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Macroeconomics Instructors Manual (Charles I. Jones)

Charles I. Jones
Anthony Laramie
Garett Jones
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W. W. Norton & Company has been independent since its founding in 1923, when William Warder Norton and Mary D.
Herter Norton first published lectures delivered at the People’s Institute, the adult education division of New York City’s Cooper Union. The firm soon expanded its program beyond the Institute, publishing books by celebrated academics from America and abroad. By midcentury, the two major pillars of Norton’s publishing program—trade books and college texts—were
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Part 1 Preliminaries
Chapter 1 | Introduction to Macroeconomics
Chapter 2 | Measuring the Macroeconomy
Part 2 The Long Run
Chapter 3 | An Overview of Long-Run Economic Growth
Chapter 4 | A Model of Production
Chapter 5 | The Solow Growth Model
Chapter 6 | Growth and Ideas
Chapter 7 | The Labor Market, Wages, and Unemployment
Chapter 8 | Inflation
Part 3 The Short Run
Chapter 9 | An Introduction to the Short Run
Chapter 10 | The Great Recession: A First Look
Chapter 11 | The IS Curve
Chapter 12 | Monetary Policy and the Phillips Curve
Chapter 13 | Stabilization Policy and the AS/AD Framework
Chapter 14 | The Great Recession and the Short-Run Model
Chapter 15 | DSGE Models: The Frontier of Business Cycle Research
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iv | Contents
Part 4
Applications and Microfoundations
Chapter 16 | Consumption
Chapter 17 | Investment
Chapter 18 | The Government and the Macroeconomy
Chapter 19 | International Trade
Chapter 20 | Exchange Rates and International Finance
Chapter 21 | Parting Thoughts
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Introduction to Macroeconomics
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.
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 is able to easily deduce a
short-run model from the long-run model, and therefore link
short-run and long-run economic analyses. By streamlining
the coverage while teaching surprisingly solid microfoundations, Chad’s text gives you a solid chance to spend more
time on intelligent, model-driven policy discussions about
growth and business cycles.
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
through 14 in a semester. How much time you spend on these
chapters, whether or not 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 third 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
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.
Chapters 1– 4 (Introduction through the basics of growth
and productivity), 8–11, and 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.
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
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2 | Chapter 1
1–8, 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.
Every chapter in this manual also has a sample lecture
that you can use, written on a topic that students typically
have a tough time with. Finally, each chapter of this manual
also contains a few case studies, often building on Chad’s
own case studies. In the case studies I provide some additional facts or theories that might help to flesh out a lecture or provoke classroom discussion. I hope you fi nd this
manual useful in getting the most out of Charles Jones’s
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)
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
through 6.3). That means that instructors can still teach the
economics of ideas (a largely math-free topic), yet avoid the
math of the Solow model.
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, I 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 GDP,
or what the Fisher equation really means.
Also, I sometimes recommend that you organize your
lecture differently than the text does—some topics just flow
together particularly well when you’re up there at the chalkboard. I always try to point out which topics you can safely
gloss over or omit, and I often mention an illustration or two
that might make your lectures a bit more relevant.
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Of great concern to the economics profession is the economic literacy of our students. In par ticular, do our students
really own an understanding of 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’s the economy? And 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’s 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? Microeconomics, the study of the individual parts of the economy,
and macroeconomics, the study of the economy as a whole
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Introduction to Macroeconomics | 3
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 U.S. 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 unemployment
rate rose from 4.6 percent in 2007 to 5.8 percent in 2008,
then to over 10 percent in 2009, and was 7.3 percent as of
October 2013 (almost two percentage points above the natural unemployment rate). 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 have been recorded; banks,
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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. auto makers 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, over $1.4 trillion in 2009, and almost $1.3 trillion in
2011. Moreover, despite bailouts and the stimulus, we have
seen the money supply (M2) grow by 8 percent in 2009, 2.5
in 2010, 7.3 in 2011, and 8.5 in 2012. The threat of worldwide
recession remains. Even as of this writing, the recovery is
slow and fragile, and the debate over austerity versus stimulus
continues to rage (see John Cassidy, “The Reinhart and Rogoff Controversy: A Summing Up,” The New Yorker, available
at http://www.newyorker.com/online/blogs/johncassidy/2013
This experience has taken the economics profession by surprise, and is currently causing us to reevaluate what we think
about how the economy works.
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
A generation ago, the business cycle section would’ve
been almost the whole course. Back then, many macroeconomists thought they could control the overall level of GDP
on a year-to-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 services
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
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4 | Chapter 1
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 on 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’ll have to 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 principle 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.
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
(The New Yorker, January 11, 2010), Lucas won the Nobel
Prize, in part, for reinventing the notion that markets are selfregulating. So Lucas’s answer is not surprising. Lucas noticed
that consumer spending—the part of our income 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 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 have
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to 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 per year to guarantee a steady
growth in your standard of living. Even when taking into
account that it’s 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 their 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; it’s 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 50 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.
1–3. Based on personal preference.
4. Ingredients: Inputs, the model itself, and outputs. We can
call these “exogenous variables,” “equations or words,” and
1. Laurence Ball and David Romer, “Real Rigidities and the Nonneutrality of Money,” Review of Economic Studies, vol. 57, no. 2, (April
1990), pp. 183–203.
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Introduction to Macroeconomics | 5
“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.
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.
wage. (Of course, you could just collapse this to equilibrium
labor supply and equilibrium wage without losing much of
(c) w* = ( − )/(1 + ā)
L* = ( − w*)
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:
Ethiopia: 1.6 percent
India: 8.4 percent
Mexico: 28.9 percent
Japan: 76 percent
(b) Botswana’s per capita growth rate between 1960 and
2010 was about 5.33 percent. China’s per capita growth rate
was somewhere between 4.62 percent and 6.02 percent
depending on which version of the data in the “snapshot”
file provided by Chad is used.
(c) Population, biggest to smallest: USA (310.2 million), Indonesia (243 million), Brazil (201.1 million), Bangladesh (156.1
million), Nigeria (152.2 million), Russia (139.4 million).
(d) Government purchases are larger in poor countries,
while investment expenditures are higher in rich countries.
(e) While 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
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 the
(d) If increases, the wage falls, and the equilibrium quantity of labor increases. This is just what we expect: The
supply of labor 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
(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 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
(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.
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Measuring the Macroeconomy
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 CobbDouglas 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
on covering 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
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 important 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, in par ticular, 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.
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Measuring the Macroeconomy | 7
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 services produced in an economy
over a certain period.” The words of this definition that can
be emphasized are “market value,” “final,” “produced,” and
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
By highlighting “final” I emphasize that one key to accurately measur ing GDP is to avoid double counting. I like
to use examples in which common sense conflicts with
Kuznets’ 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 ser vice 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 ser vices represent the largest category of consumer spending in the United
States, about two-thirds of total consumer spending. In
short, consumer services are almost half (around 47 percent)
of GDP.
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).
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It’s worth remembering that GDP is by and large an accounting measure, using accounting intuition.
Students are often confused by the rhetoric of macroeconomists. 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.
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:
• 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 have
to subtract that to make sure it doesn’t show up in our final
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
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8 | Chapter 2
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.
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.
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
Why bother with (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 valueadded 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
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
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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.
Of course, we have to 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 third 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 important 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 defi nition 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.
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Measuring the Macroeconomy | 9
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
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
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for practical 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 while 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 and how price indexes measure quality changes. Chad
provides coverage of the former later on 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 important questions
such as what causes the national budget deficit, and what
role the national budget deficit plays in affecting national
savings and gross savings.
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).
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10 | Chapter 2
Sales Tax
Cost of Inputs
+ Profit
Total Steel Sales
Sales Tax
Cost of Inputs
+ Profit
Total Truck Sales
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.
Foreign countries buy $50 worth of trucks for unknown
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.
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.
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.)
Value Added by SteelCo: Somehow, they get their raw ore
for free, so their value added is just:
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
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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.
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 that 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.
According to some economists—most prominently Robert
Hall1 of Stanford—the previous case study is completely
1. Robert E. Hall, “The Stock Market and Capital Accumulation,” American Economic Review, vol. 9, no. 5, (December 2001), pp. 1185–1202.
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Measuring the Macroeconomy | 11
wrong for an economically important reason. Hall shows
that 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), then
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
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 ser vices 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
There is a large 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
As we saw before, services are about one-quarter of U.S.
GDP. That means that much economic activity isn’t about
making things, it’s about interacting with other people.
There are two other ways of slicing up GDP that might be of
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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,” to 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 answered by persuasion. The
importance of persuasion was noted by the father of
economics himself. Adam Smith, in his Lectures on
Jurisprudence, noted, “Everyone is practicing oratory
on others thro the whole of his life” (cited in McCloskey
and Klamer).
Broadly, McCloskey and Klamer want to count up 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 up lawyers,
actors, and members of the clergy; they count up threequarters 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
1–4. These essentially summarize the entire chapter, so I
will refrain from answering them.
2. Donald McCloskey and Arjo Klamer, “One-Quarter of GDP Is Persuasion,” American Economic Review, vol. 85, no. 2, (May 1995), pp. 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).
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12 | Chapter 2
This isn’t exact, as Chad notes, but it’s good enough for our
purposes. This implies:
1. This is a worked exercise. Please see the text for the
2. (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
(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.
3. 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.)
Quantity of oranges
Quantity of
Price of oranges
Price of boomerangs
Nominal GDP
Real GDP in ‘16 prices
Real GDP in ‘17 prices
Real GDP in chained
prices, benchmarked
to 2017
Percent change
Here GDP growth only shows a tiny difference between the
various methods.
5. We’ll use Chad’s shortcut from Section 2.3.4:
growth in nominal GDP = growth in price level
(a.k.a. inflation) + growth in real GDP
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growth in nominal GDP − growth in real GDP
= inflation rate
All we need to do is add in our three definitions of “growth
in real GDP,” and we’ll have our three answers:
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
6. (a) Without taking relative price differences into account,
India’s economy is 11.9 percent of the size of the U.S. economy (78.9 trillion/45.7) / 14.5 trillion).
(b) Taking relative price differences into account, India’s
economy is 32.3 percent, or about one-third, the size of the
U.S. economy (11.9 percent/0.368).
(c) The numbers are different because many consumer
goods—food, haircuts, medical visits—are very cheap in
India when you are measur ing in U.S. dollars. This is usually true in poor countries. As we’ll see in Chapter 14, 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 while 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.
7. (a) 37.7 percent
(b) 30.3 percent
(c) The numbers are different because many goods are more
expensive in Japan than in the United States.
8. (a) If fewer people have homes, then the average person
must be worse off when it comes to homeownership—after
all, now people have to 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.
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Measuring the Macroeconomy | 13
This question illustrates a famous parable in economics,
the “fallacy of the broken window.”3 If a person breaks a shop
window, the shop owner has to 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 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 has to 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 have to
replace something. It would have been better for citizens if
the earthquake had not happened.
3. Henry Hazlitt, Economics in One Lesson, Chapters 1 and 2.
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An Overview of Long-Run Economic Growth
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
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
again 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), p.
253). When something wonderful that has never happened
before in human history begins to happen, not once, but again
and again 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. Brazil, China, Ethiopia, Japan, and the
United States receive par ticular attention, if you are looking
for countries to highlight with additional data or online
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
Finally, he 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.
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An Overview of Long-Run Economic Growth | 15
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.
Through the rest of Section 3.3.3 and all of Section 3.3.4,
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, whether
or not they were destroyed in World War II.
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 10-year growth rate they can’t just
take the total growth rate [e.g., (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 10 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 10 years, 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 pretty sanguine about the benefits of economic
growth, and emphasizes that in the views of most macroeconomists the world’s poor are in need of 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 Roadmap
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
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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
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16 | Chapter 3
students a nontechnical essay by Lucas entitled, “The Industrial Revolution: Past, Present, and Future,” available at
http:// www.minneapolisfed .org /publications _papers /pub
Suppose you have $100 in 2013 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:
y2014 = 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:
y2014 = y2013 + g × y2013.
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:
(y2014 − y2013)/y2013 = 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: height,
income, employment levels, crime levels.
You may want to emphasize how the growth rates that
come out of this calculation need to 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, and 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:
y2014 = y2013(1 + g).
With this version, we can easily ask what happens if this
grows at the same percentage rate, g, for many periods.
577-57346_ch01_5P.indd 16
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 y0:
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 again and again—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 10 years to double; it only takes 7.
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 14 years. But
how long does it take for living standards to be 8 times
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.
In Figure 3.7—a typical “convergence”-style graph—it
looks like the rich countries are growing faster than the poor
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An Overview of Long-Run Economic Growth | 17
countries, which implies a massive increase in long-term
global inequality. If present trends continue, the rich countries will tend to pull further and further away from the
poor countries—and the miracle of compounding really
will create unimaginable differences between rich and poor
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 decades.
Much of this was apparently caused by recent marketoriented economic reforms in China and India, 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 heavily when we look at the country
level, but it receives less weight when we look at the human
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.
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.
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.
While 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.
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
1. Peter Temin, “The Economy of the Early Roman Empire,” Journal of
Economic Perspectives, vol. 20, no. 1, (Winter 2006), pp. 133–151.
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18 | Chapter 3
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 trading networks, all held up until the decades after the forced
retirement of the last western Roman emperor, Augustulus.
Another interesting piece of evidence: ice core samples
from Greenland 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
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 that less specialization occurred.
That 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.
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 40-year-old today in the United States is
about twice as rich as the same person 35 years ago. This is
577-57346_ch01_5P.indd 18
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 28 years it would quadruple, and in 42 years it
would octuple. 35 years is in between—so let’s say incomes
have increased by about 6 times over that period. (In fact,
1.0535 is about 5.62, so this rough estimate only slightly
3. This is an exciting and active area of research. I’ll let you
try out some answers on your own.
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.
5. The growth rate of population plus the growth rate of GDP
per capita equals the growth rate of GDP.
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.
1. 2050 is 40 years from 2010.
(a) $1,042
(b) $1,546
(c) $3,361
(d) $7,200
So if Ethiopian living standards grew as fast as in China or
South Korea, in 40 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.
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Population in billions of people
An Overview of Long-Run Economic Growth | 19
15 22 29 36 43 50
15 22 29 36 43 50
Per capita GDP
Population in billions of people
3. This is a worked exercise. Please see the text for the
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.
2040 2060
(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.
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20 | Chapter 3
9. These are all approximations:
(a) 6 percent
Per capita GDP
(b) 2 percent
(c) −2 percent
(d) 3 percent
(e) 4 percent
2000 2020 2040 2060 2080 2100 2120 2140
10. (a) (1/3) × gk
(b) (1/3) × gk + (2/3) × gl
Per capita GDP
(f) 0 percent
(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)
2100 2150
6. This is a worked exercise. Please see the text for the
United States
United Kingdom
g rate
8. This is an essay question.
(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.
(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.
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. 7 percent annual growth is all you need to
double in 10 years—not 10 percent.
13. (a) About 251 years
(b) About $87. 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 210 years.
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A Model of Production
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 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 × L2/3 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 he 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.
A few immediate payoffs: we can show students that when
markets are competitive, wages are determined by labor
productivity. 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.
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22 | Chapter 4
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 fairly 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 important, and Chad refers to some of
the leading authors in this literature if you’re looking for supplemental readings.
tion is to consider what sort of production functions do not
fit the diminishing returns and constant-returns-to-scaleassumptions. 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
scale, let b = c = 1
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.
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 important. 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.
A good approach for students to become acquainted with
the characteristics of the Cobb-Douglas production func-
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A Model of Production | 23
Table 4.2
Table 4.3
Cobb-Douglas Production Function
Y = ĀK1/3L 2/3
Y = ĀKbLc
let A = 1, b = (1/3), c = (2/3)
let A = b = c = 1
hold L constant, L = 1
Hold L constant, L = 1
Hold K constant, K = 1
Scale: a = b = c = 1
Finally, in Table 4.3 we present the popularized CobbDouglas production function presented in the textbook. We
easily show that both diminishing returns and constant
returns to scale are evidenced.
577-57346_ch01_5P.indd 23
hold K constant, K = 1
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 get combined 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
amount of capital (machines, equipment, tools) in the economy, and L is the amount of labor—think of it as the number
of full-time 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 100th 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.
2/23/16 10:03 AM
24 | Chapter 4
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 knew 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 make sure that all the capital and labor get used?
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
Slope of production
function = Marginal
product of labor =
5,000 potatoes per
N ∗ = 100 workers
Number of workers
577-57346_ch01_5P.indd 24
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.
100 workers who will work full-time, regardless of the
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 live on. They might all meet together
at the general store one day and agree on trying to keep 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 together, 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
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 . . .
But 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 they have—
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, of agriculture, of the nature of farming: The wage
2/23/16 10:03 AM
A Model of Production | 25
A. In this model, how do you increase wages? 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.
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 selfinterest to undercut the others. In competitive markets, firm/
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.
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 Jones notes, the Cobb-Douglas model (combined with
competitive markets) has a very 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
two-thirds 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
poorest. Only in the very poorest countries is there much of
a difference from the two-thirds value our model predicts.
Fraction of GDP
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.
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
577-57346_ch01_5P.indd 25
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
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, vol. 110 (April 2002), pp. 458–74.
2/23/16 10:03 AM
26 | Chapter 4
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 plot 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: The
Free Press, 1998).)
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 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]
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: The 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.
2. Eric Hanushek and Dennis D. Kimko, “Schooling, Labor-Force
Quality, and the Growth of Nations,” American Economic Review, vol. 90,
No. 5, (December 2000), pp. 1184–1208.
577-57346_ch01_5P.indd 26
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
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.
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 while most economists will agree that the broad factors that Chad Jones discusses as drivers of TFP play a big
role in driving income differences—human capital, institutions, and technological innovations—there is much less
consensus about what those factors mean in practice. Is elementary education more important than college education?
Are political rights more important 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 per for mance 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 10—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
per for mance.)
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, vol. 94, no. 4,
(September 2004), pp. 813– 835.
2/23/16 10:03 AM
A Model of Production | 27
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 (–)
10. Whether a country is in Latin America (–)
Surprisingly, none of the top 10 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 performance. 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 10 are mostly about geography, disease, and longevity, with one bright light shining for human capital: 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 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 important for macroeconomic outcomes.
Regarding disease, health, and economic growth: the
tropical regions of the planet are hotbeds of healthdestroying infectious diseases. Modern growth researchers such as David Weil have looked into the link between
disease and economic growth and have found that indeed,
sick people are worse workers, and people with short
lifespans 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.
4. Xavier Sala-i-Martin, “I Just Ran Two Million Regressions,” American Economic Review, vol. 87, no. 2, (May 1997), pp. 178–183.
577-57346_ch01_5P.indd 27
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 America,
Australia, and New Zealand, were easier for Eu ropeans
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.
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.
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 to have 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
5. Daron Acemoglu, Simon Johnson, and James A. Robinson, “The
Colonial Origins of Comparative Development: An Empirical Investigation,” American Economic Review, vol. 91, no. 5, (December 2001), pp.
2/23/16 10:03 AM
28 | Chapter 4
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
The case study on labor shares shows that there’s actually
some good evidence of capital not being all that important
in practice.
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.
1. (a) Constant
(b) Increasing
(c) Increasing
(d) Constant
(e) 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
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: It’s 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 make sure
that all the output gets sold.)
4. This ice cream economy is a closed economy. The only
thing they make is ice cream, and the only thing they consume is ice cream, and while workers and capital owners
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).
More formally, Y = w × L + r × K
output = total wages + total rental payments
(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.)
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 very, very rapidly. That’s what the one-third
exponent on capital means: capital just isn’t that important.
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.
577-57346_ch01_5P.indd 28
6. Your guess is as good as mine. But Douglass North’s guess
is probably better than both of our guesses put together.
Y/L if 3/4
Y/L if 1/3
2. (a)
Y/L = K/L
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A Model of Production | 29
Y/L = K/L + A
Per Capital Per
Pre- TFP to
capita dicted match
person GDP person GDP
Y/L = K/L − A
3. This is a worked exercise. Please see the text for the
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:
r* = (3/4)Ā × (L/K)1/4 (more workers or ideas equals a higher
interest rate!)
w* = (1/4)Ā × (K/L)3/4 (more machines or fewer workers
equals higher wages!)
c. Y/L = Ā × (K/L)
5. (a)–(c) Please see the table below.
Per Capital Per
Pre- TFP to
capita dicted match
person GDP person GDP
124,162 41,365
110,132 37,104
100,668 31,299
136,360 38,685
101,506 26,609
9,137 3,966
29,390 12,340
35,887 11,939
2,125 1,247
(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 very quickly,
so it can’t matter that much.
577-57346_ch01_5P.indd 29
124,162 41,365
110,132 37,104
100,668 31,299
136,360 38,685
101,506 26,609
9,137 3,966
29,390 12,340
35,887 11,939
2,125 1,247
Since we now assume that capital doesn’t run into diminishing returns that quickly, the big capital differences now predict big output differences. Ethiopia and Hong Kong now
have TFPs higher than the United States.
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.
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 par ticular
country. In the third column, we’re saying that TFP differences alone make the United States Z times richer than that
par ticular country.
United States
Hong Kong
South Korea
Per capita
Implied TFP
to match data
America’s bigger capital stock makes it 3.88 times richer than
Kenya. America’s higher level of TFP makes it 8.55 times
richer than Kenya. This roughly matches the one-fourth capital-to labor (1/3.88), three-fourths TFP story that Chad tells.
2/23/16 10:03 AM
30 | Chapter 4
8. 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.
He is puzzled by this fact, 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 govern-
ment policies, culture, or education levels, there ought to be
a way to work things out, according to the (intentionally)
naïve view of the Coase theorem.
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.
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2/23/16 10:03 AM
The Solow Growth Model
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 longterm 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
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.
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32 | 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, 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.
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.
sumer goods, while the rest of the workers go to the 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, and 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 $2.0 trillion in 2012, about 12.8 percent of
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 $16 trillion, quite a bit larger than each year’s
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 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. Why this is so 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 con-
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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
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The Solow Growth Model | 33
a 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. 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 high-saving South Korea with the low-saving Philippines. In an expanded case study below, we look at another
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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—fastgrowing 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
The point Chad makes at the beginning of Section 5.4 can’t
be repeated loudly 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
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 = 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
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34 | Chapter 5
production function tells us how output (Y) is produced by
capital and labor, so let’s substitute:
ΔKt = ĀKt1/3
− 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, and 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 = 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
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
since we know that population growth hurts living standards
in this model. May be a point worth emphasizing!
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.
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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 parameter 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/.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.
Additional possibility: You could integrate the “Kindness
of Strangers” case study (below) into this part of the lecture
to show that a one-time massive give 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 coverage of steady states and convergence. After covering this,
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The Solow Growth Model | 35
you could just hand-wave your way through the rest of this
chapter without too much difficulty.
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 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 important 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 a new, lower wage—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, 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.
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). While this aid likely
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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.
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.
Lesson: A temporary change in the capital stock only
leads to a temporary change in living standards.
Bonus lesson: The only way to keep society at the new
higher post-aid capital level would be to permanently change
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36 | Chapter 5
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 longlasting changes in those deep parameters.
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 firms (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.
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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.
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
= 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 50 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 70 years. Now let the parameters , đ, Ā, and change.
For example, if s increases by 10 percent from .10 to .11, show
how the capital stock and output grow over time. Students
will learn that adjustment toward the steady state will take
over 50 years with over half of the adjustment taking place in
the first 11 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 that path to be shocked by parameter shifts over time.
1. Capital accumulation delivers growth. This makes sense
because we can see by looking around ourselves that
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The Solow Growth Model | 37
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
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 important 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.
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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
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 have to replace enormous amounts of capital each
year, and that eats up a lot of social effort.
Thus, a capital-rich economy faces two barriers to building
up the capital stock: diminishing returns and depreciation.
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.
Depreciation Line
Hi s
Lo s
New K ∗
Old K ∗
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
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
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38 | Chapter 5
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.
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
g 0.4
Investment, Depreciation, and Output
Low A Y
High A Y
Low A s ∗Y
High A s ∗Y
d ∗K
3. This is a worked exercise. Please see the text for the
(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 need to be
(b) Output per person increases as the total economy
approaches a new higher steady state level of output.
(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.
Investment, Depreciation,
and Output
577-57346_ch01_5P.indd 38
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.
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 reenforce 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
2/23/16 10:03 AM
The Solow Growth Model | 39
(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.)
Section 3.5. If you want students to use the growth rate rules
then you should allow for both answers.
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 capital-creating earthquake rather than a capital-destroying
one. It has no long-run impact on the steady-state capital
8. (a) growth rate of GDP = 1/3 × growth rate of capital stock
(a) 21/2 = 1 + gy*, so gy* = 41.42% or given that y* = ( /đ).5(Ā)1.5,
gy* = .5(gs − gd) + 1.5 × gA = 50%
(b) .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* = .5(gs − gd) + 1.5 × gA
= 15%
(d) Not at all
(e) Not at all
(b) growth rate of Y/L = (1/3) × [(s(Y*/K*) × [(K*/Kt)2/3 − 1]
The key is to substitute the solution for K*, equation 5.7, into
the final footnote equation.
(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.
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.
The approximate answer using the growth rate rules:
gy = (1/3) × (20%) = 6.66% = gC
9. Note that the question asks about the growth rate of GDP
per person, not the growth rate of capital.
(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.
(a) 3.33 percent
6. This is a worked exercise. Please see the text for the
(b) 10 percent
(c) −25 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%.
growth rate in Y/L = −33.33%. That’s the immediate fall in
Y/L from the immigrants.
7. As in exercise 5, students will be tempted to use the
growth rate rules and ignore the warning in footnote 5 in
577-57346_ch01_5P.indd 39
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40 | Chapter 5
10. (a)
Relative Per
Capita GDP
in 2000
rate during
Relative Per
Capita Steady
State GDP
(b) For countries that have growth rates greater than that of
the U.S., such as Ireland and Russia, we expect relative per
capita output to rise, and for countries that have growth rates
that are the same as that of the U.S., such as Brazil, we expect
relative per capita output to remain constant. The results for
Ireland show that its relative per capita output will rise to
more than 167% of that of the U.S. This result does not seem
plausible, as we do not expect Ireland to maintain a long-run
average growth rate of 4%.
(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.
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.
11. 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.
Investment, depreciation
Depreciation Line
577-57346_ch01_5P.indd 40
2/23/16 10:03 AM
Growth and Ideas
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 nowclassic 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 tradeoff 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
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
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 first 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, 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.
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42 | 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 important 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
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
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 that we don’t spend any time on. The At term is a “standing
1. David Landen, The Wealth and Poverty of Nations, (New York: W. W.
Norton, 1999).
577-57346_ch01_5P.indd 42
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.
Some of Chad’s research has been devoted to reminding
people that while 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 they 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 steady-state 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.
2/23/16 10:03 AM
Growth and Ideas | 43
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 through 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
we’ve spent little time on— 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 important 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 particular
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
577-57346_ch01_5P.indd 43
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 = AtKt 1/3Lyt 2/3
ΔKt + 1 = Yt – đK t
ΔAt + 1 = At L at
Lyt + L at =
L at = * ,
where the first two equations reflect the modifications to the
model while 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 = ;
and 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 = . Now the
growth rate has increased by 50% (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.
2/23/16 10:03 AM
44 | 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; i.e., K = ( /(gy + đ))Y, where
gy = gk; and recall Lyt = (1 − ) . Substitution and solving for Y/
yields yt = Yt / = [( )/(gy + đ)]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: the determinants of the total factor productivity coefficient, At=
Solow: 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) . 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.
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 ideaintensive 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.
577-57346_ch01_5P.indd 44
Average cost of pill
1 2
Quantity of pills
Average Cost
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 that one person, however rich, would pay a
billion dollars for is going to be of some substantial worth to
2/23/16 10:03 AM
Growth and Ideas | 45
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 of 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 on to teaching Problems with
Pure Competition, and then double back for the remainders 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
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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 idea 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.
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, your economy’s rate
of innovation depends on how many researchers there are—in
other words, to find gold, you 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).
2/23/16 10:03 AM
46 | 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
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 while 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 important 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.
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
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
577-57346_ch01_5P.indd 46
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 again and again 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
3. The words themselves—when in the author’s mind—are
nonrivalous. 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—all of these 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
important 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.
1. (a) nonrivalrous
(b) rivalrous
(c) rivalrous—the painting itself is a good, not an idea.
(d) nonrivalrous
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Growth and Ideas | 47
(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
doubling : 94 and 4747. The best deal so far.
3. Figure 6.2: It doubles every 20 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 10 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 in 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
6. This is a worked exercise. Please see the text for the
7. (a) This economy grows at 2 percent per year:
(1/3000) × .06 × 1000 = .02
(b) Initial level of output per person: 94. After 100 years: 681.
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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) 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:
(c) Growth rate of per capita output is 1 ⁄2 . We use the
growth-rate shortcut, and notice that the exponent on Atin
the production function is 1 ⁄2.
(d) yt = [A0 (1 +
)t]1/2 × (1 – )
The only difference from equation 6.9 is the square root term.
9. (a) growth rate of TFP: 0.02
(b) growth rate of TFP: 0.0167
(c) growth rate of TFP: 0.01.
More Exercises (Appendix 6.9)
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 = .02 = gY/L – gK/L . So g*Y/L =
gY/L = .03
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48 | Chapter 6
(b) A Latin American economy: gA = .0167 = gY/L – gK/L . So
g*Y/L = .015 < g Y/L = .0167.
(c) An Asian Economy: gA = .01 = g Y/L – gK/L . So g*Y/L = .015
< g Y/L = .06.
(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.
4. (a)
5. (a) gYt = (3/2)gAt. Given that the marginal product of capital is smaller, the amplification factor is smaller.
(b) yt = Yt / = [( ) / (gy + đ)]1/3At4/3(1 – ). Given that the marginal product of capital is smaller, the amplification factor is
capita 10
6. (a) gYt = (1/(1 – α))* gAt . In the text α = 1/3, and (1/(1 – α))= 3/2.
(b) yt = Yt/ = [(s)/(gy + đ)]α/(1–α) At1/(1–α)(1 – ). In the text,
/1–α = (1/3)/(2/3) = .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.
577-57346_ch01_5P.indd 48
2/23/16 10:03 AM
The Labor Market, Wages, and Unemployment
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 important 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
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 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%.)
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
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
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50 | Chapter 7
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. 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.
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 10 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
577-57346_ch01_5P.indd 50
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 natural level.
This conclusion is reached by ΔUt+1 = 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 important 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-to-employment ratio as .03 and the average of
new hires-to-unemployment ratio as .5 as approximate measures of and allows us to estimate the natural unemployment rate at about 5.6% for the period 2001 to 2010.
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 actually calculate the net present value of their own
future wages, and he discusses the rising value of a college
education. Once students understand 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.
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The Labor Market, Wages, and Unemployment | 51
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(.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. But 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.
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 capital1. Daniel H. Pink, “Revenge of the Right Brain,” Wired, Issue 13.02,
February 2005.
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enhanced workers. (This contradicts the “common 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 right—
one reason to spend time on the Solow model.
But does anything like that happen in the real world? David
Card and Alan Kreuger, 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 Carter 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, while 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 Kreuger 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
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52 | Chapter 7
supply increased by tens of thousands, wages quite clearly
did not fall.
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.
“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 salestype 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 that
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
A 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, vol. 28, no.
1 (July 2004), pp. 2–13. Available at www.minneapolisfed.org.
577-57346_ch01_5P.indd 52
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: The MIT
Press, 1998) show how much churn goes on in the United
States. My favorite statistic: 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
325,000 net 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 fairly 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
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The Labor Market, Wages, and Unemployment | 53
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: 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 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 particular 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 of the résumés, have meetings to decide what kind
of person you’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
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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 (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 they 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 10 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.
1. According to Table 7.1, there were about 156 million
people in the labor force in 2013. If the unemployment rate
had been 6% instead of 7.9%, the number of unemployed
would have been about 9.4 million instead of 12.3 million. In
other words, about 2.9 million more people would have been
employed. Quite a difference!
2. 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
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54 | Chapter 7
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 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.
3. 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.
4. This is a worked exercise. Please see the textbook for the
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%: 1,535.740
3%: 1,862,219
2%: 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 46 years of payments worth $50,000 per year.
(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.
8. We’ll assume that school time is four years, and that work
time is still 45 years, beginning in time 0, adding up to a
49-year noncollege work career.
(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)]}
$49,505 $45,264 $10,100 $3,958 $47,619 $30,696 $2,100 $1,917
(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
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 they think 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.
7. (a) w 0 + w 0 (1 + g) / (1 + R) + w 0 (1 + g)2 / (1 + R)2 + . . . +
w0 (1 + g)t / (1 + R)t
(c) a = (1 + g)/(1 + R)
(b) PDV = w0*[(1 + g) / (1 + R) + (1 + g)2 / (1 + R)2 + . . . + (1 + g)45
/ (1 + R)45]
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(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 + .03)]}50 / {1 − [1 /
(1 + .03)]} − 70,000{1 − [1 / (1+ .03)]}4 / {1 − [1 / (1 + .03)]}.
(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.
9. This is a worked exercise. Please see the textbook for the
10. (a) This equals a paid vacation that lasts 26 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 20th week or so, when they will start looking for a real
(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
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The Labor Market, Wages, and Unemployment | 55
a little for the first few weeks, and then start looking for
11. For the year 2010:
Italy: $106 per hour
France: $101 per hour
Germany: $89 per hour
Canada: $78 per hour
United Kingdom: $76 per hour
United States: $82 per hour
Japan: $58 per hour
Clearly, France, Italy, and Germany are more productive
than the United States on a per-hour basis. Canada, the
United Kingdom and Japan are less productive than the U.S.
on a per-hour basis.
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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
business-cycle 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 best-understood 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. CobbDouglas 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. So inflation isn’t all that
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 Inflation (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 has to 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 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 shortterm 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 them know there’s more to come so that they won’t just
forget this after the exam.
In the previous section, Chad mentions the level of currency
(C). Here he lays out the monetary base, M1, and M2. Please
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Inflation | 57
don’t make your students learn discontinued series like M3
and L—they already get the idea that lots of things have
moneylike 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?
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.
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
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 mortgage 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 left-
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hand 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 fully 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 while 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 them know that M only gets to change 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, shocks to aggregate demand are primarily caused
by changes in the money supply. 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.
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
framework to teach this—and you don’t need to, either.
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58 | Chapter 8
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 5 minutes of lecture—with minimal real payoff.
Students are primed to believe that inflation is caused by
money growth—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 them by
using the same jargon twice.
Chad’s charts in this section are great—note that the
cross-country money/inflation chart uses the ratio scale—
and these should be part of your lecture. Macroeconomists
rarely get relationships that are this precise.
This subsection is covered in a sample lecture to come.
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—have to 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 high
budget deficits, M2 grew 7.2% in 2011 and 8.6% in 2012.
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.
8.4 Costs of Inflation
8.6 The Great Inflation of the 1970s
Chad uses three people to illustrate the costs of inflation. The
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 up 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 12 inches in one year but 11 or 13
inches in another. That’s a source of confusion we could
probably live without.
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 10 years or less.
8.3 Real and Nominal Interest Rates
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:
G = T + ΔB + ΔM.
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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 have to 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 need to adjust interest rates
for inflation.
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Inflation | 59
R = i − π.
R is the real interest rate (how much real buying power you
have to 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 only have to
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, as long as 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 proinflation 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,
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. 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 important—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 flatscreen 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 stops getting made? The methods for
taking account of quality increases are constantly evolving—
and genuinely improving, but the simplest method works as
In a month when both the up-to-date and the outdated
color TV 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
up-to-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.
(Note: Consumer electronics have been one area where
rapid deflation is the norm, as your students will recognize.
Irving Fisher figured this out in the early twentieth century, and he put it into an equation (a variant of equation 8.5):
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60 | Chapter 8
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, in spite of their producers’ self-interest in charging
higher and higher prices?)
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
Interest for the year showing up on your 1099-INT: $12.
Tax you pay to government: 25% 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 quite 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.
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 and
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 take a look at the Fisher equation to see if this is right:
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,
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Inflation | 61
means that the nominal interest rate should equal zero. If the
government did that, then currency would be earning real
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. So 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.
So 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
The classical dichotomy tells us that in the long run, real
GDP growth is caused by changes in real variables: the number of ideas, the number of machines, 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, vol. 19,
no. 3 (Summer 1995), pp. 2–11. Available at www.minneapolisfed.org.
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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 all of the 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
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62 | Chapter 8
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 seignorage (changes in M). The Federal Reserve just let inflation get out of control in the 1970s,
perhaps because they didn’t know how the economy really
worked. Later chapters will give a more thorough answer to
this question—a topic which is still much debated among
9. People who hold currency and other non-interest-paying
forms of money, like most checking accounts.
Table 8.1 (2012=100)
CPI2012 /
2. This is a worked exercise. Please see the textbook for the
3. 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.
(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.
4. (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.
5. This is a worked exercise. Please see the textbook for the
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7. (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.
8. 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.
1. From Table 8.1
6. (a) 4 percent nominal
(b) 5 percent real
(c) 4 percent inflation
(d) 13 percent nominal
(e) −4 percent real
(f) 9 percent inflation
But of course, there’s a bit of fantasy involved in acting as if
business people 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. So it’s quite
reasonable to look only at the net, after-depreciation returns.
9. (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.
(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.
10. 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
have to change their behavior and react to surprises. When
bread gets 15 percent more expensive, is that more because of
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Inflation | 63
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 all of these changes
is mentally taxing. These adjustment costs are quite high.
11. 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.
12. 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
13. I used Table B71 of the 2011 Report.
(a) $149,021 million in monetary base. Currency equals
base minus reserves, so currency equals $126,578.
(b) $7.017 million was raised in revenue, 0.2 percent of 1981
(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.
14. (a) This gives us (change in M/M) × (M/PY), or money
growth times money per unit of output.
(c) i. In 1981, GDP inflation was 9.4 percent, so π + y = 11.4
percent. The data show that M/PY = 1/V = 4.7 percent (using
the monetary base in 13(a) as our measure of M). The product of these two is 0.5 percent of GDP.
This is more than double the amount from exercise 13(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 down to the
lower level predicted by the quantity theory. In fact, by 1983
it was down to 4 percent, yielding an implied inflation tax of
0.28 percent of GDP. That’s pretty close to the true level.
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 to
get the right answer.
ii. In 2005, GDP inflation was 3.2 percent, so that π + y = 6.3%
percent. Assuming a constant velocity, the growth rate in the
money supply is assumed to be 6.3%, and given that
1/V = 6.2%, the inflation tax in 2005 as a percent of GDP
was about .4%.
(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 and harder for the government to create
buying power with the printing press.
To make our story complete, we’d have to go through exercise 14’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.
15. 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.
(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
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An Introduction to the Short Run
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 pretty 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.
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 perfor mance. 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 need to be
in the habit of sorting “actual GDP” into two bins: “potential
GDP” and “short-run GDP.” We can usually identify shortrun 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.
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.
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An Introduction to the Short Run | 65
2. Draw a straight trend line through the actual path of real
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
gets 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 (Ỹt = Yt − t + t; where t is
potential output). 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 Ỹ or short-run output.
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
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. This
should give students a rough idea of how this all ties together.
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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 shortrun 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.
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:
“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”
“New bank regulations boost lending to underserved
Why emphasize long run versus short run? To let 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 right, 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 important—but
those are really the only two major macroeconomic events
of the last 50 years as far as potential GDP growth goes (and
perhaps as far as the unemployment rate is concerned as
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66 | Chapter 9
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.
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 particular, if the Phillips curve is right, then when actual GDP is
above potential GDP, inflation rises. That means policymakers 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 quite 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
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 per-
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.
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cent. Forget double-digit inflation and the natural rate of
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. So perhaps it’s worthwhile to spend some time
reading Business Week in between issues of Econometrica.
After almost 80 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 government-run 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, 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.
Randall Parker’s book Reflections on the Great Depression4
reports, according to Ben Bernanke, the current chair of the
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/
4. Randall E. Parker, Reflections on the Great Depression (Northampton, MA: Edward Elgar Publishing, Ltd., 2002).
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An Introduction to the Short Run | 67
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 important 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.
John Taylor interviewed Milton Friedman about his life and
his work for the Quarterly Journal of Economics. That
interview was republished by Paul Samuelson and Wiliam
Barnett7 in 2007. Friedman, as in Chapter 8, ascribes inflation to political rather than economic problems. Essentially,
the Kennedy administration was able to take 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’ 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 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.
5. Ben S. Bernanke, Essays on the Great Depression (Princeton, NJ:
Princeton University Press, 2004), p. 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 Barnett, William A., Inside the Economist’s
Mind (Malden, MA: Wiley-Blackwell Publishing, 2007).
577-57346_ch01_5P.indd 67
Friedman disagreed with this conclusion. Friedman thought
the mistake was not in economics but in politics.
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 of 2008 and ending in June of 2009. The peak
of the previous cycle was December of 2007 and that cycle
began in November of 2001 and lasted 71 months. This last
recession was the longest of the post–World War II era—
lasting 18 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 of 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:
(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 or not 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 committee met again in September 2010 they were 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.
2/23/16 10:03 AM
68 | Chapter 9
1. The long-run model tells us about the trend, while the
short-run model explains the relatively small fluctuations
(wiggles) around the trend.
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.
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 2007–9 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
5. We see the Phillips curve in Figure 9.5 because every time
the inflation rate crosses a grey NBER recession line, the rate
of inflation tends to fall. So when the economy drops below
potential GDP, inflation drops noticeably. (During nonrecession 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.
1. This depends on the student’s choice.
2. This is a worked exercise. Please see the text for the
3. Slope of the Phillips curve
577-57346_ch01_5P.indd 68
Change in inflation
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.
4. (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
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. So this is a tough question, one
where we can’t give a clearer answer without a clearer understanding of what the politician wants.
2/23/16 10:03 AM
An Introduction to the Short Run | 69
(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).
5. (a) True output falls to a new, lower level—in other words,
policymakers accidentally create a recession.
(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 the slow
growth was really caused by a short-term recession—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.
(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.
(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.
7. (a) 5.5 percent, 6 percent, 6.5 percent, and 7 percent,
(b) 0 percent, −2 percent, and 4 percent, respectively.
6. (a) and (b)
output t
Yt −
− 0.48
− 0.87
Short- run
output Yt
rate of
− 4.37%
− 0.53%
577-57346_ch01_5P.indd 69
2/23/16 10:03 AM
The Great Recession: A First Look
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, in particular finance majors, will
probably pick up these concepts faster than economics majors.
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 financial 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
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.
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 42 percent between 2006 and 2012.
The question is, “What caused the rise and collapse of housing prices?”
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, in particular China, and that these countries
had plenty of liquidity to invest in U.S. financial markets.
Still other economists, such as John Taylor, dispute whether
or not 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
577-57346_ch01_5P.indd 70
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The Great Recession: A First Look | 71
explaining asset (housing) price inflation. See the case study
on housing price inflation.
Here Chad provides a Minksyesque 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 important 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 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: (1) many
borrowers had little or no equity to begin with; and (2) 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.
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 risk associated with the subprime mortgages was offset by the higher rates of interest charged.
577-57346_ch01_5P.indd 71
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 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 (.2 to .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 3-month LIBOR was 4.05%;
the T-bill rate was .67%. 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, the index had fallen to 786.28 (about
a 48 percent decline).
The Federal Reserve Bank of Dallas provides an estimate of
the relationship between the price of a barrel of oil and the
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 .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 (in par ticular 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 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. In recent
years, we’ve seen oil prices rise again to between $80 and
$100 per barrel.
2/23/16 10:03 AM
72 | Chapter 10
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. The recession is evidenced by many indicators:
1. Employment fell—the economy lost 8.5 million jobs.
2. Short-term output fell below potential output by as
much as 7 percent.
3. The unemployment rate increased from about 4.5 percent in 2007 to over 10 percent in 2009, and remains
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 18-month duration is longer than the previous two
recessions in 2001 and 1991, which were each 8 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 cyclically. 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, newly industrialized countries in Asia, and Brazil. Additionally, the United
Kingdom, Italy, and Spain have double dipped into recession in 2012.
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
577-57346_ch01_5P.indd 72
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 the loan can be paid
back. 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. Most bank deposits are insured by the FDIC. 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. (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
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 would be sold at fire-sale prices, and
the liquidity crisis would turn into a solvency crisis as asset
values fell below the values of liabilities. During the last
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The Great Recession: A First Look | 73
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.
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 risk averse. This risk aversion limits investment
to only the most financially sound firms. 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 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 ser vice 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
1. Mihm, Stephen (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, The Jerome Levy Economics Institute (1992); John
Maynard Keynes (New York: McGraw-Hill, 2008); Stabilizing an Unstable Economy (New York: McGraw-Hill, 2008).
2. Keen, Steven, Debunking Economics (London: Zed Books, 2002).
577-57346_ch01_5P.indd 73
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.
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 have to 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
demand further and further increases 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 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.
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
3. Robert Shiller, Irrational Exuberance, 2nd edition (Princeton, NJ:
Princeton University Press, 2005).
2/23/16 10:03 AM
74 | Chapter 10
by using debt, or leverage, to acquire assets or to reduce
(buy back) equity. An important 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 assetto-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.
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% of its peak in 2007 to 2009. As of this writing in late 2013, stock prices have more than recovered.
2. It was the most severe recession in the post–World War II
era, lasting from January 2008 to June 2009 (18 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 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 the loan
can be paid back, 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.
577-57346_ch01_5P.indd 74
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 of examples:
Change in
as a
(Figure 10.8)
(Figure 10.9)
of GDP
Source: Federal Reserve Bank of St. Louis, FRED Economic Data.
2. For comparison purposes, see the same data for 2010 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)
− 0.3
10 Jun 2013
Source: European Central Bank Statistical Data Warehouse, http://sdw
.ecb.europa.eu /.
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)
− 0.7
− 8.0
24 Sep 2010
Source: European Central Bank Statistical Data Warehouse, http://sdw
.ecb.europa.eu /.
2/23/16 10:03 AM
The Great Recession: A First Look | 75
3. As of March 30, 2013.
Citigroup, Inc.
Goldman Sachs
In 2013, for Citibank, for each $100 of assets, $10.30 is
financed by equity and $89.70 is financed by liabilities. For
Goldman Sachs, for each $100 of assets, $8.10 is financed by
equity and $91.90 is financed by liabilities.
4. (a) Bank B, assets = 1500, liabilities = 1400, equity = 100;
Bank C, assets = 800, liabilities = 700, equity = 100
(b) Bank B, 1400/100 = 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.
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2/23/16 10:03 AM
The IS Curve
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
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: rise in interest rates causes fall in
investment demand, which hurts real 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 natural 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
11.2 Setting Up the Economy
Here, Chad sets up his simplified IS curve. Here’s what you
can’t 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
577-57346_ch02_5P.indd 76
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The IS Curve | 77
on permanent income—so he’s keeping the model quite
neoclassical to begin with. Since empirical consumption
multipliers are quite small, this rigor-driven simplification is
a quite reasonable choice.
In his notation, bars denote exogenous variables. Thus,
Ct = ā C
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 policymakers actually talk about—by contrast, few academics or policymakers 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 model. , 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
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’s 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
577-57346_ch02_5P.indd 77
it— there are a lot of good topics to cover later in this
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 us 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
started 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 semielasticity 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 go ahead and 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 ā C (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
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78 | Chapter 11
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 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?).
Section 11.4.4 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 mediumrun adjustments within the full-blown IS-MP-Phillips curve
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.
(so she can spend a little of it each year); she gets bad medical news about her long-run 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.
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
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.
11.5 Microfoundations of the IS Curve
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
For a youngish person, 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
577-57346_ch02_5P.indd 78
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.
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
Chad then covers Ricardian equivalence with intuition
alone. A number of homework problems illustrate Ricardian
2/23/16 10:04 AM
The IS Curve | 79
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
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
By and large, Chad defers the discussion of NX until
Chapter 19.
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 lifespan: “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 lifespan, 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
577-57346_ch02_5P.indd 79
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 that
we’ll apply to discussing tax cuts. Suppose your annual
aftertax income is $10 per year, and you’re going to
live for 10 years. One day, Congress tells you they’re
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 per year, 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 7 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 have to 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
In practice, as Chad notes, people appear to be quite
a bit more impatient than the PILCH implies, spending
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80 | Chapter 11
up to half of a big one-time payment right in the first
year. But there’s no serious evidence that people spend
80 to 90 percent of a big one-time payment immediately, so the average person does indeed engage in
some PILCH-like behavior.
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.
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
1. John R Hicks, “IS-LM: an explanation,” Journal of Post-Keynesian
Economics, vol. 3, no. 2 (1980), 139–54.
2. Robert Lucas, “My Keynesian Education: Keynote Address to the
2003 HOPE Conference,” History of Political Economy, vol. 36 (2004),
3. See Steven Keen, Debunking Economics (New York: St. Martin’s
Press, 2001), p. 210.
577-57346_ch02_5P.indd 80
of the money will be wasted on pet projects, high salaries,
and various inefficiencies. Therefore, businesses often choose
to finance their investment with “retained earnings,” another
word for profits.
Are there good reasons for banks and investors to be concerned about agency problems? In particular, are there good
reasons to think that when a CEO has her hands firmly on the
reins of power, 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
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,” The Financial Review, vol. 41, no. 3 (2006),
pp. 307–37.
5. Bruce Johnson, et. al., “An Analysis of the Stock Price Reaction to
Sudden Executive Deaths,” Journal of Accounting and Economics, vol. 7,
nos. 1–3, (1985), pp. 151–74.
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The IS Curve | 81
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 onetime tax changes have only small effects on consumer
Franco Modigliani, while 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 of if they do
not have heirs, then the future tax burden does not adversely
impact lifecycle (or permanent) income, and therefore does
not adversely affect consumption.
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 short-run output.
2. Because a fall in interest rates encourages businesses and
homebuyers to borrow more to purchase more investment
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: shifts right when consumers become more optimistic or foreigners demand more
U.S. goods; shifts left when government cuts purchases or
when businesses become pessimistic about the future.
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, vol. 4, 222–56 (2000), reprinted in Paul Samuelson and William Barnett, eds., Inside the Economist’s Mind (Malden, MA:
Blackwell Publishing, 2007).
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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, 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).
1. (a) Short-run output falls by .5%.
(b) rises by .25%
(c) rises by 1%
(d) falls by 2%
(e) rises by 2%
2. This is a worked exercise. Please see the text for the
3. (a) This is an increase in āi: If the government’s out 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 ser vices in the short
(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
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82 | Chapter 11
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 āC 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, ā G increases, but ā C doesn’t change at all: the
IS curve shifts to the right. More government spending
adds up to more overall demand for goods and ser vices.
Note that this is the “common sense” view of government
In a world with Ricardian equivalence, where consumers
make today’s spending decisions based on their lifetime
income (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 she has to pay off some
debt, she probably pays off a little of it every month—not all
at once. The rational consumer wants to keep her consumption smooth from year to year, if possible—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
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 they’re
doing just what rational consumers would do themselves:
paying a small price each year to pay for a big one-time
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
is exactly the same under Ricardian equivalence. (Hence the
word “equivalence.”) The effect on āC should be small: āC
577-57346_ch02_5P.indd 82
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.
āC would be pushed up since the elderly would have more
income, but āC 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
Secuirty 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 ā C 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 āC: 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
C: Consumption’s share of potential output, C/ , will stay
the same, so while consumer spending falls, it won’t fall as a
fraction of potential output. In other words, āC is fixed.
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The IS Curve | 83
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.
Y/ = C/ + I/ + G/ + NX/
= āc + Ỹ + āi + (R − ) + . . .
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.
8. (a) This is almost the same as question 7, except that the
last line will look like this:
Ỹ = [1/(1 + ñ)][ā − (R − )]
Notice that plus sign in the multiplier term!
Here’s how it goes:
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:
+ ā − (R − )
(1 − ) = ā − (R − )
Ỹ = [1/(1 + ñ)][ā − (R − )]
577-57346_ch02_5P.indd 83
(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.
9. (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 − )
(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.
10. (Parts (a) and (b) answered in text, as part of worked
(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
(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.
2/23/16 10:04 AM
Monetary Policy and the Phillips Curve
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 preFriedman-Phelps Phillips curve, and the tough love of Paul
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—
can be skipped 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 has the power to control
interest rates. It looks like a superpower.
12.1 Introduction
Again, Figure 12.1 is a great roadmap. 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, while the next chapter presents
the normative theory of optimal monetary policy.
12.2 The MP Curve: Monetary Policy and
Interest Rates
The 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 6
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, his 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.
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Monetary Policy and the Phillips Curve | 85
So Chad’s summary is very 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 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.
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 that “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
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.
Again, the MP curve is just a horizontal line telling us the
Fed’s monetary policy decision. Lay it over the IS curve, and
you’ve determined short-run output. The next subsection
applies the model to a bursting housing bubble: starting at
potential 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 latetwentieth-century macroeconomics. I’d recommend reading
the part before Section 12.3.1 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 12
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
577-57346_ch02_5P.indd 85
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
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 wellgrounded inflation expectations. A world of bad policy may
(rationally) be more adaptive in its expectations formation.
The short-run output term in PC is “demand-pull,” while ō
is “cost-push.” So both are covered in this model.
12.4 Using the Short-Run Model
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 you may find yourself coming back to.
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 slower than usual in the
1970s, Fed officials thought that the economy was below
potential. They didn’t have our Phillips curve around then,
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86 | Chapter 12
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
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
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.
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, influences 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
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
12.6 Microfoundations: How Central Banks
Control the Interest Rate
This is your basic money demand story. He 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.
Key economic idea: 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 them 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
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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 and 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.
Banks are required by the Fed 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 know 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
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Monetary Policy and the Phillips Curve | 87
lending. Typically, the Fed does not pay banks interest on
their reserves, but 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
important 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%, but if the price of the bond falls,
say to $97, the yield rises to $3/$97 = 3.1%. 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 pretty plausible.
How would you know if he/she were wrong about the
economy being weak? If he/she were wrong, you’d see
three or four years of no change in inflation—inflation
would stay at its same old 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.
Assume the Phillips curve works like this:
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/she says things have been this way for
years and years. How can you figure out whether he/she is
right or wrong?
You could try to estimate potential GDP in a couple of
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
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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?
Chad notes correctly that long-run rates are a rough average
of short-term rates. That’s how the Federal Reserve can
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88 | Chapter 12
move 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 90 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 20 years. Other researchers since then have found broadly similar results, especially
for bonds of 10 years or less. It appears that the federal funds
rate is the One Rate to Rule Them All.
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
1. Glenn D. Rudebusch, “Federal Reserve Interest Rate Targeting,
Rational Expectations, and the Term Structure,” Journal of Monetary
Economics, vol. 35 (April 1995), p. 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, vol. 24 (July 1988), p. 331−51.
3. Paul A. Samuelson and Robert M. Solow, “Analytical Aspects of
Anti-Inflation Policy,” American Economic Review, vol. 50 (May 1960),
p. 177−94.
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see that 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 “natural 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:
[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
decade, the economy might enjoy higher employment with
price stability than our present day estimate would indicate.
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.
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 grad students interview hundreds of
business leaders, and among other things they were asked
about 12 different possible explanations for sticky prices.
So, which theories did the businesspeople believe in?
The top four theories—the only ones that got a better
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
• Nonprice competition: consistent with real business
cycles and other flexible price theories. Firms might find
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.
1. The Fed’s only actual choice is to set the nominal interest rate.
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Monetary Policy and the Phillips Curve | 89
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 I done recently?” If they use that as a starting point
for discussions about price changes, that gets you 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 shortrun 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 important tool it has.
4. Friedman’s statement means that the Fed can’t use
interest rate changes to perfectly offset each and every
shock 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 6 months from
now, or it might increase it 18 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 (lasting less than six months) shocks to GDP.
The medicine won’t get there in time to cure the problem. So you have to live with some short-run GDP
Second, it tells us that good policy has to be both
forward-looking and cautious: the central bank has to
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
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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 policymakers. 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.
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.
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—
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, 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, 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,
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90 | Chapter 12
the long-term rate tends to be a rough average of shortterm 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 longterm 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.
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.
(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
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 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.
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(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
policymaker 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
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Monetary Policy and the Phillips Curve | 91
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
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 one-time 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 before to 2 percent after, 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.
• 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.
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• 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 as 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: 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
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.
2/23/16 10:04 AM
Stabilization Policy and the AS/AD
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 important 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 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
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 pa rameter (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 IS
curve quite easily; together, they give us what we now call
the aggregate demand curve:
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 AD curve.
I often emphasize that is a measure of how “mean” or
“uncaring” or “brutal” the central bank is. It shows how willing the central bank is to push the economy into recession
577-57346_ch02_5P.indd 92
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Stabilization Policy and the AS/AD Framework | 93
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 particular element of ā (such as the steady-state shares
of consumption, investment, and so on) would get absorbed
into some other component of 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.
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
The Phillips curve gets to do double duty. This equation:
When Chad draws the Phillips curve using the level of
inflation on the y-axis, he calls that the Aggregate Supply
curve. That 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 to make this clear to students? 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 to draw
something like the chart below, to clarify AS’s simple
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.
If AD crosses AS
on this side, AS
shifts down/right
next year.
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? That helps motivate a discussion and some policy
applications that fit in with conventional topics of noneconomic, real-world discussions: caring about the long run, selfcontrol, 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.
πt = πt−1 + Ỹt + ō
is Chad’s adaptive expectations Phillips curve. It is also
Chad’s Aggregate Supply curve. When discussing the equation itself, the terms are interchangeable—and in my experience, that roughly follows standard macroeconomic practice.
But when it comes to graphs, Chad makes a distinction.
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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
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94 | 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
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
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
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.
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
π t = π t−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 , 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 you can come
back to often.
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 their micro intuition
to make this point stick—so you may want to repeat it again
and again throughout the chapter.
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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).
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, this effect is summarized by the slope of the AS curve itself: 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; they’re not
trying to create a boom. They’re still putting the brakes on the
economy, but they’re no longer slamming the brakes down to
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Stabilization Policy and the AS/AD Framework | 95
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.
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.
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—longterm shares of C, I, G, and NX have to 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 to 2004 would be one recent example of a small
inflation-output loop; the period between 1975–84 would be
the biggest loop in postwar U.S. history. Chad presents data
later in the chapter—see Figure 13.18.
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 18 months to show up. Thus, a central bank has to
be reacting today to problems it might be facing in the future.
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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 will have to 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 policymakers behave just like you or I
Aside: I’ve heard more than one politician complain that
the Fed was raising rates when there was no sign of
inflation—why would she or he 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 inflationoutput 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.
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96 | Chapter 13
13.7 Modern Monetary Policy
1. Governments can make commitments
2. Prices are flexible
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
they’re 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 has to 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.
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, 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 income— 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.
I’d teach this before I teach about time consistency. This
section shows how good policy is easy if:
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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. That 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.
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
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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 going to be 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 important
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 they think inflation will be a year or
two from now. So 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 important part of the monetary policymaker’s
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.
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
time consistency parables. Kydland and Prescott’s original
one about living in a flood zone is still salient: forwardlooking 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.
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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: 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
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, 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
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98 | Chapter 13
set their prices low, then the Fed can create a boom economy. 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:
Businesses: Low
Businesses: High
Fed: Low
Fed: High
Low inflation, no
Economic boom
High inflation, no
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 (Journal of Money, Credit, and
Banking, 1993) 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
1. Alberto Alesina and Lawrence H. Summers, “Central Bank Independence and Macroeconomic Per for mance: Some Comparative Evidence,”
Journal of Money, Credit, and Banking, vol. 25 (May 1993), p. 151–62.
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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
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 Dynamics2,
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, 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 now die of cancer and heart
2. Bennett McCallum, “An Interview with Robert E. Lucas, Jr,” Macroeconomic Dynamics, vol. 3 (1999), p. 278–91.
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disease instead. But even though few humans die of infectious diseases, we still want our doctors to know how to
treat infectious diseases. So even if Lucas is right, it makes
good sense to spend our energies learning about good monetary policy.
Now let’s ask what a New Keynesian thinks about RBC.
In a 2004 paper in the Review of Economics and Statistics3,
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 percent to 25 percent of fluctuations could be
attributed to RBC-style technology shocks. But since 1980,
40 percent to 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.
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—
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
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 ser vices 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 important 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 of 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.
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
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
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.
3. Peter N. Ireland, “Technology Shocks in the New Keynesian
Model,” Review of Economics and Statistics, vol. 86 (November 2004),
p. 923–36.
4. John Fernald and Bharat Trehan, “Why Hasn’t the Jump in Oil Prices
Led to a Recession?,” NFBSF Economic Letter, November 18, 2005.
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100 | Chapter 13
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.
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 they raise it 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, they raise 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 they
“feel tough”—but they end up cutting the real rate! They’ve
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.
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.
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Also, following a rule is good for helping policymakers 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 firms
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 shortrun 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
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
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Stabilization Policy and the AS/AD Framework | 101
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 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.
1. (a) 10 percent inflation → 6 percent real, 16 percent
5 percent inflation → 3.5 percent real, 8.5 percent
2 percent inflation → 2 percent real, 4 percent nominal
1 percent inflation → 1.5 percent real, 2.5 percent
(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. From equation 13.5, the federal funds rate is:
it = Rt + πt = + πt + (πt – ).
In 2012, the inflation rate was approximately 2.1 percent. If the target inflation rate was 2 percent, and the
was 2 percent, and = .5, the predicted federal funds rate
was 4.05 percent. The actual federal funds rate was .14
percent. Apparently, our monetary policy rule doesn’t
account for continued fallout of the Great Recession.
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.
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 macro
economy 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
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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 one-time 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 expected inflation rate the AS curve moves back into its original
steady-state position.
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 level.
6. This works like an AD boom that lasts. At the moment
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
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102 | Chapter 13
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
(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) Because when inflation rises, the central bank
chooses to raise real interest rates and slow down the
(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
(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
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
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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 = .5.
Nominal interest rate
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 and 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.
Inflation rate
(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 important 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.
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?
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Stabilization Policy and the AS/AD Framework | 103
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
πt). Let us keep ā equal to zero, since there’s no AD
shock. This quickly simplifies to
πt = + ō/(1 + vmb)
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
first order 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.
Short- run output
(c) You’ll see that even after ten years, inflation is still
two-thirds 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 10 years, assuming ā stays at 2 percent
the whole time:
Short- run output
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.
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The Great Recession and the Short-Run
Students will find this chapter useful in applying what they
have learned so far in understanding the Great Recession.
This chapter introduces financial considerations, in par ticular, 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 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.
14.1 Introduction
This chapter considers the policy difficulties encountered in
stimulating the economy during a severe economic downturn. This chapter is important 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
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 10-year
treasury yield. Typically, during economic downturns financial frictions increase. During the Great Recession, financial
frictions increased dramatically to around 6 percent. 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.
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.
In the AS/AD framework, financial frictions are introduced
as an AD shock. As financial frictions rise, the real rate of
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The Great Recession and the Short-Run Model | 105
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.
To illustrate the dangers of deflation, recall the Fisher equation: it = Rt + π t. 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
14.3 Policy Responses to the
Financial Crisis
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; (2) the federal funds rate was below the predicted level from 2001 to around 2006—which may have
577-57346_ch02_5P.indd 105
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.
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.
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 effect changes in the federal funds rate.
During the financial crisis, the Fed has increased purchases
of commercial paper, other loans, and mortgage-backed
securities while more than tripling 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 interest on bank (excess) reserves. This
interest rate can be used to better control the lending activities of banks that impact the money supply.
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.
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
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106 | Chapter 14
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% of
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.
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 service its national debt this problem is
referred to as a sovereign debt crisis. Chad discusses this
problem further in Chapter 20.
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) having a systemic (risk) regulator; (2) enhanced capital requirements; (3) linking executive
compensation to performance; (4) requiring convertible debt
(debt that converts to equity); (5) requiring “living wills,” a
set of instructions for reorganizing failed banks. Many of
these features have been incorporated into the financial
reforms approved in July of 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
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of the beaver. The threat remains. Are financial institutions
like the beavers? Will putting in financial regulations
remove the systemic risk?
14.4 Conclusion
The Great Recession is different from other recessions that
have occurred during the post–World War II era. Typically
recessions are related to the Federal Reserve’s attempts to
disinflate the economy (as described by Rudi Dornbusch—
see page 400, footnote 11, 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.
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
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The Great Recession and the Short-Run Model | 107
economic stability was reduced to “How long does it take
for the economy to adjust from an out-of-full-employment
situation to a full-employment 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.
On July 21, 2010, President Obama signed the Wall Street
Reform and Consumer Protection Act, popularly known as
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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) an advance 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 http://www.banking
.senate.gov/public/_files/070110 _Dodd _Frank _Wall _Street
_Reform _comprehensive_summary_Final.pdf.
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
while 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.
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
1. 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,
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108 | Chapter 14
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 Industrials hit its record
high for the year to date.
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
“Morning 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
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 10-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
577-57346_ch02_5P.indd 108
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
short-run 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 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.
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.
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 mortgagedbacked securities, and these other assets as a means to
provide the financial system with liquidity and solvency
and reduce financial frictions.
6. The approaches policymakers are considering to
restore the financial system include (1) creating a systemic regulator; (2) enhanced capital requirements; (3)
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The Great Recession and the Short-Run Model | 109
linking executive compensation to long-term per formance; (4) requiring convertible debt; (5) requiring
“living wills.”
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.
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.
(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 longterm 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.
(d) Expansionary fiscal policy could also be considered.
2. This is a worked exercise. Please see text for solution.
3. (a) In the textbook, following Taylor’s rule: = = 1/2,
= 2%, and = 2%.
(b) The CPI inflation rate (for all urban consumers) in
2012 was 2.1%. Inflation has been relatively steady
at 2% even though the economy has been operating
below potential output (at least as reported by the
(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 for the last decade. In 2002, 2003, 2004, and
since 2007 the output has been below potential. In
2009, the actual output was more than 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:
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(e) As in the text, the predicted federal funds rate was
higher than the actual federal funds rate until 2009.
After 9/11, the Federal Reserve maintained the federal funds 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 at http://www
The June 19, 2013 statement has many interesting
discussion points. This statement can be found at http://
www.federalreserve .gov/newsevents /press /monetary
The full statement is as follows:
Release Date: June 19, 2013
For immediate release
Information received since the Federal Open Market Committee met in May suggests that economic activity has been
expanding at a moderate pace. Labor market conditions
have shown further improvement in recent months, on balance, but the unemployment rate remains elevated. Household
spending and business fixed investment advanced, and the
housing sector has strengthened further, but fiscal policy is
restraining economic growth. Partly reflecting transitory
influences, inflation has been running below the Committee’s longer-run objective, but longer-term inflation expectations have remained stable.
Consistent with its statutory mandate, the Committee
seeks to foster maximum employment and price stability. The Committee expects that, with appropriate policy
accommodation, economic growth will proceed at a moderate pace and the unemployment rate will gradually decline
toward levels the Committee judges consistent with its dual
2/23/16 10:04 AM
110 | Chapter 14
mandate. The Committee sees the downside risks to the
outlook for the economy and the labor market as having
diminished since the fall. The Committee also anticipates
that inflation over the medium term likely will run at or
below its 2 percent objective.
To support a stronger economic recovery and to help
ensure that inflation, over time, is at the rate most consistent with its dual mandate, the Committee decided to continue purchasing additional agency mortgage-backed
securities at a pace of $40 billion per month and longerterm Treasury securities at a pace of $45 billion per month.
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. Taken together, these actions
should maintain downward pressure on longer-term interest rates, support mortgage markets, and help to make
broader financial conditions more accommodative.
The Committee will closely monitor incoming information on economic and financial developments in coming
months. The Committee will continue its purchases of
Treasury and agency mortgage-backed securities, and
employ its other policy tools as appropriate, until the outlook for the labor market has improved substantially in a
context of price stability. The Committee is prepared to
increase or reduce the pace of its purchases to maintain
appropriate policy accommodation as the outlook for the
labor market or inflation changes. In determining the size,
pace, and composition of its asset purchases, the Committee will continue to take appropriate account of the likely
efficacy and costs of such purchases as well as the extent of
progress toward its economic objectives.
To support continued progress toward maximum employment and price stability, the Committee expects that a
highly accommodative stance of monetary policy will
remain appropriate for a considerable time after the asset
purchase program ends and the economic recovery strengthens. In particular, the Committee decided to keep the target
range for the federal funds rate at 0 to 1/4 percent and currently anticipates that this exceptionally low range for the
federal funds rate will be appropriate at least as long as the
unemployment rate remains above 6–1/2 percent, inflation
between one and two years ahead is projected to be no more
than a half percentage point above the Committee’s 2 percent longer-run goal, and longer-term inflation expectations
continue to be well anchored. In determining how long to
maintain a highly accommodative stance of monetary policy, the Committee will also consider other information,
including additional measures of labor market conditions,
indicators of inflation pressures and inflation expectations,
and readings on financial developments. When the Committee decides to begin to remove policy accommodation, it
will take a balanced approach consistent with its longer-run
goals of maximum employment and inflation of 2 percent.
Voting for the FOMC monetary policy action were: Ben
S. Bernanke, Chairman; William C. Dudley, Vice Chairman; Elizabeth A. Duke; Charles L. Evans; Jerome H.
Powell; Sarah Bloom Raskin; Eric S. Rosengren; Jeremy
C. Stein; Daniel K. Tarullo; and Janet L. Yellen. Voting
against the action was James Bullard, who believed that
the Committee should signal more strongly its willingness to defend its inflation goal in light of recent low inflation readings, and Esther L. George, who was concerned
that the continued high level of monetary accommodation
increased the risks of future economic and financial imbalances and, over time, could cause an increase in long-term
inflation expectations.
6. This is the student’s choice. Economic indicators can be
found at http://sdw.ecb.europa.eu/home.do?chart=t1.2.
For example:
Selected Indicators for the Euro Area
(annual percentage changes
unless otherwise stated)
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
Euro Area
− 0.4
10 Dec 2013
Source: European Central Bank Statistical Data Warehouse, http://
sdw.ecb.europa.eu /.
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2/23/16 10:04 AM
DSGE Models: The Frontier of Business
Cycle Research
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 classical 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 classical 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. So you
will have another opportunity to allow students to make
connections between core assumptions and macroeconomic
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
behaviors 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.
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
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112 | Chapter 15
features. The endogenous variables include a list that students are already familiar with: 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).
nomic 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 pa rameter is included in the
labor supply function to capture the overall magnitude of
the labor force.
Given that DSGE models are microfounded, built from the
bottom up and based on the interrelated economic decisions
of many times 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 classical 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 increase labor demand.
The labor supply schedule is microfounded in the utility maximization decisions of households. In microeco-
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 intellectual fortitude in your students.
577-57346_ch02_5P.indd 112
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
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DSGE Models: The Frontier of Business Cycle Research | 113
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).
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.
Chad provides a variant of the nominal sticky wage story
that most of us are familiar with. 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
15.5. Quantitative DSGE Models
An important feature of DSGE models is that they are
quantitative— that is, they are used to make numerical predictions as to how various shocks affect important 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.
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 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
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.
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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
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114 | Chapter 15
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, output, and the inflation rate rise.
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.
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
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:
L = (w/c).
15.6. Conclusion
To conclude, an explanation of shocks and frictions is necessary to explain cyclical fluctuations. The how shocks affect
the economy depends in part on the significance of frictions
(price, wage, and financial) in the economy. Macroeconomists over the last 50 years have increasingly relied on
models, such as the DSGE models, that incorporate Solow’s
production and transition dynamics, that are microfounded,
and in which frictions are at play to understand and 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.
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
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 + .
Assuming our representative agent is rational, the agent
consumes leisure up to the point where the marginal benefit
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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
towards the end of Chapter 6, diminishing returns can be
introduced in the production of ideas (restricting the exponent on labor to be between zero and 1 in the idea produc-
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DSGE Models: The Frontier of Business Cycle Research | 115
1. I am borrowing from Michal Kalecki, Theory of Economic Dynamics (Cambridge: Cambridge University Press, 1965).
577-57346_ch02_5P.indd 115
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
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 fi rst- 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
Case 1. x = b = 1, h = 0, a = 10, P* = 5
tion 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 while 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)]}
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
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 important. 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 real wage gaps within gaps between the bifurcated
labor markets.
2. This section was inspired by Deirdre McCloskey’s presentation at the
European Association for Evolutionary Political Economy in Antwerp,
Belgium in 1996.
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116 | Chapter 15
Case 2. x = .75 b = 1, h = 0, a = 10, P* = 5.714
equilibrium 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 decisionmaking 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 3. x = 1, b = .75, h = 0, a = 10, P* = 5.714
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-anddemand 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
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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
3. 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.
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DSGE Models: The Frontier of Business Cycle Research | 117
“uncertainty” 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 firms that do direct business with the government; 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
important 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 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?
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 macro economy that are difficult to model are those same micro foundations 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
5. Professor Colander’s testimony is available at http://www2.econ
.iastate.edu /classes /econ502 /tesfatsion /Colander.StateOfMacro.Congres
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thinking in terms of models joined to the art of choosing
models which are relevant to the contemporary world.”6
1. D = dynamic, S = stochastic, 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
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.
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118 | Chapter 15
(including nominal rigidities, adjustment costs, heterogeneity of agents, and information asymmetries).
1. This is a worked exercise. Please see the textbook for the
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 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
(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 gov-
577-57346_ch02_5P.indd 118
ernment 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
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 aftertax marginal product of
labor is (1–t)(2/3)(Y/L). The temporary reduction in the tax
rate, t, increases that aftertax marginal product of labor and
the demand for labor, and increases the equilibrium real wage
rate and the 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 very 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).
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DSGE Models: The Frontier of Business Cycle Research | 119
(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 inflation expectations) to a new lower level of inflation (as the
economy recovers).
(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). The inflation rate
stabilizes as the economy adjusts back to long-run output.
(d) The results described above are similar to the SmetsWouters model shown in Figure 15.13 as both output and
inflation stabilize over time.
(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.
8. (a) With the inflation rate on the vertical axis, and Ỹ on the
horizontal axis, a temporary increase in government purchases, shift 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 up
and to the left, and the economy returns to long-run output at
a higher rate of inflation.
(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).
(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
577-57346_ch02_5P.indd 119
2/23/16 10:04 AM
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
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’ understanding.
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).
16.1 Introduction
In the United States, personal consumption is the largest
component of GDP; it is about two-thirds of GDP and
amounts to over $10 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 income. This assumption is consistent with the microfoundations subject to certain
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 chapter, lower case y is per capita
output— students will complain that y is income in this
Given these definitions, the IBC is written in presentvalue terms where the present value of lifetime consumption
equals the present value of resources (income and wealth).
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Consumption | 121
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.
If you are interested in deriving this result using the sort
of methods used in a microtheory course please see review
question 5.
At this point an additive utility function is introduced
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:
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.
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
This section illustrates the solution to the intertemporal utility maximization problem. To maximize utility, the consumer has to 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) × Δcffuture;
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 = × (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
first-order 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 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).
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From the expression above, expressions for ctoday and cfuture
are easily found (see exercise 5 below):
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
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 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
interest-rate change.
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122 | Chapter 16
16.3 Lessons from the Neoclassical Model
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; and
$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:
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.
If borrowing constraints are not present, consumers can borrow from their future income 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.
During times of uncertainty, people save as a precaution
against an uncertain stream of income. If persons are worried about the certainty of their future income, 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
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
The implications of this result are important (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 MPC (marginal propensity to consume) out of
wealth is one divided by life expectancy.
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 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.
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The Euler equation and the permanent income hypothesis
apply to households with above-average wealth.
For low-income/low-wealth households consumption tracks
income pretty well.
Given these results, the heterogeneity of households
requires some modified description of aggregate household
Behavioral economics offers the potential for rethinking
consumption and savings behavior.
The aggregate evidence indicates that wealth effects are
important 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 permanent
income hypothesis.
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Consumption | 123
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 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), in Friedman’s view, is not a central feature of capitalist/market economies.
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 40 years, a dollar increase in
wealth (regardless of the type of wealth) increases consumption in the current year by $.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 .4 percent increase in
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consumption, whereas a similar increase in financial wealth
has no effect1.
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 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, her tastes become sated, and she values
consumption today less relative to future consumption.
4. Given the consumer’s preferences, the rate of interest,
current income, future income, and financial 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 fi rst- order utility maximization condition where
Δcfuture/Δctoday|IBC = MRSCtoday, Cfuture = 1 + R. If U = log
ctoday + β × log cfuture, then ΔU = 0 = MUCtoday × Δctoday + MU
× 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/cto= 1 + the growth rate in consumption. As such, the
Euler equation can be interpreted as the optimal growth
pattern of consumption, given R and β.
1. Karl E. Case, John M. Quigley, & Robert J. Shiller, “Comparing
Wealth Effects: The Stock Market vs. the Housing Market,” Advances in
Macroeconomics, vol. 5, no. 1 (2005), pp. 1–32.
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124 | Chapter 16
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) −.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 two-period
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.
1. This is a worked exercise. See text for solution.
human wealth = $109,524; total wealth = $159,524
ctoday = $79,762; cfuture = $83,750; Stoday = $20,238
ΔStoday = $10,000
Δctoday = $4,761
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.
2. (a)
3. (a)
ctoday = $70,000; cfuture = $70,000; Stoday = −$20,000
Δ = $10,000; Δctoday = $5,000; ΔStoday = −$5,000
Δ = $20,000; Δctoday = $10,000; ΔStoday = −$10,000
If stock market and housing wealth increase,
households increase consumption and reduce savings relative to disposable income.
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6. (a) Let the change in current taxes = –Txtoday. The
change in future taxes = Txtoday(1 + R). The beforetax intertemporal budget constraint (ignoring nonhuman wealth) is
= ytoday + yfuture/(1 + R). The
aftertax intertemporal budget constraint is = ytoday
– Txtoday + (yfuture – Txfuture)/(1 + R). The before-tax
and aftertax 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) In the following table, the savings rates were derived
from the FRED database. The household debt-toGDP ratios were calculated using the Federal
Reserve’s Flow of Funds Accounts (Table D3, line
2, “Total Household Debt”) and the BEA’s measure
of nominal GDP (Table 1.1.5, line 1).
savings rate
debt-to- GDP ratio
(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.
2/23/16 10:04 AM
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 powerful 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.
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 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; (2) investment, as illustrated in the Solow model, explains changes in
the capital stock, and therefore, is a major cause of economic
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
17.2 How Do Firms Make
Investment Decisions?
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.
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
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126 | Chapter 17
higher 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 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 simply 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.
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.
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 × pK + 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.
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
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 longrun 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 aftertax
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.
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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.
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Investment | 127
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 percents, 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).
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.
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
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this, 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.
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 twoasset 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 plus capital gains. The arbitrage equation is: R × (down
payment) = rent – đ × ph + Δph, where ph = price of the home.
From this equation rent = R × (down payment) + đ × p h – Δph).
Multiply and divide the RHS by ph. Rent = ph × [R × + đ –
Δph /ph], where = (down payment)/ph (and 1 – = leverage).
Dividing both sides by [R × + đ – Δph /ph] yields the expression for the housing price: ph = Rent/[R × + đ – Δph /ph].
Increases in the rental values of homes, increases in leverage
(decreases in ), 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.
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 intermediate
goods to complete production. Inventory investment is procyclical. (3) Stockout avoidance: firms hold inventories for transaction purposes to ensure that customers’ needs are satisfied.
Inventory investment is again procyclical. Give the confluence
of these three motives, inventory investment is expected to
be procyclical; that is, to rise and fall with short-run output.
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128 | Chapter 17
Recall that the investment schedule was important 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 10-year 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% level) were derived. The estimates show that
–b = – . . . 11 (for every 1 percentage point increase in the
interest rate spread, investment relative to potential output
fell by .11 of one percentage point), and that c = .34 (for
every one percentage point increase in Ỹ, investment relative
potential output increased by .34 of one percentage point).
This simple model explains cyclical fluctuations in investment quite well. In Figure 1, the actual changes in I/ are
compared to predicted changes in I/ .
Linear prediction
Figure 1. Comparison of Actual Changes in I/ to Predicted
Changes I/
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
Prais-Winsten AR(1) regression – iterated estimates
Coef. Std. Err.
Number of obs
F( 4, 51)
Prob > F
Adj R-squared
Root MSE
[95% Conf. Interval]
Durbin-Watson statistic (original)
Durbin-Watson statistic (transformed) 2.043467
Source: Federal Reserve of St. Louis, FRED database. http://research.stlouisfed.org /fred2 /.
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Investment | 129
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.
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
price-earnings 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 efficient market hypothesis predicts.
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
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 quite well. They conclude that such models outperform accelerator and cash-flow models. The second
1. Robert Shiller, Irrational Exuberance, 2nd ed. (New York: Doubleday, 2005), pp. 175–203.
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), p. 3–39. Available at www
.bostonfed.org /economic/neer/neer2001/.
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study, by Geoffrey Tootell and others,3 shows that estimating
disaggregated investment equations are useful in sorting out
industry-specific determinants of investment.
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 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 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
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), p. 41–58. Available at www.bostonfed.org
2/23/16 10:04 AM
130 | Chapter 17
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 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. The return on owning a house is the rent less
depreciation plus capital gains. That is: R × (down payment) = rent – đ × ph + Δph, or rent = R × (down payment) +
đ × ph – Δph. Multiplying and dividing the right-hand
side by ph yields: Rent = (R × + đ – Δph/ph) × ph, where
= (down payment)/ph. Solving for ph yields: ph = Rent/
(R × + đ – Δph/ph).
Leverage is 1 minus . The greater the leverage, the
smaller is and the greater is the housing price.
1. This is a worked exercise. Please see the text for solution.
2. (a) uc = .1467
(b) Δuc = .0267
(c) With τ = 0, Δuc = ΔR = .02. Given the tax rate of 25
percent, an increase in the interest rate of 2 percentage points causes the aftertax MPK to rise by 2 percentage points. For the aftertax MPK to rise by 2
percentage points, the pretax MPK must increase
by .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
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pretax and aftertax MPK. The increase in the user
costs lowers the investment rate.
3. (a) If τ = .20, uc = .125. If τ = .30, uc = .143.
(b) If uc = .10, τ = 0, I/Y = .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 = −.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) The increase in the TFP parameter, 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.
6. This is a worked exercise. Please see the text for the
7. (a)
Growth rate of
condo prices
Down Payment
rate, x̄
Price of Condo
(b) Condo prices are very sensitive to expected capital
gain. With no capital gain, the condo’s price is
$9,091. If condo prices are expected to increase by
10 percent per year, the condo’s price is $100,000.
(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
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Investment | 131
$16,667, but if the down payment is 5 percent, the
condo’s price is $19,048. 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.
8. (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.
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The Government and the Macroeconomy
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 IS curve (forwardlooking 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 the lives
of your students: 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 quite 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 two items—National Defense and Other—are typically
counted as part of G. The rest are transfers of income.
1. Robert J. Barro, “Are Government Bonds Net Wealth?” Journal of
Political Economy, vol. 82 (1974), p. 1095–1117.
(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/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% of GDP.
of GDP
market debt
owed by
fed. gov’t.
of GDP
Sources: National Income and Product Amounts of the United States
(BEA), and the Flow of Funds Accounts of the United States (The Federal
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The Government and the Macroeconomy | 133
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 your 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? A: Sometimes.
2. How high can the debt/GDP ratio go before a government turns to hyperinflation (seignorage) to repay the
debt? A: Higher for the U.S. government than for less
stable governments.
3. When some later generation actually has to run those
primary surpluses, won’t their taxes be really high? A:
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? A: 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 important 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
577-57346_ch02_5P.indd 133
piece2 with Robert Hall, he shows that government health
care spending is the real long-term fiscal problem. At the
same time, drawing on the Nobel Prize winner Robert
Fogel’s work, he notes that in the twentieth 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 healthcare 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 and 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.
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 a very
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 pharmaceuticals, 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 healthcare spending. And of course, in the long run, issues of slope are vastly
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), pp. 39–72.
3. Brink Lindsey, The Age of Abundance (New York: Harper Collins,
4. Alan Greenspan, “Aging Global Population” (testimony before Special Committee on Aging, U.S. Senate, February 27, 2003).
2/23/16 10:04 AM
134 | Chapter 18
more important than issues about level; Chad makes this
point with Figure 18.8.
zero. Let’s put taxes on one side and all of the spending
items—G and debt repayment— on the other:
T1 = (1 + i)B1 + G1
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 seignorage. We can
ignore seignorage for now (it’s a minor source of revenue in
rich countries, and it would be a disaster if it became an
important source), and to keep it simple we’ll just ignore
transfers or just 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
that the media pays attention to is “total deficit,” G + iB − T.
That’s primary deficit plus interest payments. It’s less important macroeconomically, as we’ll soon see.
(Aside: That’s because, in an infinite-horizon steady state,
the government must run a nonnegative primary deficit. 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
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If the government is going to meet its obligations, then revenues have to 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 quite well— and it
reminds students that paying off the debt is a real cost.
Chad writes this another way as well, to make another
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
Emphasizing that primary surpluses are the government’s
“profits” helps students use concepts they’re already familiar
with. Any business has to have some profits if it’s going to
pay down its debt. When you stretch this out to two or three
periods, all that changes is that the government can run temporary primary deficits, but on average you still have to
make a profit, or people won’t lend to you anymore. In the
long run, the government has to make enough of a primary
surplus to at least make its interest payments.
(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 have to consume less in order to at least make the minimum credit card
payment. You have to pay down your credit card with your
current income, not by borrowing. The same is true for the
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.
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The Government and the Macroeconomy | 135
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 the payment amounts are controlled by
Congress. Of course, since the elderly vote at higher rates
than other citizens, it is fairly unlikely that Social Security
benefits will ever be cut—suggesting 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, lowpaying government-guaranteed 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.
A key fiscal policy question is whether deficits hurt the overall economy. The channel we’ll focus on here is whether
long-lasting 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 Lau-
5. This section draws on “Social Security Around the World,” Washington Post Online, available at, http://www.washingtonpost.com /wp -srv
6. William G. Gale and Peter R. Orszag, “The Economic Effects of
Long-Term Fiscal Discipline” (working paper, Brookings Institution,
Washington, DC, 2002).
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bach7 and Dai and Phillipon8 argue for an effect about onethird 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 quite datadriven, using sophisticated econometrics to address the
question. Perhaps the best guess would be the median: onethird 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), longterm 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.
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 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
So one important 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 pharmaceuticals—that’s another question entirely.
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).
10. Frank R. Lichtenberg, “The Effect of Pharmaceutical Utilization
and Innovation on Hospitalization and Mortality,” The National Bureau of
Economic Research, Working Paper No. 5418, (January 1996).
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136 | Chapter 18
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.
1. This depends on current data. The data below are derived
from the 2013 ERP and my calculations:
1. This will depend on the year you answer it in, but for
some recent data please see the table on page 132 of this
manual. 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 long-term 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 has to 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 21st 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% in 2030 and 21.1% 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 a significant increase in health care
costs is driven by technological change (new medicines,
MRIs and CT, and the like). Many technological changes
are driven by preferences. Increasingly, health care
will be more and 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.
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of GDP
Per Capita
National Defense
Income Security
Social Security
Net Interest
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
2. The business’s long-run profits (primary surpluses) have
to 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 have to
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 early 1980s. So 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
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The Government and the Macroeconomy | 137
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: Economists of all political backgrounds were
surprised by the plummeting tax revenues of the early
Bush years—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
2012(estimated): 5.6% primary deficit, 7% total deficit
(Source: Economic Report of the President, 2013)
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] + G2 − T2} + G3 − 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 have to be paid off.
5. This is a worked exercise. Please see text for solution.
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. Or it can raise taxes by $110.25 billion two years
from now.
(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
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.
(c) Under the examples in (a):
1. Private savings rise this year, government savings
fall this year. No future impact. This is pure
accounting identity.
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2. Private savings rise this year, 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, government savings
fall this year. In two years, private savings fall
and government savings rise. Consumers save the
tax cut, because they know they will have to 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.
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; and again, an investment tax incentive might bring
in quite a lot of investment from overseas. For a small
economy in par ticular, 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.
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 have to pay to how many people. With health care,
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138 | Chapter 18
we have essentially promised to buy elderly people
whatever health care services get 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
to begin to think 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 be working on these issues for years to come.
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International Trade
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 wanted 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
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 wanted to focus on the static
trade issues, then, you’d omit Sections 19.4 and 19.8, two
large sections.
There’s a very 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.
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 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 important.
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
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 will have to 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.
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140 | 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 to capital. A case study below expands on
this topic.
19.7 The Costs of Trade
Churn. 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:
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
The twin deficits: 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-
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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.
Are trade deficits bad? Compared to a hypothetical world
where the United States got to keep all of these Japanese and
Chinese goods and never had to pay for them— 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 are 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 Economy, “Are Americans Saving ‘Optimally’ for
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International Trade | 141
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 of 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 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.
Production Possibilities
Frontiers with large
gains from trade
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 a proof, but it should
probably raise our confidence in the savings choices of Americans, whether talking about private saving or foreign saving.
1. John Karl Scholz, Ananth Seshadri, and Surachai Khitatrakun, “Are
Americans Saving ‘Optimally’ for Retirement?” Journal of Political
Economy, vol. 114 (2006), p. 607–43.
2. Jagdish Bhagwati, Arvind Panagariya, and T.N. Srinivasan, “The
Muddles over Outsourcing,” Journal of Economic Perspectives, vol. 18
(Fall 2004), p. 93–114.
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Production Possibilities
Frontiers with no
gains from trade
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
production-and-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 winwin 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? Shockingly, the gains have completely vanished! Global output is
clearly going to be higher than before, but North is just as
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. That 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
will raise wages by much, 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.
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142 | Chapter 19
Lutz Hendricks’s 2002 American Economic Review
piece, “How Important 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 on the order of 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
country is something located back in the home country, not
something located inside the immigrants themselves. That’s
the key reason why immigration increases global GDP.
1. This is an essay question; student’s choice.
2. When a person buys more than she earns in income, 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, 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
4. Yes, unless they have exactly 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.
5. The deficit and the United States’ debtor status would
be problems if Americans behaved recklessly in accu-
3. Lutz Hendrick, “How Important Is Human Capital for Development?
Evidence from Immigrant Earnings,” American Economic Review, vol. 92
(March 2002), p. 198–219.
577-57346_ch02_5P.indd 142
mulating 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.
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. 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,
fairly 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 would also count 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
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 fell and foreign savings fell by (roughly) equal amounts.
How can 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. So 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.
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International Trade | 143
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.
3. This is a worked exercise. Please see the text for the
4. The key assumption: people spend half their income on
apples and half on computers.
(a) Autarky
Wage, w
Price of computer, p
Consumption of
apples (per person)
Consumption of
computers (per
Fraction producing
Fraction producing
Total production of
Total production of
160 apples
8 apples
80 apples
100 apples
50 apples
50 apples
10 computers
1 computer
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
Total production
of apples
Total production
of computers
Wage, w
Price of
computers, p
of apples
(per person)
of computers
(per person)
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
low-computer-productivity world seen in Table 19.4.
Both countries benefit from the improvement in
577-57346_ch02_5P.indd 143
5. (a) Autarky
Wage, w
Price of computers, p
Consumption of
apples (per person)
Consumption of
(per person)
Fraction producing
Fraction producing
Total production of
Total production of
160 apples
10 apples
80 apples
160 apples
80 apples
80 apples
8 computers
1 computer
8,000 apples
32,000 apples
800 computers
400 computers
(b) Trade
Fraction producing
Fraction producing
Total production of
Total production of
Wage, w
Price of computers, p
Consumption of apples
(per person)
Consumption of
computers (per person)
0 apples
64,000 apples
640 apples
40 (that’s
320 apples
0 computers
160 apples
40 (that’s
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.
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144 | Chapter 19
More broadly, the Baumol effect explains why
many ser vices 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. Ser vices in the U.S.
economy are like computers in this economy: they
only became relatively more expensive.
6. 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 them to trade, since in both
countries, the price of a computer is 10 apples.
(b) This means that North gets no gains from trade. It’s
the same as if North was back in the world of
(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
7. (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
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xn /zn
xn /2
zn /2
xs /zs
xs /2
zs /2
L nxn /2
L nzn /2
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).
Fraction producing apples
Fraction producing
Total production of apples
Total production of
Wage, w
Price of computers, p
Consumption of apples
(per person)
Consumption of computers
(per person)
L nz n
L s xs
L sxs /L n
L sxs /(L nzn)
L sxs /(2L n)
L sxs /(L nzn)
xs /2
zn /2
L nzn /(2L s)
(c) This has to 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 has
to be lower than in the South (recall that x/z is the
price, in apples, of one computer). When that price is
low in the North, North is likely to stick to making
But will each country completely specialize in
apples and computers, respectively? For this to happen, North has to be able to meet all of its own computer needs, as well as South’s computer needs. And
South has to 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 those 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).
8. 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.
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International Trade | 145
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 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.
9. This is an essay question; student’s choice.
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Exchange Rates and International Finance
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 on 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 magazine’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
tradeables—and that arbitrage is the reason why 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 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 important 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 openeconomy 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 has to just pick one big country that it wants a stable
exchange rate with (Of course, small countries can pick a
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Exchange Rates and International Finance | 147
“basket” of big country currencies, but that’s too much
detail.). Then, they pick an exchange rate that they think is
the long-run exchange rate, get a big pile of big-country currency, and tell the world that 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
has to do the same. That’s because when the big country
raises rates, there will be increased world demand for that
currency. The small country has to make sure that its own
currency is just as relatively popular, otherwise the smallcountry 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 has to 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. That
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
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 performance,
the causality probably runs from performance to currency
strength, not the other way around. Since students never know
what to think about exchange rates, it’s a point worth making.
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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 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
1. Stanley Fischer, “Exchange Rate Regimes: Is the Bipolar View
Correct?” Journal of Economic Perspectives, vol. 15 (Spring 2001), p.
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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 banking lending and rising sovereign-debt-to-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%,
and real interest rates rise from 1% to 10%, can a country
afford to spend 10% 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 has to be decreased (through direct and indirect
intervention of the European Central Bank). Second, the
long-term issues deal with the relative competiveness 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, this imbalance could
have been corrected by currency devaluations in the south.
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.
There’s a common theme running through Chad’s discussion of the currency crises in Mexico, a number of nations
in Asia, and Argentina. The links run from fiscal crises
through dollar-denominated 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.
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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.
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 18 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.
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 par ticular country’s
currency, convert it into a variety of foreign currencies,
and then try to actually buy goods and services in those
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Exchange Rates and International Finance | 149
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.
various countries. The real exchange rate adjusts the
nominal exchange rate to take into account that some
things (rent, restaurant meals, health care) are more expensive in some countries, and shows how many units of one
country’s goods must be given up to purchase those same
goods in another country.
2. U.S. inflation was higher than Japanese 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.
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.
8. A country can’t simultaneously 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.
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 that
country’s exchange rate appreciate. So 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.
1. For a Big Mac to cost the same $4.37 in every country,
assuming the local price of a Big Mac stays the same in
each country, the euro must fall against the dollar by
10.42 percent. Given the current exchange rate on which
.74 euros purchases $1, euros are too expensive for
Americans to buy if they want Big Macs to cost the same
in the euro area and in the United States.
In most other countries, the currency needs to rise
against the dollar. We can tell this quickly by looking at
the “Big Mac price in dollars” column in Table 20.1. In
every country outside the euro area (excluding Norway),
the Big Mac costs less than the U.S. price.
In all cases, the “law of one price” exchange rate is
calculated by multiplying Table 20.1’s actual exchange
rate per dollar by that country’s Big Mac price in dollars, and then dividing by the U.S. price of a Big Mac.
If Big Macs are cheap in that country, then the local
currency needs to fall— and that’s just what our equation says.
Big Mac
rate per
dollar ($)
Big Mac
price in
% Change
in exchange
Euro area
South Africa
*For example, the appreciation in the Japa nese yen is measured as: [(1/73.14) – (1/91.06)]/(1/91.06).
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2. Both net exports and investment are hurt by 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.
3. (a) growth in exchange rate = growth rate in rest-ofworld prices – growth rate in home country prices.
(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. It’s not off by a factor of ten, so some might say
it’s in the ballpark.
(d) Without hard data on the local prices of goods and services in each country, it’s hard to say. I wouldn’t hazard a guess on the question, though many would argue
that the strong performance of the Japanese economy
combined with tight monetary policy has raised
demand for the yen as a safe form of hard currency.
4. This is a worked exercise. Please see the text for
5. 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 AD to the left. The
economy returns to steady state because the leftward
AD shift slows down the rate of inflation, and AS 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.
6. 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.
Ỹ = C/ + I/ + G/ + NX/
Ỹt = C/ + I/ + G/ + ā nx −
(Rt −
) − 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 + )][ā − (Rt − )]
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.
7. When people want dollars in a financial crisis, they have
to 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.
8. This is a worked exercise. Please see the text for solution.
9. 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.
10. In three years, South Korea was almost back. Mexico
was still not back; its peak was around 1981. Indonesia
was back within a year.
11. This is an essay question. Answers may vary.
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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 they 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. In
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 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—
and 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 as the United States has entered the tenth year
in the “war against terror.” 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 identify the causes of GDP growth as determined by
short-term and long-term factors, to control inflation and
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, 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 better prepared to shape the future.
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Whose ideas did we cover this semester? This list doesn’t
cover all of the macroeconomists who earned Nobel
Prizes—merely those whose ideas appeared in this text.
2012: 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
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 problems on
business investment. Stiglitz’s imperfect-competition
models help explain sticky inflation and the market for
Robert Mundell: applied our IS model to small open
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-business-cycle
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/.)
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