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PRSRT STD
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ST. LOUIS MO
PERMIT NO. 444

FEDERAL RESERVE BANK OF ST. LOUIS

REVIEW

Federal Reserve Bank of St. Louis
P.O. Box 442
St. Louis, MO 63166-0442

FIRST QUARTER 2016
VOLUME 98 | NUMBER 1

Change Service Requested

Three Challenges to Central Bank Orthodoxy
James Bullard and Kevin L. Kliesen

REVIEW

A Regional Look at U.S. International Trade
Maximiliano Dvorkin and Hannah G. Shell

Relative Income Traps
Maria A. Arias and Yi Wen

Aging and Wealth Inequality in a Neoclassical Growth Model
Guillaume Vandenbroucke

First Quarter 2016 • Volume 98, Number 1

REVIEW
Volume 98 • Number 1
President and CEO
James Bullard

Director of Research
Christopher J. Waller

Chief of Staff
Cletus C. Coughlin

1
Three Challenges to Central Bank Orthodoxy
James Bullard and Kevin L. Kliesen

Deputy Directors of Research
B. Ravikumar
David C. Wheelock

Review Editor-in-Chief

17
A Regional Look at U.S. International Trade
Maximiliano Dvorkin and Hannah G. Shell

Stephen D. Williamson

Research Economists
David Andolfatto
Alejandro Badel
Subhayu Bandyopadhyay
Maria E. Canon
YiLi Chien
Riccardo DiCecio
William Dupor
Maximiliano A. Dvorkin
Carlos Garriga
George-Levi Gayle
Limor Golan
Kevin L. Kliesen
Fernando M. Martin
Michael W. McCracken
Alexander Monge-Naranjo
Christopher J. Neely
Michael T. Owyang
Paulina Restrepo-Echavarria
Nicolas Roys
Juan M. Sánchez
Ana Maria Santacreu
Guillaume Vandenbroucke
Yi Wen
David Wiczer
Christian M. Zimmermann

41
Relative Income Traps
Maria A. Arias and Yi Wen

61
Aging and Wealth Inequality in a Neoclassical Growth Model
Guillaume Vandenbroucke

Managing Editor
George E. Fortier

Editors
Judith A. Ahlers
Lydia H. Johnson

Graphic Designer
Donna M. Stiller

Federal Reserve Bank of St. Louis REVIEW

First Quarter 2016

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Review
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ISSN 0014-9187

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Federal Reserve Bank of St. Louis REVIEW

Three Challenges to Central Bank Orthodoxy

James Bullard and Kevin L. Kliesen

Since 2007-09, the Federal Reserve has pursued a very aggressive monetary policy strategy. This
strategy has been associated with healthy labor market conditions, moderate economic growth, and
inflation—netting out the effects of a major oil price shock—that is close to the Federal Open Market
Committee’s (FOMC’s) 2 percent target. Thus, with the economy returning to normal, it is natural
for the FOMC to begin the process of exiting its highly accommodative policy. The FOMC has laid
out several well-defined steps for this process. This strategy may be called central bank orthodoxy,
since it is a natural extension of the classical view. However, three challenges to this orthodoxy have
developed. Although each challenge is interesting and potentially helpful, the orthodox view provides
a better basis for devising near- and medium-term monetary policy decisions. (JEL E52, E58, E63, E65)
Federal Reserve Bank of St. Louis Review, First Quarter 2016, 98(1), pp. 1-16.

T

he current monetary policy debate in the United States is at a crossroads. Since
2007-09, the Federal Open Market Committee (FOMC) has pursued a very aggressive monetary policy strategy. This strategy has been associated with a significantly
improved labor market, moderate growth, and inflation relatively close to target, net of a large
oil price shock. A key question now is how to think about monetary policy going forward.
The FOMC has long suggested that the appropriate exit strategy from the highly accommodative monetary policy following the 2007-09 recession would be slow and gradual and
would proceed in several well-defined steps. In the first step, the FOMC tapered and then
ended its quantitative easing (QE) program during 2014. In the second step, the Committee
waited for further improvement in labor markets and signaled that the policy rate would soon
move off the zero lower bound, albeit in small increments that would leave substantial monetary policy accommodation in place. In the third step, still in the future, the FOMC would
begin to gradually shrink the Federal Reserve’s balance sheet, most likely through an end to
reinvestments.1 The fourth step, well in the future, would see the balance sheet closer to precrisis levels and the policy rate more consistent with the FOMC’s view of its longer-term level.2
James Bullard is president and CEO of the Federal Reserve Bank of St. Louis. Kevin L. Kliesen is a research officer and economist at the Federal
Reserve Bank of St. Louis. President Bullard presented a version of this paper at the meeting of the Shadow Open Market Committee October 2,
2015, and the annual meeting of the National Association of Business Economics (NABE) October 13, 2015. The paper was published in Business
Economics (October 2015, Vol. 50, Issue 4, pp. 191-99). Copyright © 2015, Macmillan Publishers Ltd. Reprinted with permission.
The views expressed in this article are those of the author(s) and do not necessarily reflect the views of the Federal Reserve System, the Board of
Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced, published, distributed, displayed, and transmitted in
their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses, and other derivative works may be made only
with prior written permission of the Federal Reserve Bank of St. Louis.

Federal Reserve Bank of St. Louis REVIEW

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Bullard and Kliesen

The liftoff of the policy rate from near zero might be viewed by some as a momentous
event, given that the FOMC has not changed this element of monetary policy since December
2008, over seven years ago. Indeed, the FOMC has not increased its intended federal funds
rate target since the target was raised from 5 to 5.25 percent on June 29, 2006. Still, a liftoff of
the policy rate would be a relatively minor part of the normalization story we have outlined.
It is, after all, just one portion of a long-running recovery process from the events of 2007-09.
Eventually, one would surely expect to see nominal interest rates at more normal levels to be
consistent with a precrisis equilibrium in which inflation is at target and labor markets are
functioning well.
On the eve of policy rate normalization, however, the general view outlined above was
challenged from several directions. In this paper, we will provide our characterization of some
of these challenges in what we hope is an easy-to-digest format.
We will describe four broad categories of thinking about current U.S. monetary policy.
None of these four broad themes is strictly identified with any one individual or organization;
instead, the themes represent threads of arguments one often hears in financial market commentary, academia, and policymaking circles. Of these four approaches, the first will be a
“classic” interpretation of current events based on traditional ideas of successful central banking practice. This is the central bank orthodoxy referenced in the title of this paper. The other
three approaches are mildly heretical. Each claims that an aspect of the orthodoxy is clearly
deficient in the current policy environment. Each has some appeal, but also important drawbacks. Each departs from the classic view by arguing that “this time is different.”
Our conclusion will be that each challenge to orthodoxy is interesting and potentially
helpful, but ultimately has one or more drawbacks that make the orthodox view our favored
basis for near- and medium-term monetary policy decisions.
We will begin by first describing our version of central bank orthodoxy. This part of the
paper will be familiar to those who have followed recent speeches of Bullard (2015) on the
state of monetary policy. We will then move on to the three challenges to this orthodoxy that
we wish to discuss. These challenges are (i) a weakening Phillips curve relationship that can
lead to arguments for a more intense focus on inflation relative to the orthodox view; (ii) very
low real interest rates that can undermine the part of the orthodox view that claims monetary
policy is very accommodative today; and (iii) citation of ongoing globalization as a possible
reason to heed foreign economic developments distinctly and separately when making domestic monetary policy decisions. We will explain all of these challenges to orthodoxy as we proceed through these arguments.

1 A SIMPLE DESCRIPTION OF CENTRAL BANK ORTHODOXY
What we are calling the “classic” or “traditional” way to view current U.S. monetary policy
emphasizes the cumulative success that has been achieved so far with respect to FOMC goals.
The FOMC has clear objectives associated with labor market performance and inflation.
Regarding inflation, the FOMC set an official target of 2 percent beginning in 2012. Concerning labor market performance, the FOMC, through its September 17, 2015, “Summary of
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Economic Projections” (SEP), has indicated that an unemployment rate of around 4.9 percent
is likely to be consistent with longer-run equilibrium, as indicated in Table 1.3
The value of the longer-run unemployment rate has drifted down recently—it was 5.6
percent within the last few years.4
Is the FOMC achieving these objectives? The classic view emphasizes that, indeed, these
FOMC objectives are close to being met. As shown in Figure 1, the unemployment rate as of
September 2015 was 5.1 percent and has been on a downward trend. Given the large amount
of uncertainty around the concept of a long-run or natural rate of unemployment, the current
5.1 percent value is statistically indistinguishable from the FOMC’s statement of the likely
long-run level.
In the past two expansions, unemployment fell well into the 4 percent range; and, barring
a major recessionary shock, unemployment is likely to fall to similar levels in the quarters and
years ahead. This is likely regardless of the date of liftoff because monetary policy will remain
exceptionally accommodative even after normalization begins. In short, the FOMC has already
hit its objective on this dimension, as shown in Figure 1. In addition, labor markets are likely
to continue to improve going forward, barring a major negative shock.
Many have argued that other dimensions of labor market performance should be considered in the current environment. We think this is fair, since labor markets were severely
impaired in 2007-09. Indicators such as job openings and initial unemployment insurance
claims look very good, while other indicators such as working part-time for economic reasons
and long-term unemployment seem not as good. One way to get a handle on this issue is to
consider a labor market conditions index. Such an index can be constructed by combining
many different indicators of labor market performance into a single index number and then
taking that index number as a better and more informed judgment of the state of the overall
labor market than the unemployment rate alone. The Board of Governors of the Federal
Reserve System has calculated such an index (Chung et al., 2014). As shown in Figure 2, the
current level of the index is well above its average level since 1976. Labor markets might be
viewed as even better than normal according to this metric.
What about the inflation side of the Federal Reserve’s dual mandate? Inflation is certainly
low today; in fact, it is near zero on a year-over-year basis due in part to the very large decline
in oil prices beginning in 2014. In addition, recent oil price volatility suggests stabilization of
oil and related commodities prices may still be some ways in the future. Although the drop in
oil prices is a net positive for the U.S. economy, the sharp downward movement does inhibit
year-over-year readings on headline inflation. The classic view has an answer for this—it suggests looking through large oil price shocks, either positive or negative. The reason is that
energy price shocks are usually limited in their duration. Thus, relatively large increases
(decreases) tend to be followed by relatively large decreases (increases). Accordingly, at this
particular juncture, it may be more useful to consider the Dallas Federal Reserve’s trimmed
mean personal consumption expenditures (PCE) inflation measure, as seen in Figure 3. As
of August 2015, this measure was running at about 1.7 percent year over year, about 30 basis
points below the FOMC’s target. This is low, but still reasonably close to target.
The classic view, as we are outlining it here, would then say that unemployment of 5.1
percent and underlying inflation of 1.7 percent constitute values that are exceptionally close
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Table 1
The FOMC’s Summary of Economic Projections
FOMC Economic Projections Released on September 17, 2015
Median responses

Range of responses

Variable

2014
(Actual)

2015

2016

2017

2018

Longer
run

2015

2016

2017

2018

Longer
run

Real GDP

2.5

2.1

2.3

2.2

2.0

2.0

1.9-2.5

2.1-2.8

1.9-2.6

1.6-2.4

1.8-2.7

Unemployment rate

5.7

5.0

4.8

4.8

4.8

4.9

4.9-5.2

4.5-5.0

4.5-5.0

4.6-5.3

4.7-5.8

Inflation

1.1

0.4

1.7

1.9

2.0

2.0

0.3-1.0

1.5-2.4

1.7-2.2

1.8-2.1

2.0

Core PCE

1.4

1.4

1.7

1.9

2.0

—

1.2-1.7

1.5-2.4

1.7-2.2

1.8-2.1

—

Memo
Projected appropriate policy path
for federal funds rate

—

0.4

1.4

2.6

3.4

3.5

–0.1-0.9

–0.1-2.9

1.0-3.9

2.9-3.9

3.0-4.0

Federal Reserve Bank of St. Louis REVIEW

NOTE: Projections of change in real gross domestic product (GDP) and projections for both measures of inflation are percent changes from the fourth quarter of the previous year
to the fourth quarter of the year indicated. Inflation is measured using the personal consumption expenditures all items and all items excluding food and energy prices (core PCE)
price indexes.
SOURCE: Federal Open Market Committee (FOMC; projections released on September 17, 2015), Bureau of Economic Analysis (BEA), and Bureau of Labor Statistics (BLS).

Bullard and Kliesen

Figure 1
Unemployment Rate
Percent
10

Actual
FOMC Sep-15 Summary of Economic Projections:
Median Longer-Run Value
FOMC Sep-15 Summary of Economic Projections:
Central Tendency Longer-Run Value

9

8

7

6

5

4
Jan-10 Jul-10 Jan-11 Jul-11 Jan-12 Jul-12 Jan-13 Jul-13 Jan-14 Jul-14 Jan-15 Jul-15
NOTE: Last observation: September 2015.
SOURCE: Bureau of Labor Statistics and Federal Reserve Board.

Figure 2
Labor Market Conditions Index
Index Average = 0
200
150
100
50
0
–50
–100
–150
–200
–250
–300
1976

1980

1984

1988

1992

1996

2000

2004

2008

2012

NOTE: Last observation: August 2015.
SOURCE: Federal Reserve Board and authors’ calculations.

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Bullard and Kliesen

Figure 3
Inflation Rate
Year-over-Year Percent Change
2.5

FRB Dallas: Trimmed Mean PCE
FOMC Longer-Run Target
Core PCE

2.0

1.5

1.0

0.5

0
Jan-10 Jul-10 Jan-11 Jul-11 Jan-12 Jul-12 Jan-13 Jul-13 Jan-14 Jul-14 Jan-15 Jul-15
NOTE: Last observation: August 2015.
SOURCE: Bureau of Economic Analysis and the Federal Reserve Bank of Dallas.

to the objectives of the FOMC. One easy method of calculating how close the FOMC is to its
dual objectives uses a quadratic function to approximate the FOMC’s objective function. In
effect, it measures deviations of unemployment and inflation from target:
(1)

(

Distance from goals  π t − π *


) (
2

)

1

2
+ ut − u*  2 ,


where pt is the actual inflation rate at time t; p* is the FOMC’s 2 percent inflation target; ut is
the actual unemployment rate at time t; and u* is the median longer-run value of the unemployment rate from the FOMC’s September SEP (4.9 percent).5 Importantly, this version of
the objective function puts equal weight on inflation and unemployment and is sometimes
used to evaluate various policy options. Figure 4 shows that today’s combination of labor
market performance and inflation performance is about as good as it has ever been in the
past 50 years or so.6
Although the metrics concerning FOMC objectives are close to normal, the policy settings
are not. The FOMC has used two tools in the past seven years to conduct monetary policy.
One tool has been to set the policy rate—the federal funds rate—to a near-zero value, where
it remains today (see Figure 5).
Recall from Table 1 that the FOMC’s SEP indicates that participants view the longer-run
level of the policy rate to be about 3.5 percent. Thus, the current policy rate is more than 325
basis points lower than the long-run level. The other tool has been QE. As a result of several
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Figure 4
Distance from FOMC Policy Goals
9
8
7
6
5
4
3
2
1
0
Jan-60 Jan-65 Jan-70 Jan-75 Jan-80 Jan-85 Jan-90 Jan-95 Jan-00 Jan-05 Jan-10 Jan-15
NOTE: Last observation: August 2015.
SOURCE: Bureau of Economic Analysis, Bureau of Labor Statistics, and authors’ calculations.

Figure 5
Federal Funds Rate
Percent
6

Effective
FOMC Sep-15 Summary of Economic Projections:
Median Longer-Run Value

5

4

3

2

1

0
Jan-06

Jul-07

Jan-09

Jul-10

Jan-12

Jul-13

Jan-15

NOTE: Last observation: Week of September 30, 2015.
SOURCE: Federal Reserve Board.

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Figure 6
Federal Reserve Balance Sheet
$ Trillions
5.0

Total Assets
Average 2006 Value

4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0
Jan-06

Jul-07

Jan-09

Jul-10

Jan-12

Jul-13

Jan-15

NOTE: Last observation: Week of October 7, 2015.
SOURCE: Federal Reserve Board.

rounds of QE, the Federal Reserve’s balance sheet has increased from a precrisis value of about
$800 billion to about $4.5 trillion today (see Figure 6).
These considerations—objectives met, but policy settings far from normal—suggest a
policy path that will return the economy to the well understood precrisis equilibrium. Based
on central bank orthodoxy, the most prudent course of action is to begin to normalize the
policy rate slowly and gradually, under the interpretation that the FOMC will still be providing considerable monetary policy accommodation to the economy to guard against potential
pitfalls and risks as the quarters and years ahead unfold. By adopting this prudent approach
to monetary policy strategy, the FOMC may be able to lengthen the expansion longer than it
may otherwise extend. However, failure to promptly begin the process of normalization runs
the risk of settling into an equilibrium of unknown duration and uncertain consequences.7
We have set up this simple classic view because we think that, on balance, this view suggests the best path forward for U.S. monetary policy. But there are certainly other views with
considerable merit, and we will now turn to a discussion of these alternatives. Each of the
alternatives departs from an important aspect of the classic view. Again, we would hesitate to
associate these alternatives with specific individuals or organizations, as most or all of us
(including us at times) appeal to parts of these arguments when discussing contemporary
monetary policy.

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2 STRICT INFLATION TARGETING
The classic view we have outlined places heavy emphasis on the attainment of FOMC
goals with respect to labor market outcomes. A possible challenge to the classic view is that
labor markets have been overemphasized and that it is the low inflation outcomes that are
more critical today. This brings us to a second way to think about current U.S. monetary policy strategy and the first of the mildly heretical views. We will provocatively label this view
“strict inflation targeting,” a term often applied to Taylor-type monetary policy rules that
place no weight on real variables such as output or unemployment gaps.
How could labor market outcomes be overemphasized? One version of this view is that
Phillips curve relationships on which much of modern central bank practice rely have either
broken down completely or are badly damaged, meaning that further expansion of the economy
and tighter labor markets in the quarters and years ahead are unlikely to lead to more inflation.8
This being the case, one may wish to pursue substantially more monetary policy accommodation than otherwise—one may, for instance, keep the policy rate near zero longer.
Another version of this story is that the normal Phillips curve relationship remains intact,
but the inflation rate itself contains all the information one needs to determine the extent of
slack in the economy. That is, one may be able to reverse engineer the degree of slack in the
economy by considering the inflation rate alone. One does not really need to know that much
about the Phillips curve and its mysteries. The Phillips curve is temporarily dormant—it may
or may not reassert itself in the future—and we can watch inflation for signs of life in the
inflation-unemployment nexus.
Either way, whether one thinks the Phillips curve has broken down or is merely dormant,
a student of the current U.S. economy taking this broad view may tend to cite inflation alone
as the key indicator on which monetary policy should rely, and, hence, we label this view
“strict inflation targeting.” We could think of an advocate of this view as employing a Taylortype rule in which the coefficient on the unemployment gap has been set to zero.
In short, in this alternative view, policy rates should be normalized only when inflation
threatens. It challenges the classic view by dispensing with or substantially discounting the
empirical evidence on labor market improvement as a reason to begin policy normalization.
Since we are not advocates of the Phillips curve as an organizing principle for monetary economics, the strict inflation-targeting approach has some appeal for us. Taken to its logical
extreme, one could thus greatly de-emphasize current data on economic growth and labor
market performance, focusing instead on inflation developments alone in considering monetary policy strategy.
Nevertheless, we do see an important drawback with this view. This type of argument
might work better if the policy rate were not near zero, but instead were only mildly below its
long-run level. But to use this alternative to the classic view to justify a very low policy rate
near zero implies a very large elasticity between the policy rate and the inflation gap (Bullard,
2014a). One would be saying, in effect, that because a smoothed measure of inflation—such
as the year-over-year Dallas Federal Reserve trimmed mean PCE—was somewhat below the
inflation target (let’s say 50 basis points below), the policy rate itself must be set 325 basis points
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Bullard and Kliesen

Figure 7
Taylor (1999) Rule and Strict Inflation-Targeting Rule Policy Rate Paths
Percent
30
25

Taylor (1999) Rule with Smoothing
Strict Inflation-Targeting Rule
Effective Fed Funds Rate

20
15
10
5
0
–5
–10
Jan-84 Jan-87 Jan-90 Jan-93 Jan-96 Jan-99 Jan-02 Jan-05 Jan-08 Jan-11 Jan-14
NOTE: Last observation: August 2015.
SOURCE: Federal Reserve Board, the Federal Reserve Bank of Dallas, Bureau of Labor Statistics, and authors’ calculations.

below its normal value.9 The flip side would be, in the context of strict inflation targeting, that
when a smoothed measure of inflation is 50 basis points above target, the appropriate policy
rate would need to be set to something like 325 basis points above its normal value, on the
order of a 7 percent policy rate. We can think of this strict inflation-targeting rule as engineered
to justify today’s near-zero policy rate based on today’s inflation gap alone. This rule would
produce a coefficient of 10 on the inflation gap.
Figure 7 shows what such a policy rule would have recommended since 1984.10
Such a large coefficient would have implied very high policy rates at some points in the
past, including the 2000s. Given normal stochastic variation in inflation, few would have advocated this kind of policy sensitivity since it would have risked destabilizing the economy.
However, that is the implication of strict inflation targeting in the current environment: a
rapid adjustment of the policy rate in response to relatively benign inflation developments.
In short, strict inflation targeting may provide a reason to set the policy rate below its longrun level, but not all the way to zero. For this reason, we think it may be unwise to follow this
particular alternative to the classic view.

3 LOW REAL INTEREST RATES
The classic view as we have formulated it does not say anything about real interest rates.
It implicitly assumes that policy can be conducted with a standard Taylor-type policy rule in
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which the intercept term represents a constant long-run or normal value for the policy rate.
This is indeed the way Taylor-type rules were initially proposed and fit to macroeconomic
data. Still, we have to be cognizant of the evidence, and current real interest rates on government debt and related instruments are exceptionally low.11 Another alternative, and mildly
heretical, way to think about current U.S. monetary policy is to appeal to time-varying real
interest rates and to argue that the intercept term in the Taylor-type rule is exceptionally low
in the current era.
To see this, consider a generic Taylor-type monetary policy rule without too many bells
and whistles. This is shown in Equation (2):
(2)

(

)

It = R*t + π * + 1.5 π t − π * + Yt ,

where It is the long-run or steady-state level, which—according to the Taylor-type rule—
simply says that the policy rate should be equal to its long-run or steady-state level; Rt* is the
short-term real rate (which varies over time); pt is the year-over-year inflation rate; p* is the
Federal Reserve’s longer-run goal inflation rate (2 percent); Yt is the output gap and is defined
as 2.3 (u* − ut ); ut is the current unemployment rate; and u* is the long-run unemployment
rate. The rule is thus stated in linear terms, with inflation gaps and output or unemployment
gaps as key arguments. Let us suppose for purposes of discussion that these gaps are zero—
inflation is at target and unemployment is at its long-run level—so these terms go away completely. Then it is simply the sum of the short-term real rate (Rt* ) and the inflation target (p* ).
That is, the Taylor rule collapses to a Fisher relation, stating that the current value of the nominal policy rate is equal to the real rate plus (expected) inflation, which is equal to the inflation
target at the steady state. In the orthodox view, R* is a constant and equal to 2 percent; so the
recommended nominal policy rate is 4 percent.
The real interest rate argument is that Rt* is actually a very low value in the current macroeconomic environment. Let us suppose that the relevant short-term real interest rate is –2
percent. Then, given an inflation target of 2 percent and gaps which are zero, the recommended
policy rate from a Taylor-type rule in this class would be zero. This provides an argument
rationalizing today’s near-zero policy rate. In other words, inflation and unemployment are
near target, implying that the policy rate should also be near Rt*, but R* is itself zero; so, everything is exactly rationalized.
What should we make of this alternative view? First, this argument as stated says that
monetary policy is not accommodative right now. This is contrary to the orthodox view, which
was recently expressed by Fed Chair Janet Yellen.12 Most observers of monetary policy seem
to agree with Chair Yellen (via the orthodox view given earlier) that monetary policy is highly
accommodative and that it will continue to be accommodative going forward. This provides
one reason why the low-real-rates view is somewhat heretical. In other contexts, many might
say that it is the central bank actions themselves that are driving real interest rates to very low
levels.
Second, there are many competing methods for computing the real interest rate. Recall
that the orthodox view is that R* is constant. But suppose instead that one believes that R* is
time-varying (Rt* ). In the latter case, economic theory offers several methods, but we will conFederal Reserve Bank of St. Louis REVIEW

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Figure 8
Different Estimates of the Natural Real Interest Rate
Percent
4

3

Fixed (2 Percent)
Per Capita Consumption Growth
Productivity Growth + Population Growth
Laubach-Williams One-Sided Estimate

2

1

0

–1
Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 Jan-15
NOTE: Last observation: 2015:Q2.
SOURCE: Bureau of Economic Analysis, Bureau of Labor Statistics, Census Bureau, and authors’ calculations.

sider three. One method would emphasize labor force growth and the pace of technological
improvement. The pace of technological improvement is measured by total factor productivity. A second method hypothesizes that R* is the growth rate of per capita consumption. A
third method, which many employ, is based on a statistical model. As shown in Figure 8, using
these and other methods from the literature suggests that one can reasonably reach a wide
variety of conclusions about the appropriate estimate of the real interest rate.13
The bottom line is that each of these three methods produces a value for R* greater than
–2 percent. Accordingly, given the implied level of accommodation and the measurement
uncertainty surrounding the estimation of the real interest rate, we think this alternative view
suggests an unwise modification to the classic orthodoxy.

4 GLOBALIZATION
For quite a while, emerging market economies have been growing, on average, faster
than developed economies. The classic view as we outlined it did not make reference to events
outside U.S. borders. This may be viewed as a shortcoming in an age of globalization. The
third challenge to the classic view is to suggest that, because of globalization, foreign economic
developments need to be taken into account—separately and distinctly—in U.S. monetary
policy deliberations.
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It may seem obvious that increasing reference to foreign economic events will be part of
U.S. monetary policy going forward. But it has not been as popular as one might think, at least
in portions of the international monetary policy coordination literature (Bullard and Singh,
2008; Bullard and Schaling, 2009; and Bullard, 2014b). In models, the ideas are clear. There are
many countries with independent monetary policies. Each country is its own New Keynesian
economy with its own shocks. Exchange rates are flexible. Monetary policymakers in each
country attempt to stabilize their own economies as well as they can by reacting appropriately
to the shocks in their own country through a Taylor-type monetary policy rule. A general
conclusion from our reading of the literature is that in this situation, there would be little to
gain from international monetary policy coordination. Roughly speaking, if policymakers in
each country pursue the best domestically oriented stabilization policy available to them, the
global equilibrium will be as good, or nearly as good, as the fully optimal outcome that could
be attained through an appropriate coordination of monetary policy.
What does this mean in practical terms? “Domestically oriented stabilization policy”
means policymaker reaction functions include only domestic variables, and these domestic
variables contain all the information needed to pursue optimal policy, regardless of what is
occurring in the rest of the world. Alternatively, one could imagine monetary policymakers
in each country incorporating, in addition to their own output gaps and inflation gaps, foreign
output gaps in their Taylor-type rules as they conduct monetary policy. The policymakers
would then be adjusting their own policy rates in reaction to domestic inflation developments,
domestic real developments, and—separately and distinctly—foreign real developments. The
baseline result from an important class of models is that this situation does not lead to a better
global equilibrium, and all countries would be just as well off focusing only on domestic inflation and domestic real developments. Why? The short answer is that it is the job of the foreign
central bank to use stabilization policy in reaction to shocks in its own economy. That, in
conjunction with the flexible exchange rate regime, makes it unnecessary for the domestic
policymaker to react to foreign shocks.
Of course, this is just one set of models. But as a baseline, we think this provides food
for thought concerning globalization and monetary policy. The models we refer to are “fully
globalized” as the economies involved are simply carbon copies of one another with different
shocks. Even within this environment of full globalization, the gains from international policy
coordination may be small.
There is another angle on the role of foreign developments in domestic monetary policy.
This is the literature on so-called global output gaps (Borio and Filardo, 2007, and Bullard,
2012). This literature argues that the output or resource gap that is most relevant for domestic
inflation may actually be a global gap, which is sort of an average of output gaps across countries. In other contexts, one of us (Bullard, 2012) has explored the idea that especially for
China and the United States, which are linked by a managed exchange rate regime, it may be
more appropriate to think of the resource gap for the two countries jointly. Although this is
interesting and we think deserving of further research attention, in truth, the measurement
problems are all the more severe in attempting to calculate a global output gap as opposed to
simpler domestic resource gaps.
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5 CONCLUSION
In this paper, we have outlined an interpretation of current events in U.S. monetary policy
that we called the orthodox view. This view stresses the currently stark difference between
FOMC objectives, which are arguably nearly attained, and FOMC policy tools, which remain
on emergency settings. A simple and prudent approach to current policy would be to begin
normalizing the policy settings in an effort to extend the length of the expansion and to avoid
taking unnecessary risks associated with exceptionally low rates and a large Federal Reserve
balance sheet. This would be done with the understanding that policy would remain extremely
accommodative for several years. Why? Because the Federal Reserve’s policy settings are far
from anything that could reasonably be called restrictive. Thus, even as normalization proceeds, this accommodation would help to mitigate remaining risks to the economy during
the transition.
These remarks have described what we see as three important challenges to this orthodox
view. All challenges have a certain clear appeal, but also important drawbacks. All challenges
contain an element of the argument that “this time is different.”
The first challenge concerned possible overemphasis on labor market improvement in
the orthodox view. One version would be that the empirical Phillips curve relationship is
broken and, therefore, the Federal Reserve can continue a very accommodative policy without
worry of pressing inflation concerns. We called this view “strict inflation targeting.” A key
issue with this challenge to orthodoxy is that it is difficult to use this argument to justify the
exceptionally low policy rate observed in the United States today. Actually trying strict inflation targeting in the current environment would imply an exceptionally sensitive policy reaction function that might destabilize rather than stabilize the economy.
The second challenge concerned the observed low real interest rates on government debt
and related instruments in the United States and globally vs. the orthodox view that real interest rates of this type move very little and only very slowly. Time-varying and low real rates
can be used, via a Taylor-type rule, to rationalize the current policy rate setting of zero. An
important question for this challenge to orthodoxy is whether the resulting characterization
of current policy as neutral instead of accommodative is consistent with FOMC statements
and financial market interpretations of current monetary policy. In addition, simple alternative measurements of an appropriate real interest rate suggest considerable uncertainty around
this concept.
The final challenge deals with global concerns vs. the orthodoxy that de-emphasizes
international considerations. While it may seem that, with increasing globalization, policy in
one country has to take increasing account of developments in other countries, some of the
literature on international monetary policy coordination in New Keynesian models suggests
otherwise. In particular, at least as a baseline concept, the global equilibrium will be close to
optimal if each country reacts only to domestic variables and the world is characterized by
flexible exchange rates. This provides some food for thought on what globalization does and
does not imply for monetary policy strategy.
In sum, while the challenges to orthodoxy presented here are certainly tangible and interesting, we do not think they provide sufficiently robust arguments to guide U.S. monetary
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policy over the near and medium term. The U.S. economy will likely enjoy better outcomes
if the monetary policy orthodoxy we have described is preserved as the guiding principle. In
other words, the orthodox approach can best manage the risks to the U.S. economy that arise
from the dangers of maintaining policy settings in an environment where conventional gaps
have narrowed to zero. n

NOTES
1

At present, the FOMC reinvests the principal payments from its portfolio of agency debt and agency mortgagebacked securities. The FOMC also replaces (rolls over) maturing Treasury securities with new Treasury securities at
auctions.

2

See Kliesen (2013) for a discussion of the Federal Reserve’s strategy for exiting unconventional policies and the
potential challenges.

3

This was the median longer-run value of the SEP (FOMC, 2015).

4

This was the mid-point of the central tendency of the January 2012 SEP (FOMC, 2012).

5

Inflation is measured as the 12-month percent change in the PCE chain-weighted price index that excludes food
and energy prices (core PCE).

6

See Bullard (2015). More details can be found in Bullard (2014a).

7

See Bullard (2010) for an extended discussion of this possibility.

8

See, for instance, Blanchard, Cerutti, and Summers (2015). They find that in their Phillips curve specifications
across many countries, the effect of the unemployment gap on inflation is small and often not statistically distinguishable from zero. See Owyang (2015) for a discussion of recent shifts in the U.S. Phillips curve.

9

Recall that 325 basis points is the difference between the current federal funds target rate and the FOMC’s projected longer-run value of the federal funds rate from the SEP.

10 The details for the calculation of the Taylor rule with smoothing and the strict inflation-targeting rule are provided

below. A version of the Taylor-type rule in Equation (2) often used in the empirical analysis of monetary policy
allows for a gradual adjustment of the short-term interest rate to the target value: It = r × It–1 + (1 – r ) × [R * + p* +
1.5 × (pt − p* ) + Yt ], where pt denotes the Federal Reserve Bank of Dallas’s year-over-year trimmed mean inflation
rate, Yt = 2.3 × (u* − ut ) is the output gap, and ut is the unemployment rate. The values of the parameters are as follows: u* = 4.9 percent, the median long-run unemployment rate from the September 2015 SEP; p* = 2 percent, the
inflation target; r = 0.85, the smoothing parameter; and R * + p* = 3.5 percent, the long-run federal funds rate target
from the September SEP. The equation for the inflation-targeting rule is It = R *+p*+ jp × (pt − p* ). With an inflation
gap, (pt − p* ), of −0.3 percent, a federal funds rate gap, It − (R * + p*), of −3.25 percent is rationalized by a value of jp
of roughly 10. This rule implies that the nominal value of the federal funds rate (It ) would need to be 6.5 percent
with a 0.3 percent inflation gap.
11 However, real returns on capital are not (Gomme, Ravikumar, and Rupert, 2011 and 2015).
12 Chair Yellen (2015) made this statement at her September 17, 2015, press conference: “The stance of monetary

policy will likely remain highly accommodative for quite some time after the initial increase in the federal funds
rate in order to support continued progress toward our objectives of maximum employment and 2 percent
inflation.”
13 See Dupor (2015) for a more in-depth discussion of these alternative methods.

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REFERENCES
Blanchard, O.; Cerutti, E. and Summers, L. “Inflation and Activity.” Unpublished manuscript presented at the ECB
Forum on Central Banking, Sintra, Portugal, May 2015.
Borio, C. and Filardo, A. “Globalisation and Inflation: New Cross-Country Evidence on the Global Determinants of
Domestic Inflation.” BIS Working Papers No. 227, Bank for International Settlements, May 2007.
Bullard, J. “Seven Faces of ‘The Peril.’” Federal Reserve Bank of St Louis Review, September/October 2010, 92(5),
pp. 339-52; https://research.stlouisfed.org/publications/review/10/09/Bullard.pdf.
Bullard, J. “Global Output Gaps: Wave of the Future?” Remarks delivered at Monetary Policy in a Global Setting:
China and the United States, Beijing, China, March 28, 2012;
https://www.stlouisfed.org/~/media/Files/PDFs/Bullard/remarks/BullardBeijing28Mar2012Final.pdf.
Bullard, J. “Fed Goals and the Policy Stance.” Remarks delivered at the Owensboro in 2065 Summit, Owensboro, KY,
July 17, 2014a; https://www.stlouisfed.org/~/media/Files/PDFs/Bullard/remarks/BullardOwensboroKYChamber
ofCommerce17July2014Final.pdf.
Bullard, J. “Two Views of International Monetary Policy Coordination.” Remarks delivered at the 27th Asia/Pacific
Business Outlook Conference, USC Marshall School of Business—CIBER, Los Angeles, CA, April 7, 2014b;
https://www.stlouisfed.org/~/media/Files/PDFs/Bullard/remarks/Bullard-APBO-USC-Marshall-April-7-2014-Final.pdf.
Bullard, J. “A Long, Long Way to Go.” Remarks delivered at the Community Bankers Association of Illinois Annual
Meeting, Nashville, TN, September 19, 2015;
https://www.stlouisfed.org/~/media/Files/PDFs/Bullard/remarks/Bullard-CBA-of-IL-Nashville-Sep-19-2015.pdf.
Bullard, J. and Schaling, E. “Monetary Policy, Determinacy, and Learnability in a Two-Block World Economy.”
Journal of Money, Credit and Banking, December 2009, 41(8), pp. 1585-612.
Bullard, J. and Singh, A. “Worldwide Macroeconomic Stability and Monetary Policy Rules.” Journal of Monetary
Economics, October 2008, 55(Supplement), pp. S34-S47.
Chung, H.; Fallick, B.; Nekarda, C. and Ratner, D. “Assessing the Change in Labor Market Conditions.” Board of
Governors of the Federal Reserve System FEDS Notes, May 22, 2014; http://www.federalreserve.gov/econresdata/notes/feds-notes/2014/assessing-the-change-in-labor-market-conditions-20140522.html.
Dupor, W. “Liftoff and the Natural Rate of Interest.” Federal Reserve Bank of St. Louis On the Economy (blog), June 5,
2015.
Federal Open Market Committee. “Summary of Economic Projections of Federal Reserve Board Members and
Federal Reserve Bank Presidents, January 2012.” Board of Governors of the Federal Reserve System, January 2012.
Federal Open Market Committee. “Summary of Economic Projections of Federal Reserve Board Members and Federal
Reserve Bank Presidents, September 2015.” Board of Governors of the Federal Reserve System, September 2015.
Gomme, P.; Ravikumar, B. and Rupert, P. “The Return to Capital and the Business Cycle.” Review of Economic
Dynamics, April 2011, 14(2), pp. 262-78.
Gomme, P.; Ravikumar, B. and Rupert, P. “Secular Stagnation and Returns on Capital.” Federal Reserve Bank of
St. Louis Economic Synopses, 2015, No. 19; https://research.stlouisfed.org/publications/economic-synopses/
2015/08/18/secular-stagnation-and-returns-on-capital/.
Kliesen, K. “The Fed’s Strategy for Exiting from Unconventional Policy: Key Principles, Potential Challenges.”
Federal Reserve Bank of St. Louis The Regional Economist, October 2013, pp. 1-4;
https://www.stlouisfed.org/~/media/Files/PDFs/publications/pub_assets/pdf/re/2013/d/ExitStrategy.pdf.
Owyang, M. “Has the Phillips Curve Relationship Broken Down?” Federal Reserve Bank of St. Louis On the Economy
(blog), September 21, 2015;
https://www.stlouisfed.org/on-the-economy/2015/september/phillips-curve-unemployment-down-inflation-low.
Taylor, J. “A Historical Analysis of Monetary Policy Rules,” in J. Taylor, ed., Monetary Policy Rules. Chicago: University
of Chicago Press, 1999, pp. 319-41.
Yellen, J. “Transcript of Chair Yellen’s Press Conference, September 17, 2015.” Board of Governors of the Federal
Reserve System, September 17, 2015.

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A Regional Look at U.S. International Trade

Maximiliano Dvorkin and Hannah G. Shell

Economic activity at the state level varies greatly across U.S. regions, with different states specializing
in the production of particular goods and services. This heterogeneity in activity informs the geographic distribution of U.S. imports and exports. Using U.S. Census Bureau foreign trade statistics,
the authors examine the distribution of U.S. international trade at the state level, controlling for commodities and major trading partners. They find that trade activity varies greatly from state to state
and identify two factors affecting this pattern—proximity to a trading partner and geographic location of industries. This analysis is descriptive but can be seen as a step toward understanding the local
impact of globalization and asymmetric trade exposure across U.S. regions. (JEL F10, F14, R12)
Federal Reserve Bank of St. Louis Review, First Quarter 2016, 98(1), pp. 17-39.

I

n the United States, the distribution of economic activity is heterogeneous across space.
Different U.S. states tend to specialize in the production of particular goods and services.
This specialization is, in part, a result of available natural resources, such as oil in Texas
and Alaska, but also historical and man-made circumstances, such as the location of the auto
industry in Michigan or the computer and technology industries in the “Silicon Valley” of
California.
In this article, we analyze the interaction between the industry specialization of U.S. states
and the geographic distribution of U.S. international trade. We investigate which states export
and import the most, which kinds of goods they trade, and who they trade with. Understanding the regional characteristics of production and trade is important for gauging, for example,
the effects of an increase in Chinese imports on Californian labor markets or the effects of a
European recession on the auto industry in Michigan. Our analysis is descriptive but can be
seen as a step toward understanding the local impact of globalization and asymmetric trade
exposure across U.S. regions.1
For this analysis, we use import and export data at the national and state levels for 2014
from U.S. Census Bureau foreign trade statistics. We classify the goods according to the threedigit North American Industry Classification System (NAICS) and focus on the top-five

Maximiliano Dvorkin is an economist and Hannah G. Shell is a senior research associate at the Federal Reserve Bank of St. Louis.
© 2016, Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the views of
the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced, published,
distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses, and
other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.

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traded commodities, which account for roughly 58 percent of imports and exports. For the
United States, the top-four exported commodities are also the top-four imported, with a fifth
for each being energy related.
Standard theories of international trade, such as the Ricardian model or the HeckscherOhlin model, suggest that countries or regions will produce and export goods for which they
have a comparative advantage and import the rest.2 Patterns observed in U.S. data, however,
are at odds with these theories of trade. Moreover, a similar pattern holds for U.S. trading
partners—the top exporters are also the top importers. This article analyzes the top-four U.S.
trading partners, Canada, Mexico, the European Union, (EU) and China, which account for
roughly 60 percent of exports and 64 percent of imports.3
A newer generation of trade models emphasizes product differentiation and variation in
consumer tastes to reconcile the fact that a substantial volume of trade across countries is
intra-industry trade.4,5 The intuition is simple: For example, the United States both exports
and imports cars, as some consumers prefer to buy a Ford, while others a Mercedes-Benz.
A European consumer’s Ford purchase counts as a U.S. export, while a U.S. consumer’s
Mercedes-Benz purchase counts as a U.S. import. The same analogy is easily applied to purchases from Boeing (a U.S. aircraft company) and Airbus (a European aircraft company).
In addition, we find large, regional dispersion in the patterns of international trade,
which is partly explained by proximity to trading partners. For example, the states that trade
with Canada the most are the northern states bordering Canada.6 This finding is consistent
with gravity models of international trade, in which proximity (broadly defined to capture
distance) and transportation costs are important determinants of trade.7
Earlier versions of the gravity models of trade were mostly empirical and drew an analogy
to Newton’s law of universal gravitation—objects with larger mass or closer to each other will
have larger gravitational pull between them. In economic terms, countries or regions with
higher incomes or close to each other—close geographically and/or having lower tariffs or
similar lower barriers to trade—should see larger volumes of trade between them. Several
microfounded models of trade have been developed to account for gravity relationships.8
Overall, our study identifies two main forces at play that explain the regional patterns of
trade, which can be easily missed using a more aggregate approach. As discussed, proximity
to a trading partner is an important determinant of trade. However, the geographic location
of industries, perhaps due to regional comparative advantage, also affects the exposure of U.S.
states to international trade. For example, computer and electronic products are primarily
imported and exported by the western states. Proximity to a major trading partner affects
this pattern only mildly. So, while the northern states trade more with Canada overall, presumably due to proximity, California and Texas provide a larger share of U.S. computer and
electronic products exported to Canada.
This article is organized as follows. The next section analyzes total U.S. imports and
exports by major trading partner. The third section examines U.S. trade of commodities with
the world and by major trading partner. The fourth section analyzes state trade by major U.S.
trading partner and commodity. The final section discusses some caveats in the data and
concludes.
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TOTAL U.S. IMPORTS AND EXPORTS
We start our analysis by looking at the value of total exports and imports by state. We first
focus on total international trade and then analyze state trade by major U.S. trading partner.
Trade data for our analysis are from U.S. Census Bureau foreign trade statistics. We use
state and national annual imports and exports of goods by trading partner and commodity
from the USA Trade Online database. The commodities are classified at the three-digit NAICS
level. We use 2014 data only, the most recent full year of data available. We treat the District
of Columbia (D.C.) as one state but do not include U.S. territories or possessions. To facilitate
state-level comparisons, we divide each state’s total import and export values, respectively,
by the state’s population in 2014 to calculate per capita values.9 The Census data provide a
geographic distribution of import and exports of goods only. Although international trade in
services is a large component of total U.S. trade, the lack of a geographic distribution prevents
us from including services in our analysis.

Total International U.S. Imports and Exports
In 2014, the U.S. exported $1.6 trillion of goods and imported $2.3 trillion. Figure 1 shows
the distribution of per capita imports (bottom map) and exports (top map) across the 50 states
and D.C. The darkest color is the top 25 percent (first quartile) and the lightest is the bottom
25 percent (last quartile). As the figure shows, imports and exports vary quite substantially
across states. On average, states exported $4,276 per person in 2014. The biggest per capita
exporter in 2014 was Louisiana, at $13,939, followed closely by Washington, at $12,822. The
smallest was Hawaii, at $1,019.10 In terms of total U.S. exports (not per capita), Texas exported
the most overall, $288 billion, or 18 percent of the total, while D.C. exported the least.
As shown in Figure 1, the states that import the most do not necessarily export the most.
Nonetheless, imports and exports are highly correlated. The per capita average of imports
across all states was $5,757 in 2014. New Jersey, Louisiana, and Michigan imported the most
per capita: $14,137, $12,389, and $12,385, respectively. New Mexico imported the least, only
$1,072 per capita. In terms of total U.S. imports, California imported the most, around $403
billion, or 17 percent of the total; Texas was next with $302 billion, or 13 percent of the total;
and South Dakota imported the least.

Total U.S. Imports and Exports by Major Trading Partner
Table 1 shows the annual import and export values for trade in goods between the United
States and several selected countries and areas in 2014. Canada was the biggest recipient of
U.S. exports, at about $312 billion, followed by the EU, Mexico, and China.11 Overall, these
four trading partners accounted for close to 60 percent of total U.S. exports and 64 percent of
total U.S. imports. Most U.S. imports in 2014 came from China, totaling about $467 billion,
followed by the EU, Canada, and Mexico. Japan was the next-largest trading partner for imports
and exports, although the trade pattern was imbalanced: In 2014, the U.S. imported twice the
amount of goods from Japan as it exported to Japan.
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Figure 1
U.S. Exports and Imports (2014)
Exports to the World (USD per capita)

5,029.54-13,939.39
4,045.88-5,029.53
2,709.15-4,045.87
1,423.77-2,709.14

Imports from the World (USD per capita)

7,807.32-14,137.72
5,178.49-7,807.31
3,244.46-5,178.48
1,072.75-3,244.45

SOURCE: U.S. Census Bureau foreign trade statistics.

Similar to the variation in state-level imports and exports, certain states trade more with
certain trading partners. Figures 2 through 5 show the per capita spatial distribution of U.S.
exports (top maps) and imports (bottom maps) in 2014 by the four largest bilateral trading
partners listed previously.
Canada. As shown in Figure 2, U.S. trade with Canada exhibits a clear spatial pattern in
2014. In fact, there is a positive correlation between the value of per capita trade with Canada
and a state’s proximity to Canada. On average, states exported $972 per capita to Canada and
imported $1,295. The five states that imported or exported, respectively, the most per capita
to Canada in 2014 are all in the northern half of the United States. The biggest exporter per
capita was North Dakota, at $5,881, while the biggest importer per capita was Vermont, at
$5,937. In terms of total U.S. trade with Canada in 2014, Michigan imported the most, $49
billion, or 14 percent of the total, and Texas exported the most, $31 billion, or 10 percent of
the total.
China. Figure 3 shows state per capita trade with China in 2014. On average, states
exported $387 per capita to China and imported $929. Washington exported the most, $2,929
per capita, while Tennessee imported the most, $3,868 per capita, followed closely by California
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Table 1
U.S. Trade in Goods by Selected Countries and Groups (2014)
Exports (USD millions)

Imports (USD millions)

Canada

312,421

China

466,755

European Union

276,143

European Union

418,201

Mexico

240,249

Canada

347,798

China

123,676

Mexico

294,074

Japan

66,827

Japan

134,004

United Kingdom

53,823

Germany

123,260

Germany

49,363

Korea, South

69,518

Korea, South

44,471

United Kingdom

54,392

Netherlands

43,075

Saudi Arabia

47,041

Brazil

42,429

France

46,874

Hong Kong

40,858

India

45,244

Belgium

34,790

Italy

42,115

France

31,301

Taiwan

40,582

Singapore

30,237

Ireland

33,956

Taiwan

26,670

Switzerland

31,191

Australia

26,582

Vietnam

30,589

Switzerland

22,176

Brazil

30,537

United Arab Emirates

22,069

Malaysia

30,420

India

21,608

Venezuela

30,219

Colombia

20,107

Thailand

27,123

SOURCE: U.S. Census Bureau, U.S. International Trade in Goods and Services, FT900 Exhibit 13, Not Seasonally Adjusted,
Census Basis.

at $3,548 per capita. In terms of total U.S. trade with China in 2014, California imported the
most, $137 billion, or almost 30 percent of the total, while Washington exported the most,
$20 billion, or 17 percent of the total.
European Union. As shown in Figure 4, in general, EU imports in 2014 appear to be more
concentrated in northeastern states. This concentration could be because of geographic proximity or greater demand for EU imports due to cultural similarity with the EU. On average,
states exported $754 per capita to the EU and imported $1,167. Louisiana was the biggest per
capita exporter, at $2,446, while Delaware was the biggest per capita importer, at $4,631. In
terms of total U.S. trade with the EU, New Jersey and New York imported $36 and $33 billion,
respectively, together receiving 17 percent of the total. Texas exported the most, $30 billion,
or 11 percent of total U.S. exports to the EU.
Mexico. As shown in Figure 5, U.S. trade with Mexico in 2014 shows concentration
among southern states closer to the Mexican border and Midwestern states with large agricultural industries. On average, states exported $454 per capita from Mexico and imported
$571. Texas exported the most to Mexico, $3,804 per capita, while Michigan imported the
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Figure 2
U.S. Exports to and Imports from Canada (2014)
Exports to Canada (USD per capita)

1,160.94-5,881.54
779.29-1,160.93
479.84-779.28
10.35-479.83

Imports from Canada (USD per capita)

1,475.48-5,937.62
731.88-1,475.47
457.17-731.87
84.41-457.16

SOURCE: U.S. Census Bureau foreign trade statistics.

most, $4,286 per capita. In terms of total U.S. trade with Mexico in 2014, Texas was the biggest
trading partner, exporting $102 billion and importing $90 billion, or 43 percent of total exports
to Mexico and 31 percent of total imports from Mexico.12

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Figure 3
U.S. Exports to and Imports from China (2014)
Exports to China (USD per capita)

356.38-2,929.91
267.65-356.37
143.89-267.64
8.01-143.88

Imports from China (USD per capita)

1,168.55-3,868.15
808.43-1,168.54
423.33-808.42
44.15-423.32

SOURCE: U.S. Census Bureau foreign trade statistics.

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Figure 4
U.S. Exports to and Imports from the European Union (2014)
Exports to the European Union (USD per capita)

951.55-2,446.15
635.74-951.54
360.27-635.73
137.08-360.26

Imports from the European Union (USD per capita)

1,427.20-4,630.85
809.58-1,427.19
475.75-809.57
83.51-475.74

SOURCE: U.S. Census Bureau foreign trade statistics.

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Figure 5
U.S. Exports to and Imports from Mexico (2014)
Exports to Mexico (USD per capita)

523.22-3,804.43
343.56-523.21
157.82-343.55
7.31-157.81

Imports from Mexico (USD per capita)

730.06-4,286.41
412.05-730.05
145.67-412.04
14.85-145.66

SOURCE: U.S. Census Bureau foreign trade statistics.

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Table 2
U.S Imports of Goods for Selected NAICS-Based Product Codes (2014)
Product code

Imports (USD millions)

Computer and electronic products

365,805

Transportation equipment

355,720

Oil and gas

263,230

Chemicals

205,668

Machinery, except electrical

160,847

Miscellaneous manufactured commodities

111,422

Primary metal manufacturing

101,165

Electrical equipment, appliances, and components

99,793

Apparel and accessories

86,613

Petroleum and coal products

81,976

Fabricated metal products, NESOI

66,199

Goods returned

60,387

Food and kindred products

57,130

Plastics and rubber products

49,645

Other

282,086

NOTE: NESOI, not elsewhere specified or included.
SOURCE: U.S. Census Bureau foreign trade statistics.

U.S. IMPORTS AND EXPORTS BY MAJOR COMMODITY
In this section, we use three-digit NAICS product codes to examine which commodities
make up the majority of U.S. imports and exports.
Tables 2 and 3 show imports and exports, respectively, for the 15 most-traded commodity
groups in 2014. The biggest U.S. import was computer and electronic products, which include
computers and peripherals; communication, audio, and video equipment; and navigational,
control, and electro-medical instruments. In 2014, the United States imported about $366
billion of these goods, or 16 percent of total U.S. imports. Transportation equipment, which
includes automobiles, trucks, trains, boats, airplanes, and their parts, was the second-largest
U.S. import in 2014, at more than $355 billion, or 15 percent of total U.S. imports. Oil and gas,
chemicals, and machinery (excluding electrical) round out the top-five imports. Oil and gas
includes only crude petroleum and natural gas and accounted for $263 billion of U.S. imports,
followed by chemicals at over $205 billion. Chemicals include pesticides and fertilizers; pharmaceutical products; paints and adhesives; soap and cleaning products; and raw plastics,
resins, and rubber. Finally, U.S. imports of machinery totaled about $161 billion. Machinery
includes goods for ventilation, heating, and air conditioning (both for consumers and companies); power tools; and industrial equipment. These five categories together made up about
58 percent of total U.S. imports in 2014.
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Table 3
U.S Exports of Goods for Selected NAICS-Based Product Codes (2014)
Product code

Exports (USD millions)

Transportation equipment

273,637

Computer and electronic products

209,058

Chemicals

200,222

Machinery, except electrical

152,560

Petroleum and coal products

116,935

Miscellaneous manufactured commodities

81,914

Agricultural products

72,927

Food and kindred products

70,708

Primary metal manufacturing

64,040

Electrical equipment, appliances, and components

60,585

Fabricated metal products, NESOI

49,245

Special classification provisions, NESOI

43,801

Plastics and rubber products

33,877

Oil and gas

29,766

Other

161,257

NOTE: NESOI, not elsewhere specified or included.
SOURCE: U.S. Census Bureau foreign trade statistics.

In terms of total U.S. exports in 2014, transportation equipment was the largest exported
commodity, at $273 billion, or about 17 percent of the total. Four of the top-five exported commodities were the same as those imported, just in a slightly different order. The remaining
top commodity for each was energy related: More oil and gas was imported and more petroleum and coal products were exported. Petroleum and coal products include refined petroleum products, such as gasoline, lubricating oils, and asphalt, and totaled $117 billion of U.S.
exports in 2014. Another major U.S. import that is not a major U.S. export was apparel and
accessories. Instead, in 2014 the United States exported more agricultural products.
Figure 6 shows the values of the top-five U.S. imports in 2014 from the four major trading
partners. With the exception of oil and gas, the four trading partners provided around 70 percent of total U.S. imports for each of the commodities. For oil and gas, they provided 48 percent. The U.S. imported the most transportation equipment, which includes cars, from Canada,
Mexico, and the EU, with Mexico being the largest source, at $89 billion, or 25 percent of total
transportation equipment imported. Nearly half (46 percent) of U.S. imports of computer
and electronic products came from China and totaled $167 billion. The most U.S. imports of
chemicals came from the EU (44 percent) and totaled $90 billion. The most U.S. imports of
oil and gas (37 percent) came from Canada and totaled $97 billion. China and the EU export
almost no oil and gas to the United States, which is no surprise given that these countries produce little of these commodities and are net importers themselves. U.S. imports of machinery
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Figure 6
Top U.S. Imports by Trading Partner (2014)
2014 USD (millions)
180,000
Canada
China
Mexico
European Union

160,000
140,000
120,000
100,000
80,000
60,000
40,000
20,000
0
Transportation
Computer and
Equipment
Electronic Products

Chemicals

Oil and Gas

Machinery,
Except Electrical

SOURCE: U.S. Census Bureau foreign trade statistics.

Figure 7
Top U.S. Exports by Trading Partner (2014)
2014 USD (millions)
70,000

Canada
China
Mexico
European Union

60,000
50,000
40,000
30,000
20,000
10,000
0
Transportation
Computer and
Equipment Electronic Products

Chemicals

Machinery,
Petroleum and Coal
Except Electrical
Products

SOURCE: U.S. Census Bureau foreign trade statistics.

came mostly from the EU and China, $52 billion (33 percent) and $29 billion (18 percent),
respectively.
As shown in Figure 7, U.S. exports in 2014 were more evenly spread among the trading
partners than imports. The top-four trading partners together received about 60 percent of
each of the top-four exported commodities and 45 percent of the fifth—petroleum and coal
products. Canada received the most U.S. exports of transportation equipment, $65 billion
(24 percent), followed by the EU at $47 billion (13 percent). The most U.S. exports of com28

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puter and electronic products went to Mexico, $40 billion (19 percent). Similar to U.S. imports
of chemicals, the EU received the most U.S. exports of chemicals, $54 billion (27 percent).
Canada also received the most U.S. exports of machinery, $32 billion (21 percent). Lastly,
Mexico received the most U.S. exports of petroleum and coal products, $19 billion (16 percent).

STATE-LEVEL IMPORTS AND EXPORTS BY COMMODITY AND
TRADING PARTNER
We have described U.S. trade in terms of major trading partners (Canada, China, Mexico,
and the EU) and identified the major traded commodities (computer and electronic products,
transportation equipment, chemicals, and machinery).
Our state-level analysis by major trading partner shows that trade volume seems to be
influenced by proximity. However, aggregation may mask some important heterogeneity
due to the particular geographic distribution of industries. For example, given the large production of automobiles in Michigan, it is expected that exports of automobiles (or their parts)
from Michigan and imports of automobiles (or their parts) to Michigan will be large.
It is important to highlight that a sizable fraction of imports are intermediate goods.13
Therefore, the geographic location of industries will affect the geographic distribution of
imports according to the inputs they demand. To identify which goods individual states trade
the most with which major U.S. bilateral trading partners, Figures 8 through 15 show for each
commodity per capita state imports (the first figure for each) and exports (the second figure
for each) in 2014 by trading partner and for the world.

Chemicals
Figure 8. In general, states in the eastern half of the United States and the Rust Belt
imported the most chemicals per capita. Delaware and Indiana were the biggest per capita
importers of chemicals, at $4,078 and $2,010, respectively. As mentioned, most U.S. imports
of chemicals came from the EU, with many states importing the most chemicals per capita
from the EU; however, quite a few northern states such as Wyoming, Montana, and Oregon
imported most of their chemicals from Canada. Delaware imported more chemicals per capita
from the EU than any other state, at $3,612. The biggest per capita importers of chemicals from
Mexico, Canada, and China were West Virginia, New Jersey, and North Dakota, respectively.
Figure 9. In 2014, states exporting chemicals were more geographically spread out than
those importing chemicals. The biggest per capita exporters of chemicals were Delaware,
Louisiana, and Texas, at over $1,700 each. The EU received the most U.S. exports of chemicals
overall, and this relationship mostly holds at the state level: Nearly every state exports more
chemicals to the EU than any other trading partner. A few states such as Iowa, New Jersey,
and Ohio exported more chemicals to Canada, and New Mexico, Arizona, and Texas exported
more to Mexico. Oregon and Hawaii are the only states that sent the majority of their chemical
exports to China. Not surprisingly, Delaware was the biggest U.S. exporter of chemicals to
China and the EU, Texas was to Mexico, and North Dakota was to Canada.
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Figure 8
U.S. Imports of Chemicals from the World and by Trading Partner (2014)
Imports from the World (USD per capita)

Imports from Canada (USD per capita)

587.69-4,078.53
344.86-587.68
195.08-344.85
34.97-195.07

Imports from Mexico (USD per capita)

129.06-437.50
61.47-129.05
39.61-61.46
1.41-39.60

Imports from the European Union (USD per capita)

17.24-105.58
10.23-17.23
3.16-10.22
0.19-3.15
*Data for the District of Columbia are not available.

214.87-3,612.34
88.88-214.86
26.44-88.87
2.58-26.43

Imports from China (USD per capita)

66.39-171.85
31.27-66.38
10.11-31.26
0.02-10.10

SOURCE: U.S. Census Bureau foreign trade statistics.

Computer and Electronic Products
Figure 10. As stated, computer and electronic products were overall the biggest U.S.
import in 2014. Relative to states importing chemicals, states importing computer and electronic products were more spread out geographically, with slight concentration in the western
United States (Figure 10). On average, in 2014, states imported $700 per capita of computer
and electronic products. The biggest per capita importers were Tennessee, California, and
Texas, at over $2,400 each. Most states imported more of their computer and electronic products from China than any other country, while a few states, such as Delaware and Connecticut,
imported more from the EU and Colorado imported more from Mexico. Vermont was the
biggest per capita state importer of computer and electronic products from Canada, while
Tennessee was the biggest from China and Minnesota from the EU. As expected, Texas was
the biggest per capita state importer of computer and electronic products from Mexico.
Figure 11. In contrast to imports, U.S. exports of computer and electronic products in
2014 were more geographically concentrated in western states. Almost all of the top per capita
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Figure 9
U.S. Exports of Chemicals to the World and by Trading Partner (2014)
Exports to the World (USD per capita)

Exports to Canada (USD per capita)

562.68-2,274.71
372.88-562.67
234.86-372.87
41.98-234.85

Exports to Mexico (USD per capita)

128.82-387.71
64.14-128.81
32.85-64.13
0.60-32.84

Exports to the European Union (USD per capita)

64.67-395.35
28.64-64.66
14.40-28.63
0.46-14.39

141.60-1,501.71
86.56-141.59
38.52-86.55
2.89-38.51

Exports to China (USD per capita)

37.81-172.83
23.73-37.80
10.56-23.72
0.09-10.55

SOURCE: U.S. Census Bureau foreign trade statistics.

state exporters of computer and electronic products are in the same southwestern slice of the
United States. The biggest per capita exporters of these products, however, were Vermont,
Oregon, and Texas, at over $1,700 each. Most states exported more computer and electronic
products per capita to the EU than other trading partner. Exceptions included Texas and
Vermont: Texas exported more computer and electronic products per capita to Mexico, at
$921, or $24 billion overall, making Mexico the biggest recipient of these goods. Vermont
exported more computer and electronic products per capita to Canada.

Transportation Equipment
Figure 12. On average, states imported $835 per capita of transportation equipment in
2014. Most transportation imports were concentrated in a strip of states in the Midwest and
Midsouth, from Michigan down to Mississippi, where a large portion of U.S. automobile
production occurs. Michigan was the biggest per capita importer of transportation equipment,
at over $7,000, followed by Rhode Island and New Jersey, each above $2,000. In regard to total
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Figure 10
U.S. Imports of Computer and Electronic Products from the World and by Trading Partner (2014)
Imports from the World (USD per capita)

918.71-3,155.90
448.43-918.70
207.42-448.42
34.15-207.41

Imports from Mexico (USD per capita)

Imports from Canada (USD per capita)

22.48-1,967.70
15.45-22.47
10.29-15.44
4.43-10.28

Imports from the European Union (USD per capita)

107.59-778.17
28.35-107.58
7.38-28.34
0.38-7.37

112.79-256.43
71.25-112.78
36.09-71.24
8.13-36.08

Imports from China (USD per capita)

285.02-2,517.20
119.72-285.01
59.19-119.71
6.03-59.18

SOURCE: U.S. Census Bureau foreign trade statistics.

U.S. imports of transportation equipment, Mexico provided the most. At the per capita state
level, imports came fairly evenly from the EU, Mexico, and Canada. Michigan imported
approximately half of its transportation equipment from Mexico. Among states, Michigan
was not only the biggest importer of these goods from Mexico, but also from Canada and
China, while Rhode Island was the biggest importer of these goods from the EU.
Figure 13. On average, in 2014, states exported $749 of transportation equipment per
capita, with exports similarly concentrated in the auto-producing states, with the notable
exception of Washington. Washington is actually the biggest per capita exporter of transportation equipment, most likely because of Boeing’s large presence there. In 2014, Washington
exported $7,342 per capita of transportation goods, followed by Kentucky and Michigan, with
closer to $3,000 per capita each. As is the case for the nation, states exported the most transportation equipment to the EU and Canada, with Michigan sending more than any other state
to Canada. Washington, however, actually sent most of its exports of transportation equipment to China. In terms of biggest trading partners, Canada and Mexico received most of
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Figure 11
U.S. Exports of Computer and Electronic Products to the World and by Trading Partner (2014)
Exports to the World (USD per capita)

Exports to Canada (USD per capita)

705.17-4,020.40
316.30-705.16
186.71-316.29
32.53-186.70

Exports to Mexico (USD per capita)

79.68-1,743.23
45.78-79.67
20.46-45.77
2.94-20.45

Exports to the European Union (USD per capita)

53.93-921.23
18.71-53.92
9.21-18.70
0.24-9.20

122.28-399.17
75.68-122.27
41.80-75.67
6.39-41.79

Exports to China (USD per capita)

68.33-566.14
17.90-68.32
8.60-17.89
0.26-8.59

SOURCE: U.S. Census Bureau foreign trade statistics.

their U.S. transportation equipment from Michigan, China from Washington, and the EU
from Connecticut.

Machinery (Except Electrical)
Figure 14. The geographic distribution of machinery imports and exports, respectively,
in 2014 was similar to that of transportation equipment. On average, states imported $449
per capita of machinery. Machinery imports seem to be slightly more sensitive to the geographic location of trading partners. Northern states imported more machinery from Canada,
while southern states imported more from Mexico. The biggest per capita importers overall
were North Dakota ($1,286), South Carolina ($1,175), and Kentucky ($985). On a per capita
basis, the EU was the largest source of imports for most states. A few notable exceptions
include North and South Dakota, which imported more machinery per capita from Canada.
In terms of biggest trading partners, South Carolina imported the most machinery of any state
from the EU and China, Kentucky from Mexico, and North Dakota from Canada.
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Figure 12
U.S. Imports of Transportation Equipment from the World and by Trading Partner (2014)
Imports from the World (USD per capita)

Imports from Canada (USD per capita)

1,216.46-7,726.15
445.94-1,216.45
161.99-445.93
20.54-161.98

Imports from Mexico (USD per capita)

100.91-3,254.93
54.69-100.90
21.67-54.68
2.06-21.66

Imports from the European Union (USD per capita)

195.88-3,603.92
50.69-195.87
15.96-50.68
0.26-15.95

260.55-2,414.62
65.93-260.54
22.50-65.92
0.73-22.49

Imports from China (USD per capita)

50.30-249.80
22.75-50.29
7.80-22.74
1.07-7.79

SOURCE: U.S. Census Bureau foreign trade statistics.

Figure 15. Exports of machinery in 2014 were somewhat concentrated in the northern
Midwest and Texas. On average, states exported $402 per capita of machinery. The biggest per
capita exporters of machinery were North Dakota, Iowa, and Texas, at over $1,000 per capita
each. Most states sent the majority of their exports of machinery to Canada or the EU, although
Texas sent the majority of its exports to Mexico. China received most of its U.S. machinery
from Minnesota, the EU from Iowa, Mexico from Texas, and Canada from North Dakota.

CONCLUSION
The effects of globalization and international trade may be heterogeneous across industries and space. In this article, we performed a descriptive analysis of the geographic distribution of U.S. international trade in 2014. We looked particularly at which states exported
and imported the most, the types of goods they traded, and their main trading partners.
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Figure 13
U.S. Exports of Transportation Equipment to the World and by Trading Partner (2014)
Exports to the World (USD per capita)

Exports to Canada (USD per capita)

857.94-7,342.32
374.19-857.93
191.57-374.18
20.16-191.56

Exports to Mexico (USD per capita)

157.93-1,418.00
89.81-157.92
32.34-89.80
0.13-32.33

Exports to the European Union (USD per capita)

79.16-421.14
22.54-79.15
7.40-22.53
0.21-7.39

143.77-1,089.07
64.78-143.76
34.29-64.77
0.72-34.28

Exports to China (USD per capita)

41.89-1,744.64
8.08-41.87
2.15-8.07
0.03-2.14

SOURCE: U.S. Census Bureau foreign trade statistics.

We found large regional dispersion in the origin and destination of U.S. international
trade. We argue there are two important determinants of this pattern. First, proximity to trading partners influences trade volume, which is consistent with gravity models of international
trade. Second, we also found that the heterogeneous spatial distribution of industries in the
United States affects the concentration of exports and imports of individual states, which is
consistent with the large intra-industry component of trade.
It is important to highlight some data limitations in our analysis. The trade data collected
by the Census Bureau come directly from import and export records. Export data are reported
through the Automated Export System and import data through the U.S. Customs and Border
Protection’s Automated Commercial System. Because the data are a direct account of goods
and services flowing in and out of the United States, sampling error is not an issue. That being
said, certain nonsampling errors can occur.
Many of the sources for nonsampling errors are typical of any dataset. The data are subject to reporting errors, undocumented (or illegal) shipments, and data-capture errors. There
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Figure 14
U.S. Imports of Machinery (Except Electrical) from the World and by Trading Partner (2014)
Imports from the World (USD per capita)

586.31-1,286.95
415.87-586.30
264.38-415.86
54.56-264.37

Imports from Mexico (USD per capita)

Imports from Canada (USD per capita)

64.12-570.67
43.19-64.11
26.80-43.18
6.56-26.79

Imports from the European Union (USD per capita)

48.09-237.50
23.50-48.08
7.24-23.49
0.33-7.23

216.22-597.38
148.30-216.21
73.86-148.29
20.27-73.85

Imports from China (USD per capita)

106.54-320.22
52.59-106.53
32.94-52.58
1.80-32.93

SOURCE: U.S. Census Bureau foreign trade statistics.

are, however, a few additional sources of nonsampling errors worth noting that are unique to
the trade data. First, the United States does not require individual imports and exports valued
below $2,000 to be reported. To avoid omitting these data altogether, the Census Bureau estimates the annual amount of these “low-value” goods using country-specific factors. Because
the amounts are estimated, estimation error is possible. However, the methodology was
revised in 2010 and the Census Bureau regularly evaluates the methodology to make it more
effective in identifying low-value trade.
Another source of nonsampling error particularly important for our state-level analysis
is the potential misclassification in the origin of movement and state of destination. The statelevel export data are reported in terms of origin of movement, which means exports should
be attributed to the state where they start their exportation journey (not the state with the
actual exit port). However, if shipments are consolidated, which occurs when a freighter combines several individual shipments to fill space, it is possible the exports will all be attributed
to the port state. These consolidated shipments can cause port-state exports to be overstated.
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Figure 15
U.S. Exports of Machinery (Except Electrical) to the World and by Trading Partner (2014)
Exports to the World (USD per capita)

Exports to Canada (USD per capita)

575.96-1,297.27
383.42-575.95
187.25-383.41
27.34-187.24

Exports to Mexico (USD per capita)

144.09-765.55
72.30-144.08
36.38-72.29
0.23-36.37

Exports to the European Union (USD per capita)

43.18-278.11
24.65-43.17
12.33-24.64
0.00-12.32

95.73-189.85
58.11-95.72
24.85-58.10
2.86-24.84

Exports to China (USD per capita)

34.99-73.82
15.64-34.98
10.50-15.63
0.08-10.49

SOURCE: U.S. Census Bureau foreign trade statistics.

Overstatement is particularly common with agricultural exports shipped down the Mississippi
River, with agricultural exports for Louisiana tending to be overstated.
Import data are recorded in terms of the state where the merchandise is destined (the
state of destination). There are a few limitations with this form of import recording, similar
to the export issues. First, if the shipments are consolidated, they are attributed to the state
that receives the most. Such overstatement has less of a systematic bias than exports but could
overstate imports in states where major trading companies are based. Additionally, if the state
of destination is a storage or distribution point, the import destination may not reflect the
state where the goods are consumed. For example, an importer of automobiles might import
a large shipment that is meant to be distributed across the country. All the import value would
be given to the company’s home state as opposed to the states with distributing branches.
We are not aware of the magnitude of these misclassification errors or whether there is a
generally accepted procedure to correct for them. In our analysis, we take the data at face value
but recognize the potential pitfalls. n
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NOTES
1

The recent works by Autor, Dorn, and Hanson (2013) and Caliendo, Dvorkin, and Parro (2015) are examples of a
nascent literature on this important topic.

2

The costs of moving goods across space, tariffs, and regulations also affect which goods and quantities thereof
are traded.

3

When the EU is considered one trading partner, trade between the United States and the EU exceeds that between
the United States and Japan; however, Japan is a larger trading partner than any individual country in the EU.

4

See, for example, Krugman (1979), Eaton and Kortum (2002), and Melitz (2003).

5

The early works of Grubel and Lloyd (1975) and Greenaway and Milner (1983) analyze the empirical patterns of
trade across countries and find that most trade is intra-industry.

6

Similarly, states that trade more with China, Mexico, and Europe are mostly on the West Coast, in the South, and
on the East Coast, respectively.

7

See Anderson (2011).

8

See Costinot and Rodriguez-Clare (2014) for a recent survey.

9

We use annual state population data from the Census Bureau population estimate program via Haver Analytics.
Normalizing using state gross domestic product would slightly change the magnitudes reported here but would
otherwise leave the (qualitative) results virtually unchanged.

10 Although data for Hawaii and Alaska are included in our analysis, maps for these states are excluded from the

figures.
11 We include the EU in the analysis instead of its individual countries because it is a common trading bloc, with a

common trade policy with other countries and non-trade barriers among its members. Countries comprising the
EU are Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany,
Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Poland, Portugal, Romania,
Slovakia, Slovenia, Spain, Sweden, and the United Kingdom.
12 The geographic and industry concentration of U.S.-Mexico trading is also influenced by maquila production. The

maquiladora is a manufacturing operation whereby factories import foreign intermediate materials and equipment from a country free of duties or tariffs and then export the assembled, processed, and/or manufactured
products mostly back to the country of origin of the raw materials. Data from the Banco de Mexico show that
maquila-related trade accounted for almost 50 percent of all trade with Mexico in 2006, the bulk of which was
with the United States. Most of these industries are located close to the U.S.-Mexico border.
13 According to the World Input-Output Database (Timmer et al., 2015), in 2011, roughly 69 percent of U.S. imports

were intermediate goods.

REFERENCES
Anderson, James E. “The Gravity Model.” Annual Review of Economics, September 2011, 3(1), pp. 133-60.
Autor, David H.; Dorn, David and Hanson, Gordon H. “The China Syndrome: Local Labor Market Effects of Import
Competition in the United States.” American Economic Review, October 2013, 103(6), pp. 2121-68.
Caliendo, Lorenzo; Dvorkin, Maximiliano A. and Parro, Fernando. “Trade and Labor Market Dynamics.” Working
Paper No. 2015-009C, Federal Reserve Bank of St. Louis, August 2015;
https://research.stlouisfed.org/wp/more/2015-009.
Costinot, Arnaud and Rodríguez-Clare, Andrés. “Trade Theory with Numbers: Quantifying the Consequences of
Globalization,” in Gita Gopinath, Elhanan Helpman, and Kenneth S. Rogoff, eds., Handbook of International
Economics. Volume 4, Chap. 4. Oxford: Elsevier, 2014, pp. 197-261.
Eaton, Jonathan and Kortum, Samuel. “Technology, Geography, and Trade.” Econometrica, September 2002, 70(5),
pp. 1741-79.

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Dvorkin and Shell
Greenaway, David and Milner, Chris R. “On the Measurement of Intra-Industry Trade.” Economic Journal, December
1983, 93(372), pp. 900-08.
Grubel, Herbert G. and Lloyd, P.J. Intra-Industry Trade: The Theory and Measurement of International Trade in
Differentiated Products. New York: Wiley & Sons Inc., 1975.
Krugman, Paul R. “Increasing Returns, Monopolistic Competition, and International Trade.” Journal of International
Economics, November 1979, 9(4), pp. 469-79.
Melitz, Marc J. “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity.”
Econometrica, November 2003, 71(6), pp. 1695-725.
Timmer, Marcel P.; Dietzenbacher, Erik; Los, Bart; Stehrer, Robert and de Vries, Gaaitzen J. “An Illustrated User
Guide to the World Input-Output Database: The Case of Global Automotive Production.” Review of International
Economics, August 2015, 23(3), pp. 576-605.

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40

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Relative Income Traps

Maria A. Arias and Yi Wen

Despite economic growth in the post-World War II period, few developing countries have been able
to catch up to the income levels in the United States or other advanced economies. Such countries
remain trapped at a relative low- or middle-income level. In this article, the authors redefine the concept of income traps as situations in which income levels relative to the United States remain constantly low and with no clear sign of convergence. This approach allows them to study the issue of
economic convergence (or lack of it) directly. The authors describe evidence pointing to the existence
of both relative low- and middle-income traps and examine cross-country historical transitions
between income groups at the global and regional levels. Finally, they point out challenges to the
benchmark neoclassical growth theory, which predicts convergence to the developed world over time,
and discuss existing theories with the potential to explain income traps. (JEL E13, L52, O11, O47)
Federal Reserve Bank of St. Louis Review, First Quarter 2016, 98(1), pp. 41-60.

E

conomic growth during the post-World War II period lifted many low-income
economies out of absolute poverty and some middle-income economies to higher
income levels. In particular, the percent of the world population living below the
absolute poverty line in the developing world declined from 47 percent to 21 percent in the
20 years between 1990 and 2010, and the World Bank estimated this share would be 13 percent in 2015.1 However, despite such impressive global economic growth, very few countries
have been able to catch up to the high per capita income levels of the developed world and
maintain those levels. As a result, most developing countries still remain “trapped” at a
constant low- or middle-income level relative to the United States (as a representative of
the developed world).
Such a “relative income trap” phenomenon raises concern about the validity of the neoclassical growth theory, which predicts global economic convergence. Specifically, Solow
(1956) suggests that income levels in poor economies will grow relatively faster than in developed nations and eventually converge through capital accumulation, assuming that all counMaria A. Arias is a senior research associate at the Federal Reserve Bank of St. Louis. Yi Wen is an assistant vice president and economist at the
Federal Reserve Bank of St. Louis and professor of economics in the School of Economics and Management at Tsinghua University. The authors
thank Stephen Williamson, Juan Sánchez, and Ana Maria Santacreu for helpful comments.
© 2016, Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the views of
the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced, published,
distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses, and
other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.

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tries have the same access to the world frontier technologies.2 But very few low- or middleincome countries have successfully caught up to high-income countries.
Per capita income in many poor countries is 30 to 50 times lower than that of the United
States and sometimes even lower (i.e., less than $1,000 per year).3 It may take at least 170 to
200 years for such countries to catch up to U.S. living standards, assuming that the poor countries could maintain a growth rate consistently 2 percentage points above the U.S. rate (about
3 percent per year on average). Such growth would be difficult, if not impossible. It is even
harder to imagine that such countries can reach U.S. living standards within one or two generations (40 to 50 years), similar to how North American and Western European economies
caught up to Britain during the 1800s after the Industrial Revolution. To achieve that speed of
convergence today, developing countries would need to grow about 8 percentage points faster
than the United States (or about 11 percent per year) nonstop for 40 to 50 years. In recent
history, only China has come close to this growth rate; it maintained a 10 percent annual
growth rate (7 percentage points above the U.S. rate) for 35 years, but per capita income was
still only one-seventh of that in the United States in 2014. Hence, the lack of income convergence and relative income traps appear to be real problems.
We begin this article with a brief review of various definitions of “income traps” extant
in the literature. Then, we redefine the concept using a relative income measure and describe
evidence pointing to the existence of both low- and middle-income traps. We continue with
a more in-depth analysis of the income traps by finding episodes of rapid and persistent relative growth and use them to assess the relationship between relative growth and several macroeconomic variables. To test the existence of income traps based on our new definition, we
examine cross-country historical transitions between income groups using different time
horizons and look at regional transition patterns to discern possible regional-specific effects.
Finally, we discuss possible explanations for why some countries or regions remain trapped
at a relatively low- or middle-income level while others have escaped the traps and continued
to grow at a rate faster than the United States.

A BRIEF LITERATURE REVIEW
The literature on economic development provides various ways to classify countries by
income groups. In addition, definitions of the “poverty trap” and the “middle-income trap”4
can be based on subjectively defined rules of thumb, statistical approaches to find structural
breaks in the time series, or a combination of both (Kar et al., 2013).
For example, Eichengreen, Park, and Shin (2012, 2013) used per capita gross domestic
product (GDP) in constant international purchasing power parity (PPP) prices to analyze
the frequency and correlates of growth slowdowns in fast-growing middle-income countries.
They use an approach similar to that used by Hausmann, Pritchett, and Rodrick (2005) to
identify and analyze growth accelerations. Aiyar et al. (2013) used growth slowdowns to define
a middle-income trap as a large sudden and sustained deviation from the growth path predicted by a basic conditional convergence framework. Felipe (2012) took a different approach
and defined the traps in terms of the median number of years it took countries already in the
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high-income category in 1950 to transition from lower middle-income to upper middleincome and then to high-income status using GDP per capita in international dollars and the
World Bank’s income thresholds to define the income groups in analyzing these historical
income transitions.
The body of this literature has mainly focused on using absolute measures of income levels
or growth rates to characterize income gaps or to measure low- and middle-income traps.
But in doing so, this literature has ignored the more pervasive phenomenon of a lack of convergence. That is, a country’s income level can grow permanently in absolute terms but nonetheless remain permanently below the U.S. level, trapped at a lower relative income level
because its growth rate is lower than or equal to the U.S. rate.
Few articles have explored the problem from the viewpoint of relative income. For example, Im and Rosenblatt (2013) surveyed the empirical evidence for different relative and absolute definitions of middle-income traps, describing the approaches used to measure both
absolute and relative income thresholds in the literature.

REDEFINING THE INCOME TRAP
Although many so-called low- or middle-income countries have experienced persistent
economic growth, their growth rates have never surpassed the U.S. growth rate. Consequently,
these countries have been unable to close their income gaps with the United States. In other
words, they remain “trapped” at relatively lower income levels compared with the living standards of the developed countries, contrary to the neoclassical growth theory’s predictions that
they will converge because of technology spillover and international capital flows.5
The lack of relative income convergence implies that U.S. per capita income, as well as
general living standards, will continue to be 10 to 50 times higher than in low-income economies and two to five times higher than in middle-income economies. Moreover, the lack of
a clear and consistent definition of low- and middle-income traps or a standard approach to
measure and test the theory hinders the ability to easily (i) compare the results obtained
across studies and (ii) assess the validity of possible explanations behind the income trap
phenomenon.
Therefore, redefining the low- and middle-income traps as situations in which income
levels relative to those of the United States remain constantly low and with no clear sign of
convergence allows us to study the issue of economic convergence (or lack of it) more directly.
Specifically, we use income relative to that of the United States as our reference point to study
the failure of developing countries to achieve the same status as their developed counterparts.
This relative income gap perspective is important because the economies of even the
poorest countries continue to grow at some positive rate every year. Easterly (2006) noted
that relative growth is not significantly different across income quintiles over an extended
period, but unless lower-income economies grow more rapidly and persistently than developed countries, they will not be able to catch up.
Such a permanent relative income gap has important welfare implications. Although
Lucas (2000) points out that it is the growth rate that matters the most for welfare, a persistent
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income gap also matters greatly. As John Stuart Mill keenly observed, “men do not desire to be
rich, but richer than other men.”6 In particular, based on micro-level household data, Luttmer
(2005) found that, controlling for their own income, individuals reported lower levels of
happiness when their neighbors’ income was known to be higher.

Data
We use real GDP data at chained PPP rates from the Penn World Table version 8.0
(PWT 8.0) to calculate income relative to the United States for a sample of 107 countries
between 1950 and 2011.7 We first aggregate the ratio of total real GDP relative to that of the
United States for each year into six regions: Africa, Asia (excluding the Tigers, China, and
Japan), Asian Tigers (including China and Japan), Eastern Europe, Latin America, and member countries of the Organisation for Economic Co-operation and Development (OECD).
This regional aggregate of relative income is used to identify episodes of rapid and persistent
relative growth, as described below. Table 1 lists the countries in the sample for each region.
To analyze the relationship between the relative growth regimes and broader macroeconomic variables, we use a measure of gross trade (the share of exports and imports relative
to GDP), the value of terms of trade, and the share of investment relative to GDP, all obtained
from the PWT 8.0. Moreover, following Buera, Monge-Naranjo, and Primiceri (2011), we
use a proxy for market orientation calculated as the percentage of countries in the region that
are open to trade during any given year, based on the index of trade openness calculated by
Sachs and Warner (1995) and expanded by Wacziarg and Welch (2008).
Using the PWT 8.0 ratio of real GDP per capita relative to the United States for each
country in the sample, we analyze the income transitions between groups and test the income
trap hypothesis. Finally, we check the robustness of these results by repeating the income
transition analysis using the ratio of real GDP per capita relative to the United States8 with
data from the 2013 version of the Maddison-Project (Bolt and Van Luiden, 2013). Overall,
there are data for 104 of the 107 countries in our sample; for many of them the data go as far
back as 1870.

Stylized Facts
The most common examples of rapid and persistent relative income growth (leading to
convergence) are the Asian Tigers (Hong Kong, Singapore, South Korea, and Taiwan); other
examples include countries such as Spain and Ireland. Figure 1 shows a sample of these economies whose relative per capita income grew significantly faster than that of the United States.
The faster growth began in the late 1960s and continued through the early 2000s, catching
up or converging to the higher level of U.S. per capita income. In sharp contrast, per capita
income relative to the United States remained constant and stagnant—between 10 percent
and 40 percent of U.S. income—in the Latin American countries listed in the figure. Despite
their moderate absolute growth during the same period, these countries remain stuck in the
relative middle-income trap and show no sign of convergence to higher income levels.
The lack of convergence is even more striking among low-income countries (Figure 2).
For example, Bangladesh, El Salvador, Mozambique, and Nepal are stuck in a poverty trap,
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Table 1
Countries by Region
Africa
Angola
Benin
Botswana
Burkina Faso
Burundi
Cameroon
Central African Republic
Chad
Congo, Democratic Republic of
Congo, Republic of
Cote d’Ivoire
Egypt
Ethiopia
Gabon
Gambia, The
Ghana
Guinea
Guinea-Bissau
Kenya
Lesotho
Liberia
Madagascar
Malawi
Mali
Mauritania
Mauritius
Morocco
Mozambique
Namibia
Niger
Nigeria
Rwanda
Senegal
Sierra Leone
South Africa
Sudan
Swaziland
Tanzania
Togo

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Africa, cont’d
Tunisia
Uganda
Zambia
Zimbabwe
Asia (excluding Tigers)
Bangladesh
Cambodia
India
Indonesia
Laos
Malaysia
Mongolia
Nepal
Pakistan
Philippines
Sri Lanka
Thailand
Vietnam
Asian Tigers
China
Hong Kong
Japan
Korea, Republic of
Singapore
Taiwan
Eastern Europe
Albania
Bulgaria
Hungary
Poland
Romania
Turkey

Latin America
Argentina
Bolivia
Brazil
Chile
Colombia
Costa Rica
Dominican Republic
Ecuador
El Salvador
Guatemala
Honduras
Jamaica
Mexico
Panama
Paraguay
Peru
Trinidad & Tobago
Uruguay
Venezuela
OECD
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Germany
Greece
Ireland
Israel
Italy
Netherlands
New Zealand
Norway
Portugal
Spain
Sweden
Switzerland
United Kingdom

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Figure 1
Middle-Income Trap
GDP Per Capita Relative to the United States
1.2
United States

1.0

Hong Kong
0.8

Ireland
Spain

0.6

Taiwan
0.4

Mexico
Brazil

0.2
Ecuador
0
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Guatemala

SOURCE: PWT 8.0 and authors’ calculations.

Figure 2
Low-Income Trap
GDP Per Capita Relative to the United States
1.2
United States

1.0

China
0.8

India
Bangladesh

0.6

El Salvador
0.4

Mozambique
China

India

0.2

Nepal

0
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
SOURCE: PWT 8.0 and authors’ calculations.

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Arias and Wen

where their relative per capita income is constant at or below 5 percent of the U.S. level. Even
though their economies might have grown moderately in absolute terms, they have not grown
at a rate faster than the U.S. growth rate; thus, their relative income levels have not increased.
As a result, the income gap between these nations and the United States has permanently
been at least 20 times their own per capita incomes.
In comparison, China’s economy has grown relatively faster than the U.S. economy
since about the early 1980s, breaking away from the relative low-income trap and reaching
middle per capita income levels. India has also shown signs of escaping the low-income trap
since the early 1990s. However, both countries still have a long way to go to catch up to and
converge to the levels in developed economies, and both have yet to encounter the relative
middle-income trap.9

CORRELATES OF GROWTH
What potential factors could contribute to (or explain) the relative income traps? Causal
explanation is difficult in a statistical framework unless good instrumental variables are available, but this is not the case at the moment. In this section, we conduct a correlation analysis.
Specifically, we start with a filter-based approach to identify episodes of rapid and persistent relative growth using the following criteria. Relative growth episodes must be at least
five years long with at least four periods of rapid growth, where rapid growth is defined as
relative growth higher than 1 percent for non-OECD countries and 0.5 percent for OECD
countries (considering that the United States has grown at an average rate of about 2 percent
since 1950). Once a start date for the growth regime is found, the last date is defined at the
next relative growth peak, allowing for several years of slow or negative relative growth. The
shaded areas in Figure 3 represent the relative growth episodes as determined by our algorithm.
This approach relaxes the regime length constraints set in other filter-based algorithms
(e.g., Eichengreen, Park, and Shin, 2012, 2013; and Aiyar et al., 2013), allowing us to create a
dichotomous variable that identifies the entire length of the growth regime, analogous to a
variable created with a statistical model such as the Bai-Perron methodology to find structural
breaks in the time series (e.g., Jones and Olken, 2008).
Then, we examine the cross-sectional correlation between average economic growth during the growth regimes and several macroeconomic variables based on the following model:
(1)

∆ ln yi = ln xi + u ,

where yi in equation (1) is the average relative income ratio during each regime; xi is the variable of interest, computed as the average value of an explanatory variable by regime and
region (also calculated as a ratio of the individual country data relative to the United States);
and u is an error term. Specifically, the explanatory variable xi includes gross trade volume,
terms of trade (the exchange rate), investment, government expenditures, inflation (growth
of the household consumption price level), and market orientation (the share of countries in
the region determined to be “open” according to Wacziarg and Welch, 2008, as constructed
in Buera, Monge-Naranjo, and Primiceri, 2011, respectively).
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Figure 3
Relative Growth Regimes by Region
Africa

Asia (excluding Tigers)

Total RGDP Ratio

0.18

0.60

0.16

1.00

0.50
0.14
0.40
0.12
0.10

0.50

0.30
1960

1980

2000

0.20

1960

1980

0

2000

0.50

1.30

0.16

0.40

1.20

0.14

0.30

1.10

0.12

0.20

1.00

1960

1980

2000

0.10

1960

1980

2000

1980

2000

OECD

0.18

0.10

1960

Latin America

Eastern Europe

Total RGDP Ratio

Asian Tigers
1.50

0.70

0.90

1960

1980

2000

NOTE: The shaded bars indicate recessions as determined by the National Bureau of Economic Research. RGDP, real
gross domestic product.
SOURCE: PWT 8.0 and authors’ calculations.

The results summarized in Table 2 show that relative strength in trade, investment, and
market orientation has a statistically significant relationship to strength in relative income
growth rates across regimes, while that of consumer price inflation is negative and marginally
significant. This analysis shows that strong economic growth relative to the United States is
associated with a region’s relative strength in trade, investment, or market orientation but is
not associated with the exchange rate or government expenditures.

INCOME TRANSITIONS: ARE THE TRAPS REAL?
To determine the validity of our hypothesis about low- and middle-income traps, we study
the historical evidence of transitions between income groups in our sample by calculating
transition probability matrixes in the spirit of Im and Rosenblatt (2013). Assuming that relative GDP per capita follows a first-order Markov chain, we calculate the probability of a coun48

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Table 2
Regression Results
Independent variable
Gross trade

Dependent variable: average relative income
1.22***

Terms of trade

0.98

Investment

2.17***

Government expenditures

–0.63

Inflation

–0.79*

Market orientation
Constant

0.68***
–1.87***

Observations
R-squared

–0.67*

0.19

–0.36

20

–0.97***
20

–0.88***
20

20

20

20

0.59

0.01

0.42

0.03

0.21

0.43

NOTE: Average relative income is the average regional income during the growth episode, calculated as the natural
log of the aggregate of total real GDP for each region. Gross trade, terms of trade, investment, government expenditures, and inflation are also the natural log of the regional averages during the episode, and market orientation is the
average ratio of countries in the region that were open, constructed as in Buera, Monge-Naranjo, and Primiceri (2011).
* and *** indicate significance at the 10 percent and 1 percent levels, respectively.

try having a relative income in income range j today given a relative income in income range
i during the previous period. So, the probability of transitioning from income group i to income
group j can be written as

(

)

pij = Pr st = j st −1 = i .

(2)

Given N income groups, the entire matrix of transition probabilities can be written as
 p11  p1 N

P=   
 pN 1  pNN


(3)

where

∑

j



,



pij = 1.

Our analysis differs from that of Im and Rosenblatt (2013) in several ways. We divide the
sample into only three relative income groups: low (≤15 percent of U.S. income), middle
(>15 to 50 percent of U.S. income), and high (>50 percent of U.S. income).10 Moreover, we
are interested in analyzing the incidence of economies that permanently escape the relative
income traps, so we calculate three transition matrixes for period intervals spanning 10 years,
20 years, and the entire sample available (30 to 61 years, depending on data available for each
country) to assess the persistence of traps in the data.11
As shown in Table 3, the relative low-income trap is highly persistent: The probability of
an economy remaining trapped in the low-income range is 94 percent after 10 years (Panel A),
90 percent after 20 years (Panel B), and 80 percent after the entire observational period, 30 to
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Table 3
Transition Matrixes: Entire Sample (1950-2011)
A: 10-Year transition matrix

B: 20-Year transition matrix

C: Start-to-end transition matrix

0 to 15%

15 to 50%

>50%

0 to 15%

15 to 50%

>50%

0 to 15%

15 to 50%

>50%

0 to 15%

0.94

0.06

0.00

0.90

0.10

0.00

0.80

0.16

0.03

15 to 50%

0.09

0.80

0.11

0.14

0.65

0.21

0.17

0.47

0.36

>50%

0.00

0.03

0.97

0.00

0.03

0.97

0.00

0.00

1.00

61 years (Panel C). Meanwhile, the effects of a relative middle-income trap are strong in the
10-year period (with an 80 percent probability that an economy will remain in middle-income
status and a 9 percent probability that it will regress to low-income status) but dissipate in
the longer term. Still, Panel C shows that more than half of the economies with middle-income
status at the beginning of the sample remained at or below that relative income status (with a
cumulative conditional probability of 47 percent + 17 percent = 64 percent); this finding indicates that these economies had a low probability of relative income convergence to higher
levels of relative income even after moderate absolute growth during the entire 30- to 61-year
period.
In other words, the probability of an economy escaping the middle-income trap is 11 percent after a 10 years, 21 percent after 20 years, and 36 percent after 30 to 61 years. Also interesting to note is that countries almost never regress to low- or middle-income status once they
have reached high-income status: The conditional probability of remaining at high-income
status is at least 97 percent.12
Compelled to delve into this issue even further, we broke down the country sample by
region (as shown in Table 1) and repeated this exercise. We obtained interesting results that
shed light on regional growth trends commonly discussed in the development literature
(Table 4). For example, African nations share an extremely strong tendency to be trapped at
relative low- or middle-income levels. Regardless of the length of the period under consideration, the probability of remaining trapped in the low-income range in Africa is at least 95
percent. Moreover, even for those African countries that reached the middle-income range,
their historical chance of moving further up to the high-income range is zero, while their
chance of regressing to the low-income range is higher as the time period expands, reaching
40 percent at the end of the full sample.
Most Asian countries (excluding the Tigers and China and Japan) experienced similar
trends. Namely, the low-income trap is extremely stable—so much so that countries can at
most only temporarily escape from it. The probability of returning to the low-income range
is 100 percent in the long run. The exception here is the Asian Tigers, which have been able
to converge to the rich economies, transitioning into—and maintaining—a higher relative
income.13
The results for Eastern European countries are strikingly different: They show a remarkably stable middle-income trap. Countries that started in the relative low-income range have
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Table 4
Transition Matrixes by Region (1950-2011)
A: 10-Year transition matrix

B: 20-Year transition matrix

C: Start-to-end transition matrix

0 to 15%

15 to 50%

>50%

0 to 15%

15 to 50%

>50%

0 to 15%

15 to 50%

>50%

0 to 15%

0.98

0.02

0.00

0.97

0.03

0.00

0.95

0.05

0.00

15 to 50%

0.16

0.84

0.00

0.27

0.73

0.00

0.40

0.60

0.00

>50%

NA

NA

NA

NA

NA

NA

NA

NA

NA

Africa

Asia (excluding Tigers)
0 to 15%

0.96

0.04

0.00

0.91

0.09

0.00

0.83

0.17

0.00

15 to 50%

0.17

0.83

0.00

0.31

0.69

0.00

1.00

0.00

0.00

>50%

NA

NA

NA

NA

NA

NA

NA

NA

NA

0 to 15%

0.73

0.27

0.00

0.49

0.51

0.00

0.00

0.33

0.67

15 to 50%

0.00

0.57

0.43

0.00

0.15

0.85

0.00

0.00

1.00

>50%

0.00

0.00

1.00

0.00

0.00

1.00

NA

NA

NA

0 to 15%

0.50

0.50

0.00

0.05

0.95

0.00

0.00

1.00

0.00

15 to 50%

0.05

0.95

0.00

0.12

0.88

0.00

0.00

1.00

0.00

>50%

NA

NA

NA

NA

NA

NA

NA

NA

NA

0 to 15%

0.84

0.16

0.00

0.77

0.23

0.00

0.50

0.50

0.00

15 to 50%

0.13

0.85

0.02

0.20

0.77

0.03

0.23

0.77

0.00

>50%

0.00

0.90

0.10

0.00

1.00

0.00

NA

NA

NA

Asian Tigers

Eastern Europe

Latin America

OECD
0 to 15%

NA

NA

NA

NA

NA

NA

NA

NA

NA

15 to 50%

0.00

0.63

0.37

0.00

0.44

0.56

0.00

0.00

1.00

>50%

0.00

0.01

0.99

0.00

0.00

1.00

0.00

0.00

1.00

NA, not available.

a 50 percent probability of moving up to middle-income status in 10 years, and this probability
increases to 95 percent in 20 years and 100 percent at the end of the full sample. On the other
hand, countries that started in the relative middle-income range have zero probability of
escaping the middle-income trap if we do not consider the chance of regressing to the lowincome range.
The results for Latin America show a trend similar to the Eastern European countries:
They exhibit a highly stable middle-income trap. However, while all Eastern European nations
have been successful in escaping the low-income trap in the long term, this is not true for
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Latin America, where some economies have been able to temporarily reach the relative highincome range but have not been able to maintain it.
The OECD countries show a clear tendency to move up the income ladder even if they
start at a relatively lower income level. In the long run, all OECD countries become highincome nations.
Our analysis shows that (i) the relative income trap is a useful concept and (ii) the stability
of low- and middle-income traps is region dependent. When we group all countries together,
the relative middle-income trap does not seem very stable. However, once we exclude the
OECD countries from the sample, the relative middle-income trap appears as stable as the
relative low-income trap, in the sense that middle-income countries are not very likely to reach
the relative high-income range and stay there but have a positive probability of moving down
to the relative low-income range. Similarly, low-income countries have a positive probability
of reaching the middle-income level, but they are not likely to reach the high-income range.
In either case, it is far more likely for a low-income country to remain in the low-income range
than to become a middle-income nation. Similarly, it is far more likely for a middle-income
country to remain in the middle-income range than to become a poor nation again (once
OECD countries are excluded from the sample).
Evidence from Latin America and Eastern Europe shows that a low-income country can
become a middle-income country, but the means are unclear. Why are a low-income Latin
American and an Eastern European country more likely than an African country to become
middle-income countries and remain there? Why have only the Asian Tigers been able to
defy the low- and middle-income traps by moving from low-income status all the way up to
high-income status and remain there?

Further Back in History
We go further back in history to attempt to reveal more answers, yet the picture is not
much different. Following the same methodology outlined previously, we use Maddison
Project data (Bolt and Van Luiden, 2013) to calculate the income transition matrixes once
more for the entire sample, though this time for relative income data between 1870 and 2010.
The results substantiate our previous conclusion (with OECD countries included): The relative low-income trap is persistent even in the long run, and even though the effects dissipate
over time, the probability of a country remaining in a relative middle-income trap is still substantial enough that it warrants a search for further explanations (Table 5). These results also
support our hypothesis that both relative low-income and middle-income traps exist because
the probability of transitioning from low-income to middle-income status is only 5 percent,
and the probability of moving from middle-income to high-income status is only 18 percent—
even in the very long run (140 years).
An important caveat to our findings is that the transition probability is based on statistical
evidence observed in cross-country data. Such evidence overlooks the underlying processes
that give rise to the income gaps and cross-country differences in such mechanisms. Hence,
a positive transition probability of moving from middle-income to high-income status does
not necessarily imply that each particular middle-income country will necessarily become a
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Table 5
Transition Matrixes: Entire Sample (1870-2010)
A: 10-Year transition matrix

B: 20-Year transition matrix

C: Start-to-end transition matrix

0 to 15%

15 to 50%

>50%

0 to 15%

15 to 50%

>50%

0 to 15%

15 to 50%

>50%

0 to 15%

0.94

0.06

0.00

0.92

0.08

0.00

0.93

0.05

0.02

15 to 50%

0.08

0.83

0.09

0.13

0.75

0.12

0.31

0.51

0.18

>50%

0.00

0.10

0.90

0.00

0.12

0.88

0.00

0.17

0.83

high-income country given a long enough time. In other words, even if the statistically measured transition probability is 90% or higher, it does not imply that a particular low- or middleincome country will surely become a high-income country in the long run. Hence, economic
(instead of statistical) explanations of the income traps are needed.

EXPLAINING INCOME TRAPS AND ECONOMIC DEVELOPMENT
Consensus explanations for the existence of traps or the lack of rapid convergence do
not exist. In this section, we first briefly review the theories that stand out, in our view, as the
most prominent. We then provide some case studies to shed light on the existing theories.

Existing Theories
The general theme underlying most existing theories is that technology drives long-run
growth (as Solow, 1956, points out), but there are barriers to technology spillovers and frictions in resource reallocation that prevent the adoption of new technology and innovation in
low- and middle-income countries. The question is: What are these barriers?
First, as Parente and Prescott (2002) explain, a developing country’s local monopoly
power may impede the adoption of new technology and international capital flows. Interest
groups in developing countries have little incentive to open their domestic markets and allow
competition from foreign firms with more advanced technologies. There is empirical evidence
to support this theory, but it does not explain why nations remain trapped at low- or middleincome levels even when they adopt policies to open domestic markets and enact radical
economic reforms that lift barriers to international capital flows. In fact, many nations have
encouraged the attraction of foreign direct investment (FDI) but have had little success; even
if they do attract FDI, they are still unsuccessful in climbing out of the income trap. For example, Mexico adopted financial liberalization in the 1970s, accumulating a large amount of debt.
But when the United States hiked interest rates in the early 1980s, Mexico suffered a debt crisis,
partly because of its lack of capital controls. As another example, Russia also adopted dramatic
economic and political reforms to lift capital controls starting in the early 1990s, but the result
was a collapsing economy, not a reviving one.
A second popular theory to explain the income traps is the institutional theory of North
(1982, 1991) and Acemoğlu and Robinson (2012). This theory proposes that poor nations
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fail to develop because of bad political institutions, such as a dictatorship. Under bad political
institutions, the elite class builds extractive economic institutions to expropriate profits from
the grassroots population. Hence, the rule of law and private property rights are not protected,
and the private sector has little incentive to accumulate wealth and adopt new technologies
to improve productivity. Notable examples of the institutional theory are the Eastern Europe
communist countries during the postwar period before their economic reform in the late
1980s and early 1990s, as well as today’s North Korea.
The institutional economists also apply this theory to explain why the Industrial Revolution took place first in late eighteenth-century England instead of in other parts of Europe.
They argue that England had the best (most inclusive) political institutions in the world, thanks
to the 1688 Glorious Revolution, which strengthened private property rights by restricting
the British monarch’s extractive power on the British economy.
However, the institutional theory’s explanation of the Industrial Revolution based on the
notion of better private property rights has been criticized by many prominent economic
historians, such as Allen (2009), McCloskey (2010), and Pomeranz (2000). They argue that
private property rights in many countries outside England, such as eighteenth-century China,
were just as secure as (or even more secure than) those in England, yet the Industrial Revolution did not happen there.
Furthermore, Wen (2015) points out that the institutional theory (i) lacks explanatory
power for the mechanism of China’s miracle growth over the past 35 years and (ii) is highly
inadequate in explaining other instances such as Russia’s dismal failure to grow after the shock
therapy economic reform in the1990s or South Korea’s rapid growth in the 1960s and 1970s
under a dictatorship. A similar case can be made for areas with identical political and economic institutions, such as the different counties within the American cities of St. Louis or
Chicago, or the different parts of northern and southern Italy, where there are sharply contrasting pockets of extreme poverty and extreme wealth and areas of violent crime and obedience to the rule of law. Instead, both regional economic inequality and the failures or success
stories of nations that have attempted industrialization could be explained by the specific
development strategies and industrial policies adopted, rather than by the political institutions
per se, as we point out later for Ireland and Mexico.
Within the neoclassical growth model framework, Lucas (2000) and Tamura (1996) claim
that by adding the different rates of technology diffusion, one can explain income variation
across countries. Hsieh and Klenow (2010) find that 50 to 70 percent of income differences
across countries can be accounted for by variations in resource misallocations, as measured
by differences in the dispersion of the marginal product of capital (MPK). Such resource misallocation reduces aggregate total factor productivity (TFP) and, hence, national income. So,
low TFP (characterized largely by a misallocation of resources such as capital) signals high
production inefficiencies. However, this theory is incomplete because a wide dispersion of
MPK across firms can itself be the result of economic development. As the economy evolves
from an agrarian society to an industrial society, the agricultural sector with nearly identical
backward technologies across farm households bifurcates into a traditional rural sector and a
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modern industrial sector. Although the industrial sector has a much higher MPK than the
rural sector, the overall economy is far more productive than the original backward society
before the bifurcation. That is, middle-income countries tend to have a wider income dispersion than poor countries while still having higher TFP levels. The dispersion will shrink only
after all sectors of the economy are fully industrialized.
Therefore, if barriers to technology spillovers exist, developing countries can still grow
while failing to converge to the living standards of the developed world. The fundamental
question remains: Why do these barriers exist such that advanced technologies are not rapidly
adopted by developing countries? There is no consensus answer. On one hand, the institutional theory is highly inadequate because even nations that adopted radical political and
economic reforms following the Washington consensus have remained stagnant for decades
(such as many Latin American countries after the 1980s). On the other hand, the endogenous
growth theory can hardly explain why poor nations choose not to accumulate human capital.
And the dispersion theory simply describes (or measures) the outcome of the barriers of technology spillovers. Furthermore, technology is not free and is embedded in fixed tangible capital; thus, fixed investment is necessary to adopt new technologies. But investment requires
savings, which are hard to accumulate when income levels are low and goods sales are limited
by anarchic markets.
The implication is that policies that help create markets, attract FDI, and promote domestic
saving and exports of manufactured goods are more likely to overcome the barriers of technology transfers. Based on this insight, Wen (2015) uses case studies based on China and the
history of the Industrial Revolution to argue for a new stage theory (NST) of economic development, suggesting that (i) institutions are endogenous and (ii) industrialization requires the
creation of a mass market to support mass production. Furthermore, the division of labor and
formation of economic organizations are limited by the extent of the market (as per Smith,
1776), which in turn is extremely costly to create and can be created only sequentially through
several key stages—at any of which countries can get stuck. In particular, Wen (2015) attributes both the low-income trap and the middle-income trap to government failures in market
creation at critical junctures of industrialization. For example, a country will be stuck in the
low-income trap when its market size is too small (or market transaction costs are too large)
to spur the formation of proto-industries beyond artisan workshops. And a country will be
stuck in the middle-income trap if its market size is not large enough (or market transaction
costs are not low enough) to support modern heavy industries or make capital-intensive heavy
industries profitable. An example that supports this theory is that of the Asian Tigers, which
were able to escape both the low-income and middle-income traps because of their governments’ immense help in continuous market creation to support profitable operations of laborintensive industries (in their early low-income development stage) and capital-intensive
industries (in their later middle-income development stages). The NST also argues that China’s
growth miracle since its economic reform in 1978 has been driven not by technological adoption per se, but by government-led continuous market creation through a series of industrial
policies.14
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Ireland and Mexico
We investigate further the issue of why some countries have failed to climb the income
ladder and others have succeeded by looking at the diverging cases of Ireland and Mexico.
Both countries maintained a roughly similar level of development in terms of per capita
income as far back as the early 1920s. However, each took dramatically different approaches
to development in the postwar era, leading to different outcomes, especially after the 1980s.
This occurred despite the adoption of political democracy by both nations: Mexico in 1810
and Ireland in 1921.
Ireland’s economy did not experience fast growth between the 1920s and the 1950s
because of anticolonial policies based on the since-discredited strategy of import substitution
industrialization.15 However, since the 1950s, Ireland has used its state capacity developed in
the previous period and adopted industrial policies to gradually open its borders to global
markets to encourage manufacturing exports and attract FDI instead of fully liberalizing its
capital markets all at once. Moreover, special government agencies were created to guide and
steer such foreign investment through preferential policies (subsidies) and proper regulations
to nurture its manufacturing sector. Ireland also increased government spending on infrastructure and public education for all and adopted new tax, fiscal, and monetary policies to
control high government deficits and inflation. In addition, it promoted domestic investment
and targeted its exports to Europe and the United States.16
On the other hand, Mexico had a far more open economy than Ireland between the 1920s
and 1970s but lacked sufficient government discipline to develop its state capacity to steer
the economy. Mexico’s exposure to international oil markets as an oil exporter, as well as the
rapid expansion of public debt in the 1970s, made its economy susceptible to more-liquid
short-term capital flows instead of longer-term foreign investment. Its large government debt
became very expensive after U.S. interest rates were increased drastically to curb inflation,
pushing the Mexican economy into default and prompting a large currency devaluation.
Moreover, Mexico did not invest highly in education, nor did it establish government agencies to design industrial policies to promote both foreign and domestic investment in areas
consistent with Mexico’s comparative advantages. Economic reform and nationalization of
the banking system in the early 1980s prompted investors to look for financing outside the
banking system, thereby changing the financial landscape and failing to stimulate industrial
growth that would invigorate the economy.17
Comparing the divergent growth paths of Mexico and Ireland in the twentieth century
suggests that state capacity and proper industrial policies are critical in explaining the issue,
rather than differences in political institutions or vast interests of local monopolies per se.
Contrary to what the Solow growth model suggests, technology is embedded in tangible capital, which is most likely to originate from the manufacturing sector instead of the agricultural
and natural resource sector or services sector. Hence, advanced technology flows only from
developed nations to developing nations through costly fixed investment in manufacturing.
Financial capital investors from developed countries are typically interested in short-term
capital gains (especially in real estate and natural resources), not necessarily in the foreign
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country’s long-term development. Such types of capital flows should be controlled or regulated—instead of encouraged or unchecked—by the governments of developing countries.
Thus, those countries that can find ways to grow their manufacturing sector through continuous market creation, investment, and exports are more capable of achieving technological
and income convergence to the technology frontier.

CONCLUSION
In this article, we examine relative low- and middle-income traps, which we define as situations in which income levels relative to the United States remain constantly low with no
clear sign of convergence. This perspective is important because even the poorest economies
continue to grow at some positive rate each year; but unless lower-income economies persistently grow at a rate faster than the developed economies, they will not be able to catch up.
We show that the relative low-income trap is more persistent over time than the relative
middle-income trap, though the stability of both traps is region-dependent. The cases of Latin
America and Eastern Europe are proof that low-income economies can successfully escape
the relative low-income trap. In particular, Latin American countries must have escaped the
poverty trap before the 1900s since most were at a middle-income range (relative to the United
States) at that point, but the means of achieving this level remain unknown.
To this effect, we point out challenges to the benchmark neoclassical growth theory, which
predicts convergence to the developed world over time: Even in the very long run, the relative
income traps and the issue of nonconvergence are prevalent. Furthermore, we discuss existing
theories with the potential to explain income traps. We note two things: (i) To adopt modern
efficient technologies available in developed nations, the developing nations must first create
the necessary market (including the supply chains and goods distribution networks) to render
such production technologies profitable. (ii) Technologies are embedded in capital, so large
and continuous capital investments are required to adopt frontier technologies from advanced
countries, and such investment requires large and continuous savings. Hence, creating a
modern mass market is extremely costly and time consuming and thus needs to be created
in steps. Therefore, industrial policies designed to help create domestic and international
markets for domestic firms and attract foreign direct investment while promoting domestic
investment, savings, and exports of manufactured goods are more likely to overcome the
barriers of technology adoptions and transfers. n

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NOTES
1

These data are from Table 2.8.2 of the World Bank’s October 2015 update of the World Development Indicators.
The absolute poverty line is defined as the international equivalent of the purchasing power parity of $2 (PPP$2).

2

In addition, the “iron law of convergence” suggests that poor countries can constantly reduce their income gap
with the frontier economies by half every 35 years (see, e.g., Barro, 2015).

3

Per capita income in 2014 was about $54,500 in the United States, $725 in Uganda, $650 in Afghanistan, $437 in
the Democratic Republic of the Congo, $380 in the Central African Republic, and $336 in Burundi, for example.

4

The term “middle-income trap” was first used by Gill and Kharas (2007) in reference to countries that have maintained a middle-income status for decades but have failed to reach a high-income status. This concept has become
increasingly relevant in the face of slower economic growth seen in the developing world.

5

We review the institutional theories of development traps in a later section.

6

Cited in Pintus and Wen (2010, p. 6).

7

We exclude countries with a population smaller than 1 million and those with fewer than 30 observations. We
exclude Middle Eastern countries from the analysis given that most countries in the sample are oil-rich countries
with specific idiosyncrasies about their relative income that are unique to the region.

8

Even though the United States was not the richest country during the 1870s, its income per capita was more than
75 percent that of Great Britain, so it was still a good representative of the developed world. Real GDP per capita
in the United States surpassed that of Great Britain in 1904.

9

Relative per capita income in 2011 was 18.9 percent in China and 8.4 percent in India.

10 As in other studies, the income group thresholds are arbitrary. Therefore, we performed a sensitivity analysis to

check the robustness of the results by changing the low-to-middle and middle-to-high thresholds and found that
our results did not change significantly.
11 A common criticism in the literature is that using long-term average growth is an inadequate approach to deter-

mine if an economy is caught in (or will be able to avoid) an income trap. However, our focus is on the changes, if
any, to another (higher or lower) income group in the long term.
12 Since we compute the transition matrixes using statistical procedures and past data, the observations reflect cases

of countries that have escaped the traps. However, this does not mean that the measure shown is the probability
for each country to escape the trap, as some countries may remain trapped forever.
13 China and Japan are included in the Asian Tigers group, explaining the 33 percent probability of transitioning

from the lower to the middle relative income group in Panel C of Table 4.
14 Although Wen’s (2015) NST connects both the low- and the middle-income traps to developmental stages and

reveals economic mechanisms behind the Industrial Revolution itself, theoretical models built on Wen’s NST are
still lacking. Models proposed to explain the Industrial Revolution are abundant, such as those of Desmet and
Parente (2012), Hansen and Prescott (2002), Stokey (2001), and Yang and Zhu (2013), among others. However,
such neoclassical growth models of the Industrial Revolution still fall short in differentiating and explaining the
low- and middle-income traps, despite claiming to explain the Industrial Revolution based on the assumption of
exogenous technological changes in the agricultural and industrial sectors.
15 Import substitution industrialization (ISI) is a trade and economic policy that advocates replacing foreign imports

with domestic production, especially in manufactured goods. ISI has been advocated since the eighteenth century
by economists such as Friedrich List and Alexander Hamilton. ISI policies became popular after World War II among
socialist countries and Latin American nations with the intention of producing development and self-sufficiency
through the creation of an internal market. ISI works by having the state lead economic development through
nationalization, subsidization of vital industries (mostly heavy industries), increased taxation, and highly protectionist trade policies. ISI was gradually abandoned by developing countries in the 1980s and 1990s because of its
failure to promote persistent growth and the insistence of the International Monetary Fund and World Bank on
their structural adjustment programs of market-driven liberalization. For more details, see
https://en.wikipedia.org/wiki/Import_substitution_industrialization.
16 For a report on Ireland’s development process, see Dorgan (2006).
17 See Hernández-Murillo (2007).

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Aging and Wealth Inequality
in a Neoclassical Growth Model
Guillaume Vandenbroucke

In this article, the author uses a version of the neoclassical growth model with overlapping generations
of individuals to investigate the effect of aging on wealth inequality. When an economy’s population
becomes older—that is, when the proportion of individuals 65 years of age and older increases—
two effects are at work: a direct effect from the changing age composition of the population and an
indirect, equilibrium effect from the change in asset holdings by owner’s age. The main result is that
wealth inequality in an aging population may decrease or increase depending on the cause of the aging.
An increase in life expectancy tends to increase inequality, whereas a reduction in the population
growth rate tends to reduce it. (JEL E1, E2, J1)
Federal Reserve Bank of St. Louis Review, First Quarter 2016, 98(1), pp. 61-80.

1 BACKGROUND FACTS
A fraction of wealth inequality is attributable to the age composition of a population
because older individuals have had more time to accumulate wealth than younger individuals.
Figure 1 illustrates this for selected years using U.S. data from the Survey of Consumer
Finances. Young households start with little wealth and accumulate more until they reach
65 to 74 years of age. After that point, they deplete their wealth. There are large (i.e., between
fivefold and tenfold) differences in wealth between the old and the young. A question then
arises: What effect would a change in the age composition of a population have on wealth
distribution?

1.1 Aging Around the World
There are substantial demographic differences across countries, as well as demographic
transformations within particular countries over time, that motivate studying the effect of
demography on economic variables. Figure 2 illustrates this point: It shows the proportion of
the population 65 years and older in a selected sample of countries since 1960. In the United
States, for example, less than 10 percent of the population was 65 or older in 1960. In 2014,
Guillaume Vandenbroucke is a research officer and economist at the Federal Reserve Bank of St. Louis.
© 2016, Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the views of
the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced, published,
distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses, and
other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.

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Figure 1
Mean Net Worth by Age of Head of Household
Thousands of 2013 Dollars
1,200

2001
2007
2009

1,000

800

600

400

200

0

<35

35-44

45-54

55-64

65-74

75+

Age of Household Head (years)

NOTE: The figure shows the net worth by age composition within the U.S. population for the years 2001, 2007, and 2009.
SOURCE: Survey of Consumer Finances, 2013 Chartbook.

however, this proportion was almost 15 percent. This is what it means for a population to
become older.
Figure 2 reveals that populations in developed countries—such as the United States,
Japan, France, and Germany—are noticeably older than those in developing countries such
as China or India. In 2014, the proportion of people 65 and older in the latter group of countries was below 10 percent, while in the former group it was 15 percent or higher. Figure 2 also
reveals that all populations in the sample became older, albeit at different paces, since 1960.
Of particular interest is the Japanese population, the oldest population in the sample (in 2014).
Japan experienced the fastest aging process: In 1960, its share of people 65 and older was less
than that of the United States, but in 2014 Japan’s share exceeded that of the United States.
India, the youngest population in the sample, is also remarkable. Even though its share of
people 65 and older increased from less than 5 percent in 1960 to 5 percent in 2014, this
increase was small relative to that of the older economies in the sample.

1.2 Measuring Wealth Inequality
The question in this article can then be phrased as follows: “How does wealth inequality
change when the proportion of older people changes?” How does one measure inequality,
though? In this article, I use a Gini index. A simple example can help to illustrate how this
approach works. Imagine a world populated by young and old people. Suppose there are as
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Figure 2
Fraction of Population 65 Years of Age or Older














 
 
 
 
 
 

 
 
 
 
 
 

 
     
  
  
  
   



   





















 

 











NOTE: The figure shows the proportion of the population 65 years and older in a selected sample of countries since 1960.
SOURCE: FRED®, Federal Reserve Economic Data, Federal Reserve Bank of St. Louis;
https://research.stlouisfed.org/fred2/graph/?g=2pxM.

many young people as old people; the proportion of young (and old) is, therefore, 50 percent.
Suppose now that young people hold 50 percent of the total wealth and that older people hold
the remaining 50 percent. This world features no inequality: The proportion of the total wealth
held by any group of individuals is the same as the proportion this group represents in the
total population. Panel A of Figure 3 illustrates this scenario. The horizontal axis measures
the cumulative proportions of the population, and the vertical axis measures the cumulative
proportions of wealth. The distribution of wealth in the economy is represented by the straight
line overlapping the 45-degree line.
Suppose, now, that the young still represent 50 percent of the population but hold only
1/3 of the total wealth (Panel B of Figure 3). The shaded area in this panel—that is, the difference between the actual distribution and the 45-degree line (which represents perfect equality
of asset holdings)—is a measure of wealth inequality. Consider a third case: The young still
hold 1/3 of the total wealth (as in Panel B) but they now represent 2/3 of the total population
(Panel C). Again, the measure of inequality has changed relative to Panels A and B.
The curves represented in Figure 3 are so-called Lorenz curves. The Gini coefficient is
calculated as the ratio between the shaded area and the total area under the 45-degree line.
Thus, in Panel A the Gini coefficient is 0, illustrating no inequality. In panel B the Gini coefficient is 0.16. In Panel C it is 0.33.
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Figure 3
Measurement of Wealth Inequality
A.

B.
1
Cumulative Proportion of Wealth

Cumulative Proportion of Wealth

1

1/2

0

1/2
1
Cumulative Proportion of Population

1/3

0

1/2
1
Cumulative Proportion of Population

C.

Cumulative Proportion of Wealth

1

1/3

0

2/3
1
Cumulative Proportion of Population

NOTE: In this example, there is no inequality in Panel A. The shaded area in Panels B and C is a measure of inequality.

1.3 This Article
It is important to note that in the data, not all variations in wealth are explained by age.
Díaz-Giménez, Glover, and Ríos-Rull (2011) discuss measures of wealth inequality and show
substantial inequality both within age groups and across age groups. Thus, here I do not attempt
to explain overall wealth inequality. Instead, my goal is to discuss a few fundamental mechanisms that relate wealth inequality to demographic changes. In this spirit, I use a deterministic
version of the optimal growth model. The model is augmented with a simple demographic
structure of overlapping generations, which permits a sensible discussion of demographic
changes. I use this model even though it is known that, in its simple version, it does not yield
accurate quantitative predictions for the distribution of wealth. This model, however, is the
workhorse of macroeconomics and the forces at work in its simpler version are likely to be at
work in more sophisticated versions as well. Thus, the question asked here can be qualified
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as follows: “How would a change in a population’s age composition affect the distribution
of wealth, holding constant all other factors that may also affect the wealth distribution?” A
related paper by Chatterjee (1994) also uses a version of the optimal growth model to discuss
wealth inequality. His focus, however, is on the transitional dynamics of inequality and
abstracts from demographic considerations.
How does the optimal growth model help to analyze the effect of demographic changes
on the distribution of wealth? Suppose, for instance, that a world as in Panel C of Figure 3
exists, where the young represent 2/3 of the total population and hold 1/3 of the total wealth.
To assess the effect of an aging population, one could compare Panel C with Panel B, since the
only difference between them is the proportion of young people, which decreases from 2/3 in
Panel C to 1/3 in Panel B. This approach amounts to using the observed relation between age
and asset holdings and combining it with different age compositions of the population to
measure the effect of the age composition on wealth inequality. There seems to be no need
for a model. This approach may be misleading, however. Young people may no longer hold
1/3 of the total wealth when their proportion in the population changes. One key reason for
this is that, as the proportions of the young and the old change, aggregate savings changes as
well. The interest rate may increase or decrease, implying different saving behaviors. One
needs, therefore, a theory of saving decisions and of the interest rate to reliably analyze the
effects of demographic changes. The optimal growth model provides this theory. This point
is akin to the well-known Lucas critique (see Lucas, 1976).

2 THE MODEL
2.1 Demography
The economy is populated by generations of individuals living for J periods, indexed by
j = 1,…,J. The size of the age-j population at time t is denoted by ptj. The laws of motion for ptj
are
(1)

pt1 = npt1−1

(2)

ptj = ptj−−11 for j = 2 ,… , J .

Equation (1) describes the population growth: Each age-1 individual at time t “gives birth”
to n children, who become age-1 individuals in the next period. Children are economically
inactive and birth is not a choice. Equation (2) describes aging: Each individual becomes one
year older every year. Thus, the population of individuals of age j–1 at time t–1 is of age j at
time t. Let Pt denote the total population at date t:
J

(3)

Pt =

∑p .
j
t

j =1

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2.2 Technology and Profit Maximization
Aggregate output, Yt , is produced by a representative firm operating a constant returns
to scale aggregate technology:
Yt = Ktθ ( zt N t )

1−θ

,

where q ∈ (0,1), zt is labor-augmenting productivity, Kt is the aggregate stock of capital, and
Nt is labor demand. Productivity grows at the constant (gross) rate g : zt+1/zt = g. Capital depreciates at rate d ∈ (0,1). Note that the assumption of constant returns to scale implies that the
number of firms does not matter. That is, the production side of the economy would be strictly
identical if there were many small identical firms operating the same constant returns to scale
technology.
The objective of the firm is to maximize profit:
max K tθ ( zt N t )

1−θ

(4)

Kt ,N t

− wt N t − ( rt + δ ) Kt ,

where wt is the wage rate and rt is the interest rate prevailing between periods t–1 and t.

2.3 Preferences and Individual Optimization
The preferences of an age-1 individual at date t are represented by
J

(5)

∑β
j =1

j −1

(c )
j
t + j −1

1−σ

1−σ

, σ > 0,

j
where b ∈ (0,1) is the subjective discount factor and c t+j–1
is consumption at age j (date t+j–1).
The individual does not value leisure. Thus, labor supply is inelastic and equals 1 each period
when the individual works. There is an exogenously given retirement age, R. That is, from
j
age R to J, the labor supply is zero. Let a t+j–1
denote the assets owned by the individual at the
beginning of age j (date t+j–1). At age 1 the individual is endowed with zero assets. That is,
at1 = 0. The period budget constraint at age j is then

(6)

(

)

ctj+ j −1 + atj++1j = wt + j −1I ( j < R ) + 1 + rt + j −1 atj+ j −1 ,

where I(j < R) is an indicator function that takes the value 1 whenever j < R and 0 otherwise.
The left-hand side of this constraint indicates the expenditures of an age-j individual: consumption and savings. The right-hand side indicates the individual’s sources of revenue:
labor if he is not retired and revenue from past savings.

2.4 Equilibrium
An equilibrium is a sequence of wages and interest rates, {wt ,rt }, together with sequences
of capital stock and labor demand for the firm, {Kt ,Nt }, and sequences of consumption and
j+1
}, such that the following conditions are satisfied:
savings for individuals, {c tj ,a t+1
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(i) Profit maximization: The sequences {Kt ,Nt } solve the optimization problem of the
firm at each date t (equation (4)), given the sequence of wages and interest rates,
{wt ,rt }.
j+1
(ii) Utility maximization: The sequences {c tj ,a t+1
} solve the optimization problem of
age-1 individuals at each date t; that is, the sequences maximize utility (5) subject to
the sequence of budget constraints (6), given the sequence of wages and interest
rates, {wt ,rt }.

(iii) Market clearing:
(a) The labor market clears at each date t. That is, the labor demand by the firm,
R −1

Nt , equals the labor supply by working individuals:
clearing condition is

∑ p . So, the labor market
j
t

j =1

R −1

Nt =

(7)

∑p .
j
t

j =1

(b) The market for savings clears at each date t. That is, the supply of funds by
J

individuals,

∑p a

j j +1 ,
t t +1

equals the demand for capital for the following period,

j =1

Kt+1. So, the savings market clearing condition is
J

Kt +1 =

(8)

∑p a

j j +1
t t +1 .

j =1

Note that, since age-J individuals do not save, this equation can also be written
J −1

as K t +1 =

∑p a

j j +1
t t +1 ,

and since it must hold at any date t, it must hold at t–1:

j =1

J −1

Kt =

∑p

j
j +1
t −1 at . Finally, using equation (2) and the assumption that individuals

j =1

are born without assets, a1t = 0, the savings market clearing condition also reads
J

Kt =

(9)

∑p a ,
j j
t t

j =1

which means that the aggregate stock of capital is held by individuals at the
beginning of period t.
(c) The market for goods clears at each date t. The demand for goods (that is, the
J

sum of consumption and investment,

∑p c

j j
t t

+ Kt +1 − (1 − δ ) Kt , equals the

j =1

supply, Yt . So, the goods market clearing condition is
J

(10)

∑p c

j j
t t

+ Kt +1 = Yt + (1 − δ ) Kt .

j =1

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2.5 Balanced Growth
The analysis of this economy focuses on its “balanced growth path” —that is, an equilibrium where variables grow at constant (possibly zero) rates. The appendix shows the derivation of the equations characterizing the balanced growth path.
Along the balanced growth path the aggregate stock of capital, Kt , and aggregate output,
Yt , grow at the (gross) rate gn. The interest rate, rt , is constant and the wage rate, wt , grows at
the (gross) rate g. This implies that an individual’s labor income grows at rate g over his lifetime. Finally, population, Pt , grows at the (gross) rate n.
For future reference, it is useful to note one result derived in the appendix: The share of
age-j individuals in the total population is constant over time and denoted by p j ≡ ptj/Pt , where

πj =

(11)
and x (n, J ) ≡

1
,
n x ( n, J )
j −1

J

∑1 n

j −1

. To understand equation (11), consider the case where n = 1. The

j =1

equation implies that the population distribution is uniform and that p j = 1/J. That is, the
proportion of individuals of all ages is the same. This is because age-1 individuals are “born”
at the same rate at which age-J individuals “die.” When n increases above 1, age-1 individuals
are born at a faster rate than the rate at which age-J individuals die. This implies that the
proportion of young individuals increases and that that of old individuals decreases. This is
most transparent when J = 2 since, in this case, p 1 = n/(1+n), which is increasing in n, and
p 2 = 1/(1+n), which is decreasing in n.

3 QUANTITATIVE ANALYSIS
3.1 Calibration
Let age 1 in the model correspond to age 18 in the data, and let Jbench = 63. That is, people
live until the equivalent of 80 years of age. Let the retirement age be Rbench = 48 (that is, 65 years
old in the data). Let p 65+(n,J) denote the proportion of individuals age 65 and older:
J

π 65+ (n, J ) = ∑ π j .
j = 48

The benchmark population growth rate, nbench , is set at 1.015 so that p 65+(nbench ,Jbench) =
0.17, which is the proportion of the population age 65 and older in the population of individuals age 18 and older in the U.S. data in 2010. In fact, the U.S. population age 18 and older
grew from 209.13 to 234.56 million individuals between 2000 and 2010. This represents an
average growth rate of 1.1 percent per year versus 1.5 percent in the model.
The capital share of output q is set at a standard value of q = 1/3. The growth rate of laboraugmenting technological progress, g, is set so that the economy’s balanced growth path
features 2 percent growth in per capita quantities per year. Hence, g = 1.02. The investment-to68

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Table 1
Calibration of the Benchmark Economy
Parameters
Demography

nbench = 1.105, Jbench = 63, Rbench = 48

Preferences

s = 1.0, b = 0.97

Technology

q = 1/3, g = 1.02, d = 0.04

Figure 4
Profile of Assets and Population Distribution by Age and Lorenz Curve: Calibrated Economy
A. Assets by Age

B. Population by Age

Assets
14

Percent of Total Population
2.6
2.4

12

2.2
10

2.0

8

1.8

6

1.6
1.4

4

1.2
2

1.0

0
10

0.8
10

20

30

40

50
Age

60

70

80

20

30

40

50
Age

60

70

80

C. Lorenz Curve
Cumulative Proportion of Assets
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

0.2

0.4

0.6

0.8

1.0

Cumulative Proportion of Population
NOTE: The figure shows the balanced growth path distributions of assets and population by age (Panels A and B), as well as the Lorenz curve for
assets (Panel C) in the calibrated economy.

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capital ratio is gn + d –1. Following Cooley and Prescott (1995), I set the rate of depreciation
d so that the investment-to-capital ratio equals 7.6 percent; this yields d = 0.04. The period
utility index is logarithmic: s = 1. Finally, I set b = 0.97 so that the capital-to-output ratio is
3.3. The equilibrium interest rate implied by this calibration is r = 5 percent per year. This
figure compares with a 4 percent rate of return on U.S. Treasury inflation-protected securities
of various maturities (see McGrattan and Prescott, 2001).
Table 1 presents the list of calibrated parameters. Figure 4 shows the profile of assets by
age (Panel A), the population distribution by age (Panel B), and the Lorenz curve (Panel C)
in the balanced growth path of the calibrated economy. Individuals exhibit a typical behavior
for this class of models: They accumulate assets until they retire. Then they live off their savings and deplete their assets. This explains the inverted-V pattern of the asset profile. Note
that the asset profile implied by the model matches the qualitative pattern exhibited by the
empirical profiles in Figure 1. The calibrated economy features a Gini coefficient of 0.45 for
the distribution of assets.

3.2 Changes in the Age Composition of the Population
The effect of a change in the age composition of the population depends on the cause of
this change. In the context of the model developed here, there are two exogenous variables
driving the age composition: the population growth rate, n, and life expectancy, J. This transpires in equation (11).
3.2.1 The Effect of Population Growth. I consider different values for the population
growth rate, n, holding life expectancy, J, constant. For each value of n, I compute a balanced
growth path. I choose the values of n to exemplify a specific point—namely, that wealth
inequality is not monotonic in the age composition of the population.
Panel A of Figure 5 shows the Gini coefficient plotted against the share of individuals age
65 and older implied by the different values of n. The main message is that, as the proportion
of individuals age 65 and older increases because of a decreased population growth rate, wealth
inequality measured by the Gini coefficient decreases, reaches a minimum, and then increases.
In particular, Panel A of Figure 5 shows that wealth inequality is the same when the share of
individuals age 65 and older is 17 percent or 60 percent.
Table 2 reports statistics from the model’s balanced growth path for three values of n:
(nbench ,n1,n2) = (1.015,0.984,0.952). Start with the benchmark economy and contemplate what
happens when n is lowered from 1.015 to 0.984. The share of individuals age 65 and older
increases from 17 percent to 37 percent. Panel B of Figure 5 shows this by comparing the distribution of the nbench economy (black circles) with that of the n1 economy (red squares). The
lower proportion of young individuals relative to the nbench economy implies a higher stock
of capital per worker. There are two reasons for this. First, there is a direct effect: There are
fewer workers since the demography changed. Second, there is an equilibrium effect: There
is more capital in the economy to finance the consumption of the larger number of retirees.
Such a higher stock of capital per worker explains the decrease in the interest rate from 5.0
percent to 4.0 percent. At this rate future consumption is more expensive, so individuals
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Figure 5
Effect of a Change in Population Growth Rate
A. Gini

B. Proportion of Total Population
0.06

0.50
n = 1.0156

n = 0.94764

0.45

0.05

0.40

0.04

0.35
0.03
0.30
0.02

0.25

0.01

0.20
Calibrated Model
0.1

0.2

0.3
0.4
Proportion of 65+

0.5

0
10

0.6

C. Assets

20

30

40

50
Age

60

70

80

n = 1.015, Gini = 0.45
n = 0.981, Gini = 0.18
n = 0.947, Gini = 0.45

14
12
10
8
6
4
2
0
−2
−4
10

20

30

40

50
Age

60

70

80

NOTE: Panel A plots the Gini coefficient in the steady state as a function of the proportion of individuals age 65 and older. Panel B plots the population distribution by age in three selected balanced growth paths. Panel C plots the asset profiles by age in the same three steady states.

Table 2
Comparative Statistics Across Balanced Growth Paths: Selected n
Population
growth rate, n

Proportion
of 65+, p 65+

Capital
per worker, k

Interest rate, r

Gini
coefficient

nbench = 1.015

0.17

5.52

0.050

0.45

n1 = 0.981

0.37

6.45

0.041

0.18

n2 = 0.947

0.60

7.76

0.031

0.45

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accumulate fewer assets over their lifetimes. Panel C of Figure 5 shows that the asset profile
of the nbench economy is above that of the n1 economy.1
There are, therefore, two factors affecting the change in wealth inequality between the
nbench economy and the n1 economy: a change in the distribution of assets by age and a change
in the age composition of the population. In Figure 3, the former is represented, albeit in a
simplified way, by the change from Panel A to Panel B; I refer to this as the “economic effect.”
The latter is represented by the change from Panel B to Panel C; I refer to this as the “demographic effect.” I follow a procedure used by Greenwood and Seshadri (2002) and Greenwood
and Vandenbroucke (2008) to assess the contribution of these two factors. Define the Gini
coefficient as a function G(a, p), where a and p represent vectors of assets and the population
J
J
and p ≡ (p j )j=1
. The change in the Gini coefficient from
share by age, respectively: a ≡ (a j )j=1
G(a, p) to G(a¢, p ¢) satisfies
G ( a',π ' ) − G ( a,π ) = G ( a ′ ,π ′ ) − G ( a,π ′ )  + G ( a,π ′ ) − G ( a,π ) 
 

X1

X2

= G ( a ′ ,π ′ ) − G ( a ′ ,π )  + G ( a ′ ,π ) − G ( a,π )  .
 

X3

X4

Note that the terms X1 and X4 measure the effect of a change in a, holding p constant:
the economic effect. The difference between X1 and X4 is the value at which p is held: the
final value, p ¢, for X1 and the initial value, p, for X4. Similarly, the terms X2 and X3 measure
the contribution of a change in p , holding a constant at either its initial or final value: the
demographic effect. Summing the two rows of this system and dividing by 2 yields
G ( a',π ' ) − G ( a,π ) = G ( a ′ ,π ′ )  − G ( a,π ′ ) + G ( a ′ ,π ) − G ( a,π ) 2



Effect of a

G ( a ′ ,π ′ )  − G ( a ′ ,π ) + G ( a,π ′ ) − G ( a,π ) 2




Effect of π

where the economic effect, for example, is the average of the effects of a change in a holding
p constant at its initial and final values.
Table 3 shows the results of this decomposition as n changes from nbench to n1 and then
from n1 to n2. Consider the change from nbench to n1 first. The Gini coefficient decreases by 26
percentage points. Table 3 shows that the economic effect tends to raise the Gini coefficient
by 14 percentage points, while the demographic effect lowers it by 40 percentage points. The
net effect equals the total effect by construction. Why does the economic effect, the change in
the asset profile by age, contribute to more inequality? This occurs because the reduction in
asset holdings is not uniform across age groups as the interest rate decreases. Figure 6 shows
that, from one balanced growth path to the next, individuals with the most asset holdings
reduce their holdings relatively less than others. The 20-year-olds, for instance, reduce their
asset holdings by 250 percent between the nbench economy and the n1 economy, while the 60year-olds reduce theirs by less than 50 percent. Thus, given an age distribution for the population, a reduction in the interest rate results in an increased concentration of wealth, which
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Table 3
Decomposition of the Change in the Gini Coefficient with
Population Growth Rate Changes
nbench
Gini

n1

0.45

n2

0.21

0.45

Total effect

–0.26

+0.26

Effect of a

+0.14

+0.73

Effect of p

–0.40

–0.47

Figure 6
Change in Assets by Age from the nbench to the n1 Economy
Percent Change in Assets
0
−20
−40
−60
−80
−100
−120
−140
−160
10

20

30

40

50

60

70

80

Age
NOTE: From one balanced growth path to the next, individuals close to retirement age reduce their holdings relatively
less than others.

contributes to more inequality. On the other hand, the change in the age composition of the
population reduces inequality because it reduces the proportion of individuals with the least
asset holdings: the young. When comparing the nbench economy with the n1 economy, this
latter effect dominates.
Now contemplate a further reduction in n, from n1 to n2. Why does inequality increase?
Table 3 reveals that, in contrast to the previous difference between nbench and n1, the dominating effect here is the economic effect. To be precise, the economic effect increases the Gini
coefficient by 73 percentage points, while the demographic effect lowers it by 47 percentage
points.
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Figure 7
Effects of a Change in Life Expectancy
A. Gini

B. Assets
16

0.47
0.46
0.45

14

J = 83

12

0.44
0.43

J = 53, Gini = 0.37
J = 63, Gini = 0.45
J = 83, Gini = 0.46

10
8

0.42
0.41
0.40

6
4
2

0.39
0.38

0

0.37
0.05

J = 53
0.10

Calibrated Model
0.15
0.20
Proportion of 65+

0.25

0.30

−2
0

20

40

60

80

100

60

80

100

Age

C. Gini

D. Assets

0.54

16

J = 83

J = 53, Gini = 0.40
J = 63, Gini = 0.45
J = 83, Gini = 0.53

14

0.52

12

0.50

10

0.48

8
0.46

6

0.44
0.42

4
2

J = 53

0.40
0.05

Calibrated Model
0.10

0.15
0.20
0.25
Proportion of 65+

0
0.30

0

20

40
Age

NOTE: Panels A and B report the results of an experiment where life expectancy, J, changes while the age of retirement, R, remains constant at
the calibrated value, R = 48. All other parameters are also held constant at their calibrated values. Panels C and D report the results of an experiment where J and R change in the same proportion so that the fraction of life spent in retirement remains the same at the value implied in the
calibrated economy, 24 percent. All other parameters are held constant at their calibrated values.

3.2.2 The Effect of Life Expectancy. I consider different values for life expectancy, J, holding the population growth rate constant. I use values ranging from 53 to 83—that is, from 10
years below the calibrated economy to 20 years above. As in the previous exercise, I compute
a balanced growth path for each value of J.
For this exercise I distinguish two cases. First, I keep the age of retirement constant at its
calibrated value, R = 45, as J changes. This implies that the fraction of one’s life spent in retirement changes as J changes. When J = 53, for instance, one spends 9 percent (1 – 48/53 = 0.09)
of one’s life in retirement. When J = 63, as in the calibrated economy, this fraction is 24 percent. When J = 83, this fraction is 42 percent. Panels A and B of Figure 7 report these results.
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Table 4
Decomposition of the Change in the Gini Coefficient with Life Expectancy Changes
R constant
J = 53
Gini

0.37

J = Jbench

R varying
J = 83

J = 53
0.40

J = Jbench

J = 83

0.45

0.46

0.45

0.53

Total effect

+0.08

+0.01

+0.05

+0.09

Effect of a

+0.22

+0.22

+0.20

+0.29

Effect of p

–0.15

–0.21

–0.15

–0.20

In a second experiment I consider values of R that change as J changes, such that the fraction
of life spent in retirement remains constant at the value implied in the calibrated economy,
24 percent. Panels C and D of Figure 7 report these results. It is worth noting that the age composition of the population is the same regardless of whether R is held constant. It is uniquely
determined by n, which remains at its calibrated value, and by J.
The message from Figure 7 is that wealth inequality increases as a population grows older
because its life expectancy increases. Decomposing the change in the Gini coefficient between
the economic effect and the demographic effect, as in the previous exercise, reveals that the
economic effect tends to increase wealth inequality, while the demographic effect tends to
reduce it (Table 4). This is true regardless of whether the retirement age is held constant.
Remember that the economic effect is the effect on the Gini coefficient of a change in the asset
profile by age, holding the age composition constant. It increases inequality because R-old
individuals accumulate more wealth when they expect to live longer. Since R is the age at which
asset holdings are at their maximum in the first place, an increase in life expectancy results in
a concentration of wealth among the richest and thus yields a higher Gini coefficient. The
demographic effect measures the effect on the Gini coefficient of a change in the age composition of the population, holding the asset profile by age constant. Since older people tend to
be less numerous and tend to hold more wealth than younger people, an increase in the proportion of older people tends to reduce the Gini coefficient. Table 4 shows that the demographic effect tends to be small relative to the economic effect when life expectancy increases.
The results in Figure 7 contrast with those in Figure 5. To see this more precisely, consider
an increase in the proportion of individuals age 65 and older from 17 percent (the calibrated
economy) to 25 percent. Panel A of Figure 5 shows that if this increase results from a reduction
in the population growth rate, the result is a decrease in wealthy inequality: The Gini coefficient decreases from 0.45 to about 0.32. Panels A and C of Figure 7 show that if this increase
in the proportion of individuals age 65 and older results from an increase in life expectancy,
inequality increases: The Gini coefficient rises from 0.45 to almost 0.47 (Panel A of Figure 7)
or more than 0.5 (Panel B of Figure 7).
Two points are worth mentioning at this stage. First, one reason for the different results
(as emphasized above) between the two experiments stems from a stronger economic effect
in the increased life expectancy experiment than in the lower population growth experiment.
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Why is that? The main difference is that when life expectancy increases, young individuals
reduce their asset holdings so they can hold more when they reach retirement (see Panels B
and D of Figure 7). In contrast, when the population growth rate decreases, individuals of all
ages reduce their asset holdings (see Panel C of Figure 5). These differences in asset profiles
explain the stronger concentration of wealth after an increase in life expectancy.
Second, the different results between the two experiments emphasized above do not
hold everywhere. Panel A of Figure 5 shows that there are economies in which inequality
can increase as the economy’s population becomes older following a change in n. Similarly,
Panel A of Figure 7 shows that there are economies in which inequality decreases as the age
of the population increases following a change in J. Thus, the takeaway lesson from these
numerical examples is of a qualitative nature: Assessing the effect of aging on wealth inequality
depends critically on the cause of aging.
3.2.3 Optimal Retirement Age. As the previous discussion suggests, the retirement age
is an important determinant of the wealth distribution since it is at this age that wealth concentrates. In this section, I consider a version of the model in which the retirement age is optimally chosen. The key questions are these: Does the age of retirement change significantly as
the population becomes older? And if yes, then how does this change affect wealth inequality?
Here I modify the model presented earlier (see Section 2) slightly to endogenize retirement. Specifically, I let preferences be represented by
J

(12)

∑β
j =1

j −1

(c )
j
t + j −1

1−σ

1−σ

+ α ln ( J − R ) ,σ ,α > 0.

The novelty in this formulation is the introduction of a taste for the time spent in retirement:
a ln(J – R). When a = 0, which corresponds to the original model, an individual would not
retire if given the choice since working causes no disutility and retirement entails a loss of
income. When a > 0, however, the individual needs to choose his retirement age to balance
the cost associated with the loss of income against the utility benefit of a longer retirement.
I calibrate the balanced growth path of this alternative model in the same way described
in Section 3.1 with the addition that a must be given a value. I choose a so that the optimal
retirement age is R = 48, as in the calibrated model. This implies a = 3.5. All other parameters
remain the same as before.
In this alternative model, a change in n, the population growth rate, has very little effect
on the results discussed previously since the retirement age changes little.2 Changes in life
expectancy have more noticeable effects on the retirement age. When J = 53, the optimal retirement age is R = 41, while when J = 83, it is R = 62. This implies that the fraction of life spent in
retirement varies from 22 percent (when J = 53) to 25 percent (when J = 83). Thus, the results
of this experiment with endogenous retirement are very similar to the results in Panels C and
D of Figure 7, where the fraction of life spent in retirement was kept constant at 24 percent.

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CONCLUSION
In this article, I use a simple version of the optimal growth model to assess the effect of
demographic changes on wealth inequality. Two forces affect inequality when a population
becomes older: First, a demographic effect tends to reduce inequality. As the population grows
older, there are relatively fewer young individuals who typically own less wealth. This tends to
reduce the Gini coefficient of wealth. A second effect, the economic effect, acts in the opposite
direction. As the share of the older population increases, wealth tends to concentrate among
those close to retirement. This tends to increase the Gini coefficient on wealth.
I conducted two experiments using a version of the model calibrated to the U.S. economy.
When aging increases relative to current U.S. demography, wealth inequality may decrease
or increase depending on the causes of aging. When life expectancy increases, the economic
effect dominates and inequality tends to increase. In contrast, when the population growth
rate decreases, the demographic effect dominates and inequality tends to decrease.
The model used here is a simple version of the optimal growth model. An interesting
extension is to augment it with a realistic description of progressive taxation and a social
security scheme. I leave this for future research. n

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APPENDIX: THE STATIONARY ECONOMY
Demography
1
1
Equation (1) implies pt1 = n j–1pt–j+1
, and equation (2) implies ptj = pt–j+1
. It follows that the
total population, Pt , is proportional to the age-1 population:

Pt
=
pt1

J

∑
j =1

ptj
=
pt1

J

∑n
j =1

pt1− j +1

J

j −1 1
pt − j +1

=

∑n

1
j −1

.

j =1

Hence, population grows at the (gross) rate n: Pt+1/Pt = n. Define x (n, J ) ≡

J

∑1 / n

j −1

.

j =1

The share of age-j individuals in the total population, p j = ptj /Pt , is constant over time and
given by

πj =

1
.
n x ( n, J )
j −1

Technology and Profit Maximization. The output-to-capital ratio is constant along the
balanced growth path—that is, Yt /Kt = (zt Nt /Kt)1–q is constant. This implies that Kt grows at
the same rate as the efficiency units of labor employed, zt Nt . In equilibrium, labor demand
grows at the population growth rate, n. It follows that aggregate output and the aggregate stock
of capital grow at rate gn along the balanced growth path. Prices are given by marginal products; therefore,
θ

 K 
wt = (1 − θ ) zt  t  ,
 zt N t 
 K 
rt + δ = θ  t 
 zt N t 

θ −1

.

Thus, the interest rate, r, is constant and the wage rate, wt , grows at rate g. Define ŵ =
wt /zt , k = Kt /(zt Nt ), and y = Yt /(zt Nt ) = kq. Then,
ŵ = (1 − θ ) kθ ,
r + δ = θ kθ −1 .
Note that the objective of the firm, expressed in transformed variables, is to maximize
profit per efficiency units of labor:
max kθ − ( r + δ ) k − ŵ .
k

Also note that the first-order conditions associated with this problem are the same as the one
just derived.
Preferences and Individual Optimization. Since individual variables grow at rate g,
define ĉ j ≡ ctj/zt and â j ≡ atj/zt. The utility function then reads
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J

∑β

j −1

(c )
j
t + j −1

1−σ

∑β

=

1−σ

j =1

J

(ĉ z )
j

j −1

1−σ

j =1
J

∑β

=

( ĉ g
j

j −1

j −1

zt

)

1−σ

,

1−σ

j =1

J

which is equivalent to preferences represented by

1−σ

t + j −1

∑

(ĉ )

j 1−σ

β j −1

1−σ

j =1

, where b˜ ≡ b g1–s. Dividing

the period budget constraint (equation (6)) by zt+j–1 yields
ĉ j + gâ j +1 = ŵ I ( j < R ) + (1 + r ) â j .
Thus, the transformed individual’s optimization problem is

( )

1−σ

ĉ j
β j −1
1−σ
j =1
J

max

∑

s.t .

ĉ j + gâ j +1 = ŵ I ( j < R ) + (1 + r ) â j .

The first-order conditions associated with this problem imply the following Euler equation:

(c )

j −σ

=

β
(1 + r ) c j +1
g

( )

−σ

,

which equates the marginal cost of saving at age j (left-hand side) to its marginal benefit (righthand side).

Equilibrium
Dividing the market clearing condition for savings (equation (9)) by zt Nt yields
J

∑

k=

j =1

πj

∑

R −1
j =1

πj

â j .

Dividing the market clearing condition for goods (equation (9)) by zt Nt yields
J

∑
j =1

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πj

∑

R −1
j =1

π

j

ĉ j + gnk = y + (1 − δ ) k.

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NOTES
1

Since there are more older individuals, the fact that individuals save less at each age is not inconsistent with the
fact that there is more capital in the economy.

2

Details are available upon request.

REFERENCES
Chatterjee, Satyajit. “Transitional Dynamics and the Distribution of Wealth in a Neoclassical Growth Model.”
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Frontiers of Business Cycle Research. Chap. 1. Princeton, NJ: Princeton University Press, 1995, pp. 1-38.
Díaz-Giménez, Javier; Glover, Andy and Ríos-Rull, José-Víctor. “Facts on the Distributions of Earnings, Income, and
Wealth in the United States: 2007 Update.” Federal Reserve Bank of Minneapolis Quarterly Review, February 2011,
34(1), pp. 2-31.
Greenwood, Jeremy and Seshadri, Ananth. “The U.S. Demographic Transition.” American Economic Review, May 2002,
92(2), pp. 153-59.
Greenwood, Jeremy and Vandenbroucke, Guillaume. “Hours Worked (Long-Run Trends),” in Lawrence E. Blume
and Steven N. Durlauf, eds., The New Palgrave Dictionary of Economics. Second Edition. London: Palgrave
Macmillan, 2008, pp. 75-81; doi:10.1057/9780230226203.0748.
Lucas, Robert E. “Econometric Policy Evaluation: A Critique.” Carnegie-Rochester Conference Series on Public Policy,
1976, 1(1), pp. 19-46.
McGrattan, Ellen R. and Prescott, Edward C. “Is the Stock Market Overvalued?” NBER Working Paper No. 8077,
National Bureau of Economic Research, January 2001; http://www.nber.org/papers/w8077.pdf.

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