitted assumptions hold true)—then there would be
no reason for free trade.
But the overall case for free trade is undiminished by this
example: North is now no worse than under autarky. South
is vastly better off because it can consume more computers
(five computers per person, if you work it out).
So, if free trade does eventually make us all more alike,
then we may stop trading with each other. But it’s worth noting that most of the United States’ top-ten trading partners in
recent years are relatively prosperous countries that outwardly
look quite a bit like us: France, Italy, Canada, the United
Kingdom, Germany, South Korea, Taiwan, and Japan. Only
China and Mexico fall into the informal “much less productive” category. So even if globalization makes us outwardly
similar in the way we dress, the food we eat, and where we
travel, it would be surprising if all our countries also became
equally productive at everything. Diversity in productivity
seems to stay with us, even if we all eat at McDonald’s.
8. (a) Autarky
Wage, w
Price of computers, p
Consumption of apples (per person)
Consumption of computers
(per person)
Fraction producing apples
Fraction producing computers
Total production of apples
Total production of computers
North
South
xn
xn /zn
xn /2
zn /2
xs
xs /zs
xs /2
zs /2
50%
50%
L nxn /2
L nzn /2
50%
50%
L sxs /2
L sxs /2
(b) Trade
To keep it simple, we’ll assume that North is relatively
more productive at making computers. Chad discusses the
other possibilities in 7(c).
North
Fraction producing apples
Fraction producing
computers
Total production of apples
Total production of
computers
Wage, w
Price of computers, p
Consumption of apples
(per person)
Consumption of computers
(per person)
South
0%
100%
100%
0%
0
L nz n
L s xs
0
L sxs /L n
L sxs /(L nzn)
L sxs /(2L n)
xs
L sxs /(L nzn)
xs /2
zn /2
L nzn /(2L s)
(c) This must be a story about opportunity cost—because
that’s what most important trade stories are ultimately about.
Let’s first look at the outer parts of the inequality: xs/zs > xn/zn.
That’s saying that the relative price of making computers in
the North must be lower than in the South (recall that x/z is the
International Trade | 157
price, in apples, of one computer). When that price is low in
the North, North is likely to stick to making computers.
But will each country completely specialize in apples
and computers, respectively? For this to happen, North must
meet all of its own computer needs, as well as South’s computer needs. And South must meet both North and South’s
apple needs as well. One way to check this would be to ask,
“Can South produce at least as many apples as North could
have on its own? And can North produce at least as many
computers as South could have on its own?” This is a question about the actual production of the economies— the
number of computers and apples, not just their relative cost.
Here’s the mathematical way to ask these two questions:
L sxs > L n x n
L sz s < L nz n .
A few moments looking at the inequality in 7(c) should
convince you that those two formulae are already embedded within 7(c).
9. The question asks us to compare Table 19.4 against
Table 19.5. We’re considering a simple case where everyone
migrates to North. If South workers migrate to North, then
global production massively increases, but the original
North workers are worse off than under free trade— they
get the same 80 apples/8 computers consumption bundle
they had under autarky.
One way to fix this would be to charge a tax of 30 apples
per South immigrant. Thus, every four immigrants would
pay 120 apples, which would go to pay the North worker for
his or her 120 lost apples. This works because there are four
times as many South workers as North workers. South
workers will pay this because they get to consume the same
50 apples as they had under free trade (Table 19.4), but also
get 6 more computers.
10. This is an essay question; it is students’ choice.
CHAPTER 20
Exchange Rates and International Finance
CHAPTER OVERVIEW
Exchange rates in the long and short run, applying IS/MP and
AS/AD to a small open economy, the exchange rate trilemma,
and the Euro crisis—that’s the chapter.
Sections 20.1 through 20.4, on the basics of exchange rates
under flexible and sticky prices, are the only prerequisites for
the rest of the chapter— Chad has written it so that you can
pick and choose what you like after that. Further, aside from
the IS/MP and AS/AD section (20.5), there are no formal
models in these optional sections. The model-building from
earlier underlies everything, so you can build some structure
on the foundations you’ve laid during the semester.
20.1 and 20.2 Introduction and Exchange Rates
in the Long Run
The law of one price is the big story here—and Chad illustrates its strengths and weaknesses by referring to the Economist’s famous Big Mac Index. Chad’s discussion is so clear
that it’s disarming. Just stick with his notation and give a
couple of examples (selling U.S. wheat in the United States
versus in Brazil; selling Russian oil in Russia versus in
England, and so on).
If you emphasize that the law of one price only applies to
tradables—and that arbitrage is the reason the law holds—
then you’ve covered the key microeconomic idea. If you also
explain to students that the price level in each country is
determined by the money supply—and so reinforce the classical dichotomy—then you will have covered the main macroeconomic idea.
Actually, the oil example is quite useful— students can
stand to be reminded that global commodities are a clear
example where the law of one price holds. So, if students want
158
to enact policies to bring down the price of gasoline by
encouraging domestic conservation, they’ll have to make a
big enough dent in gasoline consumption to impact the global
market demand for oil— quite a large market. Cutting demand
for gas in Iowa isn’t going to cut gas prices in Iowa one cent.
20.3 Exchange Rates in the Short Run
The key point in this section is so impor tant that Chad does
something quite rare—he sets it out in an italicized block
quote: When domestic interest rates rise, the exchange rate
rises (the domestic currency appreciates). Chad spends a
while explaining how changes in nominal rates impact
exchange rates. His story is about global bond traders. When
they see that country X has raised its domestic interest rate,
they want to buy bonds denominated in country X’s currency.
That raises the demand for country X’s currency, pushing up
its price—which we call the exchange rate. This is a straightforward, traditional story, again rooted in arbitrage, as is so
much of finance.
Add sticky inflation to that, and you’ve got a complete
open-economy monetary policy mechanism. That mechanism is the key to understanding how central bank policy
impacts net exports, something Chad gets to in Section 20.5.
20.4 Fixed Exchange Rates
Some small countries don’t want their exchange rates moving around—so, what do they do? Well, the “exchange rate”
is just a ratio of the prices of two currencies—so a small
country must just pick one big country with which it wants a
stable exchange rate (of course, small countries can pick a
“basket” of big country currencies, but that’s too much detail).
Exchange Rates and International Finance | 159
Then, they pick an exchange rate that they think is the longrun exchange rate, get a big pile of big-country currency, and
tell the world they are going to exchange their small-country
currency against the big- country currency at the fixed
exchange rate.
What happens afterward? Chad sums it up by stating that
the small country must follow the monetary policy of the big
country: if the big country raises rates, the small country
must do the same. That’s because when the big country raises
rates, there will be increased world demand for that currency.
The small country must make sure that its own currency is
just as relatively popu lar, other wise the small- country
exchange rate will fall. So, the small country raises rates
along with the big country, and both simultaneously increase
their “popularity” with global bond traders. The exchange
rate stays intact.
Of course, as I noted above, one prerequisite for all of this
is that the small country first must hold a big pile of bigcountry currency— and be willing to exchange it. If the
country runs out of big-country currency, there’s a foreign
exchange crisis, something Chad discusses later and that is
covered later in a case study.
20.5 The Open Economy in the Short-Run Model
When foreigners find that your goods are cheap, they buy
more of them. When domestic consumers (or firms) find that
foreign goods are expensive, they buy less of them. This
means that a fall in the exchange rate will increase exports
(their foreign money buys more of your stuff) and decrease
imports (since your domestic money doesn’t go as far
overseas).
Since a simple interest rate channel explains exchange
rates, Chad quickly puts the exchange rate story (and a global
interest rate story) into the background and focuses on domestic interest rates. We’re back to the normal IS curve much
faster than you’d expect. You might want to emphasize to
your students that small open economies are surprisingly
similar to large closed ones: if you emphasize that their earlier IS/MP intuitions transfer over to small globalized countries, they’ll be quite appreciative.
20.6 and 20.7 Exchange Rate Regimes
and the Policy Trilemma
In a case study, Chad argues that even though strong currencies are associated with strong economic per for mance,
the causality probably runs from per for mance to currency
strength, not the other way around. Since students never know
what to think about exchange rates, it’s a point worth making.
At the same time, it’s worth emphasizing that the root
causes of exchange rate movements are one of the most hotly
debated issues in macroeconomics, with many believing that
exchange rates follow an unforecastable random walk. Of
course, the classical dichotomy explains much in the long
run, but the money growth/currency depreciation relationship
is still quite a bit weaker than the money growth/inflation
relationship. In a nontechnical National Bureau of Economic
Research (NBER) Reporter piece available at http://www
.nber.org /reporter/fall06/engel.html, Charles Engel, of the
University of Wisconsin, widely published on the topic, sums
up his views as well as the consensus view on exchange rate
movements.
While the root causes of exchange rate movements may be
controversial, the lessons of the policy trilemma have stayed
with the profession and gained near-canonical status. It seems
that you can’t simultaneously have an independent monetary
policy, a stable exchange rate, and free (financial) capital
flows. Two out of three is it. Chad’s Figure 20.7 tells the story.
The big policy debates in international macroeconomics
tend to focus on which fork of the trilemma should be given
up, although there’s a parallel debate over whether a country
can get most of all three: a fairly stable exchange rate, fairly
free financial flows, and a fair degree of monetary policy
autonomy. Indeed, the foreign exchange crises of recent years
tended to occur in countries that were trying to do some version of that. This more flexible policy often goes by the name
of “soft peg” or “dirty float” and is said to be driven by a “fear
of floating.” Stanley Fischer, former chief economist at the
World Bank and a key figure in early New Keynesian
research, discussed the benefits of such policies in a 2001
Journal of Economic Perspectives piece, “Exchange Rate
Regimes: Is the Bipolar View Correct?”1
Chad discusses the trilemma informally and with recent
historical illustrations—at this point in the semester, most of
your students should have enough macroeconomic intuition
for this to proceed smoothly.
20.8 The Euro Crisis
The Euro crisis is characterized as a new phase of the global
financial crisis. This section gives students a nice overview
of factors leading up to the financial crisis in Europe and the
short-term and long-term dimensions of the crisis.
Chad introduces students to “sovereign [government]
debt”—sovereign in the sense that no superior exists to settle
accounts in case of default. The growth in sovereign debt
across Europe, especially southern Europe, is attributed, in
part, to the creation of the eurozone. With the creation of the
eurozone, real interest rates fell for southern Europe. The fall
in real interest rates and relaxed lending standards led to the
expansion of debt, as evidenced by the increase in domestic
1. Stanley Fischer, “Exchange Rate Regimes: Is the Bipolar View Correct?” Journal of Economic Perspectives 15 (Spring 2001): 3–24.
160 | Chapter 20
banking lending and rising sovereign-debt-to-gross-domesticproduct (GDP) ratios. The financial crisis exposed European
domestic banks to insolvency. Local European governments
further increased sovereign debt, in part, to prevent a collapse
of domestic banks, resulting in high sovereign-debt-to-GDP
ratios.
The increase in debt gives rise to two concerns. First, the
near-term concerns are about stabilizing the financial sector.
The rising debt-to-GDP ratios expose European countries to
insolvency as real interest rates increase. As Chad describes
in the chapter, if the debt-to-GDP ratio is 100 percent, and real
interest rates rise from 1 percent to 10 percent, can a country
afford to spend 10 percent of its GDP on debt? Given the high
debt exposures, the financial crisis becomes self-fulfilling. If
the perception of risk is increasing, real interest rates increase,
and the ability of debtor countries to ser vice their debts
diminishes. To address the near-term concerns, the likelihood
of default must be decreased (through direct and indirect
intervention of the European Central Bank). Second, the longterm issues deal with the relative competitiveness of southern
and northern Europe. Chad explains that unit labor costs are
much higher in the south than in the north. The relatively high
wages contribute to high production cost and slow growth.
Before the creation of the euro, currency devaluations in the
south could have corrected this imbalance. With a unified
currency (holding relative total factor productivities constant),
the solution is either to increase wages in northern Europe or
to reduce wages in southern Europe.
SAMPLE LECTURE: EXPLAINING
CURRENCY CRISES
There’s a common theme running through Chad’s discussion
of the currency crises in Mexico, several nations in Asia, and
Argentina. The links run from fiscal crises through dollardenominated debt right up to the government’s store of hard
currency.
In all three cases, there were some reasons for strongly
doubting the fiscal stability of the economies in crisis. In
Mexico, it was assassinations; in Asia, banking sectors with
blurry government solvency promises; and in Argentina, an
outright government default.
In all three cases, private and public agencies had large
amounts of debt payable in U.S. dollars. That meant that if
there ever was a depreciation, then the economies would find
it even more difficult to repay their debt—after all, a depreciated currency can’t buy as many dollars. Ordinarily, depreciation is a way to boost aggregate demand—by making the
economy’s exports more attractive to foreigners. But in these
three cases, what depreciation giveth through higher exports
it taketh away with higher nominal debt repayments.
Finally, in all three cases, the only way that these governments could credibly promise to keep their exchange rates
fixed at their old levels was to have enormous amounts of U.S.
dollars on hand. But once investors foresaw that fiscal problems might be an issue, and that if depreciation occurred it
could create a massive multiplier effect, making the economy’s problems even larger, there was a rush to the exits: investors cashed out their Mexican pesos, Thai baht, and Argentine
pesos as quickly as possible. The countries ran out of dollars (or
other hard currencies) and did the only thing they could then
do: float.
The punishment that these countries suffered was far worse
than any economic “crime” they had committed—none had
the kinds of massive budget deficits or irresponsible fiscal policies seen in, say, hyperinflation-era Germany. But such is the
nature of macroeconomics: multiplier effects are everywhere.
Since Paul Krugman created our modern models of financial crises, his speech to Credit Suisse officials given in the
wake of the Asian financial crisis (available at http://web.mit
.edu / krugman /www/suisse.html) is well worth reading. He
uses the basic metaphor of a “run on a basically sound bank”
very effectively in this and other popular writings.
EXPANDED CASE STUDY: THE EURO
AND HYPERINFLATION
Remember the government’s three ways of raising funds each
period: taxes, borrowing, and printing money. Before the euro
existed, each country in Europe had all three options. Now
that the euro exists, the third option is gone. That means that
European governments now are like United States state governments. If they get in fiscal trouble, they can’t just print
money to cover their debts. These eighteen governments gave
up a powerful tool when they handed over monetary authority to the European Central Bank.
Of course, one can imagine situations where the European
Central Bank would print large amounts of money—if most
of the big countries in Europe demanded it, for example. But
clearly, the chances of hyperinflation—which is always and
everywhere a fiscal phenomenon, according to Thomas
Sargent—are lower than ever thanks to the independence of
the European Central Bank. Greece’s recent financial problems are a case in point.
REVIEW QUESTIONS
1. The nominal exchange rate tells me how many units of
one currency can be exchanged for another foreign currency.
The real exchange rate tells me how much I could buy if I
were to take one unit of one country’s currency, convert it to
a foreign currency, and then try to actually buy goods and
services in that country. The real exchange rate adjusts the
nominal exchange rate to take into account that some things
(rent, restaurant meals, and health care) are more expensive
in some countries, and it shows how many units of one
country’s goods must be given up to purchase those same
goods in another country.
Exchange Rates and International Finance | 161
7. The level of the nominal exchange rate by itself can’t
matter—that’s just the classical dichotomy. Chad’s case study
discusses this in detail.
2. U.S. inflation was higher than Japa nese inflation from
1970 to 1995. That’s reason enough for the U.S. dollar to
depreciate against the yen. Since then, inflation has been
quite low in the United States.
3. In principle as well as in practice, for tradable goods like oil
the power of arbitrage is very strong. People try to buy low and
sell high everywhere in the global economy, and by doing so,
entrepreneurs push prices up in “cheap” places and push them
down in expensive ones. For other goods, like the Big Mac
example in the textbook, some of the inputs used in making
the good, such as domestic real estate and local service labor,
are not easily tradable, and therefore we expect the price of
these goods, like the Big Mac, to vary across markets.
4. When interest rates are high in a given country, global
investors want to save money in that country’s bank
accounts. To do so, they need that country’s currency—so
they bid up the price of that currency. That makes the country’s exchange rate appreciate. Therefore, interest rates and
exchange rates tend to move in similar directions.
5. Both net exports and investment are inversely related to
higher interest rates, but for different reasons. An increase in the
home country’s interest rates raises its exchange rate and makes
the currency more expensive. That makes it more expensive for
foreigners to buy home country goods, so it hurts exports.
A rise in the interest rate just raises the cost of business borrowing, which hurts investment directly. The NX channel in
an open economy makes the IS curve flatter. A rise in rates
hurts short-run output through two channels, not just one.
United States
Norway
Euro Area
Japan
Mexico
China
Russia
South Africa
India
EXERCISES
1. For a Big Mac to cost the same $4.93 in the euro area, the
euro must appreciate against the dollar by 23.25 percent. Given
the current exchange rate where 0.93 euros purchases $1, or
3.72 euros purchases $4.00, Big Macs are a better buy in the
euro area than in the United States. At the exchange rate where
0.75 euros purchase $1 (or 1 euro purchases $1.33), 3.72 euros
purchases $4.93. In all cases, the “law of one price” exchange
rate is calculated by dividing the local-domestic price of Big
Macs by the U. S. price of Big Macs. If Big Macs are locally
cheap relative to the United States, as in most of the cases
below, then the local currency should appreciate relative to the
dollar. In most countries, the currency needs to rise against the
dollar. We can tell this quickly by looking at the “Big Mac
price in dollars” column in Table 20.1. In every country (excluding Norway), the Big Mac costs less than the U.S. price.
2. Higher interest rates hurt both net exports and investment, but for different reasons. An increase in the home
country’s interest rates raises its exchange rate and makes the
currency more expensive. That makes it more expensive for
foreigners to buy home-country goods, so it hurts exports.
A rise in the interest rate just raises the cost of business borrowing, which hurts investment directly. The NX channel in
an open economy makes the IS curve flatter: a rise in rates
hurts short-run output through two channels, not just one.
6. A rise in the foreign real rate makes the home country
real rate relatively lower, bringing in borrowers from
around the world and pushing lenders away from the home
country. This weakens the home country’s currency, which
helps exporters. For the same reason that exporters like low
home-country interest rates, they like high foreign interest
rates: because, once again, it is relative prices that matter.
Country
8. A country can’t simulta neously have a fixed exchange
rate, free capital flows, and an independent monetary policy. It can only be on one side of the triangle because it can
only have two out of three.
3. (a) growth in exchange rate = growth rate in rest-ofworld prices − growth rate in home country prices
Big Mac
Price
(local
currency)
Exchange
rate per
dollar ($)
Big Mac
price in
dollars
Exchange
to
equalize
prices
% Change
in exchange
rate*
4.93
46.80
3.72
370.00
49.00
17.60
114.00
28.00
127.00
1.00
8.97
0.93
118.65
17.44
6.56
74.66
15.81
66.80
4.93
5.22
4.00
3.12
2.81
2.68
1.53
1.77
1.90
1.00
9.49
0.75
75.05
9.94
3.57
23.12
5.68
25.76
–5.51%
23.25%
58.09%
75.47%
83.75%
222.87%
178.37%
159.31%
Adjustment
Depreciate
Appreciate
Appreciate
Appreciate
Appreciate
Appreciate
Appreciate
Appreciate
*For example, the yen-dollar exchange rate that equalizes prices of Big Macs is 1/(4.93/370), and the appreciation in the Japanese yen is measured as:
[(1/75.05 − (1/118.65)] / (1/118.65) = 58.09%.
162 | Chapter 20
(b) The dollar should have depreciated by about 2.1 percent
per year against the yen.
(c) Actually, the dollar depreciated at a much higher rate—
closer to 5 percent per year. In 1975, a dollar used to buy 300
yen, and in 1995 it bought about 100 yen. The numbers do not
match up well to the prediction generated by equation 2.3.
(d) Given Figure 20.3, for the period of 1970 to 1995, the real
exchange rate for the yen has appreciated (the real exchange
rate for the dollar has depreciated). The appreciation of Japan’s
real exchange rate for a sustained period appears to violate the
“law of one price,” but as Chad points out in the “Case Study:
Long-Run Trends in Real Exchange Rates,” the real exchange
can grow because of the growth in price level of non-traded
goods, driven by wage increases in low productivity growth
sectors. The increase in the relative price of non-trade goods
increases the price level of domestically (traded and nontraded) produced goods and increase the real exchange rate.
4. (a) I expect that most students will look at the yuan/dollar
exchange rate, so here it is:
down the rate of inflation, and aggregate supply begins to
drop. As inflation falls, the Federal Reserve slowly cuts real
interest rates, which returns the economy back to steady
state at a new, lower inflation level.
Over the longer term, the European Central Bank will
eventually have to raise the interest rate back to the level of
the marginal product of capital—it can’t stimulate forever—
and so the United States’ AD curve will get a boost, eventually completing the cycle.
7. This creates a “spending leakage,” where part of any economic boost for domestic rate cuts or foreign rate increases
convinces Americans to import more goods from abroad.
(Yt/ −(Y)) − 1 = Ỹt = (Ct/ + It/ + Gt/ + NXt/ −(Y)) − 1
and by substituting in the expressions from Chapter 11, and
assuming Rw = , yields
Ỹt = (āc + āi + ā G + ā NX −1) − ( i +
NX
)(R ) − Ỹt.
The key is to notice that the Ỹ (short-run output) is on
both sides of the equation. That’s the only real change. Our
only goal now is to solve for Ỹ. This yields
Ỹt = [1/(1 + )][(āc + āi + ā G + ā NX −1) − ( i +
NX
)(R )].
It’s a normal IS curve, with the addition of the spending
leakage term. Now a change in the interest rate will have a
smaller impact on short-run output (as the multiplier is less
than one). That’s good news if you are a central banker trying to keep the economy stable.
(b) What is interesting is in the above diagram is how the
dollar has appreciated against the yuan over time, and how
the dollar has remained “high” against the yuan for almost
twenty-five years, despite the United States’ relatively large
trade deficit with China.
(c) The reason for the relatively high value of the dollar can
be attributed to China’s central bank holding the dollar
reserves, and Chinese purchases of U.S. real and financial
assets, especially U.S. Treasury bonds. China, by managing
a low exchange rate for its country, has kept the prices of its
goods relatively low in U.S. and world markets (as many
goods traded across borders are priced in dollars).
5. This is a worked exercise. Please see the text for solution.
6. This question is the opposite of the one posed by Figure 20.4. When the euro area cuts interest rates, this makes
the United States a more attractive place for global investors
to save their money. This raises demand for U.S. dollars,
raising the price of dollars. The dollar’s new, higher value
helps Americans who want to import goods from overseas
(IM rises) and hurts Americans who want to export their
now-more-expensive goods (EX falls). All told, this clearly
shifts aggregate demand (AD) to the left. The economy
returns to steady state because the leftward AD shift slows
8. When people want dollars in a financial crisis, they must
offer their foreign currency in exchange. That will bid up the
price of dollars and bid down the price of foreign currencies.
The dollar will appreciate. In AS/AD, this helps importers
but hurts exporters. The AD curve shifts left, and so, ironically, the U.S. economy gets hurt in the short run by people’s
desire to hold more dollars.
9. This is a worked exercise. Please see the text for solution.
10. The United States may be a big enough economy that it
can ignore the trilemma: other economies may just be too
small for their financial flows to create big shocks in the United
States.
Alternatively, it may be that the United States has run
good enough economic policy that the global financial traders haven’t felt the need to make a run on the dollar, since the
dollar is perceived as good as gold. Or it could just be luck.
11. In three years, South Korea was almost back. Mexico
was still not back; its peak was around 1981. Indonesia was
back within a year.
12. This is an essay question. Answers may vary.
CHAPTER 21
Parting Thoughts
21.1 What We’ve Learned
Chad summarizes what students have learned this semester.
This only presumes that you’ve covered Chapters 1–6
(Growth) and Chapters 8–14 (Inflation and Fluctuations). At
one point, he touches on the looming entitlement crisis of
Chapter 18, but that doesn’t interrupt his overall story: macroeconomics is still about growth, business cycles, and optimal government policy. If you’ve covered the bulk of those
chapters, you should assign this one.
He also emphasizes that there are still big, important questions to be answered—and his opening quote by prominent
physicist Brian Greene conveys the sense of wonder that macroeconomists often feel toward the aggregate economy. This
chapter gives you an excellent opportunity to spend a day—
perhaps even half a lecture—letting students know what you
think the key areas of future research are, what the major
puzzles are, and what you think are the most important ideas
for them to take away from the course.
Then, and only then, can students start asking you what’s
on the final.
21.2 Significant Remaining Questions
Chad introduced you and your students to most of the big
macroeconomic questions of the day, and he has given you a
rigorous and intuitive set of models for thinking about these
questions. In this concluding chapter Chad gives you some
more things to think about. Some of these issues flow directly
from the models developed in the text. Some, like rising
health care expenditures, have significant implications for
how the economy will evolve into the future. Going forward,
we will need a deeper understanding of some of the issues.
In Chapters 4–6, Chad describes the growth factors—such
as the total factor productivity coefficient, the depreciation
rate, and the savings rate—but a deeper understanding of the
factors that determine the growth factors is required. Ultimately, this discussion will get us into the role of institutions
and cultural values. In economic development courses, we
see, for example, that the transition from state socialism to
markets has not been the same for all countries— China and
Russia, for example, have had quite different experiences.
This raises the question, “What social institutions are best for
economic growth?” The question of what institutions best
promote growth will become increasingly relevant for the
United States. How does prolonged war affect the institutions
of economic growth and prosperity?
In Chapters 10–14, Chad examines short-run fluctuations in
actual output relative to a constantly moving potential output.
Knowing potential output is important in getting macroeconomic policy right. Economists will have to continue to identify the causes of GDP growth as determined by short-term
and long-term factors, to control inflation and unemployment.
Finally, as we are still learning lessons from the Great
Recession, we will continue to debate the role of deficits,
debt, rules, and discretion, income distribution and taxation,
regulation, and deregulation and reregulation. These are the
sort of topics that, as seasoned teachers, we recognize come
and go—where old ideas become new, but recast in new
terms. However, the future is not just about recasting the old
in new terms. We have seen significant changes in the world,
things that we would never have predicted. As teachers, we
send our students out into an uncertain world—a world that
poses both risks and opportunities. After completing this
course, we hope our students better understand the world, are
better able to cope with what the future brings, and are better prepared to shape the future.
163
164 | Chapter 21
SAMPLE LECTURE: NOBEL PRIZE WINNERS
IN MACROECONOMICS
Whose ideas did we cover this semester? This list doesn’t
cover all the macroeconomists who earned Nobel Prizes—
merely those whose ideas appeared in this text.
2013: Robert Shiller: awarded the prize for empirical analysis of asset pricing. Shiller is cited in Chapter 14 for
using price-to-earnings ratios to predict bubbles in
stock markets. His analysis has also been applied to
other markets, including the housing market.
2011: Thomas Sargent: recognized for the art of distinguishing cause and effect in the macroeconomy. Sargent is cited in Chapter 8 for the fiscal causes of high
inflation.
2008: Paul Krugman: awarded for analysis of trade patterns
and firm location, explaining what goods are produced
where. Krugman is cited for the policy trilemma in
open economies in Chapter 20.
2006: Edmund S. Phelps: awarded for the core of New
Keynesian models—the natural rate hypothesis;
explained education’s role in helping poor countries
adopt the ideas of rich countries.
2004: Finn Kydland and Edward Prescott: recognized for
their work on real business cycles and time
inconsistency— cited at length in Chapter 15 for their
contribution to real business cycle and DSGE models.
2001: George Akerlof and Joseph Stiglitz: Akerlof’s
“Market for Lemons” explains the impact of agency
1999:
1995:
1993:
1987:
1985:
1984:
1976:
1972:
1970:
problems on business investment. Stiglitz’s
imperfect-competition models help explain sticky
inflation and the market for ideas.
Robert Mundell: applied our IS model to small open
economies.
Robert Lucas: brought rational expectations into
business-cycle research—showed that sticky inflation must be due to surprises in monetary policy.
Douglass C. North: made economic institutions a
central focus of growth research.
Robert Solow: developed the Solow growth model.
Franco Modigliani: invented the life-cycle hypothesis of consumer spending.
Richard Stone: recognized for his role as a founder of
national income accounting.
Milton Friedman: awarded the prize for his work on
the permanent-income hypothesis, the natural rate of
unemployment, and monetary policy rules.
John Hicks and Kenneth Arrow: Hicks formulated
the IS/LM model. Arrow’s general equilibrium theories underlay Kydland and Prescott’s real-businesscycle theories.
Paul Samuelson: formalized an early Phillips curve;
created the earliest mathematical models of much of
modern economics in both macro and trade. His pedagogical style shaped all macroeconomics textbooks
from the 1940s onward—including this one.
(More information is available about the Nobel Prize winners
at http://nobelprize.org/nobel_prizes/economics/laureates/.)