INSTRUCTOR’S MANUAL
Charles I. Jones
Macroeconomics
FIFTH EDITION
Anthony Laramie
BOSTON COLLEGE
CHAPTER 1
Introduction to Macroeconomics
CHAPTER OVERVIEW
This is a conventional first chapter of a textbook: it defines
macroeconomics, it mentions a few in­ter­est­ing topics, it
explains what a model is, and it lays out the book’s separation into sections on the long run, short run, applications,
and microfoundations. It is quite a short chapter with few
surprises, so rather than summarizing it, I ­will instead talk a
­little about what makes this book dif­fer­ent and lay out a few
dif­fer­ent ways you can use it in your course.
WHAT MAKES THIS BOOK DIF­FER­ENT
run growth—­
This book offers solid coverage of long-­
including endogenous growth—­while simplifying the New
Keynesian business cycle dramatically, and it does all this
without any calculus. Author Charles (Chad) Jones shows
how long-­run macroeconomic growth models have evolved
and how tweaking the assumptions of ­these models 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 thereby 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.
HOW TO USE THIS TEXTBOOK
they 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 you omit coverage of any of them,
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, you might have to tread lightly over some of the math in
the growth-­and labor-­market models, which are self-­contained
and d­ on’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 and fourth editions of the book provide an innovative chapter on dynamic stochastic general equilibrium
(DSGE) models. This chapter provides a bridge between
long-­run economic growth and short-­run economic fluctuations, and it fits in nicely at the end of Part 3 of the textbook
to remind us of the links between the long run and the short
run. I’d recommend that you make time in the semester to
include Chapter 15 as a capstone to a semester course.
ONE-­QUARTER COURSE OR ONE-­SEMESTER COURSE WITH
MANY OUTSIDE READINGS AND PROJ­ECTS
In this case the best choice would be Chapters 1–4 (the
introduction through the basics of growth and productivity),
8–11, 15 (inflation, business cycles, and DGSE models), and
two of the following: Chapters 5, 6.1–6.3, and 7, or 12–14,
and Chapters 18–20.
CONVENTIONAL ONE-­SEMESTER CLASS
TWO-­QUARTER COURSE OR TWO-­SEMESTER COURSE
In this day and age of assessment, we are ever-­conscious of
what we teach, how we teach it, who our students are, what
In this case the best choice would be the entire book, spending one quarter or semester on long-­r un growth, ­labor mar1
6 | Chapter 1
Table 1. PER CAPITA REAL GDP GROWTH RATES AND
INCOME IN­EQUALITY: EASTERN EU­RO­PEAN EU COUNTRIES
Country
Czech Republic
Estonia
Slovak Republic
Croatia
Hungary
Poland
Bulgaria
Slovenia
Latvia
Romania
Lithuania
Per Capita Real
GDP Growth
Rate (2018)
Ratio of the Share of
Income of the Top
Quintile to the Bottom
Quintile (2017)
5.14%
5.83%
6.16%
6.44%
6.62%
6.76%
6.79%
6.84%
6.99%
7.00%
7.42%
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
3.4
5.4
9.4
5.0
4.3
4.6
8.2
4.3
6.3
6.5
7.3
.
.
.
.
Data sources: Eurostat and author’s calculations.
Table 2. PER CAPITA REAL GDP GROWTH RATES AND
INCOME IN­EQUALITY: THE REST OF THE EU COUNTRIES
Country
Per Capita Real
GDP Growth
Rate (2018)
Ratio of the Share
of Income of the Top
Quintile to the Bottom
Quintile (2017)
3.73%
3.74%
3.94%
4.45%
4.59%
4.62%
4.63%
4.68%
4.74%
4.84%
4.86%
5.21%
6.13%
4.5
4.1
6.6
5.0
4.0
4.3
4.2
6.1
3.4
3.5
5.7
4.6
4.6
France
Denmark
Germany
Luxembourg
Netherlands
Austria
Malta
Greece
Spain
Finland
Portugal
Cyprus
Ireland
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Data sources: Eurostat and author’s calculations.
recognizing that the rising income in­equality can generate
underinvestment in education and skills, as, for example,
evidenced by the decline in numeracy skills of low-­income
­people as income in­equality increases. The OECD suggests
that the solution to the dual prob­lem of growth and income
in­equality is a radical rethinking of the educational pro­cess:
providing more equal and meaningful educational opportunity to the poor.
CASE STUDY: INCOME IN­EQUALITY IN THE
EUROPEAN UNION AND ECONOMIC GROWTH
Following the OECD report on income in­equality (described
in the previous paragraphs), we can use a popu­lar mea­sure
of income in­equality that was reported by Eurostat5 to take
a snapshot of income in­equality in the Eu­ro­pean Union
(EU) and per capita GDP growth rates. The Eurostat mea­
sure of income in­equality is the ratio of the income share of
the top quintile to the income share of the bottom quintile.
­Table 1 reports the per capita GDP growth rate and the
quintile ratios for the Eastern Eu­ro­pean countries of the
EU. ­Table 2 reports the same data for rest of the Eu­ro­pean
countries.
For the Eastern Eu­ro­pean members, we can see, that
with the exception of the Slovak Republic and Bulgaria,
the three countries with the highest growth rates have the
highest degrees of income in­equality. For example, Lithuania has a per capita real GDP growth rate of just over
7.4% and the top quintile share of income is over seven
times greater than the income share of the bottom quintile.
For the rest of Eu­rope, Germany and Greece have the
5. https://­ec​.­europa​.­eu​/­eurostat​/­statistics​-­explained​/­index​.­php​?­title​=­In
come​_­poverty​_ ­statistics
highest degree of income in­equality; Greece’s growth rate
reflects its recovery from the debt crisis. In Eastern Eu­rope,
the Czech Republic reports a low degree of income
in­equality and is on par with Spain and Finland. Clearly,
the relationship between income in­equality and growth is
hard to decipher from a “snapshot,” but we do see some
evidence, as stated by the Kuznets hypothesis, of industrialization leading to income in­equality.
REVIEW QUESTIONS
1–3. Based on personal preference.
4. Ingredients: Inputs, the model itself, and outputs. We can
call t­hese “exogenous variables,” “equations or words,” and
“endogenous variables,” respectively. The best short summary of the power of models is Robert Lucas’s 1988 speech,
“What Economists Do,” which is available widely on the
Web. This is possibly his best line: “I’m not sure w
­ hether
you w
­ ill 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.
EXERCISES
1, 2. Based on personal preference.
3. (a) From www​.­stanford​.­edu​/­~chadj​/­snapshots​.­pdf:
Ethiopia: 2.9%
India: 11.8%
Mexico: 31.7%
Japan: 73.7%
Introduction to Macroeconomics | 7
(b) Botswana’s per capita growth rate between 1960 and
2017 was about 5.5%. China’s per capita growth rate was
somewhere around 3.9%.
(c) Population as of 2017, biggest to smallest: United States
(324.5 million), Indonesia (264.0 million), Brazil (209.3
million), Nigeria (190.9 million), Bangladesh (164.7 million), Rus­sia (144.0 million).
(d) Government purchases are likely to be larger in poor
countries, while investment expenditures are likely to be
higher in rich countries. Using the UN H
­ uman Development
Report to compare the five most highly developed countries
with the five least developed countries reveals:
THE FIVE HIGHEST ­HUMAN DEVELOPMENT COUNTRIES
Country (2017)
I/Y
(­percent)
Norway
Switzerland
Australia
Ireland
Germany
28.5
27
24.4
28.4
19.8
G/Y
(­percent)
5.8
7.23
15.8
8.3
15.7
Exchange
Rate
8.27
0.985
1.3
0.89
0.89
the wage. (Of course, you could simply collapse this to equilibrium ­labor supply and equilibrium wage without losing
much of interest.)
( f − ℓ)
(1 + a )
L* = ( f − w* )
(c) w* =
This might be a good time to review the importance of the
associative rule: students often forget about the importance
of parentheses when ­doing algebra.
(d) If ℓ 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 w
­ ere
willing to work the same number of hours at a lower wage.
In equilibrium, firms decide to hire more workers at a new,
lower wage.
(e) This is an increase in demand: the quantity and wage of
­labor ­will both rise in equilibrium. The wage rises a bit, to
which workers respond by supplying more l­abor.
THE FIVE LOWEST ­HUMAN DEVELOPMENT COUNTRIES
Country (2017)
I/Y
(­percent)
Niger
Central Africa
Republic
South Sudan
Chad
Burundi
G/Y
(­percent)
Exchange
Rate
25.7
10.3
18.1
11.2
582.07
582.07
30.4
11
6.14
10.6
6.7
31.96
6.68
582.07
1729.05
Source: UNHDR 2018.
(e) While t­here are many exceptions, it appears that money
in poorer countries has less value per unit compared to
money in richer countries (see the exchange rate data provided previously, in part d). This is largely b­ ecause some
poor countries have a history of high inflation, so that one
unit of their currency becomes worth very ­little compared to
the dollar. High inflation is rare in rich countries and much
more common in poor countries.
4. Based on personal preference.
5. This is a worked exercise. Please see the text for the
solution.
6. (a) ā tells us how the quantity of ­labor supplied responds
to wages. Informally, it tells us how sensitive workers are to
wages when deciding how much to work.
(b) This is the same as in 5: quantity of ­labor supplied,
quantity of ­labor demanded, equilibrium ­labor supply, and
7. (a) QD = demand for computers = F(P, X )
X is exogenous and captures consumers’ understanding
of how to use computers.
QS = supply of computers = G(P, Y )
Y is exogenous and captures the manufacturing skill of
the computer industry.
In equilibrium, QS = QD = Q*, so this model is r­eally
three equations and three variables (unknowns, QS, QD, and
P). If the demand and supply functions are straight lines,
then ­there must be a unique solution.
(b) QD = demand for classical m
­ usic = F(P, X )
X is exogenous and captures consumers’ interest in classical ­music.
QS = supply of classical m
­ usic = G(P, Y )
Y is exogenous and captures the technology for recovering and cleaning up old classical ­music recordings.
(c) QD = demand for dollars = F(P, X )
X 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, Y )
Y is exogenous, and captures the Federal Reserve’s supply
of currency.
CHAPTER 2
Mea­sur­ing the Macroeconomy
CHAPTER OVERVIEW
By and large, this is a conventional “What is gross domestic
product (GDP)?” chapter. Jones runs through the production, expenditure, and income approaches and emphasizes
that the ­labor share in the United States is roughly constant
(a point well worth emphasizing, since it helps justify the
Cobb-­Douglas production function that plays a major role
­later).
­There’s a particularly clear discussion of how to compare
GDP numbers across countries; even if you d­ on’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 countries).
Interest rates and the unemployment rate are deferred to
­later chapters, so you can focus your energies on an intellectual triumph that we economists usually take for granted:
the definition of GDP.
2.1 Introduction
Chad starts off by emphasizing just how hard it is to mea­
sure “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 he
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 r­ eally is one
of the ­great intellectual contributions to economics. What
did we ever do without it? Bad macro policy: that’s what we
8
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
­ hese definitions are impor­tant in framing
by definition. T
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 w
­ ill 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 par­tic­u­lar, 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 b­ ecause 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.
Mea­sur­ing the Macroeconomy | 15
CASE STUDY: COMPENSATION TO EMPLOYEES’
SHARE IN THE EU AND THE EU28 COUNTRIES
Data on the Eu­ro­pean economy and on the economies of its
member states can be found at https://­ec​.­europa​.­eu​/­eurostat.
Eurostat provides a search engine for finding data on the
national income and product accounts of the Eu­
ro­
pean
Union and its member states. Chad reports in the textbook
that compensation to employees in the United States is about
two-­thirds of GDP, trending down in recent years. A quick
look at the Eu­ro­pean Union shows compensation to employees’
share of GDP has been quite stable (with the exception of
Ireland) between 2009 and 2018. Compensation to employee’s share since the ­Great Recession ranges from a high of
52.2% for France to a low of about 34% for Greece. For a
summary of how Eurostat calculates the wage share, see
­Table 2. AVERAGE WAGE SHARES:
EU AND EU28 COUNTRIES
Country
France
Denmark
Germany
Belgium
Slovenia
United
Kingdom
Luxembourg
Finland
Netherlands
Spain
Eu­ro­pean
Union
Austria
Estonia
Sweden
Croatia
Cyprus
Portugal
Latvia
Hungary
Malta
Lithuania
Czechia
Italy
Bulgaria
Slovakia
Poland
Ireland
Romania
Greece
Standard
Average deviation
Max.
Min.
Standard
deviation
as a
p
­ ercent of
the average
52.20%
52.13%
51.42%
50.50%
50.21%
49.84%
0.18%
1.08%
0.80%
0.83%
1.24%
1.02%
51.92%
51.37%
50.11%
49.42%
48.74%
48.80%
52.41%
54.91%
52.93%
51.56%
52.30%
51.62%
0.35%
2.08%
1.56%
1.64%
2.48%
2.06%
49.40%
48.89%
48.70%
48.22%
47.74%
1.12%
1.23%
0.79%
1.43%
0.36%
48.26%
46.81%
47.73%
46.93%
47.29%
51.81%
50.24%
49.96%
50.89%
48.56%
2.27%
2.51%
1.63%
2.96%
0.76%
47.38%
47.20%
47.09%
47.06%
45.72%
45.16%
43.84%
43.36%
42.93%
41.72%
40.69%
39.81%
39.42%
38.23%
37.77%
36.03%
34.45%
34.07%
0.39%
1.76%
0.79%
1.11%
2.00%
1.39%
2.96%
1.07%
1.67%
2.33%
0.97%
0.31%
3.12%
1.53%
0.68%
5.75%
2.49%
1.32%
46.53%
44.74%
45.42%
45.96%
43.16%
43.72%
39.47%
41.01%
40.30%
38.91%
39.63%
39.42%
35.40%
36.96%
37.05%
28.79%
31.76%
32.91%
47.73%
50.49%
48.05%
49.48%
48.10%
47.66%
47.29%
45.05%
44.75%
44.82%
42.99%
40.36%
43.21%
41.10%
39.16%
43.74%
39.89%
36.34%
0.83%
3.73%
1.67%
2.36%
4.37%
3.08%
6.75%
2.47%
3.88%
5.59%
2.37%
0.79%
7.91%
4.01%
1.79%
15.97%
7.24%
3.87%
Sources: Wage data: https://­ec​.­europa​.­eu​/­eurostat ​/­databrowser​/­view​
/ ­TEC00013​/­default ​/­table; GDP data: https://­ec​.­europa​.­eu​/­eurostat
Eurostat; wage share: author’s calculations.
https://­ec​.­europa​.­eu ​/­eurostat ​/­statistics​-­explained ​/­index​.­php​
/ ­Wages​ _­a nd​ _­l abour​ _­c osts#Labour​ _­c ost​ _­c omponents.
­These income shares appear to be considerably lower than
what Chad reports for the United States However, the difference in the EU versus the U.S. share must largely account
for differences in the health care systems: see https://­ec​
.­europa​.­eu ​/­eurostat ​/­statistics​-­explained ​/­i ndex​.­php​/ ­Wages​
_­and​_­labour​_­costs. In the United States, health insurance is
employer provided, whereas in the EU, health care is largely
provided by the state, and therefore is excluded from compensation to employees.
Looking at ­Table 2, we can see that the wage shares are,
for most countries, stable during the post ­Great Recession
era in the EU. The standard deviations (relative to the averages) in the wage share during the 2009–2018 period are
quite small—­for most countries less than 3%. The countries
with the most volatile wage shares include Ireland, Latvia,
Bulgaria, Romania, and Lithuania. Countries such as Ireland, Latvia and Lithuania have experienced above-­average
volatility in unemployment.
M. Kalecki (1968) used the wage share (a “distributive
­factor”) to derive the relationship (multiplier effect) between
business profits and national income. If the wage share = the
wage bill/national income, and if national income = the
wage bill + gross profits, then (national income) * the wage
share = wage bill, and since the wage bill equals national
income − gross profits, national income − gross profits equals
the wage share * national income; solving for national income
yields: national income = gross profits/(1 − wage share).6
Given gross profits, national income is pushed up to the
point where the wage bill is paid and profits are realized.
Based on Kalecki’s work, the profit multiplier ranges from
about 2 for France, Denmark, Germany, Belgium, Slovenia,
and the United Kingdom, to about 1.5 for Poland, Ireland,
Romania, and Greece.
REVIEW QUESTIONS
1–4. ­These essentially summarize the entire chapter, so I
­will refrain from answering them.
EXERCISES
1. (a) Real GDP 2018 is $18,638.2 billion; nominal GDP
2018 is $20,580.3 billion. T
­ hese numbers are dif­
fer­
ent
­because real GDP is valued in 2012 (chained) prices whereas
nominal GDP is valued in 2018 (current) prices.
(b) Real GDP 1970 is $4,951.2 billion; nominal GDP 1970 is
$1073.1 billion.
6. M. Kalecki, Theory of Economic Dynamics (London: George Allen &
Unwin, 1965; rev. 2nd ed., New York: Monthly Review Press, 1968).
16 | Chapter 2
(c) The ratio of real GDP 2018 to real GDP 1970 is about 3.8;
the ratio of nominal GDP 2018 to nominal GDP 1970 is
about 19.2.
5.
2020
(d) The difference between the two ratios can be explained
by the inflation ­factor between 1970 and 2015, reflected in
the growth of the GDP deflator. Letting Pt = GDP deflator in
time t, and Yt = real GDP in time t, we know that P2018Y2018/
P1970Y1970 = 19.2, and that Y2018/Y1970 = 3.8, so that P2018/
P1970 = 19/2/3.8 = 5.1; in other words, the GDP deflator has
grown by a ­factor of 5.1.
2. This is a worked exercise. Please see the text for the
solution.
3. (a) GDP rises by $2 m)illion (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 w
­ asn’t produced that year. They ­aren’t part of national income, ­either).
(c) No impact. This is a government transfer payment, not a
government purchase of a good or ser­vice. If the government hired the unemployed and paid them to dig ditches or
program in C++, then their wages would count as a government purchase.
Quantity of oranges
Quantity of
boomerangs
Price of oranges
(dollars)
Price of boomerangs
(dollars)
Nominal GDP
Real GDP in 2020
prices
Real GDP in 2021
prices
Real GDP in chained
prices, benchmarked to 2021
100
20
2021
105
22
1
1.10
3
3.10
Percentage
change
2020–2021
5
10
10
3.33
160
160
183.7
171
14.8
6.9
172
183.7
6.8
171.9
183.7
6.85
­ ere GDP growth only shows a tiny difference between the
H
vari­ous methods.
6. ­We’ll use Chad’s shortcut from Section 2.3:
growth in nominal GDP = growth in price level
(aka inflation) + growth in real GDP
As Chad notes, this ­isn’t exact, but it’s good enough for our
purposes. This implies that:
growth in nominal GDP − growth in real GDP
= inflation rate
(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.
All we need to do is add in our three definitions of “growth
in real GDP,” and w
­ e’ll have our three answers:
(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).
Paasche: 14.8% − 6.9% = 7.9%
Laspeyres: 14.8% − 6.8% = 8%
Chained: 14.8% − 6.85% = 7.95%
(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.
7. (a) Without taking relative price differences into account,
India’s economy is 13.2% of the size of the U.S. economy
[(152 trillion rupees/65.1)/16.5 trillion = $2.34 trillion/$17.7
trillion.]
4. Real GDP in 2027 in 2025 prices: $5,950; 19% growth
between 2026 and 2027.
Real GDP in 2025 in 2027 prices: $6,500.
Real GDP in chained prices, benchmarked to 2027: $6,483.
(Note: The 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.)
(b) Given that prices in the United States are higher by a
­factor of 3.6 (=1/.277) and India’s GDP in U.S. dollars in U.S.
prices equals $12.34 trillion, then India’s GDP in U.S. dollars
and U.S. prices is $2.36 times 3.6 = $8.44 trillion. Taking
relative price differences into account, India’s economy is
47% of the U.S. economy ($8.44 trillion/$17.7 trillion).
Mea­sur­ing the Macroeconomy | 17
(c) The numbers are dif­
fer­
ent ­
because many consumer
goods—­for example, food, haircuts, and medical visits—­
are very cheap in India when you are mea­sur­ing in U.S. dollars. This is usually true in poor countries. As ­we’ll see in
Chapter 20, when we look at The Economist’s “Big Mac
Index” of exchange rates, the same McDonald’s hamburger
is much cheaper in poor countries than in rich countries
when you compare prices in U.S. dollars. Wages, rents, and
taxes cost less in poor countries, which makes it cheaper to
produce a hamburger, a haircut, or even a doctor’s visit.
That means that while India is a poor country, the Indian
economy is quite large. It is one-­half the size of the U. S.
economy.
8. (a) $.052 trillion/$17.7 trillion = .3%
(b) ($.052 trillion/1.11)/$17.7 trillion = .26%
(c) The numbers are dif­fer­ent ­because many goods are more
expensive in Sweden than in the United States.
9. (a) If fewer ­people have homes, then the average person
must be worse off when it comes to homeownership: ­after
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. T
­ hese
wages for workers and purchases of materials (which are
mostly wages for other workers, prob­ably) all show up in
GDP.
This question illustrates a famous parable in economics,
the “fallacy of the broken win­dow.”7 If a person breaks a
shop win­dow, the shop owner has to pay to repair that win­
dow. 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 win­
dow. So he w
­ ould’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.
Therefore, 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 the
citizens if the earthquake had not happened.
7. Henry Hazlitt, Economics in One Lesson (New York: Harper, 1946),
Chapters 1 and 2.
CHAPTER 3
An Overview of Long-­Run Economic Growth
CHAPTER OVERVIEW
This short chapter lays out the basic facts of the wealth of
nations. Chad makes it clear that higher GDP per person usu­
ally means real improvements in ­people’s lives—­something
that more than a few undergrads might need to remember.
He also covers the s­ imple and increasingly common math­
ematical shortcuts that macroeconomists and finance profes­
sors 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 too much 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 pro­
gress, and Chad hits a few of them quite quickly: higher lev­
els 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 hap­
pened before in ­human history begins to happen, not once,
but again and again in many countries, the word “miracle”
18
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. Of course,
many students and academics are concerned about in­equality
and climate change, and, increasingly, students w
­ ill want to
contextualize the “miracle” to address the concerns of their
generation.
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 dif­fer­
ent places. Argentina, China, Ghana, the United Kingdom,
Japan, and the United States receive par­tic­u­lar attention, if you
are looking for countries to highlight with additional data or
online photos.
We also learn that centuries-­long peaks and valleys have
occurred in the past—­which raises the question of ­whether the
developed world’s current prosperity could be just another
local maximum. (Two case studies that follow cover the
Roman economy’s golden age and collapse—­a cautionary tale
as well as one of the ­great puzzles of ­human history).
Fi­
nally, he introduces the term “­
Great Divergence,”
coined by Harvard’s Lant Pritchett to summarize the enor­
mous new gap in living standards between the world’s rich­
est and poorest inhabitants.
An expanded case study l­ ater in the chapter looks at ­whether
the world ­really is experiencing a ­great divergence: As Steven
Parente and Nobel Prize winner Ed Prescott have shown in
their work, and as Xavier Sala-­i-­Martin has shown in separate
work, the rapid growth in East and South Asia throws doubt
on the ­Great Divergence—or at least makes a strong case for
nuance.
An Overview of Long-­Run Economic Growth | 23
­Table 1. GROWTH RATES IN THE EU­RO­PEAN UNION
Country
Per Capita
Real GDP
Growth Rate
Real GDP
Growth
Rate
Population
Growth
Rate
Austria
Belgium
Bulgaria
Croatia
Cyprus
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Ireland
Italy
Latvia
Lithuania
Luxembourg
Malta
Netherlands
Poland
Portugal
Romania
Slovak Republic
Slovenia
Spain
Sweden
U.K.
4.62%
3.45%
6.79%
6.44%
5.21%
5.14%
3.74%
5.83%
4.84%
3.73%
3.94%
4.68%
6.62%
6.13%
3.70%
6.99%
7.42%
4.45%
4.63%
4.59%
6.76%
4.86%
7.00%
6.16%
6.84%
4.74%
3.50%
3.04%
5.21%
3.88%
6.01%
5.19%
6.36%
5.45%
4.33%
6.12%
5.03%
3.92%
4.28%
4.42%
6.42%
7.14%
3.52%
6.13%
5.95%
6.44%
8.10%
5.20%
6.78%
4.68%
6.38%
6.31%
6.89%
5.04%
4.79%
3.71%
0.56%
0.41%
−0.73%
−1.17%
1.10%
0.30%
0.56%
0.27%
0.18%
0.18%
0.33%
−0.25%
−0.20%
0.96%
−0.17%
−0.81%
−1.37%
1.92%
3.35%
0.58%
0.01%
−0.18%
−0.58%
0.14%
0.05%
0.28%
1.25%
0.65%
capita GDP as the differences between the two growth rates.
To provide an example, consider the countries that make up
the Eu­ro­pean Union. Real purchasing power parity GDP in
dollars, as defined in Chapter 2, is provided by the IMF, and
population data are provided by Eurostat.2 As shown in
­Table 1, the growth rates across the Eu­ro­pean Union have
recovered since the ­
Great Recession, where the average
growth rate in per capita real GDP was about 5.2%. Figure 1
demonstrates that some countries that experienced above
average rates of growth in per capita GDP have also experi­
enced population declines. See, for example, Croatia, Hun­
gary, Latvia and Lithuania. Countries such as Greece, Italy,
and Portugal, experienced below average per capita real
GDP growth rates and population declines. Some of the
most developed countries in Eu­
rope, such as the U.K,
2. Population data can be found at: https://­appsso​.­eurostat​.­ec​.­europa​.­eu​
/­nui​/­setupDownloads​.­do. Real Purchasing Power Parity GDP data can
be found at: https://­www​.­i mf​.­org​/­external ​/­pubs​/­f t ​/­weo​/­2018​/­02​/­weodata​
/­w eorept​.­a spx​?­p r​.­x ​= ­6 8&pr​.­y ​=­11&sy​=­2 017&ey​=­2 018&ssd​=­1&sort​
=­country&ds​=­​.­&br​=­1&c​=­946%2C137%2C122%2C181%2C124%2C918%
2C138%2C964%2C182%2C960%2C423%2C935%2C968%2C128%2C93
9%2C936%2C961%2C172%2C132%2C184%2C134%2C174%2C144%2C
944%2C178%2C136%2C112%2C941&s​= ­N GDPD%2CPPPGDP&grp​
=­0&a​= ­#download.
Figure 1. Per Capita Real GDP Growth Rates and Population
Growth Rates in EU (see footnote 1 for data sources, graph
constructed using STATA).
France, and Germany experienced relatively lower growth
(we ­will return to pos­si­ble explanations in Chapter 5, when
we study Solow’s transition dynamics, for example, well
developed countries are in rich in physical capital, caus­
ing depreciation to be relatively high and net investment
relatively low to the capital stock). Of t­hese more devel­
oped countries, only Italy experienced a population
decline. Fi­nally, the U. K. recorded the lowest per capita
real GDP growth rate, and the next to lowest real GDP
growth rate (Italy had the lowest)—­this relatively lower
growth rate is prob­
ably attributed to some degree to
­ ill also return to when we discuss
Brexit—­which we w
international macroeconomics—­when we study interna­
tional economic relations, we ­will consider the effects of
trade relations on direct foreign investment.
REVIEW QUESTIONS
1. The first sustained economic growth occurred in ­England
in the late 1700s, and spread across western Eu­rope over the
next few de­cades. A thousand years ago, living standards
­were quite equal across countries—­Robert Lucas summed it
up by saying incomes differed by a ­factor of maybe two.
­Today, living standards differ by a f­actor of 30, perhaps as
high as 50, across countries.
2. The average 40-­year-­old ­today in the United States is
about twice as rich as the same person 35 years ago. This is
confirmed by applying the rule of 70: living standards grew
about 2 ­percent per year, so 70/2 = 35 years.
The text notes that South K
­ orea 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
24 | Chapter 3
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 overstates.)
3. This is an exciting and active area of research. I’ll let you
try out some answers on your own, but I generally direct
students to three ­things: a) the development of trade and
markets; b) a shift in epistemology—­the Galileo example;
and c) fossil fuel based industrialization—­where a barrel of
oil generates about 5.8 million BTUs.
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 dis­
cussing fairly constant exponential growth: the first takes care
of the ­simple math and the second takes care of the ­simple
graphs.
(d)
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.
EXERCISES
1. 2050 is 33 years from 2017.
(a) $16,664
(b) $23,067
(c) $43,781
(d) $82,087
So if Ethiopian living standards grew at 1%, then in 33 years,
Ethiopia’s living standard w
­ ill almost approach the living
standard of 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.
(c)
3. This is a worked exercise. Please see the text for the
solution.
4. (a) Age 25: $33,455. Age 30: $44,771. Age 40: $80,178.
Age 50: $143,587. Age 65: $344,115.
(b) 5 ­percent: Age 25: $31,907. Age 30: $40,722. Age 40:
$66,332. Age 50: $108,048. Age 65: $224,625.
(c) 7 ­percent: Age 25: $35,063. Age 30: $49,178. Age 40:
$96,742. Age 50: $190,306. Age 65: $525,061.
The shift from 5 ­percent to 7 ­percent more than doubles the
value of the retirement portfolio by age 65.
An Overview of Long-­Run Economic Growth | 25
(c)
(d)
5.
(a)
(b)
(c)
6. This is a worked exercise. Please see the text for the
solution.
26 | Chapter 3
10. (a) (1/3) × gk
7.
United States
Canada
France
U.K.
Italy
Germany
Japan
Ireland
Mexico
Brazil
Indonesia
Keyna
India
China
Ethiopia
1980
2017
29219
24647
22394
19991
19928
19552
18977
12826
12225
5307
2212
2052
1169
826
724
54807
42540
38841
39135
37242
46445
40250
77160
17070
13795
10598
3069
6420
15288
1596
Growth Rate
1.71%
1.49%
1.50%
1.83%
1.70%
2.37%
2.05%
4.97%
0.91%
2.62%
4.33%
1.09%
4.71%
8.21%
2.16%
8. This is an essay question.
9. ­These are all approximations. Side note: students often
have prob­lems with this question ­because they fail to recog­
nize the equation as a growth pro­cess (as the initial value of
x and y are implied as 1). It might help to remind students of
this point and that gx is 4% and gy is 2%.:
(a) 6 ­percent
(b) 2 ­percent
(c) −2 ­percent
(d) 3 ­percent
(e) 4 ­percent
(f) 0 ­percent
(b) (1/3) × gk + (2/3) × gl
(c) gm + (1/3) × gk + (2/3) × gl
(d) gm + (1/4) × gk + (3/4) × gl
(e) gm + (3/4) × gk + (1/4) × gl
(f) (1/2) × (gm + gk + gl)
(g) (1/4) × gk + (1/4) × gl − (3/4) × gm
11. (a) Time 0: 2. Time 1: 2.04. Time 2: 2.081. Time 10:
2.44. Time 17: 2.8. Time 35: 4.
(b) Time 0: 1. Time 1: 1.05. Time 2: 1.1025. Time 10: 1.638.
Time 17: 2.29. Time 35: 5.52.
(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 268 years (= ln(61000/300)/ln(1.02))
(b) About $99 (= 61000/(1.03)217). 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 p­ ercent rate for 217 years.
A Model of Production | 35
­Table 1. DERIVING THE IMPLIED RELATIVE TOTAL
PRODUCTIVITY COEFFICIENT OF EU28 COUNTRIES: 2017
Country
Austria
Belgium
Bulgaria
Croatia
Cyprus
Czechia
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Ireland
Italy
Latvia
Lithuania
Luxembourg
Malta
Netherlands
Poland
Portugal
Romania
Slovakia
Slovenia
Spain
Sweden
United
Kingdom
GDP
Per Capita
(Billions of Capital Stock
Capital Stock
2011
(Billions of
(Billions of
Chained
2011
Population 2011 Chained
U. S.
Chained U. S.
(Millions) U. S. Dollars)
Dollars)
Dollars)
8.7
11.4
7.1
4.2
0.86
10.6
5.8
1.3
5.5
67.2
82.1
11.1
9.7
4.8
59.4
1.9
2.9
0.58
0.43
17
38.2
10.3
19.7
5.5
2.1
46.4
9.9
66.2
1,867.60
2,619.80
366.80
477.50
144.30
1,949.50
1,329.80
175.30
1,103.90
12,670.50
15,656.60
1,667.10
1,137.00
1,182.60
12,681.20
287.30
273.70
191.90
48.50
3,669.60
2,311.30
1,947.70
1,727.50
531.70
313.00
9,047.50
1,864.80
10,439.20
450.10
531.70
141.90
102.10
27.50
382.90
263.00
40.60
237.00
2,754.60
4,035.20
283.20
267.60
349.00
2,343.00
51.90
89.40
58.4
18.00
852.20
1,084.80
278.40
497.10
165.80
70.60
1,725.90
474.60
2,788.70
214,666.67
229,807.02
51,661.97
113,690.48
167,790.70
183,915.09
229,275.86
134,846.15
200,709.09
188,549.11
190,701.58
150,189.19
117,216.49
246,375.00
213,488.22
151,210.53
94,379.31
330,862.07
112,790.70
215,858.82
60,505.24
189,097.09
87,690.36
96,672.73
149,047.62
194,989.22
188,363.64
157,691.84
Germany’s. If France and Germany employ the same technology (have inputs that are equally productive), then France
should have a per capita output that is about 99% of Germany’s. However, France’s a­ ctual per capita output is about
83% of Germany’s per capita output. Clearly, France’s inputs
are less productive than Germany’s inputs (in this case, 84%
as productive as Germany’s inputs).
REVIEW QUESTIONS
1. Macroeconomic models are also toy versions of the real
world that (hopefully) contain the key moving parts to give
us an idea about how the real world ­really works.
In order to generate real insights, a model of ice cream
production only needs 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
returns to ideas, but it is incredibly s­ imple. It helps us forget
about the (hopefully) extraneous details about real life: the
­human emotions, the need for health care and nutrition, the
distribution of income, natu­ral resources, and so forth. Economics has progressed as a science when it has left ­things
out. Economists are reluctant to add new tools to their toolkit: we work with the small number of tools we have.
2. Hire workers ­until the cost of one more worker (in wages)
is just equal to the benefit of having one more worker (in
extra output). When you have only a 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 continues
to fall u­ ntil extra workers ­aren’t worth the cost.
The same argument holds for capital: buy machines ­until
the marginal rental cost of one more machine equals the
marginal benefit of one more machine.
3. An equilibrium occurs when businesses want to hire
exactly the number of workers they have and want to rent
exactly the number of machines they have.
In our model the number of workers and machines in
society is fixed (or perfectly inelastic)—so what ­really
adjusts ­isn’t the quantity of machines and workers: It’s
the price of machines and workers. Prices adjust so that
the quantity supplied equals the quantity demanded.
­ e’ll see that the price of output—­ice cream—­
(­Later w
adjusts as well, to make sure that all the output gets sold.)
4. This ice cream economy is a closed economy. The only
t­ hing it makes is ice cream and the only t­ hing it consumes is
ice cream, and while workers and capital o­ wners may get
paid in money, ­there’s only one t­ hing 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 c­ an’t drive big income differences. Why
not? B
­ ecause our usual model assumes that diminishing
returns to capital set in extremely rapidly. That’s what the
CHAPTER 4
A Model of Production
CHAPTER OVERVIEW
This chapter puts the Cobb-­Douglas production function
front and center in our study of economic growth. At the
same time, it provides the opportunity to tell your students
an honest yet understandable story about general equilibrium, as well as the chance to show how productivity
accounting can give real insight into the reasons why some
countries are so rich while o­ thers 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. Macro­
economists make “toy models” of a complex world and then
check to see if the models match 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 dif­
fer­ent 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 section covers the work­horse 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 × L 2/3 throughout, so you can dispense with the alphas. He illustrates the constant returns
property before taking us to a ­simple general equilibrium
setup.
The only real maximization prob­lem to consider is profit
maximization for the firm. Since Chad assumes l­abor and
capital are in fixed supply, it’s a very straightforward setup.
He assumes no calculus, so you can just hand students the
formula for the marginal product of ­labor or capital, show
that it’s intuitive, and then move on to the real economics
that grow out of the model.
A few immediate payoffs are that 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 p­ eople’s
quasi-­Luddite intuition, so it may be a point worth driving
home. Also, as I show l­ater in this chapter, 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.
Fi­
nally, 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 psy­chol­
ogy: 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 f­ actors, such
as the supply of savings, the supply of ideas, and the supply
of ­labor.
27
36 | Chapter 4
Country
Austria
Belgium
Bulgaria
Croatia
Cyprus
Czechia
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Ireland
Italy
Latvia
Lithuania
Luxembourg
Malta
Netherlands
Poland
Portugal
Romania
Slovakia
Slovenia
Spain
Sweden
United Kingdom
Per Capita GDP
(Billions of 2011
Chained U. S.
Dollars)
Relative (to
Germany)
per Capita
Capital Stock
51,735.63
46,640.35
19,985.92
24,309.52
31,976.74
36,122.64
45,344.83
31,230.77
43,090.91
40,991.07
49,149.82
25,513.51
27,587.63
72,708.33
39,444.44
27,315.79
30,827.59
100,689.66
41,860.47
50,129.41
28,397.91
27,029.13
25,233.50
30,145.45
33,619.05
37,196.12
47,939.39
42,125.38
1.13
1.21
0.27
0.60
0.88
0.96
1.20
0.71
1.05
0.99
1.00
0.79
0.61
1.29
1.12
0.79
0.49
1.73
0.59
1.13
0.32
0.99
0.46
0.51
0.78
1.02
0.99
0.83
Relative (to Germany)
per Capita GDP
Predicted Relative
(to Germany) per
Capita GDP
(Assuming a
Wage Share = .5)
Implied
Relative
Total ­Factor
Productivity
Coefficient
1.05
0.95
0.41
0.49
0.65
0.73
0.92
0.64
0.88
0.83
1.00
0.52
0.56
1.48
0.80
0.56
0.63
2.05
0.85
1.02
0.58
0.55
0.51
0.61
0.68
0.76
0.98
0.86
1.06
1.10
0.52
0.77
0.94
0.98
1.10
0.84
1.03
0.99
1.00
0.89
0.78
1.14
1.06
0.89
0.70
1.32
0.77
1.06
0.56
1.00
0.68
0.71
0.88
1.01
0.99
0.91
0.99
0.86
0.78
0.64
0.69
0.75
0.84
0.76
0.85
0.84
1.00
0.58
0.72
1.30
0.76
0.62
0.89
1.56
1.11
0.96
1.03
0.55
0.76
0.86
0.77
0.75
0.98
0.94
Sources: FRED Database, Penn World ­Tables, and author’s calculations.
one-­third exponent on capital means that capital just ­isn’t
that impor­tant. If you run through a s­imple example, you
can show students that a 1% rise in capital c­ auses only a
1/3% rise in output: a small effect.
The case study on l­ abor shares shows that t­ here’s actually
some good evidence that capital is not that impor­tant in
practice.
6. Your guess is as good as mine. But Douglass North’s
guess is prob­
ably better than both our guesses put
together.
EXERCISES
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) ­There are decreasing returns to scale at the beginning,
toward constant returns as inputs increase.
but moving ­
(Hint: The A term gives a l­ittle extra productivity, whose
impact diminishes as K and L rise.)
(g) ­There are increasing returns to scale at the beginning,
but moving t­oward constant returns as inputs increase.
2. (a)
A Model of Production | 37
(b)
5. (a)–(c) Please see the following t­ able.
ki/
kusa
yi/yusa
175,075 54,807
1.00
1.00
1.00
1.00
153,390 42,540
136,004 38,841
154,766 40,603
0.88
0.78
0.88
0.78
0.71
0.74
0.96
0.92
0.96
0.81
0.77
0.77
142,891 36,521
0.82
0.67
0.93
0.71
26,620 10,598
41,589 16,469
41,866 17,070
4,179 3,069
2,938 1,596
0.15
0.24
0.24
0.02
0.02
0.19
0.30
0.31
0.06
0.03
0.53
0.62
0.62
0.29
0.26
0.36
0.49
0.50
0.19
0.11
K/L
United
States
Canada
France
Hong
Kong
South
­Korea
Indonesia
Argentina
Mexico
K
­ enya
Ethiopia
(c) + (d)
Y/L
Predicted Implied
yi/yusa Ai/Ausa
(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 c­ an’t m
­ atter that much.
6.
ki/
kusa
yi/yusa
175,075 54,807
1.00
1.00
1.00
1.00
153,390 42,540
136,004 38,841
154,766 40,603
0.88
0.78
0.88
0.78
0.71
0.74
0.91
0.83
0.91
0.86
0.86
0.81
142,891 36,521
0.82
0.67
0.86
0.78
26,620 10,598
41,589 16,469
41,866 17,070
4,179 3,069
2,938 1,596
0.15
0.24
0.24
0.02
0.02
0.19
0.30
0.31
0.06
0.03
0.24
0.34
0.34
0.06
0.05
0.79
0.88
0.91
0.92
0.62
K/L
3. This is a worked exercise. Please see the text for the
solution.
4. (a) Y = A K3/4L1/4
Rule for hiring capital: (3/4) × Y/K = r
Rule for hiring ­labor: (1/4) × Y/L = w
Capital demand equals capital supply: K = K
­Labor demand equals l­abor supply: L = L
(b) The in­ter­est­ing answers are:
r* = (3/4) A × (L/K)1/4 (more workers or ideas equals a higher
interest rate!)
w* = (1/4) A × (K/L)3/4 (more machines or fewer workers
equals higher wages!)
(c) Y/L = A × (K/L)3/4
United
States
Canada
France
Hong
Kong
South
­Korea
Indonesia
Argentina
Mexico
­Kenya
Ethiopia
Y/L
Predicted Implied
yi/yusa Ai/Ausa
Since we now assume that capital ­doesn’t run into diminishing returns that quickly, the big capital differences now predict big output differences. With the change in the capital
exponent, the implied total ­factor productivity coefficient
increases for Canada, South ­Korea, Indonesia, Argentina,
Mexico, ­Kenya, and Ethiopia.
Prob­lems 5 and 6 are useful in showing students how a
choice we make early on—­the choice of exponent—­has a
big impact down the road when we try to draw conclusions
from the model. Assumptions ­matter.
38 | Chapter 4
7. (a) In the first column, ­we’re now saying that the United
States is X times richer than a par­tic­u­lar country. In the second
column, ­we’re saying that capital differences alone make the
United States Y times richer than that par­tic­u­lar country. In the
third column, w
­ e’re saying that TFP differences alone make
the United States Z times richer than that par­tic­u­lar country.
(b)
United States
Canada
France
Hong Kong
South ­Korea
Indonesia
Argentina
Mexico
­Kenya
Ethiopia
yusa/yi
Predicted
yusa/yi
Implied
Ausa/Ai
1
1.29
1.41
1.35
1.50
5.17
3.33
3.21
17.86
34.34
1
1.05
1.09
1.04
1.07
1.87
1.61
1.61
3.47
3.91
1
1.23
1.30
1.30
1.40
2.76
2.06
1.99
5.14
8.79
(b) Amer­i­ca’s bigger capital stock makes it 3.47 times richer
than ­Kenya. Amer­i­ca’s higher level of TFP makes it 5.14
times richer than ­Kenya. For K
­ enya, the U.S. TFP is about
1.5 times (5.14/3.47) as impor­tant as capital per person in
explaining relative per capita income.
(c) Amer­i­ca’s bigger capital stock makes it 3.91 times richer
than Ethiopia. Amer­i­ca’s higher level of TFP makes it 8.79
times richer than Ethiopia. For Ethiopia, the U.S. TFP is
about 2.25 times as impor­
tant as capital per person in
explaining relative per capita income.
8. (a)
(b) For the second quarter of 2019, the index was 101.02.
The index from 1965 to 1980 was about 111, so l­abors share
for the second quarter of 2019 was about 61%.
(c) The production can still be Cobb-­Douglas, but the exponents on capital and l­abor have been shifting: which is capital getting a higher share of income and l­abor getting a
smaller share of income than in the past.
9. Olson is referring to the fact that even if p­ eople are individually smart, they may make poor (or nonsensical) group
decisions. The classic ­simple example would be Condorcet’s
paradox, which many students w
­ ill 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 p­ eople
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 c­ an’t ­people
in poor countries come to some agreement to start acting
more like the rich countries? If they need to change government 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”
were poorer. Government bureaucrats, u­nion
when they ­
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
­ ill win and who w
­ ill lose in the transifighting over who w
tion to prosperity (­Will I lose my government job? ­Will I get
laid off at the factory? ­Will my education in communist economics become worthless?) rather than creating the prosperity in the first place. This, to Olson, is a puzzle that
deserves further study.
CHAPTER 5
The Solow Growth Model
CHAPTER OVERVIEW
Chad lays out the simplest pos­si­ble version of the Solow
with no technology growth and no population
model—­
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 cap­
i­tal­ist countries grow quickly for a while and then slow
down. At the same time, students ­will understand why long-­
term growth in living standards in cap­i­tal­ist socie­ties c­ an’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 y­ ou’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 in 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 ­will be grinding through the mod-
els 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, ­t hings get a ­l ittle tougher
­t here, 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, which you can omit in this course without feeling too deceptive. The key point I emphasize when
introducing the Solow model is that w
­ e’re g­ oing 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 g­ oing 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 t­ hese 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.
39
46 | Chapter 5
­Table 1. EXPLAINING CAPITAL AND INCOME DIFFERENCES IN THE EU28 COUNTRIES
Country
Bulgaria
Croatia
Romania
Greece
Portugal
Latvia
Hungary
Poland
Slovakia
Lithuania
Estonia
Cyprus
Slovenia
Czechia
Spain
Italy
France
Malta
United Kingdom
Finland
Denmark
Belgium
Sweden
Germany
Netherlands
Austria
Ireland
Luxembourg
K (2017, billions 2001
chained U.S Dollars)
Y (2017, billions 2001
chained U. S. Dollars)
Average I/Y
1990–2017
Per Capita Real
GDP, 2017
(Purchasing Power
Parity U. S. Dollars)
366.80
477.50
1,727.50
1,667.10
1,947.70
287.30
1,137.00
2,311.30
531.70
273.70
175.30
144.30
313.00
1,949.50
9,047.50
12,681.20
12,670.50
48.50
10,439.20
1,103.90
1,329.80
2,619.80
1,864.80
15,656.60
3,669.60
1,867.60
1,182.60
191.90
141.90
102.10
497.10
283.20
278.40
51.90
267.60
1,084.80
165.80
89.40
40.60
27.50
70.60
382.90
1,725.90
2,343.00
2,754.60
18.00
2,788.70
237.00
263.00
531.70
474.60
4,035.20
852.20
450.10
349.00
58.40
0.13
0.215
0.194
0.247
0.274
0.216
0.209
0.179
0.232
0.165
0.253
0.304
0.272
0.258
0.29
0.258
0.43
0.281
0.23
0.28
0.255
0.297
0.269
0.23
0.232
0.3
0.267
0.359
19,985.92
24,309.52
25,233.50
25,513.51
27,029.13
27,315.79
27,587.63
28,397.91
30,145.45
30,827.59
31,230.77
31,976.74
33,619.05
36,122.64
37,196.12
39,444.44
40,991.07
41,860.47
42,125.38
43,090.91
45,344.83
46,640.35
47,939.39
49,149.82
50,129.41
51,735.63
72,708.33
100,689.66
Source: Penn World T
­ ables, Federal Reserve Bank of St. Louis Database, and author’s calculations.
tries between 1990 and 2017 and the respective per capita
GDPs in 1990 are compared. Based on Solow’s transition
dynamics, in 1990, countries with high growth rates ­were
relatively far away from their steady states, while countries
with low growth rates ­were relatively close to their steady
states. Ireland, Estonia, Malta, Romania, and Poland had
average per capita real GDP growth rates in excess of 4%
and relatively low levels of per capita real GDP in 1990. In
contrast, real per capita real GDP in Lithuania was about
$24,000 in 1990, and it increased to almost $31,000 in 2017,
where the average growth rate was about .9%. This suggests
that Lithuania was relatively close to its steady state in 1990
and that its steady-­state conditions have not changed as significantly as ­those of the other countries of the EU28.
Figure 2. Growth Rates in the EU28 Countries, 1990–2017
Source: Penn World ­Tables, Federal Reserve Bank of St. Louis, and
author’s calculations.
and vari­ous other countries around the world in Section 5.7
of the textbook. The Penn World Database for many of the
Eastern Eu­ro­pean EU countries begins in 1990. In Figure 2,
the average per capita GDP growth rates of the EU28 coun-
REVIEW QUESTIONS
1. Capital accumulation delivers growth. This makes sense
­because we can see by looking around ourselves that using
machines helps 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.
The Solow Growth Model | 47
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 becomes, the harder it is to produce
more (­there are diminishing returns), while a larger amount
of capital depreciates (­there is a constant depreciation rate).
Together, ­these two forces mean that capital ­can’t be the true
cause of long-­r un growth in a cap­i­tal­ist economy.
2. K6 = 1,469
I6 = 200
dK 6 = 147
change in capital: 53 = 200 − 147
3. The gap is “net investment” or “how much the capital
stock grows in this period.”
s 1/2
4. C*/L = c* = (1 − s )A3/2 ⎛ ⎞ .
⎝d⎠
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 (which is good for raising
consumption), but it means ­there’s less to consume. In a
more advanced course, you w
­ ill learn to find an optimal
savings rate if your goal is to maximize long-­r un 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%. 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
­r unning from tech to capital. Some economists focus on the
route by which capital creates technology, but most researchers currently think that’s a less impor­tant channel.
6. If s , d , or A shifts, then a curve ­will shift. If K or L shift,
then ­you’re moving along the fixed savings and depreciation
curves. S and A shift the savings curve (more of each pushes
it up), while a rise in d makes the depreciation curve steeper.
7. The princi­ple of transition dynamics is that any time an
economy is away from the steady-­state capital-­labor ratio,
forces ­will naturally return the economy to the steady state.
When the economy is far from the steady state, it w
­ ill move
t­ here quickly, but as it gets closer to steady state, the pro­cess
slows down.
The Solow model has this property b­ ecause of two features:
diminishing returns to capital combined with the constant
depreciation rate. The more capital-­rich the economy becomes,
the harder it is to build t­hose extra units of capital: that’s
diminishing returns. Also, the richer the economy becomes,
the bigger its capital stock must be: and the more capital you
have, the more capital you have that is 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.
EXERCISES
1. The capital stock ­will immediately start falling ­toward its
new steady-­state level. At first, the drop ­will be rapid, but
then it w
­ ill slow down, and eventually it w
­ ill come to rest at
the new, lower level.
Before the drop in savings, the capital stock was at Old K*.
Then p­ eople became more impatient, and immediately the savings curve dropped to “Lo s.” The capital stock does not make
the same immediate drop, but it does start dropping quickly.
The double-­thick dashed line shows the immediate gap
that opens up that year between the massive amount of
depreciation and the lower amount of saved capital. That
shows how much the capital stock w
­ ill 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 w
­ ill
also drop: imagine pushing that double-­thick dashed line to
the left, and you’ll see that it ­will become a shorter line. As
a result, 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
f­ actor productivity coefficient Ā permanently increases. The
48 | Chapter 5
increase in Ā has a direct effect of increasing current output,
and an indirect effect, whereby the increase in current output increases the level of savings and investment above the
level of depreciation: the resulting change in the capital
stock leads to further changes in output, subject to diminishing returns, as the economy then adjusts to new, higher,
steady levels.
(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.
(d) A onetime technology transfer stimulates growth, but
the growth rate w
­ ill diminish to zero as the economy moves
into a new, higher, steady state. In this case, for the economy
to continue to grow, new technology transfers need to be
continuous.
3. This is a worked exercise. Please see the text for the
solution.
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.”
However, in fact, the story ­doesn’t change at all if we divide
every­thing by L , 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 onetime drop in
K
, but now that’s happening, not b­ecause K falls, but
L
­because L 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 percentage 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. If you want to reinforce the growth
rate rules and sacrifice some precision, you might encourage
students to simply apply the growth rate rules to derive the
answers. Thus, both sets of answers are provided ­here.
(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%. So consumption increases by 10%.
How did I get this result? 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 the ratio in
(1 − s )Y after
equation 5.12 :
. Since s , Ā, and � are all the
[(1 − s ) × Y after ]
The Solow Growth Model | 49
same for both “before” and “­after,” they cancel out. All that
is left in the ratio is the difference in K.
The approximate answer: if the growth rules are used, then
recall that the gY = (1/3) × gk, and that gK = 33%, which
means that gY = 11%, and gC = gY = 11%.
Long-­run consumption ­will not change at all. That’s a
key insight h­ ere: 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-­r un impact on the steady-­state
capital stock.
(b) The precise answer: Consumption ­
will immediately
increase by 6.3%, 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, of course, consumption
­will not change at all.
The approximate answer using the growth rate rules w
­ ill
be: gy = (1/3) × (20%) = 6.66% = gC.
(c) Foreign aid that shifts only the capital stock w
­ ill only
help an economy temporarily b­ ecause it ­will only raise consumer spending temporarily.
We can hope that the Solow model is too s­ imple. Perhaps
a rise in foreign aid could help an economy to raise its level
of technology, or it could be used to educate p­ eople in the
value of saving money. If the aid can somehow permanently
raise A or s, then aid could have a permanent impact on living standards and consumer spending.
If we want foreign aid to have a permanent impact, then it
needs to be used to change the deep par­ameters, not the size
of the capital stock.
6. This is a worked exercise. Please see the text for the
solution.
7. (a)
(b) The average investment share of GDP between 1980 and
2006 is 18%. The average share of investment between 2012
and 2018 is 17.1.
(c) The average investment share declined by 5% between
­these two periods. Applying the growth rate rules from
Chapter 3 to equation 5.9 yields: gy = (1/2)*(gs − gd) + (3/2)
gA. Substituting −5% in for gs and holding other ­things constant yields gy = −2.5%. Alternatively students might calculate gy = (.171/.18).5 − 1 = 2.53%.
(d) This is a question about the determinants of the savings
rate in the U.S. economy. If, for example, as Chad describes in
Chapter 14, the exogenous risk premiums increase, the real
rate of interest increases, and the investment rate decreases.
However, if the risk premiums return to “normal,” we can
expect that the investment rate ­will return to “normal” levels.
8. As in exercise 5, students ­will be tempted to use the
growth rate rules and ignore the warning in footnote 5 in
Section 3.5. If you want students to use the growth rate
rules, you should allow for both answers.
.5
s
(a) 21/2 = 1 + gy*, so gy* = 41.42%, or given that y* = ⎛ ⎞ (A)1.5
⎝d⎠
, 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
9. (a) growth rate of GDP = 1/3 × growth rate of capital
stock
(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.
Note: As Kt falls 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 rises to infinity (through generous foreign
aid, for example), the growth rate of output can only be as
sY *
low as one-­third of d , the depreciation rate (where d =
).
K*
No ­matter how rich you become, the only way to grow
poorer is to wear down your capital stock.
10. Note that the question asks about the growth rate of GDP
per person, not the growth rate of capital.
(a) 3.33%
(b) 10%
(c) −25%
50 | Chapter 5
(d) Note that our growth equation is not in per capita terms,
yet the question asks about growth in per capita income.
Using the growth shortcut, 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%, which is the immediate
fall in Y/L from the immigrants
11. (a)
Country
United States
Italy
Mexico
Brazil
China
India
Vietnam
Zimbabwe
Per capita
GDP (United
States = 100),
2017
Growth rate
during
2007–2017
(%)
Per capita
GDP (United
States = 100),
steady state
100
70
30
20
15
8
7
2
2.0
1.0
2.5
3.0
8.0
7.0
5.0
6.0
100
50.16
35.44
27.91
110.84
42.36
19.03
7.59
(b) As long as the savings line is higher than the depreciation
line—in other words, as long as sA is greater than d —­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 a rate of � A − d . That
is also the growth rate of the capital stock.
Proof:
(b) For countries that have growth rates greater than that of
the United States, such as China and India, we expect relative per capita output to rise.
12. This is known, unsurprisingly, as an “AK model.” Much
theoretical work has been done on this kind of growth
model.
(a) The slope of the savings line is sA.
K t +1 = K t + I t − dK t (by definition of capital stock),
K t +1 = K t + sYt − dK t (by definition of investment),
K t +1 = K t + s AK t − dK t (by definition of production
function),
(K t +1 − K t ) /K t = s A − d (moved K t over, divided both
sides by K t ).
And by our growth shortcuts, we know that since the exponent on Kt is one in the production function, the growth rate
of capital equals the growth rate of output.
CHAPTER 6
Growth and Ideas
CHAPTER OVERVIEW
­ ere we discuss a key source of productivity growth: new
H
ideas. Most textbooks cover this material with a bit of hand
waving, but Chad takes the time to outline two ­simple models that w
­ ill let students understand the basics of the ecoThese two models underlie Paul
nomics of innovation. ­
Romer’s now-­classic model of endogenous growth.
The first model shows how an entrepreneur has a strong
incentive to spend money to discover profitable new ideas.
At the same time, this model shows that since idea discovery creates a (perhaps temporary) mono­poly, the invisible
hand fails and we land in a world of the second best. The
second model illustrates a key trade-­off society f­aces: how
many workers should make ideas rather than final products?
In the fifth edition of the textbook, Chad incorporates the
case study “Globalization and Ideas” into the text of Section 6.3, and he adds two new and very topical case studies,
“On the Possibility of Pro­gress” in Section 6.3 (where he
discusses natu­ral resource price trends before and a­ fter the
year 2000), and “Is Economic Growth Slowing Down?” in
Section 6.5 (as illustrated in the growth-­accounting exercise). In the latter case study Chad speculates about changes
in the nature of inventions and innovations possibly contributing to the slowdown and considers the potential effects of
artificial intelligence on pos­si­ble ­future growth trends. The
chapter concludes by pointing out how the Romer and Solow
models together can explain much of what we see, and it
also runs through the basics of growth accounting.
6.1 and 6.2 Introduction and the Economics of Ideas
We want to understand long-­term economic growth, and
Chapter 5 just explained that long-­term growth is driven by
technological pro­gress, which in turn is (usually? always?)
driven by the 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 he repeatedly uses Romer’s distinction between “objects”
(which are subject to diminishing returns) and “ideas” (which
are subject to increasing returns).
These sections sound a lot like microeconomics, and
­
some instructors ­will be tempted to give them short shrift in
their rush to cover the s­imple general-­equilibrium Romer
model. My sense is that you’ll ­really do your students a
disser­vice if you omit Sections 6.1 and 6.2, which cover the
economics of ideas at a solid microprinciples level. ­These
are microfoundations that undergraduates can h­ andle.
The idea diagram at the beginning of Section 6.2 prob­
ably 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 t­ hese
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 very
many dif­fer­ent kinds of food. Students prob­ably have some
experience with that. The r­ ecipe 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
51
Growth and Ideas | 57
­Table 1. GROWTH ACCOUNTING IN THE EU28 COUNTRIES, 1990–2017
Country
Austria
Belgium
Bulgaria
Croatia
Cyprus
Czechia
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Ireland
Italy
Latvia
Lithuania
Luxembourg
Malta
Netherlands
Poland
Portugal
Romania
Slovakia
Slovenia
Spain
Sweden
United Kingdom
Growth
in Capital
Stock
Growth
in ­Labor
Growth
in Output
Growth
in the
TFP
Growth in the TFP
as a Percentage of
Growth in Output
1.96%
1.77%
4.26%
1.44%
2.35%
1.30%
1.22%
2.16%
1.81%
1.82%
1.36%
1.33%
1.58%
4.70%
1.47%
0.56%
1.84%
2.57%
4.63%
1.70%
3.80%
2.04%
2.19%
2.00%
1.87%
3.02%
0.95%
1.69%
0.45%
0.49%
−0.79%
−0.49%
1.47%
0.11%
0.48%
−0.77%
0.35%
0.51%
0.14%
0.31%
−0.26%
1.07%
0.15%
−1.29%
−0.90%
1.58%
0.66%
0.46%
0.02%
0.11%
−0.65%
0.14%
0.18%
0.62%
0.52%
0.54%
3.20%
2.79%
1.72%
2.08%
3.09%
1.93%
2.58%
3.44%
2.38%
2.39%
2.58%
1.99%
2.67%
6.51%
1.84%
0.84%
0.00%
4.86%
4.94%
2.91%
4.77%
2.45%
4.08%
2.29%
2.30%
3.51%
2.67%
2.81%
2.00%
1.66%
−0.02%
1.60%
1.18%
1.22%
1.73%
2.74%
1.30%
1.22%
1.83%
1.17%
2.01%
3.63%
1.03%
1.21%
−0.47%
2.79%
2.29%
1.83%
2.86%
1.38%
3.31%
1.22%
1.27%
1.70%
1.93%
1.70%
62.31%
59.58%
−0.99%
77.14%
38.08%
63.58%
67.06%
79.70%
54.51%
50.99%
70.99%
58.86%
75.20%
55.74%
55.97%
143.34%
57.35%
46.45%
62.84%
59.96%
56.23%
81.13%
53.33%
55.35%
48.27%
72.33%
60.34%
Sources: Penn World ­Tables, Federal Reserve Bank of St. Louis Database, and author’s calculations. All data are mea­sured as growth rates in 2011 U.S.
dollars, constant country prices.
REVIEW QUESTIONS
1. Ideas can be copied ­free of charge but objects cannot.
Ideas include ­
recipes for food, ideas for inventions, the
words in novels or plays, musical scores, and philosophical
concepts. Objects include cookbooks, printed novels or
plays, motorcycles, and tubas.
2. Nonrivalry exists when one person’s use of a good leaves
just as much of that good for someone ­else. A nonrivalrous
good ­can’t be “used up,” since no m
­ atter 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 incurring any extra cost. As the scale grows larger, the average
cost of producing the nonrivalrous good always falls. The
more it gets used, the better.
The standard replication argument fails in this case: having two “idea factories” to produce the same good is inefficient. It’s more efficient to have one person pay the price of
invention once and then replicate it 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, so you might
as well just create one military force to defend every­one.
3. Words themselves—­when in the author’s mind—­are nonrivalrous. But it can be expensive to print a hardcover book.
The physical book is an object. The words in the book are
ideas—­free to replicate. If the novel is sold at marginal
the cost of just printing another book—­
then the
cost—­
author w
­ on’t get paid for the effort of writing the book. That
gives the author 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 b­ ecause ideas are nonrivalrous.” Thus, ideas are used twice in the same model:
once to create output and once to create new ideas.
58 | Chapter 6
5. Equation 6.7 calls this ��� (�, the letter “�,” and then �).
The variable � is a mea­sure of how efficiently researchers
can use the old stock of ideas to create valuable new ideas;
the variable � is the fraction of the workforce devoted to creating ideas rather than creating goods; and the variable � 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.
5. The planet with more knowledge is always twice as rich.
That’s all. It’s an upward shift. The following graph is on a
ratio scale, so constant growth rates show up as a straight
line.
6. Growth accounting gives us a first look at why a par­tic­u­
lar economy is growing over time. Is it ­because the economy
added p­eople? Machines? Ideas? How much of each?
Growth accounting taught economists that ideas ­were much
more impor­
tant than many wanted to believe—­
capital
­wasn’t the driving force ­behind “capitalism,” ­after all—­and
this understanding eventually encouraged economists to
build good models of where ideas come from.
EXERCISES
1. (a) nonrivalrous
(b) rivalrous
(c) rivalrous—­the painting itself is a good, not an idea.
(d) nonrivalrous
(e) rivalrous—­each fish I eat means less for o­ thers. If one
de­cided that the number of fish was “close to infinite,” then
I’d be comfortable saying fish are nonrivalrous.
2. This is a worked exercise. Please see the text for the
solution.
6. This is a worked exercise. Please see the text for the
solution.
7. (a) This economy grows at 2% per year: (1/3,000) × .06
× 1,000 = .02.
(b) Initial level of output per person: 94. ­After 100 years it’s
681.
(c) Doubling A0: 188 and 1,362.
doubling A! : 88 and 4,444 (remember to change it in the
technology growth and output equations!),
3. Figure 6.2: it doubles ­every 20 years, so by the rule of 70,
we would guess that the growth rate must be 3.5% per year.
Figure 6.3: Let’s round the number a ­little and say that it
almost doubles between 2000 and 2020: that’s a 3.5%
growth rate. It ­really looks like a bit less: 3% perhaps? ­After
the break, it doubles ­every 10 years: this is a 7% growth rate.
Figure 6.4 looks like the same story: a bit less than 3.5%
before the break and 7% afterward.
doubling z : 94 and 4,747. This is the best deal so far.
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
types of experimentation. In some socie­ties, certain kinds of
medical tests involving stem cells or animals might be
banned—­and in such socie­ties, z might be lower.
8. (a) The answer to the question of how Chinese economic
growth ­will affect the United States and the rest of the world
is quite speculative. In the context of Romer’s growth model,
as China becomes more integrated into the world economy,
the number of p­eople creating and sharing new ideas
increases. The major benefit to the United States and the rest
of the world, in Romer’s growth model, is an increase in the
growth rate of the total ­factor productivity coefficient and
per capita output.
doubling �: 94 and 4,747. This is the same as doubling z!
This shows scale effects at work: more ­people mining for
idea-­gold means finding more idea-­gold than all humanity
can eventually use.
(d) This is a personal choice.
(b) The potential costs for the United States could come in
both the pecuniary and technical externalities: the pecuniary externalities, as Chad speculates in the case study, “The
Growth and Ideas | 59
Possibility of Pro­gress,” might come in the form of increasing natu­ral resource prices, and the technical externalities
might come in the form of rising carbon emissions or pollution in general.
(b) The growth rate of knowledge is the same as before: z l L.
(c) As Lord John Eatwell has suggested, global stabilization
requires new rules aligning the geographic and l­ egal dimensions of markets. The creation of new rules w
­ ill require
more international coordination, not less.
(c) The growth rate of per capita output is (1/2) z l L . We use
the growth-­rate shortcut. Recall that per capita output is
written as yt = At1/2(1 − l ) and notice that the exponent on At
in the production function is 1/2 and that the growth rate in
output is solely driven by A, the total f­actor productivity
coefficient. As a result, the growth rate in per capita output
is ½ times the growth rate in A, as (1 − l ) ­doesn’t change.
8. (a)
(d) yt = [A0(1 + z l L )t]1/2(1 − l )
The only way this differs from equation 6.9 is in 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.
(b) Intellectual property products’ share of GDP has
increased on a trend over the last 60 years. In our textbook
model, this trend can be attributed to three f­actors: z, the
technology production coefficient—­the United States has
become more productive at producing intellectual property;
l , the ­percent of the ­labor forced engaged in the production
of ideas—­the United States has more workers, given the
size of the ­labor force, producing intellectual property; and
L, the size of the ­labor force—­the United States’ larger ­labor
force c­ auses more workers to be engaged in the production
of intellectual property.
(c) We expect that the growth rate in real GDP and per capita output ­will have increased. However, we suspect that
long-­run growth rates ­will have not increased as intellectual property’s share of GDP has increased. One pos­si­ble
explanation, as described in the next exercise, is that ideas
run into diminishing returns. The growth rate effects of
new ideas diminish. This result, as in the Solow model,
­causes the growth rate to fall as the economy moves to a
higher level of output and per capita output. For example if
ΔAt+1 = z At(1/2)LAt, then by dividing both sides of the equation by At, we ­will get gAt, = z At(–1/2)LAt, which means that
the growth rate in ideas diminishes as new ideas are
discovered.
9. (a) Ideas run into diminishing returns: you find the best
ideas first, and then you find less useful ideas down the road.
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 s , d , z , l , or L—­can alter the growth rate temporarily,
but, as in the Solow model, due to diminishing returns to
capital, the economy w
­ ill transition back to a balanced rate
of growth. The further the economy is below its balanced-­
growth per capita output, the higher ­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 . Therefore,
g*Y/L = gY/L = .03.
(b) A Latin American economy: gA = .0167 = gY/L − gK/L .
Therefore, g*Y/L = .015 < gY/L = .0167.
(c) An Asian economy: gA = .01 = gY/L − gK/L . Therefore,
g*Y/L = .015 < gY/L = .06.
60 | Chapter 6
4. (a)
5. (a) gYt = (4/3)gAt. Given that the marginal product of capital is smaller, the amplification ­factor is smaller.
(b) yt = Yt /L = [s/(gy + d)]1/3(At)4/3(1 − l ). Given that the
marginal product of capital is smaller, the amplification
­factor is smaller. See footnote 26 in the text.
6. (a) gYt = (1/(1 − α))* gAt. In the text, α = 1/3, and [1/(1 − α)]
= 3/2.
(b) yt = Yt /L = [s/(gy + d)][α/(1−α)(At)1/(1−α)(1 − l ). In the text,
α/1 − α = (1/3)/(2/3) = .5, and 1/(1 − α) = 1/(2/3) = 1.5.
(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.
(c) [1/(1 − α)] shows the amplifying or multiplier effect of a
1 percentage point increase in the total f­actor productivity
growth rate. A 1 percentage point increase in the growth
rate ­today increases output by 1 percentage point ­today.
Subsequently, the increase in the growth rate in output leads
to more savings and more investment and more capital and
more output. Due to diminishing returns to capital, the
amplifying effect approaches zero over time.
CHAPTER 7
The L
­ abor Market, Wages, and Unemployment
CHAPTER OVERVIEW
At first glance, you’ll think this is a conventional ­labor market
chapter: it covers shifts in supply and demand, defines “unemployment,” and notes that Eu­rope and the United States have
dif­fer­ent unemployment rates. Many of you ­will want to simply define the unemployment rate, mention a few key facts
about the ­labor market, and move on—­and given the time
constraints, I ­wouldn’t blame you if you did just that.
But ­there are a few extra topics h­ ere that many of you w
­ ill
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 (7.6), a lengthy discussion of
the college wage premium (7.7), and a discussion of how the
benefits of economic growth are distributed across income
groups. Most likely, your department ­won’t require students
to take ­either a finance course or a ­labor economics course
for the economics degree, and t­ hese are practical and impor­
tant topics.
To students and voters, “the economy” is often indistinguishable from “the job market.” The time you spend h­ ere
might not feel like the cutting edge of economic theory, but
it may be the part of the course that your students think
about most 10 years from now.
7.1 Introduction and 7.2 U.S. ­Labor Market Facts
The key fact to start off with is that real wages have grown
over the past few de­cades. Chad draws this out by recycling
the fact that the ­labor share has been stable across the
de­cades: if GDP per capita has grown by about 2% per year
and if the wage share is a stable two-­thirds of GDP per capita, then wages must have grown, on average, by about 2%
per year.
Note: Wages did not grow at two-­thirds of 2% per year: if
real GDP per capita grew at 2%, then its two subcomponents, wage income and capital income, must have both
grown at 2% annually: 2% × (2/3) + 2% × (1/3) = 2%, for
the income shares to be unchanged.)
The second fact Chad emphasizes in Figure 7.1 is that the
fraction of the population employed (the E-­
Pop, as it’s
known) has also risen over the past few de­cades, driven by
the increase in w
­ omen 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 per­for­mance, we
have to explain how wages and employment can both
increase. Our long-­r un 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.
­A fter 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. ­
T hese folks ­
don’t count as
unemployed.
It’s worth noting that the U.S. government keeps track of
­these p­ eople 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 a­ fter 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
61
68 | Chapter 7
CASE STUDY: EU28 ­LABOR
MARKET CONDITIONS AND TREND
UNEMPLOYMENT RATES
A number of data sources are available to examine EU ­labor
market conditions. For example, FRED provides harmonized unemployment rates for most of the EU28 countries.7
Eurostat also provides access to its ­labor market survey.
See, for example: https://­ec​.­europa​.­eu​/­eurostat​/­web​/­lfs​/­data​
/­database. For a description/explanation of recent developments in the EU and euro area ­labor market, see: https:
//­e c​ .­e uropa​ .­e u ​ /­e urostat ​ /­s tatistics​ -­explained ​ /­i ndex​ .­p hp​
/­Unemployment​_­statistics#recent​_­developments. This link
provides up-­to-­date information on unemployment in member states, including youth unemployment, longer unemployment trends, and male and female unemployment and
describes the vari­ous data sources.
Chad in the textbook uses the bathtub model to mea­sure
the “natu­ral” unemployment rate. The natu­ral unemployment rate is defined as the rate of unemployment when the
economy is neither expanding nor contracting. As Chad
shows in the textbook, the natu­ral unemployment rate can
be expressed as the ratio of the separations rate to the sum of
the separations and hiring rates. For example, if the institutional features of the economy that generate structural
unemployment are increasing, the hiring rate decreases and
the natu­ral unemployment rate increases.
To approximate changes in the under­lying determinants
of the natu­ral unemployment rate, the trend unemployment
rates ­were calculated using the harmonized unemployment
sured by OECD and published in the Federal
rates mea­
Reserve Bank of St. Louis database, the Federal Reserve
Economic Database (FRED). The trend unemployment
rates ­were found by converting the annual unemployment
rates to natu­ral logs, regressing the natu­ral logs on time,
then generating a log linear prediction, and then converting
that log linear prediction into an estimate of the trend unemployment rate; in other words, trend unemployment rate =
2.71828^(log linear prediction).
Of the 23 countries for which harmonized unemployment
rates ­were available, five countries have positive growth
rates in the trend unemployment rate that w
­ ere statistically
7. Data ­were not available at FRED for Bulgaria, Croatia, Cyprus,
Malta, or Romania. According to the OECD. “Harmonised unemployment rates define the unemployed as ­people of working age who are
without work, are available for work, and have taken specific steps to
find work. The uniform application of this definition results in estimates
of unemployment rates that are more internationally comparable than
estimates based on national definitions of unemployment. This indicator
is mea­sured in numbers of unemployed ­people as a percentage of the
­labour force and it is seasonally adjusted. The l­abour force is defined as
the total number of unemployed p­ eople plus t­hose in civilian employment.” See OECD, “Harmonized Unemployment,” https://­d ata​.­oecd​.­org​
/­u nemp​/ ­harmonised​-­u nemployment​-­rate​-­hur​.­htm.
dif­fer­ent than zero at the 95% confidence interval or higher.8
See Figure 1, which follows. Greece and Portugal have the
highest trend unemployment rates, with Greece’s trend
unemployment rate growing at about 5.5% per year, and
Portugal’s trend unemployment rate growing at about 1.5%
per year. Austria, Sweden and Luxembourg, with much
lower trend unemployment rates, have seen their trend
unemployment rates growing at about 1.2%, 3.2% and 3.2%
per year.
Figure 2 shows the trend growth rates for countries in
which the trend growth rates w
­ ere not statistically significant from zero at the 95% confidence interval. Lithuania, for
example, has an estimated trend growth rate of just over
−2%, but the standard error of the estimate is about .0155,
causing a failure of the rejection of the null hypothesis. The
average unemployment rates, standard deviations, minimum
and maximums are summarized in ­Table 6. Given that the
trend growth rates in the unemployment rates are not statistically dif­fer­ent from zero across t­hese countries, the average unemployment rates, as provided in T
­ able 6, are used to
approximate the trend unemployment rates. ­These unemployment rates range from a low of 6% for Czechia to a high
of 11.8% for Latvia.
Figure 3 shows the trend growth rates for countries in
which the trend growth rates are negative and statistically
dif­
fer­
ent from zero. Poland, Slovakia, and Luxembourg
show the highest rate of decrease in the trend unemployment
rates, with yearly decreases of about 5.2%, 3.5%, and 3.2%,
respectively. Estonia, the United Kingdom, Ireland, and
Germany had respective rates of decrease of about 2.6%,
2%, 2.1%, and 2.5%. The Netherlands’ trend unemployment
rate decreased at about 1.5% per year, while France and Belgium both showed modest decreases in the trend unemployment rates of about .3% and .7%, respectively.
REVIEW QUESTIONS
1. The rise in the employment-­to-­population ratio is largely
driven by ­women entering the ­labor market. The civilian
employment-­
to-­
population ratio (for noninstitutionalized
civilians) fell from 62.4% in 2008 to 58.4% in 2011, a fall of
4.0 percentage points. For each percentage point decline in
this ratio, about 2.4 million jobs dis­appear. So, in total,
about 10 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.
8. The database and estimates are available on request.
The ­L abor Market, Wages, and Unemployment | 69
Figure 1. EU Member States with Trend Unemployment (Rate)
Growth Rates That Are Positive and Statistically Dif­fer­ent
Than Zero
Figure 3. EU Member States with Negative Trend
Unemployment (Rate) Growth Rates
Sources: Federal Reserve Bank of St. Louis Database; OECD,
“Harmonized Unemployment Rates”; author’s calculations, vari­ous
starting dates to 2018.
­Table 6. AVERAGE HARMONIZED UNEMPLOYMENT
RATES: EU MEMBER STATES WITH ZERO TREND
GROWTH RATES IN THE UNEMPLOYMENT RATE
Figure 2. EU Member States with Trend Unemployment (Rate)
Growth Rates That ­Were Not Statistically Dif­fer­ent from Zero
Sources: Federal Reserve Bank of St. Louis Database; OECD,
“Harmonized Unemployment Rates”; author’s calculations, vari­ous
starting dates to 2018.
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.
labor supply increases, holding demand constant,
If ­
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.
Country
Time
Period
Czechia
Finland
Italy
Latvia
Denmark
Hungary
Lithuania
Slovenia
1993–2018
1988–2018
1983–2018
1999–2018
1983–2018
1996–2018
1999–2018
1996–2018
Average
Harmonized
Unemployment
Rates
Std. Dev. Min. Max.
6.0
9.2
9.5
11.8
6.1
7.6
11.2
7.0
1.870335
3.293901
1.685595
3.631277
1.478059
2.208518
4.176078
1.470608
2.2
3.1
6.1
6.05
3.5
3.7
4.25
4.4
8.8
16.6
12.6
19.47
9.5
11.2
17.83
10.2
Sources: Federal Reserve Bank of St. Louis Database; OECD, “Harmonized Unemployment Rates”; author’s calculations.
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,
an equation that makes it 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
70 | Chapter 7
look at all of the résumés, have meetings to decide what
kind of person ­you’re looking for, meet all the applicants,
and check their backgrounds.
Structural unemployment is unemployment caused by
medium-­term shifts in the economy. In princi­ple, it can be
positive or negative. If the auto industry is declining, then
­there are ­going to be a lot of ­people with car-­making skills
who might find it very tough to transition: their “friction” in
the ­labor market is big enough and noticeable enough that
we create a new category for it. That’s an example of positive frictional unemployment. Negative frictional unemployment would happen if a big new industry moved to town and
started hiring lots of workers: “friction” would be much
lower than usual. This ­wouldn’t last forever, since the new
industry (an auto assembly line in Ohio; a movie industry in
Vancouver, British Columbia; government hiring during a
time of war) would prob­ably just need to grow quickly to a
certain level, and then would just start acting like a normal
industry—­hiring and firing at a regular “frictional” rate.
Cyclical unemployment can be positive or negative, and it
reflects changes in unemployment caused by the temporary,
two-­to-­three year fluctuations in the overall economy we
call the “business cycle.” Cyclical unemployment is positive (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. The hours worked per person in Eu­rope are
much lower than in Eu­rope. This may be ­because wage taxes
and sales taxes are higher and ­labor markets are more regulated in Eu­rope than in the United States. In Eu­rope, it is
much harder to fire workers in most countries than it is in the
United States. Therefore, Eu­ro­pean businesses need to be
very sure about the quality of a worker. By contrast, an American business can take a chance on someone new since it’s
easy to fire a person if it ­doesn’t work out. Thus, American
firms tend to hire p­ eople 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 40 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.
EXERCISES
1. According to the FRED Database, in August 2019, the
Civilian ­Labor Force was 163.922 million persons. The unemployment rate is 3.7%, meaning that about 6.1 million p­ eople
are unemployed. If the ­actual unemployment rate ­were 10%,
the ­actual number of p­ eople unemployed would be about 16.4
million persons, a difference of 10.3 million ­people!
2. (a)
(b) During the post–­World War II baby boom, many ­women
left the ­labor force and re­entered ­after their ­children had grown.
The stagflation events of the 1970s further caused w
­ omen to
enter the ­labor force to maintain f­ amily living standards. Chad
also mentions in the case study “Supply and Demand Shocks in
the U. S. ­Labor Market” that “changing social norms and technological pro­gress . . . ​and reduced discrimination” contributed
to growth in female ­labor force participation rate.
(c) Since 2000, the trend for ­women has flattened out to the
point that about 55% of the female population is working. This
could be due to a lack of job opportunities for ­women as the
employment growth stagnated in the first de­cade of the twenty-­
first c­ entury, and as a consequence of baby boomers retiring.
3. A marginal tax cut increases ­labor supply and drives
down the wage: but it w
­ ill increase the after-­tax wage for the
worker. The employment-­population ratio ­will also increase.
This is just a standard “rise in supply” story.
The effect on unemployment is quite ambiguous—­I’m
inclined to say that if the economy is at the natu­ral rate of
unemployment, it is likely to stay ­there—­there are always
some ­people entering and leaving employment relationships.
It’s hard to imagine that a change in the tax rate would
impact that “job creation and destruction” pro­
cess very
much, a­ fter 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
­ ere completely out of the ­labor
the tax cut, many ­people who w
force could start searching for work—so they would count as
The ­L abor Market, Wages, and Unemployment | 71
unemployed ­until they find jobs. The ­people ­were already
unemployed but their searching w
­ ill prob­ably become less
picky now that they get to take home more money each week,
­ ill tend to push unemployment down. In the very
so that w
short run, the net effect could go e­ ither way.
4. This is likely to raise l­abor demand, since firms ­will be
able to produce output more efficiently within the non-­oil-­
producing country. The rise in ­labor demand ­will increase
wages and the employment-­to-­population ratio.
5. This is a worked exercise. Please see the textbook for the
solution.
6.
1%
5%
a
b
c
d
a
b
c
d
$49,505 $45,264 $10,100 $3,958 $47,619 $30,696 $2,100 $1,917
7. (a)
1%
2%
4%
5%
$2,296,693
$1,895,037
$1,357,577
$1,175,754
(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 world of high interest rates.
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. As a result,
the “pre­sent discounted value” of my f­uture earnings c­ an’t get
me a good bank loan when ­future interest rates are high.
8. (a) w 0 + w 0 (1 + g)/(1 + R) + w 0 (1 + g)2/(1 + R)2 + . . . + ​
w0 (1 + g)t / (1 + R)t
(b) PDV = w 0*[(1 + g)/(1 + R) + (1 + g)2/(1 + R)2 + . . .+
(1 + g)45 / ​(1 + R)45]
(c) a = (1 + g)/(1 + R),
PDV = w0{1 − [(1 + g) / (1 + R)]45} / {1 − [(1 + g) / (1 + R)]}.
It’s essentially equation 7.10 with “1 + g” on top of “1 + R.”
(d)
4%: 1,535.740
3%: 1,862,219
2%: 2,300,00
At a 2% growth rate, the effects of the growth rate and the
discount rate cancel each other out, and w
­ e’re simply adding
up 46 years of payments worth $50,000 per year.
(e) As the discount rate decreases, the pre­sent value of the
f­ uture 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.
9. W
­ e’ll assume that school time is four years, and that work
time is still 45 years, beginning in time 0, which adds up to
a 49-­year noncollege work c­ areer.
(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)]}.
(b) Pre­
sent 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 $1,587,113 = 70,000{1 − [1/(1 + .03)]}50/
{1 − [1/(1 + .03)]} − 70,000{1 − [1/(1 + .03)]} 4 /{1 − [1/
(1 + .03)]}.
(c) If t­ hese numbers are close to the truth, the value of a college education is still massive, even if the student has to pay
his or her own tuition at a private school.
10. This is a worked exercise. Please see the textbook for the
solution.
11. (a) This equals a paid vacation that lasts 26 weeks: but you
can only get the paid vacation if you ­don’t get a job. Many
workers w
­ ill choose to stay unemployed ­
until about the
20th week or so, when they ­will start looking for a real job.
(b) Workers would have a strong incentive to start looking for
work quite quickly. They might spend some money on a quick
vacation. ­After all, you d­ on’t want to take a vacation as soon
as you start a new job: it looks bad. So they might vacation a
­little for the first few weeks and then start looking for work.
12. For the year 2017:
Country
United States
Italy
France
Germany
United Kingdom
Japan
South ­Korea
Hrs. % of
United Hrs. per Per Capita Real GDP
States
Person RGDP ($s) per Hour
100
85
75
85
96
111
127
800
680
600
680
768
888
1,016
5,4748.8
38,000
39,461
47,556
39,128
40,374
36,265
68.44
55.88
65.77
69.94
50.95
45.47
35.69
Clearly, on a per-­hour basis, the United States, Germany,
and France are more productive than the United Kingdom,
Japan, and South K
­ orea.
CHAPTER 8
Inflation
CHAPTER OVERVIEW
In this chapter, you get to cover one of the t­ hings 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. Cobb-­
Douglas could, just conceivably, fade away someday—­but
it’s hard to imagine a ­future without the quantity theory
of money (QTM). (As an 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 on historical circumstances.
­These circumstances are outlined in this chapter.)
8.1 Introduction
Most of our students have no experience with inflation that
is consistently above 3% per year. As a result, by letting
them know that the United States had a fairly recent de­cade
of 7% 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
72
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 Inflation1. I think ­there’s room for
some gloating h­ ere: our profession won this b­ attle—at least
for the time being and for the developed countries—­and no
one is g­ oing to trumpet our victories but ourselves. As further evidence of lower inflation rates, across countries, Chad
tracks the percentage of countries experiencing high (greater
than 25%) inflation rates. Chad shows that the percentage of
countries with high inflation peaked in the 1990s at around
30% and then fell below 5% in recent years.
Chad mentions a few hyperinflations in the introduction,
and he includes 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. I’ve
included an expanded case study ­here that 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
­ ere you go: this is the first or second most controversial
H
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 short-­
term business cycles all in one. We only cover the first part
now, and Chad drops some hints about the second part. You
1. Prince­ton, NJ: Prince­ton University Press, 2001
78 | Chapter 8
AVERAGE 10-­YEAR CONSTANT MATURITY TREA­SURY
BOND YIELDS, AVERAGE CORE PCE INFLATION RATES,
AND AVERAGE REAL INTEREST RATES
Time Period
1980 to 1989
1990 to 1999
2000 to 2009
2010 to 2015
Average 10-­Year
Average
Constant
Core
Maturity Trea­sury PCE Inflation
Bond Yield
Rate
10.6%
6.7%
4.5%
2.5%
5.7%
2.4%
1.9%
1.5%
Average
Real
Interest
Rate
5.3%
4.3%
2.6%
1.0%
Sources: Author’s calculations; FRED Database.
CASE STUDY: ACCOUNTING FOR INFLATION
IN THE EU EURO AREA AND THE EU28
INFLATION EXPERIENCES
As Chad describes in equations 8.2 and 8.3 of the textbook,
the equation of exchange, MV = PY, can be used to account
for the rate of inflation, which is the rate of growth in prices.
Using the con­ve­nient growth rate rules introduced in Chapter 3, Chad shows that price inflation can be written as the
rate of growth in the money supply plus the rate of growth in
velocity minus the rate of growth in real GDP. Using the
Federal Reserve Bank of St. Louis database, mea­sures of
­these variables can be found for 1995 to 2016 for the Euro
Area countries.3 The rate of inflation for the Euro Area is
defined as the rate of change in the implicit GDP deflator,
which is the ratio of nominal Euro Area nominal GDP to
real GDP. The rate of growth in the money supply is defined
as the rate of growth in M2, defined by ECB as “M1 plus
deposits with maturity up to two years and deposits redeemable at notice up to three months”4. The velocity of M2 is
defined as nominal GDP divided by M2. T
­ able 1 shows the
accounting for the rate of inflation.
As shown in ­Table 1, with the exception of 1997, the
inflation rates are positive, and t­here is a general trend
­toward disinflation through 2010. Thereafter, the inflation
3. The Euro area countries include Austria, Belgium, Cyprus, Estonia,
Finland, France, Germany, Greece, Ireland, Italy, Latvia Lithuania, Luxembourg, Malta, Netherlands, Portugal, Slovenia, Slovakia, and Spain.
4. https://­fred​.­stlouisfed​.­org​/­series​/­CLVMEURSCAB1GQEA19#0
rate fluctuates around 1%. During the period of disinflation,
the growth in M2 ranged from over 4% in 1997 to over 10%
in 2007 and 2008. The real GDP growth rates are positive,
with the exception of 2009, suggesting, of course, that the
velocity of money has falling through most of this time
period. The relationship between money growth and inflation is illustrated in Figure 1. which shows that the rate of
growth in M2 is much greater than price inflation, but M2
growth and inflation are positively related. As Chad shows
in the text, decreases in velocity (and real GDP growth) offset the inflation tendencies created by increases in the
money supply. Figure 2 illustrates the be­hav­ior of the velocity for the Euro Area. When monetary policy is discussed
in a ­later chapter we ­will return to determinants of the
velocity of money and Eu­ro­pean Central Bank’s monetary
policy.
The Saint Louis Federal Reserve Bank database also
provides data on consumer inflation for the EU28 countries. As explained in exercise 3 of the following homework assignments, using the FRED database’s search
engine, typing in the country’s name followed by inflation
­will retrieve a number of inflation options. If you type in,
for example, “Austria inflation,” you ­
will retrieve consumer prices for Austria, as published by the World Bank:
https://­f red​ .­s tlouisfed​ .­o rg​ /­s eries​ / ­F PCPITOTLZGAUT.
­T hese inflation rates ­were gathered for all the EU28 countries except Cyprus (Cyprus data ­were not available). Figures 3, 4, and 5 provide consumer price inflations for
countries with the highest inflation rates, next highest
inflation rates and lowest rates of inflation. One of the patterns that emerges is that as the Eu­ro­pean area has integrated over the last 25 years, the inflation rates have
converged at much lower levels.
REVIEW QUESTIONS
1. Inflation is a general increase in all prices in the economy,
including wages. Inflation eats away at the real buying
power of currency, so ­those hundred-­dollar bills w
­ ill 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 and 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 M and V raise the price level; an increase in
Y 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
Inflation | 79
­Table 1. ACCOUNTING FOR INFLATION
IN THE EURO AREA: EU19
Year
Inflation
Rate
Rate of
Growth
in M2
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2.61%
−0.24%
1.17%
1.71%
1.25%
2.44%
2.48%
2.22%
2.14%
1.76%
1.89%
2.48%
2.17%
0.96%
0.70%
1.00%
1.22%
1.20%
0.92%
1.46%
0.86%
5.29%
4.40%
5.38%
7.06%
4.70%
6.88%
6.48%
7.14%
6.03%
8.11%
8.98%
10.19%
10.31%
5.31%
1.97%
2.38%
3.48%
3.74%
2.84%
6.09%
5.08%
Rate of Growth
in the Velocity
Real GDP
of M2
Growth Rate
−0.97%
−1.90%
−1.26%
−2.31%
0.54%
−2.09%
−2.87%
−3.95%
−1.66%
−4.19%
−3.36%
−4.21%
−7.08%
−8.44%
0.77%
0.33%
−2.98%
−2.67%
−0.46%
−2.47%
−2.21%
1.61%
2.67%
2.85%
2.83%
3.97%
2.15%
0.93%
0.67%
2.09%
1.79%
3.37%
2.99%
0.32%
−4.49%
2.03%
1.70%
−0.82%
−0.23%
1.43%
1.98%
1.88%
Figure 2. Velocity and Its Rate of Growth for the Euro Area
Sources: Federal Reserve Bank of St. Louis Database; author’s
calculations.
Sources: Federal Reserve Bank of St. Louis Database; author’s
calculations.5
Figure 3. Consumer Price Inflation: Bulgaria and Croatia
Sources: Federal Reserve Bank of St. Louis Database; World Bank.
Figure 1. Euro Area: M2 Growth and Inflation
Sources: Federal Reserve Bank of St. Louis Database; author’s
calculations.
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
5. Recall that the growth rate rules are an approximation. The precise
mea­sure of the inflation rate is the rate of growth in the money supply plus
the rate of growth in velocity minus the rate of growth in real GDP plus the
products of the rates of growth in the money supply and velocity minus the
products of the rate of growth in real GDP and the inflation rate.
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% or 20% annual interest.
80 | Chapter 8
7. Government spending = change in money supply + taxes
+ change in bonds.
When the government ­doesn’t want to raise taxes, and when
it ­can’t borrow any more ­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.
Figure 4. Consumer Price Inflation: Estonia, Slovenia, Latvia,
Poland, Lithuania, Hungary and Romania
Sources: Federal Reserve Bank of St. Louis Database; World Bank.
8. No, it does not: the U.S. government raises only a tiny
amount of revenue from seigniorage (changes in M). The
Federal Reserve just let inflation get out of control in the
1970s, perhaps ­because they ­didn’t know how the economy
­ ater chapters ­will give a more thorough
­really worked. L
answer to this question—­a topic that is still much debated
among economists.
9. ­People who hold currency and other non-­interest-­paying
forms of money, like most checking accounts.
EXERCISES
1. From ­Table 8.1.
­Table 8.1 (2018 = 100)
(a)
(b)
(c)
(d)
(e)
Year
CPI
1900
1930
1950
1960
1970
3.24
6.65
9.59
11.8
15.47
Current
Constant
CPI2015/CPIt dollar prices dollar prices
30.86
15.04
10.43
8.47
6.46
$1,000.00
$80,000.00
$0.05
$0.55
$2.25
$30,864.20
$1,203,007.52
$0.52
$4.66
$14.54
2. This is a worked exercise. Please see the textbook for the
solution.
Figure 5. Consumer Price Inflation: Rest of the EU28
Countries (Excluding Cyprus)
3. (a)
Sources: Federal Reserve Bank of St. Louis Database;
World Bank.
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 impor­
tant: 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.
(b). China has, in the recent past, had lower inflation than
India. China’s average (consumer price) inflation rate from
2014 to 2018 is about 1.8%, and India’s average (consumer
price) inflation rate for the same time period is about 4.9%.
4. The price level is the key endogenous variable in the
quantity theory: it is the only ­thing that responds to changes
in the money supply, velocity, or real output.
Inflation | 81
(a) The price level doubles.
(b) The price level rises by 10%.
(c) The price level falls by 2%.
(d) Nothing: the two increases in money and output simply
balance out.
5. (a) 2% annual inflation
(b) 7% annual inflation
(c) 97% annual inflation
(d) 0% inflation: stable prices
(e) 3% inflation
(f) 3% annual inflation. Technological innovation might
make it easier for ­people to pay bills online, so they spend
their money faster.
6. This is a worked exercise. Please see the textbook for the
solution.
7. (a) 4% nominal
(b) 5% real
(c) 4% inflation
(d) 13% nominal
(e) −4% real
(f) 9% inflation
8. (a) 9% nominal
(b) Bank A w
­ ill be flooded with business.
(c) Bank B w
­ ill be flooded with customers: no one ­will
invest in machines and they w
­ ill save money at banks
instead. Of course, it’s tough to imagine how the bank ­will
actually come up with that 12% nominal interest if the nominal return in the private sector is 9%.
9. ­There ­will be a 14% nominal return: 6% ­will go ­toward
replacing the worn-­out capital, while the extra 8% w
­ ill go to
the investor who bought the machine.
The Fisher equation is 3% real (net) return = 8% nominal
return − 5% inflation.
But of course, t­ here’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 c­ an’t sell for as
much afterward. That 6% 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.
10. (a)
(b) As Irving Fisher has taught us, ­every nominal rate of
interest contains an inflation premium. As the inflation rate
declines, so does the inflation premium.
(c) The vertical distance between the 10-­year yield and the
inflation rate is a mea­sure of the real rate of interest.
11. (a) Real interest rates can be negative any time the nominal interest rate is less than inflation. This was true in the
United States during much of the 1970s.
(b) It’s essentially impossible for nominal interest rates to be
negative. If a bank offered −1% nominal interest for a savings account, p­ eople would just hold their money in the
form of currency—­colored pieces of paper—­instead. Currency earns 0% nominal interest.
Aside: In the worst days of Japan’s deflation in the 1990s,
nominal interest rates on short-­term government bonds w
­ ere
briefly negative. Apparently, investors thought that the
safety of government bonds was well worth paying for.
­After all, who wants to put millions of dollars of currency in
a safe? It’s easier to just hold a few government bonds. In
addition, since 2014, the Eu­ro­pean Central Bank has maintained its benchmark interest rate (the Main Refinancing
Operations yield) at negative levels.
12. This is a m
­ atter of judgment, so I w
­ ill leave most of this
to you. Constant inflation has the kinds of costs listed in
review question 6. But surprise inflation means that p­ eople
have to change their be­hav­ior and react to surprises. When
bread gets 15% more expensive, is that more ­because of
inflation or more b­ ecause bread is just harder to make t­ hese
days? ­Will I get a cost of living increase big enough to
cover the spike in prices, or w
­ ill 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.
13. In a hyperinflation, ­people often start using safer foreign
money or they use barter, both of which are difficult to do.
82 | Chapter 8
­ hese practices occur ­because governments ­can’t or ­won’t
T
raise funds through taxes or borrowing.
base in 15a as our mea­sure of M). The product of ­these two
is 0.58% of GDP.
14. Sargent has noticed that the government bud­get constraint is the key driver of hyperinflation: Governments get
themselves in a fiscal bind, and resort to the “printing press”
to make their trou­bles go away.
This is ­really a po­liti­cal conclusion made by Sargent, an
economist. He has concluded that since high, per­
sis­
tent
inflation is socially costly, the only reason a government
would create high, per­sis­tent inflation would be if it received
some benefit to offset ­those costs. And the only benefit
around is the power of the printing press to solve troublesome fiscal prob­lems.
This is about 41% more the amount from exercise 15(b). I’d
guess the reason is ­because inflation is “sticky,” as ­we’ll see
­later. It took a year or two for inflation to fall down to the
lower level predicted by the quantity theory. Remember,
just to keep it ­simple we completely ignored velocity shifts.
So our “inflation tax” equation gets us close to the truth: we
may just have to wait a ­couple of years for the nominal
shocks to work out to get the same answers.
15. (a) $170,681 million in the monetary base. The currency
equals $144,399 million.
(b) The (GDP Implicit Price Deflator) inflation rate in 1981
was 9.34%. The inflation tax is .0934 * $144,399 = 13,486.9
million—­about 0.41% of 1981, 4th quarter GDP of $3,280.8
billion.
(c) The only special t­hing I noticed about 1981 was that it
was lower than the years immediately surrounding it: it
was the year that the rate of inflation peaked in the United
States.
16. (a) This gives us (change in M/M) × (M/PY), or money
growth times money per unit of output.
(b) I w
­ ill use lowercase for growth rates, and uppercase for
levels. As usual, I ­will assume velocity growth is zero.
(π + y) × M/PY
(c) i. In 1981, GDP inflation was 9.34%, so π + y = 11.34%.
The data show that M/PY = 1/V = 5.1% (using the monetary
ii. In 2018, GDP price inflation was about 2.44%, so that
π + y = 5.4%%, and assuming a constant velocity and given
that 1/V = 15%, the inflation tax in 2005 as a ­percent of GDP
was about .81%.
(d) All through this inflation tax discussion, w
­ e’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 the
formulas in this exercise 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.
­ ill leave to you to
17. This is an essay response that I w
answer. Suffice it to say that Friedman and Schwartz’s book
is a classic, which is still read and respected by economists
from a variety of po­liti­cal and economic viewpoints.
CHAPTER 9
An Introduction to the Short Run
REVIEW AND PRELUDE
This might be a good time to review what has come before:
perhaps take a minute or two to remind students that the
previous story was largely a supply-­side model: each year,
­there’s a fixed number of workers, machines, and ideas:
markets work well enough to make sure they all get used
efficiently. In real life, this might not be a good model of
how t­hings work at e­ very moment, but economists tend to
think it’s a pretty good explanation on average.
Now, for the next six chapters, demand is in charge. W
­ e’re
now entering an upside-­down world, and the ultimate goal
­will be to explain how t­hings can be driven by demand in
the short run and supply in the long run. The last chapter in
this section, Chapter 15, synthesizes the analyses of the
short run and the long run.
CHAPTER OVERVIEW
In this short chapter, you get to explain what business cycles
are, why they m
­ atter, and what c­ auses 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. The
details w
­ ill come ­later.
9.1 Introduction and 9.2 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 noted in a case study l­ater in this chapter, 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 b­ ecause
of the academic innovations of men like Keynes and the
po­
liti­
cal entrepreneurship of men like Franklin D.
Roo­se­velt.
Chad consistently uses the term “short-­r un 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 w
­ ill 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
short-­r un GDP ­after the fact, ­because if ­there’s too much of
it, inflation rises. That’s learning the hard way, of course,
and so a case study below focuses on how former Federal
Reserve chairman Alan Greenspan and the editors of Business Week magazine did the job in real time.
MEASURING POTENTIAL OUTPUT AND CYCLICAL
FLUCTUATIONS
­There are two ways to mea­sure potential GDP:
1. Use the production function: find out the size of the
workforce, the capital stock, and the level of technology,
and estimate how much GDP would be produced if the
economy worked efficiently. This is what the Congressional Bud­
get Office (CBO) does when it mea­
sures
“potential GDP,” and yes, it takes a lot of hard work
combined with some intelligent guesswork.
83
An Introduction to the Short Run | 89
Figure 3. The Short-­Run Phillips Curve: The Euro Area
Figure 4. Okun’s Law: The Euro Area
Sources: Federal Reserve Bank of St. Louis Database; author’s
calculations.
stand the size and sign of short-­r un output, long-­r un output
has to be known.
­Table 4 and Figure 4 provide the estimated Okun’s law relationship. As with the Phillips curve estimates, the data ­were
first differenced to satisfy the stationarity condition. From
­Table 4, the change in the cyclical variation in output relative to the change in the a­ctual unemployment rate is
−1/.32 = 3.125. For the EU area, a 1% increase in the unemployment rate relative to the natu­ral unemployment rate
reduces short-­r un output by about 3.125%. The Okun’s law
relationship for the Euro Area thus appears to be larger than
for the United States, which indicates that the cost of unemployment is higher in the Euro Area than in the United
States.
REVIEW QUESTIONS
1. The short-­r un model is used to explain fluctuations in output around potential output. The long-­run model explains
the level and growth in potential output. In order to under-
2. One reason is that the size of the short-­r un output fluctuations tends to be constant in percentage terms: positive output shocks are in the 3% range, not in, say, the $300 billion
range. In other words, expressing short-­
r un output as a
­percent of potential output allows for comparisons across
time. A $100 billion fluctuation in short-­r un 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–
1982 recession was almost −8%. In comparison, Ỹ, at its
worse in the 2007–9 recession was about −7%. However, the
cumulative effects of ­these recessions have been quite dif­
fer­ent. Following the 1981–1982 recession, the recovery in Ỹ
was quite sharp, adjusting to within about 1% of potential
real GDP by 1984. In contrast, short-­run output was still
more than 2% below real GDP in 2014.
Table 4. OKUN’S LAW: THE EURO AREA
Source
SS
df
MS
Model
Residual
Total
.000719601
.000221613
.000941214
1
19
20
.000719601
.000011664
.000047061
Δ(ut − un)
Coef.
Std.
Err.
t
−.3188351
−.0010705
.5884923
.0406169
.0017011
−7.85
−0.63
0.000
0.537
ΔȲ
_cons
rho
=
=
=
=
=
=
Number of obs
F(1, 19)
Prob > F
R-­squared
Adj R-­squared
Root MSE
21
61.70
0.0000
0.7645
0.7522
.00342
P>|t|
[95% Conf. Interval]
−.4038472
−.0046309
−.233823
.0024898
C
Sources: Federal Reserve Bank of St. Louis Database; author’s calculations.
Notes: Prais-­Winsten AR(1) regression: iterated estimates; Durbin-­Watson statistic (original): 1.021720;
Durbin-­Watson statistic (transformed): 1.934667.
90 | Chapter 9
4. In 2010, recent shocks included high oil prices and the
collapse of the subprime mortgage market (which pushed
down stock prices and tightened credit markets), and a fall
in new home buying. In 2018–2019, rising tariffs and
increasing federal government bud­get deficits appear to generate opposing effects on the macroeconomy.
4. Slope of the Phillips curve.
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. Therefore, when the economy drops below potential GDP, inflation drops noticeably.
(During periods, inflation is more of a random walk, just
based on this ­simple graph.)
6. Okun’s law is handy b­ ecause typical voters care about
unemployment rates more than they care about the GDP
numbers. Our model focuses on short-­r un GDP, but we can
speak to the person on the street by ­running our model
through Okun’s law. Also, since unemployment rates tend to
fall a year or so ­after GDP starts to rise, one can use ­today’s
GDP growth to forecast changes in the unemployment rate
over the next year.
EXERCISES
1. (a)
(b)
(a) In the steep (solid) economy, a boom c­ auses 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. Therefore, if we redrew the trend line but only used
­those outliers as data, we’d have a somewhat steeper line
than we see in Figure 9.7. It’s not a major difference, but
perhaps the line grew flatter in the past two de­cades as
Americans grew used to low, stable inflation.
5. (a) The slope is +1/2. For each option, in year 1, for e­ very
2 percentage point decrease in Ỹ, the change in inflation is
−1 percentage point.
(c) As Chad writes in the textbook section, “Mea­sur­ing
Potential Output,” the slowdown in investment means a
slowdown in the accumulation of capital goods and decrease
in the rate at which potential output grows.
2. This depends on the student’s choice.
3. This is a worked exercise. Please see the text for the
solution.
(b) If I only care about the cumulative lost output, as Chad
does in the text, then I c­ an’t decide between the three. In all
three cases, all three years of lost output add up to 6%. 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 c­ an’t give a clearer answer without a
clearer understanding of what the politician wants.
An Introduction to the Short Run | 91
(c) H
­ ere, 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 (usually a good ­thing) is
to create a recession (almost always a bad ­thing).
6. (a) True output falls to a new, lower level: in other words,
policy makers accidentally create a recession.
(b) Inflation falls.
(c) If the central bank was too optimistic instead, then it
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-­r un 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 correct: the boom led to higher inflation for most years in the
1970s.
7. (a)
Year
­Actual
Y
2023Q1
2023Q2
2023Q3
2023Q4
2024Q1
2024Q2
2024Q3
2024Q4
2025Q1
2025Q2
2025Q3
2025Q4
25.00
25.20
25.40
25.30
25.20
25.15
25.13
25.30
25.50
26.00
26.80
27.10
Growth Rate of
Potential
­Actual Y
Short-­
­Actual Y,
Y
–P
­ otential Y run Y %Change in Y
25.00
25.16
25.31
25.47
25.63
25.79
25.95
26.11
26.28
26.44
26.61
26.77
0.00
0.04
0.09
−0.17
−0.43
−0.64
−0.82
−0.81
−0.78
−0.44
0.19
0.33
0.00
0.00
0.00
−0.01
−0.02
−0.02
−0.03
−0.03
−0.03
−0.02
0.01
0.01
0.80%
0.79%
−0.39%
−0.40%
−0.20%
−0.08%
0.68%
0.79%
1.96%
3.08%
1.12%
(b) The growth rate for each quarter is (1.025.25 − 1) or
approximately .025/4 = .00625.
(c) The economy is in recession in 2023Q4 to 2025Q2. Note
that u­ nder our definition of “recession,” at any time output is
below potential, w
­ e’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 t­ hings about being a central banker.
8. (a) 4.5%, 5%, 5.5%, and 6%, respectively.
(b) −2%, −4%, and 2%, respectively.
CHAPTER 10
The G
­ reat Recession: A First Look
REVIEW AND PRELUDE
This chapter makes the study of macroeconomics topical.
Leading news stories are brought into the classroom. How
the economy worked itself into the G
­ reat Recession and how
government reacted to the G
­ reat Recession are reviewed.
Students are introduced to the importance of balance-­sheet
decisions in affecting spending flows and aggregate economic activity. Business majors, and in par­tic­u­lar finance
majors, ­will prob­ably pick up ­these concepts faster than economics majors.
stand the ­causes and cures of the crisis and our ­f uture 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 G
­ reat Recession.
HOUSING PRICES
CHAPTER OVERVIEW
This chapter examines some of the major ­causes of the
financial crisis that began in summer 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 ­G reat Recession is the longest and deepest recession the United States has experienced since the ­G reat
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 ­G reat 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 under92
­ ere we see the familiar story of the inflation of housing
H
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% per year. Housing price inflation was greater in
some markets (such as Boston, Los Angeles, New York City,
and San Francisco) than ­others. Housing prices peaked in
2006, then dropped by 36% between 2006 and 2012. The
question is, “What caused the rise and collapse of housing
prices?”
THE GLOBAL SAVINGS GLUT
The global savings glut is tied to the international financial
crises of the 1990s. Some countries, like Mexico, Rus­sia,
Brazil, and Argentina, switched from being 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 savings
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.
96 | Chapter 10
ior 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.
CASE STUDY: LEVERAGE AND PROFITABILITY
A common mea­sure of profitability is the rate of return on
equity (ROE). The ROE is defined as profits/net worth. Multiplying and dividing ROE by assets and rearranging terms
yields ROE = (profit/assets) × (assets/equity). If we assume
that businesses can manage the profit-­
to-­
asset ratio (it’s
roughly fixed), then they can increase their ROE by increasing their asset-­to-­equity ratio. The asset-­to-­equity ratio can
be increased by using debt, or leverage, to acquire assets or
to reduce (buy back) equity. An 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 asset-­to-­equity ratio, and the less profitable is
the business. Securitization of assets that result in high
investment grades, such as AAA, therefore results in lower
capital requirements, higher asset-­
to-­
capital ratios, and
higher profits. The pressure t­ oward higher profitability allegedly created a moral ­hazard in the securities-­rating business
whereby risk was underestimated in the pursuit of higher
profits.
CASE STUDY: BUSINESS CYCLE DATING IN THE
EURO AREA, AND WHAT THE EURO AREA
LEARNED FROM THE ­GREAT RECESSION
The Centre for Economic Policy Research (CEPR) in London dates business cycles, peaks, troughs and recessions for
the Euro Area5. The National Bureau of Economic Research
(NBER) in Cambridge, Mas­sa­chu­setts, dates business cycles
for the United States6. NBER dates the G
­ reat Recession, the
general contraction in economic activity, as beginning in
December 2007, the peak of the last cycle, and ending in
June 2009, which marks the trough that marked the beginning of the current expansion. The CEPR shows that the
Euro Area had a double recession following the financial
crisis. The first recession began in the first quarter of 2008
and ended in the second quarter of 2009. The second reces5. See https://­cepr​.­org​/­content​/­euro​-­area​-­business​-­cycle​-­dating​-­committee
6. See https://­www​.­nber​.­org​/­cycles​/­cyclesmain​.­html
sion followed two years ­later, beginning in the third quarter
of 2011, and ended in the first quarter of 2001. Why did the
Euro Area have two recessions whereas the United States
had only one?
Antonio Fatas (2018) of the CEPR summarizes three
answers to this question:7 (1) central bank choices, whereby
the ECB was slow to lower interest rates or embrace quantitative easing; (2) fiscal policy, whereby the EU area countries
embrace fiscal austerity, where fiscal austerity is procylical,
re-­
enforcing the downturn in the Euro Area economy;
(3) politics, whereby “bailouts” ­were inconsistent with Euro-­
treaties and the savings paradox was operative. Fatas concludes that the Euro Area has few options to address the
next economic crisis, both ­because interest rates remain low
and also ­
because the po­
liti­
cal institutions necessary to
implement countercyclical macroeconomic fiscal policies
across the Euro Area have not been developed.
REVIEW QUESTIONS
1. From Figure 10.1: 42.5% (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 percentage change in real
GDP relative to potential real GDP was about −7%. 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 c­ auses 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%, the return on the investor’s equity position
in the stock is 200% ($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
7. Antonio Fatas, “What Has the Eurozone Learned from the Financial
Crisis?” Harvard Business Review, September 28, 2018, https://­hbr​.­org​
/­2018​/­09​/­what​-­has​-­the​-­eurozone​-­learned​-­from​-­the​-­financial​-­crisis.
The ­Great Recession: A First Look | 97
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.
EXERCISES
1. This is a student choice question, so the answers as to how
the economy has evolved w
­ ill be quite varied. H
­ ere are a
­couple of examples:
Real
Change in
GDP
Nonfarm
Core
CPI
CPI
Growth Unemploy-­ Employment Inflation Inflation
Federal
Bud­get
Rate
a % of GDP
−753
3.8
2.0
−3.11668
9.3
−5,936
−0.3
1.2
−9.77711
9.6
−952
1.6
1.4
−8.63373
1.6
8.9
1,585
3.1
1.6
−8.36154
Rate
2008
−0.1
5.8
2009
−2.5
2010
2.6
2011
(Annual percentage changes
unless otherwise stated)
Euro
Area
Reference
Period
Inflation rate (Harmonised Index
of Consumer Prices [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)
0.8
2019Sep
5.7
1.2
2019Aug
2019Q2
2.2
342
7.4
2019Q2
2019
2019Aug
−0.0
1.43
1.1128
−0.7
86.4
2019Q2
2019Q2
24 Oct 2019
2019Q2
2019Q2
Deficit as
Rate
ment Rate (Thousands)
Year
SELECTED INDICATORS FOR THE EURO AREA
2012
2.2
8.1
2,235
2.1
1.9
−6.64674
2013
1.8
7.4
2,200
1.5
1.5
−4.04993
2014
2.5
6.2
2,567
1.6
1.6
−2.76594
2015
2.9
5.3
2,885
0.1
1.2
−2.42505
2016
1.6
4.9
2,522
1.3
1.6
−3.12396
2017
2.4
4.4
2,263
2.1
1.6
−3.40915
2018
2.9
3.9
2,454
2.4
2.0
−3.78586
2. (a)
(b) In the 1990s, the average price of oil was about $20 per
barrel. In 2019, the average price of oil was about $57.
(c) The price of oil fell from a recent height of over $106 in
2013. The oil market is influenced by a number of geopo­liti­
cal and economic ­factors. The recent fall in oil prices can be
explained by OPEC countries increasing oil production, and
the invention of fracking technologies in the U.S.
3. For comparison purposes, see the same data for 2013, as
shown in the following t­able. Students should incorporate
­these data into their two-­paragraph answers.
The ECB “marginal lending rate” was about .25% in 2019.
4. As of December 31, 2015 (thousands of dollars).
Citigroup, Inc.
Assets
Equity
Equity/Assets
$1,917,288,000
$196,220,000
10.2%
Goldman Sachs
$931,796,000
$90,185,000
9.7%
In 2018, for Citibank, for each $100 of assets, $10.20 is
financed by equity and $89.80 is financed by liabilities. For
Goldman Sachs, for each $100 of assets, $9.70 is financed by
equity and $90.30 is financed by liabilities.
5. (a) Bank B, assets = 1,500, liabilities = 1,400, equity =
100;
Bank C, assets = 800, liabilities = 700, equity = 100.
(b) Bank B, 1,400/100 = 14/1; Bank C, 700/100 = 7/1.
(c) Bank C, NW = −200.
(d) Bank B’s net worth declines.
(e) The value of any financial asset is backed by a promise to
pay. In this case, Bank C fails to meet its promise to pay and
reduces the value of assets held by Bank B. Systematic risk
occurs when a failure of one business, like Bank C, ­causes
the failure of another business, like Bank B.
6. (a) A capital requirement sets the maximum asset-­to-­
equity ratio. Recall that the asset-­to-­equity ratio is sometimes called rate of return on equity multiplier, ­because the
ROE = (Profits/Equity)*(Assets/Assets) = (Profits/Assets) *
(Assets/Equity).
98 | Chapter 10
(b) A higher capital requirement means that firms must
maintain more equity relative to assets. With more equity on
hand, firms have a greater cushion against asset devaluations and insolvencies.
7. This is an open-­choice essay question. However, please
note that “In­equality, Pop­u­lism, and Re­distribution” was
discussed on October 9, 2019. T
­ here ­were two parts: (a) rising in­equality is straining the health of liberal democracy;
and b) enacting more redistributive expenditures and policies would be likely to limit the rise of pop­u­lism.
CHAPTER 11
The IS Curve
CHAPTER OVERVIEW
­Here you get to derive a version of John Hicks’s famous IS
curve. This version builds on more orthodox microfount hose used by Hicks that include the
dations than ­
permanent-­income/life-­cycle hypotheses and the user cost
theory of investment. You can keep this chapter s­ imple if
you like—­Sections 11.1 through 11.4 tell the main story—
or you can go further and pre­sent intuition-­d riven microfoundations for the permanent income hypothesis and
Ricardian equivalence.
You’ll want to pay close attention to Chad’s s­ imple definitions of demand for C, I, G, and NX in Section 11.2: they
clear out a lot of baggage that has accumulated in the IS
curve over the de­cades, and they let you focus on real economics or, if you choose, on the social hydraulics, like the
states of confidence and expectations.
11.1 Introduction
Chad tells the big story of the IS curve first, and I recommend you do the same: a rise in interest rates ­causes a fall in
investment demand, which hurts real 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 may pay dividends. I like to note that in
the long run, we tend to believe that every­thing w
­ ill find its
price: wages w
­ ill 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.
In the short run, however, t­ hings ­aren’t so s­ imple. 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 d­ on’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 courses, 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, however. 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.
Therefore, 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 and differences that only add up to a few
­percent of GDP.
11.2 Setting Up the Economy
­ ere, Chad sets up his simplified IS curve. This is what
H
you ­can’t forget: in his basic model, consumer spending
depends on potential GDP, not ­actual GDP. That means
99
The IS Curve | 107
­Table 1. (Continued)
Shares of
GDP/Year
Portugal
C
I
NX
G
Romania
C
I
NX
G
Slovakia
C
I
NX
G
Slovenia
C
I
NX
G
Spain
C
I
NX
G
Sweden
C
I
NX
G
United Kingdom
C
I
NX
G
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
0.675
0.231
−0.076
0.169
0.669
0.236
−0.096
0.191
0.666
0.208
−0.069
0.195
0.668
0.211
−0.076
0.197
0.658
0.186
−0.042
0.197
0.655
0.157
−0.005
0.193
0.642
0.146
0.011
0.200
0.652
0.153
0.001
0.194
0.643
0.159
0.007
0.191
0.639
0.158
0.011
0.191
0.629
0.172
0.010
0.189
0.624
0.182
0.001
0.194
0.635
0.313
−0.141
0.192
0.600
0.331
−0.129
0.198
0.658
0.272
−0.064
0.134
0.624
0.271
−0.064
0.169
0.601
0.281
−0.058
0.176
0.606
0.270
−0.051
0.176
0.572
0.256
−0.008
0.180
0.569
0.247
−0.004
0.189
0.563
0.251
−0.006
0.192
0.573
0.233
−0.009
0.203
0.570
0.233
−0.021
0.217
0.554
0.642
0.282
0.004
0.072
0.583
0.284
−0.018
0.151
0.597
0.205
−0.002
0.200
0.567
0.239
−0.003
0.198
0.530
0.252
0.007
0.210
0.515
0.207
0.055
0.223
0.503
0.209
0.056
0.232
0.498
0.217
0.048
0.236
0.490
0.243
0.031
0.236
0.503
0.231
0.029
0.237
0.503
0.230
0.022
0.245
0.492
0.234
0.020
0.254
0.575
0.330
0.546
0.329
−0.021
0.146
0.577
0.235
0.014
0.175
0.584
0.224
0.011
0.181
0.577
0.217
0.012
0.194
0.579
0.188
0.034
0.199
0.554
0.196
0.047
0.203
0.545
0.194
0.068
0.194
0.538
0.192
0.080
0.190
0.540
0.184
0.085
0.190
0.520
0.201
0.089
0.191
0.507
0.211
0.083
0.200
0.619
0.304
0.595
0.285
−0.047
0.167
0.594
0.233
−0.009
0.181
0.595
0.223
−0.010
0.192
0.589
0.206
0.003
0.203
0.588
0.184
0.021
0.207
0.577
0.172
0.039
0.212
0.580
0.179
0.031
0.210
0.572
0.190
0.030
0.208
0.571
0.188
0.040
0.202
0.565
0.194
0.036
0.205
0.555
0.204
0.027
0.214
0.451
0.247
0.057
0.245
0.458
0.246
0.053
0.244
0.522
0.208
0.051
0.219
0.454
0.227
0.049
0.270
0.420
0.235
0.044
0.300
0.405
0.224
0.046
0.325
0.401
0.224
0.040
0.335
0.416
0.232
0.035
0.317
0.415
0.240
0.040
0.304
0.415
0.243
0.037
0.305
0.411
0.254
0.032
0.303
0.428
0.508
0.182
−0.020
0.329
0.575
0.170
−0.022
0.276
0.645
0.145
−0.016
0.226
0.609
0.157
−0.020
0.255
0.595
0.156
−0.009
0.258
0.547
0.157
−0.012
0.307
0.568
0.164
−0.013
0.281
0.528
0.171
−0.014
0.315
0.473
0.170
−0.014
0.370
0.533
0.170
−0.016
0.313
0.562
0.171
−0.012
0.279
0.557
−0.032
0.024
−0.018
Sources: National Income and product Accounts, Eurostat, at https://­ec​.­europa​.­eu​/­eurostat ​/­web​/­euro​-­indicators​/­national​-­accounts; author’s calculations.
REVIEW QUESTIONS
1. First and foremost, the IS curve tells us how changes in
the real interest rate impact GDP. The letter “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 experienced by C, I, G, or NX,
interest rates still have a power­ful role to play in determining the level of short-­r un output.
2. It’s ­because a fall in interest rates encourages businesses
and homebuyers to borrow more to purchase more investment goods.
3. Movements along the IS curve: the central bank raises the
real interest rate or cuts the real interest rate.
Examples of shifts in the IS curve: it shifts right when consumers become more optimistic or foreigners demand more
U.S. goods; it shifts left when government cuts purchases or
when businesses become pessimistic about the ­future.
4. If we want to be able to read the newspaper, it’s useful to
know that shifts in the curve (that is, changes in the ā term)
can be caused by many dif­fer­ent ­factors: foreigners, government, businesses, consumers all play a role in determining
the level of short-­r un 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 �t ≠ 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.
108 | Chapter 11
6. As John Hicks reminded us, 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 (aka the trade deficit).
EXERCISES
1. (a) Short-­r un output falls by .5%.
(b) It rises by .25%.
(c) It rises by 1%.
(d) It falls by 2%.
(e) It rises by 2%.
2. This is a worked exercise. Please see the text for the
solution.
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 ser­vices in the short run.
(b) This is an increase in āEX. Foreigners want to buy more
U.S.-­produced goods: This shifts the IS curve to the right.
(c) An increase in āIM. This raises imports—­which, holding
every­thing e­ lse on the demand side equal, means the GDP
­will fall. This shifts the IS curve to the left!
(d) A fall in āi. Remember, new homes are part of I, investment purchases. This shifts the IS curve to the left.
4. To keep t­hings ­simple, let’s focus on the case where the
rise in government purchases is temporary. Also, in this
answer and in answers 5 and 6, I am using the simplest version of the IS model, that of Section 11.2, to answer the
question: that means that short-­
r un consumer spending
depends only on potential GDP, not on a­ ctual 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 āG 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 w
­ on’t
shift very much, but it w
­ ill 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 u­ ntil they get to the f­uture.
That means that consumers ­
will have the same pay as
before, so their consumer spending ­will be the same as
before. Now, āG increases, but āC ­doesn’t change at all: the
IS curve shifts to the right. More government spending adds
up to more overall demand for goods and ser­vices. Note that
this is the “common sense” view of government spending.
In a world with Ricardian equivalence, where consumers
make ­today’s spending decisions based on their lifetime
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, āG 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 l­ ittle 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 b­ ehind Ricardian
equivalence.
If the government decides to borrow to pay for the temporary boost in G, and if the government raises taxes slightly
over the next few de­cades to repay the debt, then ­they’re
­doing just what rational consumers would do themselves:
paying a small price each year to pay for a big one-­time
purchase.
If instead the government decides to raise taxes immediately to pay for the temporary boost in G, then even though
consumers have a temporarily higher tax bill, they still have
a choice about how much money to spend on consumer
goods. They can just borrow some money t­ oday 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 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 w
­ e’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.
The value of āC would be pushed up since the el­derly
would have more income, but it 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.
The IS Curve | 109
If Ricardian equivalence does not hold, so that consumers
make this year’s spending decisions based just on this year’s
income, then we need to know how the government is ­going
to pay for the extra Social Security payments.
If the government borrows money to pay for social security ­today but d­ oesn’t raise taxes to pay for it ­until the distant
­future, then el­derly consumers ­will have more income and
spend more (pushing āC up) but workers w
­ ill keep on spending just like before. So for the overall economy, the net
effect is a rise in āC: the IS curve shifts to the right.
If instead the government permanently raises taxes just
high enough to pay for the extra benefits, then t­here is
next to no impact on ā C: The el­derly consume some more,
the workers consume a ­l ittle less, and the two forces balance out.
6. A
­ fter an earthquake, potential GDP w
­ ill fall. Think about
the supply side: y­ ou’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-­r un 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 a­ fter
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 w
­ ill rise as well (two
negatives make a positive). It works just like an increase in the
intercept term: as the investment demand curve goes, so goes
the entire IS curve. This pushes the IS curve to the right.
C
C: Consumption’s share of potential output,
, ­will stay
Y
the same, so while consumer spending falls, it w
­ on’t fall as a
fraction of potential output. In other words, āC is fixed.
Thus, the earthquake’s overall impact on short-­r un output
is positive.
­Actual GDP is the sum of potential output and short-­run
output, so the earthquake’s impact on a­ ctual 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 t­ hey’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 the “earthquake” in Eu­rope
known as World War II. Even a country like France, which
lost relatively few soldiers during the war, had low GDP for
a few years. It took strong rebuilding efforts just to get GDP
back up to where it was before the war.
7. (a)
(b) During recessions, like the G
­ reat Recession, real government purchases increase relative to real GDP. A
­ fter the
­Great Recession, real government purchases decreased as
real GDP increased.
(c) The data are open to interpretation. One interpretation is
that the increase in real government purchases dampened
the fall in real GDP during. A second interpretation is that
the increase in real government purchases crowds out private spending and has dampened the increase in real GDP.
(d) In order to understand which interpretation is correct,
we need a fully specified theory so we can test, holding
other ­things constant, the effects of changes in government
purchases and changes in the government bud­get stance on
real GDP. A cursory look at other recessions, like t­hose of
1953 and 1969, suggests that government purchases fell during the recession and recovered as the economy recovered.
In addition, the increase in government purchases seems to
be playing an impor­tant role in the post-2001 recovery.
8.
Y C I G NX
= + + +
Y Y Y Y
Y
= ac + xY! + ai + b ( R − r ) + …
Subtract 1 from both sides and collect all the ā’s (minus 1)
into a single ā term:
110 | Chapter 11
Y! = + x Y! + a − b (R − r )
(1 + x )Y! = a − b (R − r )
⎡ 1 ⎤
Y! = ⎢
⎥ [a − b (R − r )]
⎣ (1 − x ) ⎦
10. (a) As always, start with the definition of GDP, and
divide both sides by �:
Y C I G NX
= + + +
.
Y Y Y Y
Y
Plug in your definitions of the components of GDP:
A graph of the IS schedule ­will show that it is flatter: a
change in interest rates w
­ ill now have a bigger impact on
short-­
r un 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.
= ac + bc (R − r ) + ai + b (R − r ) + !.
9. (a) This is almost the same as question 8, except that the
last line w
­ ill look like this:
Collect the ās and subtract one from both sides to yield the
final answer:
Y = a − (b + bc )(R − r ).
(b) Now, a cut in interest rates helps short-­r un output in two
ways: it spurs more investment-­good demand and it spurs
more consumer-­good demand. The IS curve is now flatter.
⎡ 1 ⎤
Y! = ⎢
⎥ [a − b (R − r )]
! ⎦
⎣ (1 + n)
11. Parts (a) and (b) are answered in text, as part of a worked
exercise,
Notice that plus sign in the multiplier term!
(c) I’ll cut my consumer spending by $1,000 each year
forever:
­Here’s how it goes:
$10,000 × 0.10 = $1,000.
Y C I G NX
= + + +
Y Y Y Y
Y
"
= ac + ai + b (R − r ) + ! + aIM + nY
Subtract 1 from both sides and collect all the ās (minus one)
into one ā term:
Y! = + xY! + a − b (R − r )
(1+ x )Y! = a − b (R − r )
⎡ 1 ⎤
Y! = ⎢
⎥ [a − b (R − r )]
! ⎦
⎣ (1 − n)
(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.
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% interest. I use that money to pay the
tax. Now I have a $10,000 debt, and I’ll pay $1,000 in interest payments ­every year, forever, to the bank.
(d) I’ll put the money in the bank and spend only $1 million
each year—­I’ll just spend each year’s interest on the $10
million.
(e) We’ve got to figure out the pre­sent value of the $10 million. That’s $10 million/(1.15), or $6.2 million right now. So
if I went to the bank and promised them that they could have
the $10 million when it arrived in five years, they would be
willing to pay me $6.2 million right now for that privilege.
Now the question reduces to this: if I get $6.2 million
­today, how ­will that change my consumer spending? The
answer is that I ­
will raise my consumer spending by
$620,000 each year, starting right now.
What happens to my consumer spending in year five and
­after? Nothing! I keep spending my $620,000 just as before.
The bank takes its $10 million—­that was our agreement
­after all—­and it d­ oesn’t impact my life at all.
CHAPTER 12
Monetary Policy and the Phillips Curve
CHAPTER OVERVIEW
We cover the IS-­MP-­Phillips curve model ­here. Figure 12.1
provides a ­great outline of the theory, and I’d start the lecture with that. But along the way, you have an excuse to follow Chad’s lead and cover the basics of the term structure,
oil shocks, the profession’s collective ­mistake of the pre-­
Friedman-­Phelps Phillips curve, and the tough love of Paul
Volcker.
The two microfoundations sections—on the pos­
si­
ble
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 choose the second topic. 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 g­ reat 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-­
r un 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 (it’s always denoted Rt).
Chad uses an arbitrage argument to explain how the Fed
can set one par­tic­u­lar 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 r­ eally does? Does it r­ eally borrow
and lend money to banks at the fed funds rate? Yes, the 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) in 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 d­ oing 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
111
Monetary Policy and the Phillips Curve | 117
exchange rates in terms of the Euro, the state of the ­labor
market, and consumer confidence. This discussion provided
a context for macroeconomic projections in the Euro Area.
GDP growth was projected at 1.9% in 2019, 1.2% in 2020,
and 1.4% in 2021 (­these projections reflected downward
revisions to previous forecasts).
The second part of the “account” of the policy meeting
emphasized the GC’s discussion of monetary policy decisions. Given the projections of slower growth, and inflation
rates below target rates, the GC considered lower ECB interest rates and restarting the Asset Purchase Program (APP),
which is the ECB’s quantitative easing program) Fiscal policy stances of vari­ous member ­were also discussed. In short,
“members agreed to easing” the monetary policy stance and
to restart the APP and “to lower the rate of deposit fa­cil­i­ty
by 10 basis points to −.50%.” The report ends with communication of the monetary policy decisions.
As Chad describes in the chapter, the monetary policy
decisions of the central bank can be reflected in the yield
curve. The yield curves for government AAA bonds for the
Euro Area are summarized in Figure 1 below for selected
years. Recall the Euro Area had a “double-­dip” recession
spanning 2008–2009 and 2011–2013. Prior to the 2008–
2009 recession, the 2007 yield curve was relatively flat,
reflecting yields around 4%. In 2010, a­ fter the first recession
the yield curves shifted down, with short-­term rates falling
significantly more than long-­term rates, creating a relatively
steep yield curve. This situation was similar to what happened in the U.S., and, as is well known, triggered the Fed’s
quantitative easing program (designed to reduce the longer-­
term yields). The 2014 and 2018 yield curves continued to
shift down, and became flatter, where short-­term yields fell
into negative territory, as a consequence of the high pre-
mium that bonds ­were selling for. In 2014, the five-­year
bond was still generating a positive yield, but by 2018, the
five-­year bond’s yield had turned negative. Given, the GC’s
September report, we can prob­ably expect the yield curve to
continue to shift down and flatten out over the coming year.
REVIEW QUESTIONS
1. The Fed’s only a­ ctual choice is to set the nominal interest rate.
Since the inflation rate is given, this determines the
real interest rate (real = nominal − inflation). The Fisher
equation shows us this relationship, and the real rate is
the horizontal (so far) line known as the MP curve.
(More realistic versions of the MP curve w
­ ill occur
­later: they slope upward.)
The real interest rate determines short-­r un output, �.
The IS curve shows us this relationship.
If output is above potential (positive short-­run output), then inflation rises in the f­ uture. If output is below
potential (negative short-­r un 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-­r un output), they might raise prices more than last
year. If t­ hings have been especially slow (negative short-­
run output), they might raise prices a l­ ittle 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. It does so by raising or lowering the nominal interest
rate. That’s the only impor­tant tool it has.
Figure 1. Euro Area Selected Government AAA Bond Yield
Curves
Sources: https://­sdw​.­ecb​.­europa​.­eu​/­browseSelection​.­do​?­node​
=­9 689726; author’s calculations.
Note: The daily yield curves ­were averaged to derive annual yield
curves.
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-­r un 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 fact. First, you definitely c­ an’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 fluctuations.
Second, it tells us that good policy has to be both
forward-­looking and cautious: the central bank has to
118 | Chapter 12
set the interest rate ­today based on what interest rates it
thinks the economy w
­ ill need 6 to 18 months from
­today. Since the ­future is always hazy, ­r unning a central
bank is much like driving into a fog. And the first rule of
driving in fog is “slow down.” That prob­ably means to
slow down your rate cuts as well as your rate increases.
Alan Blinder formalized this line of thinking—­a sort of
“precautionary princi­ple”—in his short, nontechnical
book, Central Banking in Theory and Practice (Cambridge, MA: MIT Press, 1999).
Overall, Friedman’s statement is a counsel of humility
for economic policy makers. The fluctuations ­
will
always be a ­factor. 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 a­ fter 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 prob­
lems 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 (πe), and on “demand
conditions,” that is, how much (�) a short-­r un boom or
bust (�) c­ auses 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.
EXERCISES
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, the long-­
term rate tends to be a rough average of short-­term rates,
and when the Fed changes short-­term rates, it tends to e­ ither
keep them at the new level for a while, or it tends to keep
making even more moves in the same direction. So the Fed
has a form of “inertia” when it changes the short-­term rate.
­People in financial markets know this, so when the short-­
term rate changes ­today, many long-­term rates tend to move
in the same direction: not days or weeks l­ater, but on the
very same day.
2. The MP curve shifts down, and so it crosses the IS curve
down and to the right of its old location. This stimulates
investment spending, which increases short-­r un 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-­r un output.
(b) A central bank that cared about keeping short-­r un 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 d­ on’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-­r un output is the same as before the
consumption boom.
4. This is a worked exercise. Please see the text for the
solution.
because any time output
5. This is an appropriate goal ­
moves away from potential, one of two bad ­things happens:
if you let output fall below potential, then you have unused
unemployed workers and machines. This is
resources—­
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 p­ eople unhappy. To make ­matters worse, the only
reliable way to get rid of the higher inflation is by creating a
­ ill, again, make citizens unhappy. In the
recession, which w
short-­r un model, “­free lunches” are hard to come by—so it’s
best to stick close to potential output.
Monetary Policy and the Phillips Curve | 119
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) u­ ntil the corresponding real interest rate again equals the marginal product of capital. This is the same as raising MP ­until Ỹ equals
zero again.
(c) IS shifts to the right. The Fed should raise MP u­ ntil 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
­ ill naturally start
Solow “long-­run” world, the economy w
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-­r un output.
Step 3: When short-­r un 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% before, it might per­sis­tently be
8% afterward.
If the central bank instead keeps the nominal interest rate
constant a­ fter the oil shock, then t­ hings get in­ter­est­ing. Now,
the rise in inflation w
­ ill 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 w
­ ill 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 m
­ atters
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%, and the oil price
shock raised inflation by 3%, then I need to raise the nominal rate by 1% + 3% = 4%. I am not likely to be a popu­lar
central banker if I do this. You can see why in the 1970s,
U.S. central bankers in the 1970s w
­ ere reluctant to undo the
effects of the oil price shocks.
Surprisingly Volcker, who fi­
nally did raise rates high
enough, has had a very successful ­career since then as an
adviser to banks. So, in the United States at least, some
forms of po­liti­cal bravery are rewarded.
In graphs, the Phillips curve rises due to the oil shock for
one period, and then goes back—­here, nothing is changed.
On the IS-­MP side, raise MP for one period to create a
recession, then put MP back to its old level.
9. I’ll just discuss the Phillips curve, since that’s the only
clear direct impact. I’ll also assume that the immigration is
a 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% before to 2%
­after, but it would stay at 2% 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-­r un model.
10. Assume we start with zero short-­r un output.
(a) If the Fed keeps the nominal rate unchanged, then a
rightward shift in the IS curve c­ auses the following:
• IS-­MP immediate effect: IS shifts right but MP stays
fixed. This yields positive short-­r un output.
• Phillips curve immediate effect: positive short-­r un 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 8a.)
120 | Chapter 12
• Phillips curve next period effect: the boom is even bigger now, so inflation rises even faster than last year. If
inflation was 2% beforehand, it might have been 4% the
first year but is now 8% this year!
• Further effects: you can see where this is headed—an
even lower real rate, since inflation is even higher.
­There’s a bigger boom, which ­causes higher inflation,
which cuts the real rate again, and so on—­all from a
one-­time boom in consumer spending that the Fed just
let pass on by.
• Summary: in this case, the IS curve only shifts once,
and it only shifts at the very beginning (rightward), due
to the consumption boom. The Phillips curve never
shifts. MP, by contrast, keeps falling ­every period, as
higher inflation accidentally reduces the real interest
rate ­every period.
(b) Assuming the goal is stable prices and production, as in
3(b) ­earlier, if the central bank raises the real rate of interest
in response to the autonomous increase in consumption, so
that short-­run output is unchanged, the rate of inflation is
unchanged and the economy remains as its initial position
on the Phillips curve.
11. With a bigger �, it’s easier to cut 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 u­ nions might make it easier to
cut wages during a recession; more trust between ­unions
and firms might convince u­ nions to take a temporary wage
cut in order to save jobs (­there’s some evidence that Scandinavian ­unions and firms cooperate this way); decentralized
firms might sell directly to the consumer (­there’s some evidence that goods that pass through many hands on their way
to the consumer have stickier prices).
12. This is a worked exercise. Please see the text for the
solution.
13. Inflation was stable in the late 1990s, so it appears that
short-­run output was close to zero. If the new economy
boom was largely due to positive short-­r un 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. The development of e-­commerce has made it much easier
to keep money outside of checking accounts, which prob­
ably reduces 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 of the time. At the end of the month,
when the bills arrive, I can quickly move money from savings into checking (no impact on M2, but increasing M1),
and then pay my bills. Of course, I need no currency for
­these transactions, so e-­commerce puts downward pressure
on the demand for currency (part of ­every definition of
money). In a world of unpredictable financial innovation,
shifts in money demand are quite likely. This is a good
argument for targeting the nominal interest rate rather than
a fixed money supply.
CHAPTER 13
Stabilization Policy and the AS/AD Framework
CHAPTER OVERVIEW
This is the third s­ imple dynamic general equilibrium model
­we’ve covered this semester: first we looked at 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: Taylor’s monetary policy rule.
This chapter contains an impor­
t ant invisible hand
result: a monetary policy rule that only focuses on keeping inflation close to its target ­will also stabilize short-­r un
output, as if by an invisible hand. Students might have
thought that in order to stabilize short-­r un 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 w
­ ill 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 f­ uture inflation rates can cause the AS
schedule to be unstable with re­spect to cyclical variations in
output.
13.1 and 13.2 Introduction and Monetary Policy
Rules and Aggregate Demand
­ ere, we introduce a ­simple Taylor rule (Chad just calls it a
H
“­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 all ­there is to it:
Rt − r = m(π t − π ).
The term � is simply a pa­ram­e­ter (1/2 in Taylor’s rule) that
shows how strongly the Fed reacts to inflation. A bigger �
means a bigger reaction.
Note that Chad has set this up so that it plugs into his IS
curve quite easily; together, they give us what we now call
the aggregate demand curve:
Y! = a − (b × m)(π − π ).
t
t
You r­ eally should keep � and � separate in your equations:
that gives you a chance to show how short-­
r un 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-­r un 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,”
“uncaring,” or “brutal” the central bank is. It shows how
121
130 | Chapter 13
uses the dispersion variables to create an interaction variable, in which increases in the dispersion of economic conditions results in increases in the coefficient relating the
current interest rate to the previous period’s interest rate.
Second, the dispersion variables are included as additional explanatory variables, modifying the effects of inflation and output gaps on the overnight lending rate of
interest. Klose predicts that the greater the dispersion of
economic conditions the less strong ­will be the ECB’s reaction to inflation and the output gap: the reaction has to be
dampened to build a voting consensus. Klose estimates
vari­ous reaction functions for the time period 2000–2014,
varying the combinations of EC voting members with and
without the dispersion interaction lagged interest-­rate coefficient and with and without inflation and output gap dispersion variables. He concludes that the dispersion of
economic circumstances across the Euro Area countries
does influence the ECB reaction function. In fact, the
greater is the dispersion in national economic circumstances, the stronger is the relationship between the current
overnight lending rate of interest and the past period’s lending rate of interest, and the weaker is the relationship
between the lending rate of interest and the inflation and
output gap targets. To quote Klose, “council members try to
reach a consensus by simply reacting less if country dispersion is high with re­spect to fundamentals.”
REVIEW QUESTIONS
1. Thinking of policy in terms of a rule is helpful ­because it
helps the private sector to form accurate expectations about
the ­future. If the central bank can reduce uncertainty by following a rule, then private businesses and workers ­will be
better able to plan for the ­future, which may improve economic stability.
Also, following a rule is good for helping policy makers
to think clearly. When you use a rule, you can run economic
simulations where you compare your favorite rule against
other policy rules. That way, you can find out which rule is
best. Rules are easy to compare to one another, while discretion is hard to compare to anything.
Fi­nally, it’s good to remember that even if you use pure
discretion, you are still following a rule: you just may not
know what the rule is yourself. The time consistency lit­er­a­
ture 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.” But as you’ll see, you just wind up with high
inflation and an average economy.
2. AD slopes downward b­ ecause of the link ­running from the
Taylor rule to the IS curve. If inflation is high, the Fed w
­ ill 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 b­ ecause it’s just the Phillips curve: positive short-­run
output ­causes firms to raise prices more aggressively.
This is like a standard supply-­and-­demand model b­ ecause
a quantity mea­sure is on the x-­axis while a price-­related
mea­sure is on the y-­axis. It’s unlike a supply-­and-­demand
model ­because the only reason AD slopes downward is
­because of a government policy decision to hurt short-­run
output when inflation is high. In markets, a high price for an
individual good generally ­causes consumers to substitute
over into buying other, cheaper goods. In brief, AD is about
government policy.
3. AD shocks: government spending shocks, investment optimism, consumer optimism, foreign recession; AS shocks: oil
price shocks, ­union wage hikes, cheap imports.
4. The AS curve is our fundamental source of dynamics, as
discussed previously. 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-­r un output equal to zero.
5. They are counterclockwise ­because the cycle is boom-­
bust, 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 w
­ ill be high, they demand
higher prices, and so the inflation expectations become
self-­fulfilling.
If the Fed can convince businesses that it w
­ ill not tolerate
inflation, then businesses know that their competitors are
unlikely to raise prices, and so each business itself w
­ ill
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.
EXERCISES
1. (a) 10% inflation → 6% real, 16% nominal
5% inflation → 3.5% real, 8.5% nominal
2% inflation → 2% real, 4% nominal
1% inflation → 1.5% real, 2.5% nominal
Stabilization Policy and the AS/AD Framework | 131
(b) 20% nominal, 10% real
10% nominal, 5% real
4% nominal, 2% real
2% nominal, 1% real
This rule implies a central bank that is tougher on
inflation. It also implies a flatter AD curve.
2. (a) The 2018 inflation rate, mea­sured as the percentage
change in the Core PCE (chained) price index, was 1.9%.
(b) The 2018 inflation rate, mea­sured as the percentage
change in the core CPI (chained, including food and energy)
price index was 2.1%.
(c) The price of energy, especially oil and gasoline, has
caused the PCE inflation rate to be greater than the core
PCE inflation rate.
(d) From equation 13.5, the federal funds rate is:
it = Rt + π t = r + π t + m(π t – π ).
In 2018, the inflation rate was approximately 1.9%. If the
target inflation rate was 2%, and the � was 2%, and � = .5,
the predicted federal funds rate would be 3.95%. The ­actual
federal funds rate was 1.83%. This monetary policy rule is
based on contemporaneous values of the rate of inflation. If
the policy makers are forward-­looking in setting interest
rates, the federal funds rate might be set in anticipation of a
slowdown in the economy.
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, c­ auses 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-­r un 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-­r un output.
In Chad’s model, the current period’s expected inflation
rate is based on last period’s ­actual inflation. With no further increases in the price of oil, the oil shock has dissipated,
but inflationary expectations remain higher than what they
­were in the steady state; as such, the AS schedule shifts
down and to the right, but not all the way back to the steady
state, ­because of the higher inflationary expectations. The
result is a decrease in the inflation rate in the second period.
The decline in the inflation rate in the second period reduces
inflationary expectations in the third period, which further
shifts the AS curve down and to the right. Eventually,
through reductions in inflationary expectations, the AS
curve shifts back into its steady-­state position. During this
adjustment, the economy ­will experience disinflation and an
increase in short-­r un 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 c­ auses 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 the opposite of positive aggregate demand shock in the textbook.
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.
either Eu­
ro­
pean or Japa­
nese economies
Eventually, ­
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.
132 | Chapter 13
6. This works like an AD boom that lasts. At the moment
that the central bank implements the new π ′, it’s cutting
the real rate. A
­ fter all, π ′ is now higher than πt, the current
inflation rate. This shifts AD outward. Higher AD means a
move along the fixed AS curve for the first year—so
demand pressures push inflation up a bit, but not quite high
enough to be in steady state. Over the next few years, AD
stays in its same (new) position, and AS slowly creeps
upward: the boom creates more inflationary pressures, so
firms raise prices more and more each year. Eventually, the
economy winds up back at zero short-­r un output, with π ′
equal to πt. The central bank then ends the boom: we are
now in a new steady state.
7. (a) The AS slopes upward ­because positive short-­r un output creates pressures for price hikes on the demand side.
With positive short-­r un output, firms are selling more than
they want to at current prices. Therefore, they raise prices
more than the previous year. If the average firm does this,
then overall inflation increases.
(b) A steeper AS would mean that output would fluctuate
less, but inflation would fluctuate more ­under AD shocks.
(c) A steeper AS would mean that both output and inflation
would fluctuate less for a given oil price shock. (Note that
the oil price shock is a y-­intercept shock.)
10. Rt − r = ( 1b ) (a). Inserting this into the IS curve,
Y!t = a − b (R − r ), yields:
b
Y!t = a − ⎛⎜ ⎞⎟ a = 0.
⎝ b⎠
­Every time ā shifts one way, the Fed instantly counteracts it
by changing the real interest rate. A positive AD shock c­ auses
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 = (r + π) + (1 + m)πt .
The slope is greater than 1. As noted in the manual, this
concept is known as the Taylor princi­ple. In the following
graph, r = π = 2%, m = .5.
(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 u­ nions, 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 economy.
(b) Note that ā is an x-­intercept. ­Under a steeper AD curve,
a shock to ā has a bigger effect on output and inflation.
That’s worse on both counts!
(c) ­Under a steeper AD curve, a shock to ō creates a smaller
swing in output, but a bigger swing in inflation.
(d) A Fed that d­ oesn’t care much about inflation c­ auses AD
to be steeper. Also if investment responds only weakly to
shifts in interest rates, or if the consumption and investment
multipliers get smaller, then AD gets steeper.
9. This is a worked exercise. Please see the text for the
solution.
(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 r­ ose, and it (perhaps accidentally) cut real
rates. When setting policy, it’s impor­t ant to remember that
Stabilization Policy and the AS/AD Framework | 133
as a rule, real rates impact spending, while nominal rates
do not.
13. This is a worked exercise. Please see the 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% interest-­rate credit card, and making minimum payments for years: can that ­really be worth it?
The only way, in this s­imple model, to keep unemployment permanently low would be to keep increasing inflation
forever. But of course we know from looking around the
world that countries with hyperinflation are poor, not rich.
So our New Keynesian model i­sn’t ­really useful for understanding per­sis­tently increasing inflation. For that, you have
to go back to Chapter 8.
16. (a) Take πt−1 as π , 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 =
π+o
(1 + vmb)
and
⎛
⎞
o
Y!1 = a − bm ⎜
⎟
⎝ (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 =
(π t −1 )
(1 + vmb)
+
π × vmb
,
(1 + vmb)
which is a ­simple first-­order difference equation. ­Here are
the figures for the first 10 years, just to be safe.
Time
0
1
2
3
4
5
6
7
8
9
Inflation
Short-­run output
2.00
3.77
3.57
3.40
3.24
3.10
2.97
2.86
2.76
2.67
0.00
−0.44
−0.39
−0.35
−0.31
−0.27
−0.24
−0.22
−0.19
−0.17
(c) You’ll see that even ­after 10 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% the
­whole time):
Time
0
1
2
3
4
5
6
7
8
9
Inflation
Short-­run output
3.00
3.80
4.44
4.95
5.36
5.69
5.95
6.16
6.33
6.46
0.00
1.60
1.28
1.02
0.82
0.66
0.52
0.42
0.34
0.27
You can see by looking at the pa­ram­e­ter values that the
new steady-­state inflation rate ­will be 7%: 3% + ā/(bm) =
3% + 2%/0.5.
A long-­lasting 2% ā shock ­doesn’t result in a 2% boom,
even in the first year. Why is that the case? It’s ­because even
in the first year, inflation rises, which forces the Fed to
immediately start cooling off the economy with higher real
rates.
CHAPTER 14
The G
­ reat Recession and the Short-­Run Model
CHAPTER OVERVIEW
Students ­will find this chapter useful for applying what they
have learned so far in understanding the ­Great Recession.
This chapter introduces financial considerations, in par­tic­u­
lar 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. Fi­nally, Chad
introduces the concept of secular stagnation, and discusses
­whether or not the United States and Eu­rope, like Japan,
have entered into an era of secular stagnation.
14.1 Introduction
This chapter considers the policy difficulties encountered in
stimulating the economy during a severe economic downturn. This chapter is 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
134
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—­the “normal” spread is about 2 percentage
points—­see Figure 14.1 in the textbook. Typically, during
economic downturns financial frictions increase. During the
­Great Recession, financial frictions increased dramatically:
the BAA/10-­yearTreasury spread increased to around 6 percentage points. To incorporate financial frictions into the IS/
MP model, the real rate of interest, R, is simply defined as
the real federal funds rate, Rff, plus the effects of the financial
frictions, �. During normal times � is assumed to be zero.
FINANCIAL FRICTIONS IN THE IS/MP FRAMEWORK
Following a collapse of housing prices, negative wealth
effects result in lower consumption, a reduction in ā, pushing the IS curve to the left. ­Under normal circumstances, the
Federal Reserve reduces the federal funds rate and other
interest rates follow suit, shifting down the MP schedule to
counteract the adverse demand shock. However, during a
severe downturn, financial frictions increase, and as the federal funds rate decreases, the long-­term rates increase, in
effect shifting the MP schedule upward, causing further
declines in short-­r un output.
The ­Great Recession and the Short-­Run Model | 139
CASE STUDY: THE EU, THE ­GREAT RECESSION,
AND THE FLIGHT TO QUALITY.
Chad describes how financial frictions create a “spread”
between the central bank lending rate and the long-­term rate
of interest. In the case study on page 399, financial frictions
are shown to increase the difference between the real rate of
interest R and the marginal product of capital, r-­bar. By
examining “convergence series” interest rates (yields on
government bonds of around a 10 year maturity) across the
EU, we can see how financial frictions, in this case reflecting the risk structure of interest rates, over time have differential effects on EU members (see http://­appsso​.­eurostat​.­ec​
.­europa​.­eu​/­nui ​/­show​.­do​?­dataset​=­i rt​_­lt​_­mcby​_­a&lang​= ­en).
During the period from 2001 to 2018, the interest rates for
the vari­ous EU members ­were compared to the average rate
of interest for the EU28 countries (no data w
­ ere available for
Estonia) to ascertain the spread between the EU member’s
interest rate and the EU28 interest rate. See Figures 1a to 1f.
Figures 1a to 1d show mainly EU members with positive
interest rate spreads—­countries with yields in excess of the
EU28 yield. Figures 1e and 1f show mainly EU members
with negative interest rate spreads—­countries with yields
less than the EU28 yield.
As mentioned in previous chapters, the EU had a “double-­
dipped” recession, where the first recession began in 2008,
Q1, and ended in 2009, Q2, and the second recession began
in 2011, Q3, and ended 2013, Q1. As shown in Figure 1a,
Ireland, Spain and Greece all initially had yields in line with
the EU28 yield. When the first recession occurred the yield
spreads increased, and as the Eu­ro­pean sovereign debt crisis
especially
exploded, the spreads increased significantly—­
for Greece of course—­where by 2013 the yield spread was
well above 15%. Figure 1b shows that the yield spread for
Lithuania and Latvia increased dramatically for the first
recession, and then has fallen below zero in recent years.
The sovereign debt crisis increased Cyprus’s yield spread,
but to a much lesser degree than what happened in Greece.
Figure 1c shows that Portugal had yields very much in line
with the EU28 yield, but, following the first recession and
then with second recession and the sovereign debt crisis, its
yield spread ­rose above 6%. Hungary’s yield spread was
above 2% and spiked to above 4% with the first recession.
Poland’s yield spread, while increasing with the first recession, has remained positive but does not seem to fluctuate as
much as other newer members to the EU. Figure 1d shows
similar but less dramatic changes—­with Romania’s yield
spread increasing during the first recession, and Slovenia’s
yield spread increasing during the second recession. Slovakia, in contrast, had a yield that followed the EU28 yield,
and has turned negative in recent years. Figures 1e and 1f
show that Germany, Belgium, Denmark, France, the Netherlands, Finland, Luxembourg, and Austria all have negative yield spreads; that Czechia’s yield spread has been very
countercyclical, fluctuating around zero (rising in recent
years); and the UK’s yield spread has been higher in recent
year (prob­ably a Brexit effect). The negative yield spreads
are interpreted as a “flight to quality” especially during the
sovereign debt crisis years, where investors ­were moving
investments from crisis countries to noncrisis countries—­
looking for relatively safer investments.
In recent years, we can see a tendency for the yield spread
for most of the EU members to begin to converge t­oward
zero. As Paul Krugman (2018) writes: “Once Mario Draghi
[announced] that the ECB would do “what­ever it takes,” (to
control the sovereign debt crisis) bond spreads rapidly
dropped.” The convergence of the bonds spreads ­toward
zero illustrates the success of ECB in containing the sovereign debt crisis, and in coordinating monetary policy across
the EU. The impor­tant question remains as to ­whether the
EU has the policy apparatus in place to end (as opposed to
control) secular stagnation6 and ­whether the EU can effectively act, when ECB’s overnight lending rate is close to
zero, to ­counter the next recession7 ?
REVIEW QUESTIONS
1. Financial frictions are a cause of disruptions to financial
markets. Financial frictions result in shortages of liquidity
and insolvencies. Financial frictions are evidenced in rising
spreads in yields between risky securities (such as corporate
bonds) and relatively safe securities (such as government
securities). For example, the difference in yields between a
10-­year BAA corporate bond and a 10-­year Trea­sury security reflects the potential risk that the corporate bond issuer
­will not meet its promised payments. If the yields on the two
bonds ­were the same, investors would choose the government bond ­because it has no risk of default. To induce investors to hold the corporate bond, the yield ­will have to rise to
encourage them to take the added risk to purchase the
bonds.
In the IS/MP diagram, financial frictions affect the real
rate of interest. As financial frictions increase, the real rate
of interest rises, in effect shifting up the MP schedule, and
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 predictable pattern: like rais6. See https://­www​.­gc​.­cuny​.­edu​/­CUNY​_­GC​/­media​/­LISCenter​/­pkrugman​/
­Its​-­baaack​.­pdf
7. See https://­www​.­piie​.­com​/ ­blogs​/­realtime​-­economic​-­issues​-­watch​/­euro
​-­a reas​-­fiscal​-­ability​-­handle​-­another​-­recession​-­limited
140 | Chapter 14
(a)
(d)
(b)
(e)
(c)
(f)
Figure 1. Convergence Yield Spreads (EU Member’s Convergence Yield Less EU28 Convergence Yield)
Sources: http://­appsso​.­eurostat​.­ec​.­europa​.­eu​/­nui​/­show​.­do​?­dataset​= ­irt ​_­lt ​_­mcby​_ ­a&lang​= ­en; author’s calculations.
The ­Great Recession and the Short-­Run Model | 141
ing 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: 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 interr un
est rates, discourages spending, and leads to short-­
declines in output. Short-­run declines in output generate
further deflation and further increases in the real rate of
interest. Real interest rates may 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 mortgaged-­
backed securities, and ­these other assets as a means to provide the financial system with liquidity and solvency and
reduce financial frictions.
6. Capital requirements set the minimum equity-­to-­asset
ratio and, therefore, limit financial institutions’ exposure to
the risk of insolvency. For example, a financial institution
with a 2% equity-­to-­asset ratio w
­ ill become insolvent following a 3% market devaluation in its assets whereas a firm
with a 10% equity-­to-­asset ratio remains solvent following
the 3% market devaluation.
7. Fiscal stimulus could be justified when monetary policy
ceases to be effective in increasing short-­r un output during
a recession. This occurs during a liquidity trap, as was
described in question 3.
EXERCISES
1. (a) In the IS/MP diagram, with the economy initially at
potential GDP, the real rate of interest equal to the marginal
product of capital, and a stable inflation rate, a mild financial crisis that increases financial frictions and raises the
interest rate from zero to 2% shifts the MP schedule up and
­causes a movement along the IS schedule to the left, which
depends 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-­r un 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 long-­term rates by purchasing long-­
term securities (quantitative easing). Purchasing long-­term
Trea­sury securities, for example, w
­ ill 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 the text for the solution.
1
3. (a) In the textbook, following Taylor’s rule: m = n = ,
2
π = 2%, and � = 2%.
(b) The Core CPE inflation rate in 2018 was 1.9%. The Core
PCE inflation rate is the rate of inflation all consumer
“goods” (excluding food and energy) mea­
sured by the
Bureau of Economic Analy­sis and reported in the National
Income and Product Accounts of the U.S.
(c) The short-­run mea­sure of output, Ỹt, equals the difference between ­actual and potential output divided by potential output. Annual mea­sures of Ỹt are provided from 2001
to 2018. Short-­run output has been negative from 2008 to
2017. In 2009, the ­actual output was almost 5.6% below
potential. See the ­table that follows.
(d) Using Taylor’s rule, it = πt + rt + .5(πt − �) + .5Ỹt = it
= πt + 2% + .5(πt − 2%) + .5Ỹt generates the following predictions of the federal funds rate:
142 | Chapter 14
Year
π
Federal
Funds
Rate
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
−1.66
−5.57
−4.18
−3.84
−3.08
−2.90
−2.13
−1.03
−1.14
−0.49
0.55
2.00
1.16
1.36
1.58
1.90
1.53
1.57
1.25
1.59
1.63
1.95
1.93
0.16
0.18
0.10
0.14
0.11
0.09
0.13
0.40
1.00
1.83
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Predicted
Federal
Funds
Rate
3.17
−0.05
0.94
1.46
2.30
1.84
2.29
2.36
2.82
3.19
4.20
.
.
.
.
.
.
.
.
.
.
.
(e) The predicted federal funds rates are higher than the
­actual federal funds rate in all years except 2009. 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 secular stagnation, and
that the Fed perceives Taylor’s rule as specified above to be
the incorrect monetary rule!
4. This is the student’s choice.
5. Students can find the FOMC minutes and press releases at:
https://­www​.­federalreserve​.­gov​/­newsevents​/­press​/­monetary​/­
2016monetary​.­htm.
The October 30, 2019. press release is as follows (the
actions are emphasized in italics):
Information received since the Federal Open Market Committee met in September indicates that the l­abor market
remains strong and that economic activity has been rising at
a moderate rate. Job gains have been solid, on average, in
recent months, and the unemployment rate has remained low.
Although ­house­hold spending has been rising at a strong
pace, business fixed investment and exports remain weak.
On a 12-­month basis, overall inflation and inflation for items
other than food and energy are ­r unning below 2%. Market-­
based mea­
sures of inflation compensation remain low;
survey-­based mea­sures of longer-­term inflation expectations
are ­little changed.
Consistent with its statutory mandate, the Committee
seeks to foster maximum employment and price stability. In
light of the implications of global developments for the economic outlook as well as muted inflation pressures, the
Committee de­cided to lower the target range for the federal
funds rate to 1-1/2 to 1-3/4 ­percent. This action supports the
Committee’s view that sustained expansion of economic
activity, strong ­labor market conditions, and inflation near
the Committee’s symmetric 2 ­percent objective are the most
likely outcomes, but uncertainties about this outlook
remain. The Committee w
­ ill continue to monitor the implications of incoming information for the economic outlook
as it assesses the appropriate path of the target range for the
federal funds rate.
In determining the timing and size of f­ uture adjustments
to the target range for the federal funds rate, the Committee
­will assess realized and expected economic conditions relative to its maximum employment objective and its symmetric
2 ­percent inflation objective. This assessment w
­ ill take into
account a wide range of information, including mea­sures of
­labor market conditions, indicators of inflation pressures and
inflation expectations, and readings on financial and international developments.
6. This is the student’s choice. Economic indicators can be
found at Eu­
ro­
pean Central Bank Statistical Data Ware­
house, http://­sdw​.­ecb​.­europa​.­eu​/­.
(Annual percentage changes
­unless other­wise stated)
Euro
Area
Reference
Period
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)
ECB Lending Rate of Interest (see
https://­w ww​.­ecb​.­europa​.­eu​/­stats​
/­policy​_­and​_­exchange​_­rates​
/­key​_­ecb​_­interest​_­rates​/­html​
/­index​.­en​.­html)
0.7
5.5
1.2
2019Oct
2019Sep
2019Q3
2.2
342
7.5
2019Q2
2019
2019Sep
0.1
1.43
2019Q3
2019Q2
1.1059
–1.7
20-­Nov-19
2019Q2
86.4
.25%
2019Q2
2019
CHAPTER 15
DSGE Models: The Frontier of
Business Cycle Research
CHAPTER OVERVIEW
This chapter provides a synthesis of the long-­r un and short-­
run 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
labor market analy­
sis); and an
extension to neoclassical ­
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 l­ abor market analy­sis. Some novel extensions to the neoclassical ­labor market model are introduced
through the DSGE models, and ­these extensions give new
(read dif­fer­ent) explanations for economic fluctuations that
­were not likely taught in princi­ples. The section on the
impulse response functions ­will require some hand-­waving
class time, but Chad provides some excellent end-­of-­chapter
exercises that enable students to qualitatively map out the
reaction of variables to vari­ous shocks. As in all good learning exercises, the reactions of the variables clearly depend
on the under­lying assumptions of the model. So you ­will
have another opportunity to allow students to make connections between core assumptions and macroeconomic
be­hav­iors.
15.1 Introduction
­ ere Chad defines DSGE models: Dynamic b­ ecause the
H
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 per­
sis­tent changes in TFP.
FROM REAL BUSINESS CYCLES TO DSGE
As real business cycle models ­were extended and refined to
explain public-­, foreign-­, and monetary-­sector events and
the effects of both nominal and real shocks for dif­fer­ent
degrees of price and wage stickiness, the real business cycle
models evolved into DSGE models.
In coming full circle back to Chapter 1 (where we said
that models include endogenous variables, exogenous variables, and par­ameters), the components of DSGE models
are explained to include endogenous variables, shocks, and
143
150 | Chapter 15
Figure 1. Real GDP and Estimated Real Potential GDP: Eu­ro­
pean Union 28 Countries
Figure 3. Growth in Estimate Potential Output: Eu­ro­pean
Union 28 Countries
Sources: Federal Reserve Bank of St. Louis Database, millions of
2010 chained euros; author’s calculations.
Sources: Federal Reserve Bank of St. Louis Database, millions of
2010 chained euros; author’s calculations.
2. Real Business Cycle (RBC) models preceded DSGE
models. RBC models emphasized the effects of real shocks,
for example TFP shocks, in explaining economic fluctuations. DSGE models incorporate the insights derived from
RBC models, but also incorporate the effects of nominal
shocks, due to shifts in monetary policy or changes in financial frictions. In short, RBC models are a special case within
DSGE models.
3. Both TFP shocks and monetary policy shocks ­
under
sticky prices lead to movements in macro variables that
resemble business cycles: that is, the real wage rate, output,
and employment move in the same direction over the business cycle.
Figure 2. Short-­Run Output: Eu­ro­pean Union 28 Countries
Sources: Federal Reserve Bank of St. Louis Database, millions of
2010 chained euros; author’s calculations.
potential output recovered somewhat, rising to almost
1.35%.
REVIEW QUESTIONS
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 b­ ecause random shocks, given the “features”
of the economy, are the primary source of economic fluctuations. DSGE models are general equilibrium b­ ecause the
effects of random shocks affect equilibriums across markets: ­labor, capital, output, and financial.
4. Agents at the micro level make decisions to save, consume, invest, work, or enjoy leisure based on current and
expected f­ uture 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.
DSGE Models: The Frontier of Business Cycle Research | 151
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
(including nominal rigidities, adjustment costs, heterogeneity of agents, and information asymmetries).
EXERCISES
1. This is a worked exercise. Please see the textbook for the
solution.
2. (a) A positive temporary TFP shock—­for example, favorable weather conditions—­increases the marginal product of
­labor and the demand for ­labor. With no rigidities, assuming
“normal”-­shaped ­labor demand and ­labor supply schedules,
the equilibrium real wage rate and employment w
­ ill increase.
(b) If prices are sticky, then aggregate demand ­
will be
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.
© ­Labor demand shifts to the right, and ­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 ­will be perfectly price
inelastic. The decline in government spending, if financed
by a reduction in ­future taxes, increases current consumption and reduces ­labor supply. The reduction in ­labor supply
increases the equilibrium real wage rate as employment is
unchanged.
(c) The impulse response function in Figure 15.12 shows the
effects of an increase in government purchases financed by
a ­future increase in taxes. In Figure 15.12, the increase in
government purchases financed by f­uture taxes stimulates
the economy in the short term by reducing permanent
income and increasing l­ abor supply. The increase in employment generates higher levels of output, with lower levels of
consumption. In this case, we have just the opposite effect.
The decrease in government purchases temporarily ­causes a
reduction in output, by reducing employment (via the wealth
effect of a lower ­future tax burden), but increases current
and ­future consumption.
5. (a) A decline in the value-­added tax is the opposite of the
example given in the textbook (the increase in the sales or
excise tax). Assuming that the tax rate is t and that businesses bear the ­legal tax incidence, the 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 thus 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 would
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 w
­ ill increase and the equilibrium
level of employment ­will decrease.
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
the 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).
152 | Chapter 15
(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).
(d) The results described previously are similar to the
Smets-­Wouters model shown in Figure 15.13 as both output
and inflation stabilize over time.
8. (a) With the inflation rate on the vertical axis, and Ỹ on the
horizontal axis, a temporary increase in government purchases,
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. However, if the central bank maintains its pre-­
fiscal stimulus inflation target, the central bank increases the
interest rate, causing a leftward shift in the aggregate demand
schedule, causing short-­run output and inflation to decrease.
The decrease in the inflation rate eventually reduces expected
inflation causing the aggregate supply schedule to shift to the
right, and the economy returns to long-­run output at the target
inflation rate. This adjustment pro­cess is described In Section 13.6 of the textbook (inflation-­output loops).
(b) A graph of the impulse response function for output
shows a temporary expansion (caused by the increase in
government purchases) and a contraction (caused by an
increase in the expected inflation rate and/or the central
bank’s monetary policy rule).
(c) A graph of the impulse response function for inflation
shows an acceleration of inflation (initially caused by the
increase in government purchases and subsequently caused
by an increase in inflation expectations). Assuming the central bank maintain its inflation target, the real interest ­will
increase to stabilize the inflation rate at the central bank’s
target level.
(d) The results described previously are similar to the
Smets-­Wouters model shown in Figure 15.13. As in the previous prob­lem, inflation and output stabilize over time with
re­spect to the shock.
(e) In the AD/AS model, the increase in aggregate demand
increases short-­
r un output, and through Okun’s law the
increase in short-­r un 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. T
­ hese
results are shown in Figure 15.12; as short-­run output expands,
employment increases, and as short-­run output contracts, so
does employment.
CHAPTER 16
Consumption
CHAPTER OVERVIEW
This chapter is the first of the last six chapters providing
applications and microfoundations. The combination of
rigor and intuition makes this chapter pleasing to teach. The
intertemporal utility maximization model is developed.
From this model, the growth rate in consumption is related
to the real rate of interest. Given that the long-­run growth
rate is determined by deep par­ameters in the Solow-­Romer
models, the determinants of the long-­run interest rate are
pinned down. In addition, through the permanent income
hypothesis, consumption is related to wealth. Exceptions to
the permanent income hypothesis, such as borrowing constraints and precautionary savings, are discussed. Borrowing constraints and precautionary savings increase the
sensitivity of current consumption to changes in current
income. The chapter concludes by examining the empirical
evidence on consumption.
16.1 Introduction
In the United States, personal consumption is the largest
component of GDP; it is over two-­
thirds of GDP and
amounts to over $12 trillion. In this chapter, the neoclassical
theory of consumption is considered. In the neoclassical
approach, a representative consumer chooses a consumption
pattern over his or her lifetime to maximize utility, subject
to a lifetime bud­get constraint. The microfoundations of
utility maximization are related to aggregate consumption
be­
hav­
ior, 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 exceptions, such as borrowing constraints and
precautionary savings.
Many students who have studied 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 for this chapter, the macroeconomic
theory of consumption is placed in the historical context of
the debate between proponents of policy activism and ­those
of 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. Therefore, U = U(c­today,c­future).
THE INTERTEMPORAL BUDGET CONSTRAINT (IBC)
The IBC shows that lifetime consumption must equal lifetime income. To illustrate, consumption t­ oday and consumption in the ­future are defined. Consumption ­today is defined
as income, y, ­today plus financial wealth, �, ­today less savings
(where savings is financial wealth in the f­uture), and consumption in the ­future is defined as income in the ­future plus
financial wealth plus interest earnings on that wealth).
(Note: In the growth chapters, lower-­case y is per capita
output: students w
­ ill notice that y is now the income of a
representative consumer.)
Given ­these definitions, the IBC is written in pre­sent
value terms where the pre­sent value of lifetime consumption
153
Consumption | 157
­Table 2. HOUSE­HOLD SAVINGS RATES: SELECTED EURO
AREA COUNTRIES, 2007 TO 2018
Variable
Austria
Belgium
Estonia
Finland
France
Germany
Greece
Ireland
Italy
Luxembourg
Netherlands
Portugal
Slovakia
Slovenia
Spain
Std.Dev./
Mean
(­Percent)
Mean
Std.
Obs (­Percent) Dev.
12
12
11
12
12
12
11
11
12
12
12
12
11
12
12
8.86
7.86
4.38
0.309
9.17
10.22
−10.22
5.11
4.05
14.05
7.41
0.01
1.72
4.27
3.15
2.08
2.69
4.11
1.58
0.9
0.496
6.21
2.79
2.08
1.66
2.58
1.98
0.982
2.56
1.88
23.476298
34.2239186
93.8356164
511.326861
9.81461287
4.85322896
−60.763209
54.5988258
51.3580247
11.8149466
34.8178138
19800
57.0930233
59.9531616
59.6825397
Min
Max
(­Percent) (­Percent)
6.74
4.84
−6.91
−1.35
8.13
9.29
−17
−0.97
1.47
11.25
1.75
−2.42
0.21
0.02
0.67
12.41
12.17
7.88
3.29
10.59
10.95
−1.13
9.6
7.81
16.1
10.25
4.07
3.03
8.85
6.83
Figure 1. Belgium: House­hold Savings Rate and House­hold
Debt-­to-­Disposable Income Ratio, 2007–2018
Sources: OECD; author’s calculations.
Sources: OECD; author’s calculations.
of ­house­hold debt to disposable income. Recall, as Chad
shows, that in the United States, as h­ ouse­hold debt-­to-­GDP
ratio increased, the personal savings rate fell, and since 2009,
as ­house­holds in the U.S. have “deleveraged,” the personal
savings rate has increased. For most of the Euro Area nations,
Chad’s casual observations about the relationship between
the savings rate and the debt-­to-­disposable income ratio are
not well borne out. However, Belgium, Greece, and Slovenia
appear to follow the pattern that Chad describes for the
United States. See Figures 1 to 3 for a cursory look at the
relationship between savings rates and the debt-to income
ratios for Belgium, Greece, and Slovenia and see Figure 4 for
the same relationship for the United States. For Belgium and
Greece (shown in Figures 1 and 2), as the debt-­to-­income
ratio has increased in recent years, the savings rate has fallen.
For Slovenia and the United States (shown in Figures 3 and
4), the savings rate has increased in recent years as the debt-­
to-­income ratio has fallen.
REVIEW QUESTIONS
1. The neoclassical consumption model is based on the
assumption that a representative consumer maximizes utility derived from lifetime consumption subject to a lifetime
(intertemporal) bud­
get 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 pro­
cess 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
Figure 2. Greece: House­hold Savings Rate and House­hold
Debt-­to-­Disposable Income Ratio, 2007–2018
Sources: OECD; author’s calculations.
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
158 | Chapter 16
relative to current consumption is given as: c­future/
c­today = β × (1 + R), where c­future/c­today = 1 + the growth rate
in consumption. As such, the Euler equation can be interpreted as the optimal growth pattern of consumption, given
R and β.
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.
Figure 3. Slovenia: House­hold Savings Rate and House­hold
Debt-­to-­Disposable Income Ratio, 2007–2018
Sources: OECD; author’s calculations.
Figure 4. United States: House­hold Savings Rate and House­
hold Debt-­to-­Disposable Income Ratio, 2007–2018
Sources: OECD; author’s calculations.
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 f­ uture 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%), and the other half next
year. But if you w
­ ere denied access to credit this year, you
would spend the ­whole bonus next year (an MPC of 100%).
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.
8. In recent de­cades as housing wealth and financial wealth
increased, the personal savings rate decreased. The decrease
in the savings rate means that h­ ouse­holds are spending more
relative to their incomes. In order to spend more relative to
income, indebtedness increased.
EXERCISES
1. This is a worked exercise. See the text for the solution.
consumer maximizes utility by smoothing consumption
over the lifetime. This pro­
cess of utility maximization
reduces the sensitivity of current consumption to anticipated
changes in income. The consequence is that consumption is
relatively stable and the Keynesian multiplier effects are
relatively small (close to zero).
5. The Euler equation is derived as a consequence of
the first-­order utility maximization condition where Δc­future/
Δc­today|IBC = MRSC­today, C­future = 1 + R. If U = log c­today + β × log
c­future, then ΔU = 0 = MUC­today × Δc­today + MUC­future × 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
2. (a) ­human wealth = $109,524; total wealth = $159,524
(b) c­today = $79,762; c­future = $83,750; S­today = $20,238
(c) ΔS­today = $10,000
(d) Δc­today = $4,761
(e) ΔX = − $434; Δctoday = − $217; ΔStoday = $217
­These effects are smaller in exercise 1 ­because the college professor’s f­ uture income is $10,000 as compared to the
student’s f­ uture 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.
Consumption | 159
3. (a) c­today = $70,000; c­future = $70,000; S­today = −$20,000
(b) ΔX = $10,000; Δctoday = $5,000; ΔStoday = − $5,000
(c) ΔX = $20,000; Δctoday = $10,000; ΔStoday = − $10,000
(d) If stock market and housing wealth increase, ­house­holds
increase consumption and reduce savings relative to disposable income.
4. (a) Using the Euler equation, c­future/c­today = β(1 + R);
where c­future/c­today = 1 + consumption growth rate, so the
consumption growth rate = 5%.
(b) −.25%
(c) R = 7.4%
⎛ 1 ⎞
⎛ β ⎞
× X; c future = ⎜
5. (a) ctoday = ⎜
⎟
⎟ X × (1 + R)
⎝ (1 + β ) ⎠
⎝ (1 + β ) ⎠
1
1
(b) If β = 1, then ctoday = ⎛⎜ ⎞⎟ X; and cfuture = ⎛⎜ ⎞⎟ X × (1 + R),
⎝ 2⎠
⎝ 2⎠
(c) If β < 1, C­today increases and c­future decreases; ­because
less utility is derived from f­ uture consumption, the rational
consumer substitutes current consumption for ­
future
consumption.
6. (a) Let the change in current taxes = −Tx­today. The change
in ­future taxes = Tx­today(1 + R). The before-­tax intertemporal bud­
get constraint (ignoring nonhuman wealth) is
ytoday + yfuture
. The aftertax intertemporal bud­get conX=
(1 + R)
– Txtoday + ( yfuture – Tx future )
y
straint is X = today
. The before-­
(1 + R)
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.
⎛ 1⎞
7. (a) For β = 1, the consumption function is c = ⎜ ⎟ × X,
⎝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 w
­ ill 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
1
c = ⎛⎜ ⎞⎟ X + MPC × Yunanticipated , and assuming that the MPC
⎝T⎠
of the poor is greater than the MPC of the rich, the consumption of the poor increases relative to the rich.
8. (a) Recent data provided by FRED are as follows.
Year
Personal
Savings
Rate
House­hold
Debt/GDP
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
3.74
4.98
6.11
6.55
7.16
8.83
6.41
7.35
7.61
6.76
6.95
7.69
96.22
97.35
96.90
92.00
87.88
83.81
81.34
79.16
77.48
77.06
76.39
74.92
(b) T
­ hese results are more or less anticipated. As wealth
decreases (increases), current consumption declines (increases)
relative to current income. The savings rate increases and the
debt-­to-­GDP ratio falls.
CHAPTER 17
Investment
CHAPTER OVERVIEW
This chapter teases out the neoclassical theory of investment
in an intuitive but rigorous way. Chad uses an arbitrage
equation to intuitively develop the user cost theory of invest­
ment. The result is a parsimonious but power­ful model for
explaining capital investment decisions. The arbitrage
approach is applied to understanding equity prices (the price
of corporate stocks), asset price ­bubbles, and information­
ally efficient markets. The arbitrage approach 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 invest­
ment as the acquisition of capital goods. Capital goods are
goods used in making other goods. Investment in capital
goods, as defined in the national income and product
accounts, includes nonresidential fixed investment like
equipment, structures, and intellectual property products,
like software; residential fixed investment; purchases of
homes; and inventory investment, the change in the stock of
inventories. The term financial investment refers to pur­
chases 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 between
current income and ­future consumption.
Investment in capital goods receives par­tic­u­lar attention
for two reasons: (1) investment share of output is highly vol­
atile compared to other components of output; (2) invest­
160
ment, as illustrated in the Solow and Romer models, explains
changes in the capital stock (objects and ideas), and there­
fore is a major cause of economic growth.
This chapter focuses on the microfoundations of invest­
ment decisions. The user cost theory of investment is devel­
oped 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 b­ ubbles. The theory of inventory investment is also
reviewed.
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, �, a
capital gains rate, ΔpK/pK, where pK is the price of capital,
and a corporate tax rate, τ.
REASONING WITH AN ARBITRAGE EQUATION
A ­simple example is used to illustrate the user cost theory
of investment. In this example, an investor is considering
an investment of a sum of money in a bank account or in
pizza ovens. Differences in the risk associated with dif­fer­
ent investments are assumed away to simplify the discus­
sion. Ultimately the goal of the investment is to maximize
the return on an investment portfolio that consists of finan­
cial 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
Investment | 165
ering the marginal tax rates, but the variations in user costs
across countries appear to be even smaller when the mar­
ginal tax rates are applied to mea­sur­ing user costs.
REVIEW QUESTIONS
1. Physical investment is the acquisition of capital goods.
Capital goods (equipment, structures and software) are
goods used in making other goods. Financial investment is
acquisition of financial assets (capital). Financial assets rep­
resent a store of wealth that connects pre­sent income flows
to ­future consumption.
2. The arbitrage equation states that profit seekers ­will maxi­
mize profits when the returns are equalized across assets. In
the text, a two-­asset model was used. If the return on a sav­
ings account is greater than a return on an investment in phys­
ical capital, resources w
­ ill be reallocated away from physical
capital into the savings account. The reduction in the invest­
ment 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 �,
and (inversely) capital gains. If the user cost is less than MPK,
the firm can increase profits by hiring additional units of capi­
tal (undertaking investment in excess of depreciation).
5. Tobin’s q is a mea­sure of the market value of the com­
pany’s stock relative to the value of capital. When the mar­
ket 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 invest­
ment portfolio, the return on the savings account should
equal the return on the stock investment. The return on the
stock investment is the dividend and the capital gains gener­
ated 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). B
­ubbles 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 a­ ctual 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 ran­
dom, 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 depos­
ited in a savings account) to the return on owning a ­house;
namely, R * down payment = Rent − �*Phouse + ΔPhouse −
R(1 − τ)(Phouse − down payment). By solving for Rent in the
arbitrage equation, by multiplying and dividing that solution
by Phouse, and by defining � = down payment/Phouse, and
solving for Phouse, yields Phouse = Rent/(Rτ� + R(1 − τ)
+ � − ΔPhouse/Phouse)). Leverage is 1 minus �. The greater the
leverage, the smaller is � and the greater is the housing price.
EXERCISES
1. This is a worked exercise. Please see the text for the
solution.
2. (a) uc = .1467
(b) Δuc = .0267
(c) With τ = 0, Δuc = ΔR = .02. Given the tax rate of 25%, 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 inter­
est rate ­because of the tax wedge between the 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.
I
(d )
,
(b) If uc = .10, τ = 0, I/Y = .30, gk = 0, = .30 =
Y
(3 × .10)
d = .09.
If τ = .20, I/Y = .09/(3 × .125) = .24. If τ = .30, I/Y =
.09/(3 × .143) = .21.
166 | Chapter 17
I (gK + d )
. As illus­
=
Y (3 × uc)
trated in ­Table 17.1, variations in corporate tax rates result in
relatively smaller variations in user costs; therefore, varia­
tions 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 + d )/3[R + −(Δpk /
pk)]} Δ τ. If Δτ = .10 and Δ(I/Y) = −1/3 × Δτ = −.033.
(c) The investment rate is given as
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 ) − d (1 − ITC).
(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.
(b) uc = (R − d )
5. (a) 10% = (1/(1-­τ)) * .0792 = (1/.79)*.0792
(b) From 17.13, I/Y = (gk + �)/3*uc; therefore gI/Y = −guc.
The reduction in the corporate tax rate from 34% to 21%
reduced user cost from 12% to 10%; therefore,
guc = −2/12 = −16.67% = gI/Y. If the investment rate ­
were
20% prior to the tax cut, the investment rate ­after the tax cut
is 20%*(1.1667) = 23.33%
(c) Holding other ­things equal, following the tax cut, the
growth in steady state per capita income, gY/L = (1/2)
(gI/Y) = (1/2)(16.67%) = 8.33%
(d) If the corporate tax cuts ­
were permanent, and the
financed out of government bud­get deficits, the real rate of
interest and the user costs of investment ­
will prob­
ably
increase. The increase in the real rate of interest ­will dampen
the increase in the investment rate, and the growth in per
capita income.
6. (a)
private and government investment in physical capital rela­
tive to GDP).
(c) The ratio derived in this figure shows that investment in
physical capital relative to GDP has been declining on a
long-­r un trend since late 1970s, and that this ratio has sig­
nificantly declined since its last cyclical peak round 2006.
­These data provide evidence of the secular stagnation men­
tioned in Chapter 14.
7. (a) The increase in the TFP pa­ram­e­ter, A, 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.
I (gK + d )
(c) The investment rate is given as:
. In the
=
Y
3 × uc
long run, as in the Solow model, gK = 0. Given no change in
d and uc, the investment rate is unchanged.
8. This is a worked exercise. Please see the text for the
solution.
9. (a)
Growth rate of
condo prices
0.00%
2.00%
5.00%
10.00%
5.00%
5.00%
5.00%
Down payment
rate, x̄ (­percent)
20.00%
20.00%
20.00%
20.00%
100.00%
10.00%
5.00%
Price of condo
$7,462.69
$8,771.93
$11,904.76
$29,411.76
$10,000.00
$12,195.12
$12,345.68
(b) Condo prices are very sensitive to expected capital gain.
With no capital gain, the condo’s price is about $7,463. If
condo prices are expected to increase by 10% per year, hold­
ing the down payment constant, the condo’s price rises to
about $29,412.
(c) Condo prices are likewise sensitive to the down payment
rate. If condo prices grow at 5% and the down payment is
20%, the condo’s price is about $11,905, but if the down pay­
ment rises to 100%, the condo’s price is $10,000. The use of
leverage, the decrease in the down payment, increases the
return on the condo relative to the bank account and
increases the demand for the condo.
(b) What is being added and subtracted can be seen in the
header of the graph presented in (a). The result is ratio of
the sum of gross private domestic and government invest­
ment less the respective investments in intellectual prop­
erty products to GDP (a rough mea­sure of the ratio of
10. (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,
provided the profit is generated in perpetuity.
CHAPTER 18
The Government and the Macroeconomy
CHAPTER OVERVIEW
It’s best if you cover this chapter a­ fter you cover Chap­
ter 8 on inflation (due to the link between hyperinflation
and the government bud­get) and Chapter 11 on the IS
looking be­
hav­
ior and Ricardian equiva­
curve (forward-­
lence). Also, this chapter makes extensive use of net pre­sent
value, which was covered in Chapter 7 (valuing h­ uman capi­
tal) 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 w
­ ill 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 w
­ ill prob­ably be the
government bud­get constraint. It is in­ter­est­ing that Chad
sets up his bud­get constraint so that you can quite easily
answer the question posed by the title of Barro’s classic arti­
cle on Ricardian equivalence: “Are Government Bonds Net
Wealth?”1
18.2 U.S. Government Spending, Revenue, and
Debt and 18.3 Foreign Government Spending,
Revenue, and Debt
This covers the basic facts that e­ very voter or international
businessperson should know. You may want to point out
that of all the spending items on T
­ able 18.1 (the U.S. bud­
get), only two items—­National Defense and Other—­a re
typically counted as part of G. The rest are transfers of
income.
(Note: Medicare is a bit ambiguous on that count as 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 empha­
size that the experience of World War II is quite solid evi­
dence 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 govern­
ment deficit was over 25% of GDP and the debt/GDP
ratio was greater than 1, yet the post–­World War II period
from 1946 ­u ntil 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—­when federal government debt was more than 100% of
GDP.
The discussion of other developed countries demon­
strates 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 finan­
cial assets.
1. Robert J. Barro, “Are Government Bonds Net Wealth?” Journal of
Po­liti­cal Economy, vol. 82 (1974), pp. 1095–1117.
167
172 | Chapter 18
a decline in multilateralism. To address ­these issues, EFB
proposals include: (1) a medium-­term debt ceiling and one
operational target (a ceiling on the growth rate of primary
expenditures net of discretionary revenue) with an “escape
clause”; (2) more flexibility to better reconcile sustainability
and stabilization; and (3) less reliance on uniform rules and
more efforts to make bud­get targets more country specific.
(See EFB report, p. 81.)
For an in­ter­est­ing paper on the macroeconomic effects of
fiscal rules in EU that foreshadows the conclusions of EFB’s
report, see the work by Creel, Hubert, and Saraceno (2012),15
who simulated the effects of four bud­get rules on three EU
countries (France: low debt; Belgium: medium debt; and
Italy: high debt). The four rules considered are: (1) the
Maastricht Rule—­where the deficit is capped at 3% of GDP;
(2) the fiscal compact—­where the structural deficit is capped
at .5% of GDP; (3) the debt rule—­where debt is reduced by
5% of the spread between the debt-to -­GDP ratio and the
target debt-­to-­GDP ratio of 60%; and (4) the Golden Rule
where structural deficit is balanced net of a 1% deficit per
year to finance public investment. Not surprisingly, the
Golden Rule generates the smallest cumulative economic
loss. One of the findings of the EFB report is that public
investment should not be procyclical during an economic
downturn (EFB report, p. 4).
REVIEW QUESTIONS
1. This ­will depend on the year you answer it in. 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, pri­
mary 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 pay­
ments. 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 savings (Y − C − T), public savings (T − G), or
foreign savings (− NX). Crowding out savings, national and/
15. Jerome Creel, Paul Hubert and Francesco Saraceno (2012), “The
Eu­ro­pean Fiscal Compact: A Counterfactual Assessment,” Journal of
Economic Integration, vol. 27, no. 4 (December 2012), 537–63.
or foreign, are diverted from investment to finance the gov­
ernment borrowings.
5. The fiscal prob­lem of the twenty-­first c­ entury is summa­
rized in Figure 18.6. Entitlement programs, for example,
social security, Medicare, and Medicaid, are growing faster
than GDP, increasing federal government spending’s per­
centage of GDP relative to federal government revenue’s
percentage of GDP. T
­hese programs’ share of GDP is
expected to rise to about 14% in 2030 and 21.1% in 2075. Pos­
si­ble solutions for social security focus on revenue enhance­
ments, for example, raising social security contributions,
and reduced benefits by increasing the retirement age. Solu­
tions for Medicare/Medicaid are quite difficult, since a sig­
nificant increase in health care costs is driven by
technological change (new medicines, MRIs and CT scans,
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.
EXERCISES
1. This depends on current data. The following data are
derived from the 2019 ERP (­Table B-47) and my calculations.
Dollars
2019
Percentage
per
(Projected)
of GDP*
Person**
Total Expenditures
​Health (including
Medicare)
​Social Security
​National Defense
​Income Security
​Net Interest
​Other
4,529.2
1,252.2
21.16
5.85
13,601.20
3,760.36
1,047
684.6
533.2
393.5
618.7
4.89
3.20
2.49
1.84
2.89
3,144.14
2,055.86
1,601.20
1,181.68
1,857.96
Total Revenues
3,437.7
16.06
10,323.42
​Personal Income Tax
​Social Insurance and
Retirement
​Corporation Income
Tax
​Other
1,698.4
1,242.4
7.94
5.80
5,100.30
3,730.93
216.2
1.01
649.25
280.7
1.31
842.94
Bud­get Deficit
1,091.5
5.10
3,277.78
*Projected GDP is based on a 4% growth rate in nominal GDP.
**Based on a population of 330 million.
In comparison to T
­ able 18.1, spending’s share and the defi­
cit’s share of GDP are rising and revenue’s share of GDP
falling. From a macroeconomic perspective, the Federal Gov­
ernment Bud­get stance appears to be procyclical—­with the
bud­get deficit as a percentage of GDP projected to increase.
The Government and the Macroeconomy | 173
2. The business’s long-­run profits (primary surpluses) have to
be big enough to pay off the investors’ (the government’s)
debt. This applies to the primary bud­get balance, not the 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 exist­
ing 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.
5. This is a worked exercise. Please see the text for the
solution.
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% in the late
1970s, dropping to 17.4% at their lowest in the early 1980s.
So tax changes apparently ­weren’t the prob­lem. Spending
increased from about 20.5% to about 22.5% of GDP over the
same period—so clearly, spending hikes ­were the bigger
change. The two biggest increases in spending w
­ ere defense
and interest on the debt.
The opposite was true in the 2000s. Taxes fell from 19.5%
of GDP in the late 1990s to perhaps 17% between 2002 and
2006. Government spending also r­ ose, but not by as much: it
went from perhaps 19% to perhaps 20% 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.
­ ere sur­
(Aside: Economists of all po­liti­cal backgrounds w
prised by the plummeting tax revenues of the early George W.
Bush years: The Bush-­era 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.)
(b) To keep this s­imple, let’s assume that all government
spending is pure transfers. Other­wise, we get into the ques­
tion of ­whether cuts in G raise lifetime income.
­Under the PIH, rational consumers do not change their
consumption be­hav­ior at all: consumer spending depends on
lifetime Y. If so, then t­hese changes are a “tax shift” to the
­future.
1985: 2% primary deficit, 5.1% total deficit
1999: 3.8% primary surplus, 1.3% total surplus
2006: .01% primary deficit, 1.8% total deficit
2010: 7.65% primary deficit, 9% total deficit
2015: 1.2%% primary deficit, 2.43% total deficit
Source: Economic Report of the President, 2013, 2015.
4. (a) B2 = (1 + i)B1 + G1 − T1
B3 = (1 + i)B2 + G 2 − T2
B4 = (1 + i)B3 + G 3 − T3
(b) B4 = 0
(c) 0 = (1 + i)[(1 + i)B2 + G 2 − T2] + G 3 − T3
(d) 0 = (1 + i){(1 + i)[(1 + i)B1 + G1 − T1] + G 2 − T2} + 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.
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.
(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.
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, b­ ecause 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 gov­
ernment savings rise. Consumers save the tax cut,
­because they know they ­will have to pay $110.25 bil­
lion a year from now. The government side is account­
ing 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 deci­
perhaps the
sions if needed. Investors may be wrong—­
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 w
­ ill they spend it on con­
sumer 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 sav­
ings are unlikely to be enough to make this work.
174 | Chapter 18
Perhaps, just perhaps, the tax cuts w
­ ill 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 evi­
dence 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
par­tic­u­lar, 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 coun­
tries. 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, we have essentially prom­
ised 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, w
­ ill be to rethink, rational­
ize, 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 t­ hese 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 allo­
cate 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 prob­
lem 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 c­ auses ­people to consider some sort of public pol­
icy response, like the Health Care and Education Reconcili­
ation Act of 2010. In short, ­there are many answers to this
question. Our best minds w
­ ill be working on ­these issues for
years to come.
CHAPTER 19
International Trade
CHAPTER OVERVIEW
This chapter covers the real side of international trade;
exchange rates are in the next chapter. The intuition you
built up in previous chapters about intertemporal bud­get
covering the permanent income hypothesis
constraints—­
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). T
­ hose sections cover static two-­country production
and the costs of globalization, and they comprise over one-­
third of the chapter.
Alternatively, if you like to get vigorous classroom debate
­going, few ­things work as well as telling students that Greg
Mankiw was pretty much right when he said that outsourcing is just another way to reap the benefits of comparative
advantage. If you 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 d­ oesn’t require economics majors to take
an international trade course; in that case, this w
­ ill likely be
their only relatively sophisticated exposure to a crucial policy area.
19.1 Introduction and 19.2 Some Basic Facts
about Trade
The first two sections contain no surprises. By Eu­ro­pean
standards, the United States is not well 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 b­ ecause they like the engravings of Washington and Jefferson.
175
178 | Chapter 19
­will raise wages by much, much more than the f­ ree flow of
capital. Getting workers to the high-­TFP places is more useful than getting capital to the low-­TFP workers.
Lutz Hendricks’s 2002 American Economic Review
piece, “How Impor­tant Is H
­ uman 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%.
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.
CASE STUDY: EU TRADE AND INVESTMENT
For an excellent introduction and discussion of globalization
as it pertains especially to Eu­rope, see: “Globalization Patterns in EU Trade and Investment,” 2017 edition, Luxembourg, Publication Office of the Eu­
ro­
pean Union4. This
report introduces the definition of globalization: “the closer
economic integration of countries due to falling trade barriers and decreasing transportation costs” (p. 8). The report is
divided into six major parts: (1) global developments in
trade and investment (which describes world trade in goods
and ser­vices and direct investment patterns; (2) international
trade in goods for the EU; (3) international trade in ser­vices
for the EU; (4) foreign direct investment (describing intensity, flows, stocks and rates of return); (5) foreign affiliates
(examines the owner­ship of foreign controlled businesses in
the EU); and (6) enterprise statistics (industrial surveys of
insourcing and outsourcing).
Each part of the report begins with a summary of the
main findings. For example, the conclusions of part 1 include
that for 2016, the EU28 countries had the highest share of
global exports at 17.6% (including 23.9% of the global share
of ser­vice exports), and the EU28 accounted for 37% “of the
world’s investment outflows” (p. 18). In part 2, the United
States, China, and Switzerland ­were identified as the main
3. Lutz Hendrick, “How Impor­tant Is ­Human Capital for Development?
Evidence from Immigrant Earnings,” American Economic Review, vol. 92
(March 2002), pp. 198–219.
4. https://­ec​.­europa​.­eu​/­eurostat ​/­documents​/­3217494​/­8533590​/­KS​- ­06 ​-­17​
-­380 ​-­EN​-­N​.­pdf​/­8b3e000a​-­6d53​- ­4089​-­aea3​- ­4e33bdc0055c
export markets for the EU28, and following the financial
crisis, EU28 exports increased at a faster rate than EU28
imports. Germany had the highest trade surplus, and “70%
of imports” entered the EU at zero or reduced tariffs (p. 60).
In part 3, the main conclusions w
­ ere that the EU28 trade in
ser­vices had recently stagnated, the main importer of ser­
vices from the EU was the United States, much of the trade
in ser­vices ­were business ser­vices, including “management
consultancy, architectural, engineering and scientific ser­
vices, or real estate” (p. 134), the EU28 ran a surplus in 11 of
the 12 ser­vice categories, and “Ireland accounted for a large
trade surplus in ser­vices with offshore financial centres”
(p. 134).
In part 4, the report concluded that the flows of “inward
and outward” foreign direct investment (FDI) w
­ ere increasing, the EU28’s principal partner in both inward and outward FDI was the United States, and FDI was especially
impor­tant in the “small economies of Luxembourg, Cyprus
and Ireland” (p. 162). In part 5, the main findings w
­ ere that a
small percentage (1.2%) of nonfinancial corporations ­were
foreign controlled (p. 180), for most EU28 countries (excluding Slovenia and the United Kingdom) more than half of the
foreign enterprises w
­ ere from other EU28 countries, and
about 60% of “persons employed in EU foreign affiliates
abroad . . . ​­
were located in countries outside the EU”
(p. 180). Fi­nally, in part 6, the report found that outsourcing
was mostly done by industrial rather than ser­vice enterprises, that support functions (production of goods and ser­
vices not directly intended for market) rather than core
functions (related to the production of final goods and ser­
vices intended for market) are more likely to be outsourced
(France being an exception [p. 202]), that half the world’s
trade was in intermediate goods, and “that a growing share
of the EU’s value added may be attributed to imports of
intermediate goods” (p. 202).
REVIEW QUESTIONS
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 t­ hose 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 ­great numbers of ­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
International Trade | 179
dislocated workers, plus the fact that voters appear to intrinsically dislike receiving products from foreigners.
4. Yes, u­ nless 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 accumulating
this debt. T
­ here are good and bad reasons for accumulating
any debt, and in many real-­world, personal examples, borrowing money can be the best (or the same t­hing, the “least
bad”) solution. Since Americans seem to be prudent savers
on average, it’s reasonable to believe that the United States
is being prudent in accumulating this debt.
EXERCISES
1. Most fast-­growing countries run trade deficits to pay for
their investment, but China ­isn’t ­doing that. For some reason, the p­ eople and government of China have massively
high savings rates and choose to invest some of their savings
overseas. High savings rates are a feature of all East Asian
economies.
2. (a)
balance has grown on a long-­r un trend since the 1980, and
we can see that China’s external balance is more marked by
cyclical fluctuations than Germany’s external balance.
3. A
­ fter the devastation of World War II, much of Western
Eu­rope was poor, but it was likely to recover quickly. Thus,
Americans w
­ ere 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 ­r unning 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 shipmade investment goods overseas. “I” fell, but
ping U.S.-­
“EX” r­ ose. That gave us a big trade surplus.
­There are many stories one can tell of the postwar recovery using t­hese two identities, so clearly ­there’s more than
one way to answer this question correctly.
4. This is a worked exercise. Please see the text for the
solution.
(b) China has experienced more or less sustained growth in
its external balance since the 1980s. Germany’s external
5. The key assumption: p­ eople spend half their income on
apples and half on computers.
180 | Chapter 19
(a) Autarky
(b) Trade
Wage, w
Price of computer, p
Consumption of apples
(per person)
Consumption of computers
(per person)
Fraction producing apples
Fraction producing
computers
Total production of apples
Total production of
computers
North
South
160 apples
8 apples
80 apples
100 apples
50 apples
50 apples
10 computers
1 computer
50%
50%
50%
50%
8,000 apples
20,000 apples
1,000 computers 400 computers
Only the left column changes. The key ­here is figuring out the
new price of computers. Price of computer = slope of the production possibilities frontier = 160 apples/20 computers =
8 apples per computer.
(b) Trade
Fraction producing
apples
Fraction producing
computers
Total production of
apples
Total production of
computers
Wage, w
Price of
computers, p
Consumption of
apples
(per person)
Consumption
of computers
(per person)
North
South
0%
100%
100%
0%
0 apples
40,000 apples
2,000 computers
0 computers
400 apples
(40K/100 ­people)
20 apples
(that’s 40K/2K)
200 apples
100 apples
(40K/400 ­people)
20 apples (that’s
40K/2K)
50 apples
10 computers
2.5 computers
(c) Both countries get more computers compared to the low-­
computer-­productivity world seen in ­Table 19.4. Both countries benefit from the improvement in technology.
6. (a) Autarky
Wage, w
Price of computers, p
Consumption of apples
(per person)
Consumption of computers (per person)
Fraction producing apples
Fraction producing
computers
Total production of apples
Total production of
computers
North
South
160 apples
10 apples
80 apples
160 apples
80 apples
80 apples
8 computers
1 computer
50%
50%
50%
50%
8,000 apples
800 computers
32,000 apples
400 computers
Fraction producing
apples
Fraction producing
computers
Total production of
apples
Total production of
computers
Wage, w
Price of
computers, p
Consumption of
apples (per
person)
Consumption of
computers (per
person)
North
South
0%
100%
100%
0%
0 apples
64,000 apples
1,600 computers
0 computers
640 apples
40 (that’s 64K/
1.6K)
320 apples
160 apples
40 (that’s 64K/
1.6K)
80 apples
8 computers
2 computers
(c) Now, the rise in apple productivity means that workers in
North and South both get more apples. Prob­ably the most
surprising t­ hing 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 e­ lse. E
­ very time a quarterback gets better at throwing
long passes relative to short passes, that’s the same as saying
he’s getting relatively worse at throwing short passes—­
compared to long ones.
This is sometimes known as the Baumol effect, and it
helps explain, for example, why medical innovation can
make doctor visits more expensive. When doctors get relatively more productive at inventing new drugs, it means
­they’re getting relatively less productive at meeting with
patients. The opportunity cost of making computers is
very high in our model economy, as is the opportunity cost
of having a doctor meeting patients rather than sitting in a
lab testing new drugs. More broadly, the Baumol effect
explains why many ser­vices have become more expensive
in recent de­cades in the rich countries. It’s ­because the
other major sector, manufacturing, has become so much
more productive. Ser­vices in the U.S. economy are like
computers in this economy: they only became relatively
more expensive.
7. This Samuelson article is discussed in a case study for this
chapter, and is illustrated with principles-­level production
possibility frontiers.
(a) No, North loses its comparative advantage. T
­ here ­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 ­were back in the world of autarky.
International Trade | 181
(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 f­ ree trade. But the overall case for f­ ree 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 10 trading partners in recent years have been 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 every­
thing. Diversity in productivity seems to stay with us, even
if we all eat at McDonald’s.
L sxs > L n x n;
L sz s < L nz n .
8. (a) Autarky
Wage, w
Price of computers, p
Consumption of apples (per person)
Consumption of computers (per person)
Fraction producing apples
Fraction producing computers
Total production of apples
Total production of computers
(c) This has to be a story about opportunity cost—­because
that’s what most impor­
tant 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 computers.
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. H
­ ere’s the mathematical way to ask t­ hose
two questions:
North
South
xn
xn /zn
xn /2
zn /2
50%
50%
L nxn /2
L nzn /2
xs
xs /zs
xs /2
zs /2
50%
50%
L sxs /2
L sxs /2
(b) Trade
To keep it s­ imple, w
­ e’ll assume that the North is relatively
more productive at making computers. Chad discusses the
other possibilities in 7(c).
North
South
Fraction producing apples
0%
100%
Fraction producing computers
100%
0%
Total production of apples
0
L s xs
Total production of computers
L nz n
0
Wage, w
L sxs /L n
xs
Price of computers, p
L sxs /(L nzn) L sxs /(L nzn)
Consumption of apples (per person)
L sxs /(2L n)
xs /2
Consumption of computers (per person)
zn /2
L nzn /(2L s)
A few moments looking at the in­equality in 8(c) should
convince you that t­ hose two formulas are already embedded
within 8(c).
9. The question asks us to compare ­
Table 19.4 against
­Table 19.5. W
­ e’re considering a s­ imple 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 f­ ree trade—­they get
the same 80 apples/8 computers consumption bundle they
had u­ nder autarky.
One way to fix this would be to charge a tax of 30 apples
per South immigrant. Thus, ­every four immigrants would
pay 120 apples, which would go to pay the North worker for
his 120 lost apples. This works b­ ecause t­ here are four times
as many South workers as North workers. South workers
­will pay this ­because they get to consume the same 50
apples as they had ­under ­free trade (­Table 19.4), but also get
6 more computers.
10. This is an essay question; student’s choice.
CHAPTER 20
Exchange Rates and International Finance
CHAPTER OVERVIEW
Exchange rates in the long and short run, applying IS-­MP
and AS/AD to a small open economy, the exchange rate trilemma, and the euro crisis: that’s the chapter.
Sections 20.1 through 20.4, on the basics of exchange rates
­under flexible and sticky prices, are the only prerequisites for
the rest of the chapter: Chad has written it so that you can
pick and choose what you like ­after that. Further, aside from
the IS-­MP and AS/AD section (20.5), ­there are no formal
models in ­these optional sections. The ­earlier model building
underlies every­thing, so you can build some structure on the
foundations ­you’ve laid during the semester.
20.1 Introduction and 20.2 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 the United Kingdom, and so on).
If you emphasize that the law of one price only applies to
tradables—­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
­ ill have covered the
the classical dichotomy—­then you w
main macroeconomic idea.
Actually, the oil example is quite useful: students can
stand to be reminded that global commodities are a clear
example in which the law of one price holds. So if students
182
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 y­ ou’ve got a complete
open-­e conomy 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 d­ on’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 Rates and International Finance | 185
CASE STUDY: REAL EFFECTIVE
EXCHANGE RATES AND MACROECONMIC
IMBALANCE PROCEDURE
Following the 2008–2009 financial crisis, the Eu­
ro­
pean
Commission created the Macroeconomic Imbalance Procedure (MIP)4.
The MIP identifies, assesses, and addresses potential
imbalances in Eu­
ro­
pean Union Countries “to support
macro-­financial stability” (MIP, 2016, p. 7).5 In identifying
macroeconomic imbalances, the EU in part assesses trade
per­for­mance and competitiveness of member states. Three
main indicators are used to assess trade per­for­mance and
competitiveness: 1) export market share; 2) real effective
exchange rates, and unit ­labor costs6. .
As Chad describes in the textbook, the real effective
exchange rate can be used to mea­sure the rate at which a
good in country i trades for a good in country j. For example,
country i’s real (effective) exchange rate can be mea­sured as
country i’s currency exchange rate, Ei, multiplied by the ratio
of price level in country i to the price level in country j, Pi/Pj;
such that the real (effective) exchange rate equals Ei*(Pi/Pj).
For countries in the Euro Area, Ei = 1, and the real exchange
rate is simply based on relative prices (Pi/Pj). In the MIP,
decreases in the real (effective) exchange rate reflect improvements in country i’s competitiveness. For example, as Chad
describes it, increases in productivity in country i reduce unit
­labor costs, and, given wage rates, reduce prices in country i,
increasing the competitiveness of country i relative to country j. A quick look at Eurostat’s databases shows that Eurostat derives a number of mea­sures of the real (effective)
exchange rate using dif­
fer­
ent price deflators, such as a
weighted price index or a weighted unit l­abor costs index of
vari­ous trading partners7. The real effective exchange rate
used in the MIP is weighted by inflation rates of 42 trading
partners (“the EU-28 plus 14 relevant world economies”).8 A
potential macroeconomic imbalance in the competitiveness
is defined as a “+/− 5%” change in the real exchange rate (see
fn. 2). Following the recession of 2013, most Euro Area
members are within the “+/−” threshold. In 2016, for example, Estonia, Latvia, and Lithuania ­were outside the “+5%”
threshold due to depreciation of the ruble (where Rus­sia is a
4. https://­ec​.­europa​.­eu​/­info​/­publications​/­economy​-­finance​/­macroeconomic​­imbalance​-­procedure​-­rationale​-­process​-­application​-­compendium ​_­en
5. See “The Macro Imbalance Procedure, Rational, Pro­cess, Application: A Compendium,” Institutional Paper 039, November 2016, Eu­ro­pean
Commission.
6. MIP, 2015, p. 104. For a nice description of how the real effective
exchange rates are used in the MIP, see: https://­www​.­europarl​.­europa​.­eu​
/­RegData​/­etudes​/­ATAG​/­2017​/­602099​/­I POL ​_­ATA(2017)602099​_­EN​.­pdf
7. https://­appsso​.­eurostat​.­ec​.­europa​.­eu​/­nui​/­show​.­do​?­dataset​= ­ert​_­eff​_ ­ic​
_­a&lang​= ­en
8. See (again) https://­www​.­europarl​.­europa​.­eu​/ ­RegData​/­etudes​/­ATAG​
/­2017​/­602099​/­IPOL ​_­ATA(2017)602099​_­EN​.­pdf.
Figure 1. Index of Real (Effective) Exchange Rates: EU28 and
Euro Area 19 (2010 = 100) deflator: unit l­abor costs in the total
economy -­37 trading partners -­industrial countries
Source: https://­appsso​.­eurostat​.­ec​.­europa​.­eu​/­nui​/­submitViewTable
Action​.­do.
main trading partner). In contrast, Ireland was outside the
“−5%” threshold due to depreciation of the euro vis a vis the
dollar and the pound (as the United States and the United
Kingdom are two of Ireland’s main trading partners).9
Figure 1 illustrates the EU28 and Euro Area 19 real effective exchange rates from 1999 to 2018, where the nominal
exchange rate is deflated by the respective unit ­labor costs.
As shown in Figure 1, the real (effective) exchange rate for
the EU28 peaked during the first recession (2008–2009) and
­rose again during the second recession (2011–2013) and has
fallen in recent years.
REVIEW QUESTIONS
1. The nominal exchange rate tells me how many units of
one currency can be exchanged for another foreign currency.
The real exchange rate tells me how much I could buy if I
­were to take one unit of one par­tic­u­lar country’s currency,
convert it to a foreign currency, and then try to actually buy
goods and ser­vices in that country. The real exchange rate
adjusts the nominal exchange rate to take into account that
some ­things (rent, restaurant meals, 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
9. See “The Macro Imbalance Procedure, Rational, Process, Application: A Compendium,” Institutional Paper 039, November 2016, European
Commission.
186 | Chapter 20
depreciate against the yen. Since then, inflation has been
quite low in the United States.
3. In princi­ple as well as in practice, for tradable goods like
oil the power of arbitrage is very strong. ­People try to buy
low and sell high everywhere in the global economy, and by
­doing so, entrepreneurs push prices up in “cheap” places
and push them down in expensive ones. For other goods,
like the Big Mac example in the textbook, some of the
inputs used in making the good, such as domestic real
estate and local ser­vice ­labor, are not easily tradable, and
therefore we expect the price of ­these goods, like the Big
Mac, to vary across markets.
4. When interest rates are high in a given country, global
investors want to save money in that country’s bank
accounts. To do so, they need that country’s currency—so
they bid up the price of that currency. That makes 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.
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.
Big Mac
price in
local Currency
United States
Norway
Euro Area
Japan
Mexico
China
Rus­sia
South Africa
India
5.58
50
4.05
390
49
20.9
110.17
31
178
7. The level of the nominal exchange rate by itself ­can’t
­matter ­because it’s just the relative nominal price of goods
in two countries (i.e., 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.
EXERCISES
1. For a Big Mac to cost the same $5.58 in the Euro Area,
the euro must appreciate against the dollar by 19.87%. Given
the current exchange rate where .87 euros purchases $1, or
4.05 euros purchases $4.66, Big Macs are a better buy in the
Euro Area than in the United States. At the exchange rate
where .725 Euros purchase $1 (or 1 euro purchase 1.38),
4.05 Euros purchases $5.58. In all cases, the “law of one
price” exchange rate is calculated by dividing the local-­
domestic price of Big Macs by the U.S. price of Big Macs. If
Big Macs are locally cheap relative to the United States, as
in most of the following cases, then the local currency
should appreciate relative to the dollar. In most countries,
the currency needs to rise against the dollar. We can tell this
quickly by looking at the “Big Mac price in dollars” column
in ­Table 20.1. In e­ very country (excluding Norway), the Big
Mac costs less than the U.S. price.
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
Exchange
rate per
dollar
Big Mac price
in dollars
Exchange
rate to
equalize price
Percentage
change in
exchange rate
Adjustment
1
8.53
0.87
108.44
17.31
6.85
66.69
17.87
69.69
5.58
5.86
4.66
3.60
2.83
3.05
1.65
1.73
2.55
1
8.96
0.725
69.89
8.78
3.74
19.74
5.55
31.89
.
−4.81%
19.87%
55.15%
97.12%
82.89%
237.78%
221.66%
118.47%
.
depreciates
appreciates
appreciates
appreciates
appreciates
appreciates
appreciates
appreciates
*For example, the yen-­dollar exchange rate that equalize prices of Big Macs is 69.89 = 390/5.58, and the appreciation in the Japa­nese yen is mea­sured as:
[(1/69.89) − (1/108.44)]/(1/108.44) = 55.15%.
Exchange Rates and International Finance | 187
rates hurts short-­run output through two channels, not just
one.
3. (a)
growth in exchange rate = growth rate in rest-­of-­
world prices − growth rate in home country prices.
(b) The dollar should have depreciated by about 2.1% per
year against the yen.
(c) Actually, the dollar depreciated at a much higher rate—­
closer to 5% per year. In 1975, a dollar used to buy 300 yen,
and in 1995 it bought about 100 yen. The numbers do not
match up well to the prediction generated by equation 2.3.
(d) Given Figure 20.3, for the period of 1970 to 1995, the
real exchange rate for the yen has appreciated (the real
exchange rate for the dollar has depreciated). The appreciation of Japan’s real exchange rate for a sustained period
appears to violate the “law of one price,” but as Chad points
out in the “Case Study: Long-­Run Trends in Real Exchange
Rates,” the real exchange can grow ­because of the growth in
price level of non-­traded goods, driven by wage increases in
low productivity growth sectors. The increase in the relative
price of non-­trade goods increases the price level of domestically (traded and nontraded) produced goods and increase
the real exchange rate.
4. (a) I expect that most student w
­ ill look at the yuan/dollar
exchange rate, so ­here it is:
5. This is a worked exercise. Please see the text for solution.
6. This question is the opposite of the one posed by Figure 20.4. When the Euro Area cuts interest rates, this makes
the United States a more attractive place for global investors to save their money. This raises demand for U.S. dollars, raising the price of dollars. The dollar’s new, higher
value helps Americans who want to import goods from
overseas (IM rises) and hurts Americans who want to export
their now-­more-­expensive goods (EX falls). All told, this
clearly shifts 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 c­ an’t stimulate forever—­
and so the United States’ AD curve ­will get a boost, eventually completing the cycle.
7. This creates a “spending leakage,” where part of any economic boost for domestic rate cuts or foreign rate increases
convinces Americans to import more goods from abroad.
⎛ Yt ⎞ − 1 = Y! = ⎛ Ct + I t + Gt + NX t ⎞ − 1;
⎜⎝
⎟
t
⎝Y ⎠
Y Y Y
Y ⎠
Y!t = (ac + ai + aG + aNX − 1) − (bi + bNX )(R − r ) − nY!t .
The key is to notice that the Y (short-­run output) is on
both sides of the equation. That’s the only real change. Our
only goal now is to solve for Y . This yields:
⎡ 1 ⎤
Y!t = ⎢
⎥ [(ac + ai + aG + aNX − 1) − (bi − bNX )(R − r )].
⎣ (1 + n) ⎦
(b) What is in­ter­est­ing is in the above diagram is how the
dollar has appreciated against the yuan over time, and how
the dollar has remained “high” against the yuan for almost
25 years, despite the United States’ relatively large trade
deficit with China.
(c) The reason for the relatively high value of the dollar can
be attributed to China’s central bank holding the dollar
reserves, and Chinese purchases of U.S. real and financial
assets, especially U.S. Trea­sury Bonds. By managing a low
exchange rate for its country, China has kept the prices of its
goods relatively low in U.S. and world markets (as many
goods traded across borders are priced in dollars).
It’s a normal IS curve, with the addition of the spending
leakage term. Now a change in the interest rate w
­ ill have a
smaller impact on short-­r un output (as the multiplier is less
than one). That’s good news if you are a central banker trying to keep the economy stable.
8. When ­people want dollars in a financial crisis, they have
to offer their foreign currency in exchange. That w
­ ill bid up
the price of dollars and bid down the price of foreign currencies. The dollar ­
will appreciate. In AS/AD, this helps
importers but hurts exporters. The AD curve shifts left, and
so, ironically, the U.S. economy gets hurt in the short run by
­people’s desire to hold more dollars.
9. This is a worked exercise. Please see the text for the
solution.
188 | Chapter 20
10. The United States may be a big enough economy that it
can ignore the trilemma: other economies may just be too
small for their financial flows to create big shocks in the
United States.
Alternatively, it may be that the United States has run
good enough economic policy that the global financial traders ­haven’t felt the need to make a run on the dollar, since
the dollar is perceived as good as gold.
11. In three years, South K
­ orea was almost back. Mexico
was still not back; its peak was around 1981. Indonesia was
back within a year.
12. This is an essay question. Answers may vary.
CHAPTER 21
Parting Thoughts
21.1 What We’ve Learned
Chad summarizes what students have learned this semester.
This only presumes that ­
you’ve covered Chapters 1–6
(Growth) and Chapters 8–14 (Inflation and Fluctuations). At
one point, he touches on the looming entitlement crisis of
Chapter 18, but that ­doesn’t interrupt his overall story: macroeconomics is still about growth, business cycles, and optimal government policy. If ­you’ve covered the bulk of ­those
chapters, you should assign this one.
He also emphasizes that ­there are still big, impor­tant
questions to be answered—­and his opening quote by prominent physicist Brian Greene conveys the sense of won­der
that macroeconomists often feel ­toward the aggregate economy. This chapter gives you an excellent opportunity to
spend a day—­perhaps even half a lecture—­letting students
know what you think the key areas of ­future research are,
what the major puzzles are, and what you think are the most
impor­tant ideas for them to take away from the course.
Then, and only then, can 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 t­ hese
questions. In this concluding chapter Chad gives you some
things to think about. Some of t­hese issues flow
more ­
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 w
­ ill need a deeper understanding of some
of the issues.
In Chapters 4–6, Chad described 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 w
­ ill 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 ­w ill become increasingly relevant for the United States as the United States has
entered the 10th year in the “war against terror.” How
does prolonged war affect the institutions of economic
growth and prosperity?
In Chapters 10–14, Chad examined short-­r un 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
unemployment.
Fi­nally, as we are still learning lessons from the G
­ reat
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
189
190 | Chapter 21
able to cope with what the f­ uture brings, and better prepared
to shape the ­future.
SAMPLE LECTURE: NOBEL PRIZE WINNERS
IN MACROECONOMICS
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.
2018: William Nordhaus and Paul Romer: awarded the
prize for integrating innovation and climate into the
analy­
sis of long-­
r un economic growth. Romer’s
endogenous growth theory is introduced in Chapter 6—­the novelty and clarity of Chad’s pre­sen­ta­tion
is one of the distinguishing ele­ments of this textbook.
Nordhaus (with Paul Samuelson) is quoted at the
beginning of Chapter 2 (“national income accounts
are one of the ­great inventions of 21st ­century”), and
his work on economic well-­being is cited l­ater in
Chapter 2.
2013: Robert Shiller: awarded the prize for empirical
analy­sis of asset pricing. Shiller is cited in Chapter 14 for using price-­to-­earnings ratios to predict
­bubbles in stock markets. His analy­sis has also been
applied to other markets, including the housing
market.
2011: Thomas Sargent: recognized for the art of distinguishing cause and effect in the macroeconomy. Sargent is cited in Chapter 8 for the fiscal ­causes of high
inflation.
2008: Paul Krugman: awarded for analy­sis of trade patterns and firm location, explaining what goods are
produced where. Krugman is cited for the policy trilemma in open economies in Chapter 20.
2006: Edmund S. Phelps: awarded for the core of New
ral rate hypothesis;
Keynesian models: the natu­
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
ideas.
1999: Robert Mundell: applied our IS model to small open
economies.
1995: Robert Lucas: brought rational expectations into
business-­cycle research—­showed that sticky inflation must be due to surprises in monetary policy.
1993: Douglass C. North: made economic institutions a
central focus of growth research.
1987: Robert Solow: developed the Solow growth model.
1985: Franco Modigliani: in­ven­ted the life-­cycle hypothesis
of consumer spending.
1984: Richard Stone: recognized for his role as a founder of
national income accounting.
1976: Milton Friedman: awarded the prize for his work on
the permanent income hypothesis, the natu­ral rate of
unemployment, and monetary policy rules.
1972: John Hicks and Kenneth Arrow: Hicks formulated
the IS-­LM model. Arrow’s general equilibrium theories underlay Kydland and Prescott’s real-­business-­
cycle theories.
1970: 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.1
1. More information is available about the Nobel Prize winners at http://
nobelprize.org/nobel_prizes/economics/laureates/.)</