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What’s Driving Wage
Inequality?
Aaron Steelman and John A. Weinberg

M

ost of the time, we assess an economy’s performance using broad
aggregate measures of output and wealth. In this regard, the United
States is doing quite well. It is the richest country in the world.
U.S. gross domestic product exceeded $11 trillion last year—roughly $38,000
per capita. And despite the slowdown associated with the 2001 recession, the
economy has expanded at an average annual rate of more than 3 percent
over the past 10 years. The way people actually feel about the economy’s
performance is shaped by their individual experiences, however, and here there
is always great diversity. Indeed, there remains substantial anxiety about the
direction the economy is heading, especially in regard to the growing disparity
in income. The gap in real wage rates between those at the higher end of the
distribution and those at the lower end has been widening for some time.
In addition, the real wages of workers at the lowest part of the distribution
were stagnant or falling during much of this extended period of growing wage
inequality.
This essay will explain why wage inequality has been increasing in the
United States; in doing so, we will draw upon the scholarly literature, including
work done by Richmond Fed economist Andreas Hornstein with Per Krusell
of Princeton University and Giovanni Violante of New York University. We
also will discuss the associated policy implications—that is, what can be done
to better assure that all Americans have the opportunity to secure well-paying
jobs, as well as which policies may hinder that goal.
Overall, we will argue that technical innovation has significantly affected
the wage distribution in the United States. But the direction of that effect has
This article first appeared in the Bank’s 2004 Annual Report. The authors are, respectively,
editor of the Bank’s quarterly magazine, Region Focus, and Senior Vice President and Director
of Research. Tom Humphrey, Andreas Hornstein, Ned Prescott, and John Walter provided
valuable comments. The views expressed are the authors’ and not necessarily those of the
Federal Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 91/3 Summer 2005

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Federal Reserve Bank of Richmond Economic Quarterly

not been uniform. In the early part of the twentieth century, various technical
innovations had the effect of compressing the wage structure. Since the 1970s,
however, technical innovation—particularly the introduction and widespread
use of information technology—has produced wage dispersion.
Another force to which many have attributed recent labor market developments is globalization. We conclude that international trade and immigration,
while significant trends, are not by themselves the primary force behind growing wage inequality. To some extent, globalization is itself a result of advances
in information technology, which allow the production of goods and services
to take place over a broader geographic area.
As for public policy, research suggests that increased emphasis on education is a sound response to recent trends in wage inequality, particularly
education early in life and programs focusing on general, broadly applicable
skills. Early skill acquisition yields rewards over a relatively long period
of time because individuals can recoup their investment in human capital
throughout their working lives. In addition, such training tends to build on
itself: acquiring skills early in life makes it easier to acquire additional skills
later in life. In contrast, policies that would aim to slow the growth in wage
inequality by imposing barriers to globalization, such as trade restrictions,
would likely do little to achieve their intended goal, while lowering aggregate
income and overall social welfare.
Before discussing why wage inequality has been growing and the steps
policymakers may wish to consider in response, it is necessary to look at the
facts. In the next section, we present data on wage inequality from the early
twentieth century to the present.

1. THE FACTS
Most economists agree that wage inequality has been increasing in the United
States recently.1 But this has not always been so. Wage inequality was large
during the first part of the twentieth century, decreased during the middle part
of the century, and accelerated again toward the end of the century.
During the early part of the twentieth century, several factors contributed to
a decline in the demand for less-skilled workers. For instance, the widespread
introduction of electricity and new hoisting equipment in the 1910s greatly
reduced the need for common laborers who moved goods to and within factories.2 The lower demand for these workers’ services put downward pressure
on their wages. At the same time, the rise of large businesses increased the
demand for the relatively small subset of workers with higher education to fill
1 For an exception, see Lerman (1997).
2 Goldin and Katz (1999, 9).

A. Steelman and J.A. Weinberg: What’s Driving Wage Inequality?

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managerial roles, thus driving up their wages. As a result, wage inequality
grew during the first quarter of the twentieth century.
By the 1940s, wage structures began to change significantly, however, so
much in fact that Claudia Goldin and Robert Margo have called this period
“The Great Compression,” describing the general decline in wage inequality.3
On the supply side, the once small number of college graduates began to face
increased competition, as thousands of American military personnel came
back from World War II and took advantage of the GI Bill. This influx of
newly minted graduates most likely helped depress the relative earnings of
college-educated workers. In addition, the quality of education at the high
school level became less variable during this period, meaning that the skill
differentials between high school graduates in different parts of the country
probably decreased, thus reducing the disparity in wage rates among this group
of workers.
On the demand side, more low-skilled labor was needed in the nation’s
industrial centers to produce goods for the war effort, therefore driving up the
relative wages of these workers. In addition, government intervention through
the National War Labor Board almost certainly contributed to the compression
of the wage structure.4
It is interesting to note that there is also evidence of wage compression
in the United Kingdom during the Industrial Revolution of the eighteenth and
nineteenth centuries. Goods that were once produced by artisans in relatively
small numbers over relatively long periods of time were produced in factories following industrialization.5 This meant that more-skilled workers were
replaced by less-skilled workers, who because of the introduction of interchangeable parts and other production techniques could perform their tasks
efficiently with little training. The demand for low-skilled workers, then, increased during this period, demonstrating that not all technological innovations
are necessarily “skill-biased.” Some, in fact, have been “skill-replacing.”
That brings us to the last half of the twentieth century. In particular, we
will focus on the period from 1970 onward. As stated earlier, this has been a
period of growing wage inequality. Consider the following observations.6
3 Goldin and Margo (1992).
4 The National War Labor Board was created in 1942 in an effort to stabilize wages during

World War II. According to two authors who worked at the agency, “no changes in wage rates
could be made except upon approval of the National War Labor Board; and ... the Board could
approve wage increases only on four narrowly circumscribed grounds, and wage decreases on only
two grounds.” See Henig and Unterberger (1945, 319–20).
5 For more on the introduction of new technology in England during the Industrial Revolution,
see Mokyr (1994).
6 These observations are taken from Hornstein, Krusell, and Violante (2004), which surveys
empirical work up to 1995. Recently, Eckstein and Nagyp´ l (2004) and Autor, Katz, and Kearney
a
(2004) have updated some of these observations. Instances in which the more recent observations
differ from the older observations are noted in the text.

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Federal Reserve Bank of Richmond Economic Quarterly
• The 90-10 weekly wage ratio, which compares the wages of workers
at the 90th and 10th percentiles of the wage distribution, rose from
1.20 to 1.55 for males and from 1.05 to 1.40 for females from 1965 to
1995. Similar growth in inequality was found elsewhere in the wage
distribution, though dispersion in the lower wage groups (for instance,
the 50-10 ratio) seems to have stabilized recently.
• Average and median real wages have changed little since the mid-1970s.
But real wages in the bottom 10 percent of the wage distribution fell
sharply during much of this period before experiencing modest growth
recently. Meanwhile, the real wages of those at the top of the distribution, especially the top 1 percent, have risen sharply.
• The returns gained from education fell in the 1970s, but have increased
since. The college wage premium—defined as the ratio between the
average weekly wage of a college graduate and a worker with a high
school diploma or less—was 1.35 in 1975, 1.5 in 1985, and 1.7 in 1995.
• The returns from experience also grew in the 1970s and the 1980s but
flattened in the 1990s. For instance, the ratio of weekly wages between
workers with 25 years of experience and workers with five years of
experience increased from 1.3 in 1970 to 1.5 in 1995.
• The returns from white-collar occupations relative to blue-collar occupations increased by about 20 percent from 1970 to 1995.
• Inequality across race and gender has declined since 1970. The blackwhite differential and the male-female differential have both dropped.
Also, labor force participation of women increased dramatically during
this period.

The last three points all involve “between-group” comparisons—that is,
comparisons of workers classified by observable characteristics, such as education, experience, occupation, race, and gender. But it is also true that wage
inequality “within groups”—that is, among workers with similar education or
experience, for instance—has risen. This trend seems to have started about a
decade prior to the trend of increasing returns from college education.7 Looking abroad, recent trends in wage inequality in the United Kingdom tend to
resemble those in the United States. Things in continental Europe are quite
different, though. There has been almost no increase in wage inequality there.
Indeed, wage inequality has even declined in Belgium, Germany, and Norway.
7 Juhn, Murphy, and Pierce (1993, 412).

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2. THE ARGUMENT
What is driving the increasing disparity in wages in the United States? The
evidence strongly suggests that there has been skill-biased technical change
that has benefited the more-skilled workers over the past 30 years. By skillbiased change, we mean advancements in technology that have boosted the
productivity of skilled labor relative to that of unskilled labor.
To determine why this is the case, it is important to understand that the
relative wages of workers at different skill levels are determined by the relative
supply of and demand for those types of workers; that supply is determined by
the relative number of more-skilled and less-skilled workers; and that demand
for those workers’labor is determined by the current state of technology, which
in turn largely determines the productivity of different types of labor.
At first, this explanation may appear to fit awkwardly with the facts. After
all, the relative supply of more-skilled workers, measured as a fraction of
the workers with a college education, has risen sharply during this period.
Wouldn’t this increased supply tend to depress wages, as seemed to happen at
mid-century? Standard theory would suggest yes: with a given demand, more
supply of a good would tend to drive down its relative price. And for a while
this seems to have been the case with skilled labor. During the 1970s, the
number of college graduates rose sharply and effectively flooded the market,
driving down the returns gained from education. But by the 1980s, moreskilled workers were able to command a wage premium.
What accounts for the change? In large measure, the development of new
technology. In particular, information technology, which began to make its
way into the workplace in the 1970s but did not become widespread until
the 1980s, the same time as the returns from skill began to increase. What
is it about information or computer technology that increases the demand
for skilled workers? According to David Autor, Frank Levy, and Richard
Murnane, two mechanisms—substitution and complementarity—are at work:
Computer technology substitutes for workers in performing routine tasks
that can be readily described with programmed rules, while complementing
workers in executing nonroutine tasks demanding flexibility, creativity,
generalized problem-solving capabilities, and complex communications.
As the price of computer capital fell precipitously in recent decades, these
two mechanisms—substitution and complementarity—have raised relative
demand for workers who hold a comparative advantage in nonroutine
tasks, typically college-educated workers.8

Autor, Levy, and Murnane conclude that information technology can explain between 60 and 90 percent of the estimated increase in relative demand
8 Autor, Levy, and Murnane (2003, 1322).

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for college-educated workers from 1970 to 1998. So while the relative supply of more-skilled workers certainly increased during this period—which,
all else being equal, would have tended to depress the relative wages of such
workers—the demand for such labor increased even more because of technical
change.
Consider a few examples that may help to illustrate their point. Advances
in manufacturing, such as the introduction of computer-controlled machinery,
have often meant fewer workers on the factory floor with those remaining
needing a higher level of skill to operate the increasingly sophisticated equipment. A similar process is at work in the division of labor between architects
and draftsmen. Before the advent of computer-aided design—or “CAD”—a
draftsman would create and revise plans under the guidance of an architect.
With CAD, however, the architect can easily generate and manipulate plans on
the computer, resulting in the employment of fewer draftsmen, while boosting
the productivity of the overall design process.
Some economists have suggested that the increasing supply of skilled
workers may have actually induced the development and implementation
of new technologies that require higher levels of skills. In short, as Daron
Acemoglu has argued, “When developing skill-biased techniques is more profitable, new technology will tend to be skill-biased.”9 Conversely, when developing skill-replacing techniques is more profitable, new technology will tend
to be skill-replacing. This, arguably, is what happened in England during the
Industrial Revolution. The migration of large numbers of less-skilled workers
to the English cities from rural areas and Ireland made the implementation of
skill-replacing technologies profitable. “So, it may be precisely the differential changes in the relative supply of skilled and unskilled workers that explain
both the presence of skill-replacing technical change in the nineteenth century
and skill-biased technical change during the twentieth century.”10
Thus, overall, the best explanation for the increase in wage inequality
appears to be skill-biased technical change. But there are some potential
challenges to this theory.

3. THE CHALLENGERS
Not all economists are persuaded that increasing returns from skill were the
principal driver of wage inequality during the 1970s. Some have offered competing explanations, many of which are centered around institutional change.11
One explanation, for example, is the erosion of the real value of the minimum
wage and the decline in unionization in the United States. Other theories focus
9 Acemoglu (2002, 9).
10 Ibid., p. 12. Also, see Acemoglu (1998).
11 See, for instance, Card and DiNardo (2002).

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on globalization—specifically, increased trade with less-developed countries
(LDCs) and immigration of less-skilled workers to the United States. Finally,
some point to evidence from other countries. If skill-biased technical change
is causing growing wage inequality in the United States, they ask, why isn’t
wage inequality also growing rapidly in Western Europe since all developed
countries have access to basically the same technology? We will address those
issues in turn.
The nominal value of the minimum wage remained constant throughout
much of the 1980s, meaning that as prices rose its real value dropped. Because
the minimum wage may be expected to raise the wages of low-paid workers, the
decline in its real value could be responsible for increased wage inequality.12
There are three problems with this hypothesis, though. First, the number of
U.S. workers—especially male workers—affected by the minimum wage is
quite small, less than 10 percent of all workers between the ages of 18 and 65.
Second, the erosion in the real value of the minimum wage occurred in the
1980s, while the general trend of rising wage inequality began in the 1970s.
One would expect the two to coincide more closely if the decline in the real
value of the minimum wage were indeed a significant factor. Third, a large
share of the increase in wage inequality is due to rapid gains by workers at
the top of the wage distribution. For these people, the minimum wage is not
a binding constraint.
Timing is also a problem in theories that focus on declining unionization.13
The 1950s, as we have discussed, was a time of wage compression, not growing
wage inequality. Yet it was during this decade that unionization began its
steady decline. To be sure, the decline of unionization in the private sector
picked up pace during the 1970s and 1980s. But at the same time, the public
sector workforce became increasingly unionized, compensating for some of
the loss in the private sector. In addition, wage inequality has increased quite
rapidly in some sectors of the economy that were never highly unionized, such
as the legal and medical professions.
There is, however, some evidence that technical change may have been
partially responsible for the decline in unionization since the 1950s.14 Such
a decline could have caused the real wages of low-skilled workers to fall (a
point that we will return to in the next section), but its effect on increasing
wage inequality would have been only indirect, with technical change starting
the whole process.
Popular opinion often attributes increased trade with LDCs as the principal
cause of increasing wage inequality in the United States—an explanation that
12 Lee (1999) argues that this has, in fact, occurred.
13 For a recent paper that argues that there is a significant relationship between unionization

and wage inequality, see Card, Lemieux, and Riddell (2003).
14 See Acemoglu, Aghion, and Violante (2001).

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some economists have argued is consistent with the data. Indeed, standard
trade theory, based on the principle of comparative advantage, would seem
to predict just that. Since LDCs have relatively large numbers of unskilled
workers, an increase in trade would act like an increase in the relative supply
of unskilled workers in the United States, thus potentially increasing wage
inequality. And trade between the United States and the developing world
has indeed increased substantially during the past 30 years, the period during
which wage inequality has been increasing.
The relative price of skill-intensive goods has not increased over the period
of rising inequality, however, as one would have expected if trade were a
significant factor in wage dispersion. Perhaps more telling, the total volume
of trade with LDCs is arguably too small to have had a significant effect on
U.S. wages. The effects of trade flows on “relative skill supplies have not been
substantial enough to account for more than a small proportion of the overall
widening of the wage structure over the past 15 years and have played only a
modest role in the expansion of the college-high school wage differential in
the United States,” conclude George Borjas, Richard Freeman, and Lawrence
Katz.15
As for immigration, the total number of newcomers to the United States
during the period under review also is probably too small to have had a large
effect on the wage structure. For instance, during the 1970s, immigration
added 2 million new workers to the U.S. labor force. But because of the baby
boom and the increased participation of women in the workplace, roughly 20
million new native workers also entered the labor force during that period. In
addition, even during the 1980s, a period of relatively high immigration, the
immigrant share of the total labor supply increased by only 1 percentage point,
from 7 to 8 percent. “These magnitudes can be taken to mean that immigration
is unlikely to have large effects on the overall distribution of wages,” concludes
Robert Topel.16
Finally, some have argued that if technical change is a significant cause of
wage inequality, then it ought to have affected the wage structure in Western
Europe in the same way that it has in the United States since those countries
have access to much the same technology and arguably employ it in similar
ways to American firms. But, as we know, wage inequality has not increased
as rapidly in Western Europe as it has in the United States. Does this cause
significant problems for the skill-biased technical change explanation of wage
inequality? Some have suggested so. We think otherwise, however. The
observations from Western Europe can be explained by factors that do not
contradict the skill-biased technical change argument.
15 Borjas, Freeman, and Katz (1997, 67).
16 Topel (1997, 62).

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As many commentators have noted, Western Europe has significantly less
flexible labor market policies than the United States, including more comprehensive employment protection, longer and more generous unemployment
benefits, and greater restrictions on wage bargaining. Those policies likely
have had the effect of compressing wages. Thus, while similar technical
change may have been introduced at roughly the same time in the United
States and Europe, different labor market policies have resulted in different
effects on the respective wage structures.17
In addition, Europe’s labor market policies combined with rapid technological change arguably have led to greater unemployment. In the 1960s, the
United States and Europe had roughly the same unemployment rates. Since
then, Europe’s labor market policies have not changed substantially—those
policies have been restrictive for many decades—but its unemployment rate
has risen sharply. Why?
Strict employment-protection laws make it difficult for companies to terminate workers in Europe. But over time some workers will leave voluntarily,
perhaps encouraged by generous social-welfare benefits. Those workers’skills
become dated quickly as technology changes, just as they do for unemployed
workers in the United States. But the principal difference is that the strict European employment-protection laws that made those same workers difficult
to terminate in the first place also have the effect of keeping them out of the
workforce longer than they would have been otherwise. Employers, knowing
that all new hires are possibly lifelong employees, will look very carefully for
a good match. Those workers whose skills are not up-to-date will have difficulty finding new employment. And the longer they are out of work, the more
difficulty they will have, because multiple generations of technology will have
been introduced and replaced during their absence from the workforce. Also,
the generous welfare benefits those workers receive reduce their incentives to
acquire new skills on their own.
In the United States, where it is easier to terminate workers, employers
do not have to be as careful when hiring new employees. The cost of taking a
chance on a worker whose skills may be somewhat dated is potentially much
smaller than in Europe. As a result, the U.S. unemployment rate has not risen
steadily over the past 30 years, as it has in most European states.18

4. THE PROBLEMS
We have argued that the most compelling single explanation for the rise of wage
inequality in the United States since the 1970s has been skill-biased technical
change. In addition, we have argued that other proposed explanations—such
17 See Krugman (1994).
18 For a complementary explanation, see Ljungqvist and Sargent (1998).

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as institutional change and globalization—do not appear very persuasive. Yet
there remain two unresolved issues.
First, as we previously noted, the growth of wage inequality within groups,
sometimes referred to as “residual inequality,” is quite large and may not be
adequately explained by skill-biased technical change alone. Second, and also
mentioned earlier, real wages for those at the lowest end of the distribution
declined during much of the last 30 years. Yet, as Acemoglu has argued,
it is unclear how “sustained technological change can be associated with an
extended period of falling wages of low-skill workers.”19 How can these
developments be explained?
Perhaps the most compelling explanation for the increase in residual inequality is that there are unmeasured differences in the skills among workers
within groups. Consider, for example, two economists that have nearly identical profiles: both are 50-year-old, white males; hold graduate degrees from
similar institutions; and have worked as university professors for 20 years. To
an outside observer, it is impossible to distinguish between the two workers.
But to their colleagues and students, there may be very substantial differences.
One economist simply may have more natural talent than the other, producing
innovative research across a number of fields. Or he may be a more gifted
teacher who inspires students in the classroom. In either case, he is a more
valuable worker than his counterpart and consequently may receive a higher
wage. We should not be surprised by such a wage differential, but according
to our measures of worker characteristics, both economists fall into the same
group—thus leading to an increase in residual inequality. Skill-biased technical change increases the premium paid to skilled workers, even if skills are
not well-measured by such characteristics as education or experience.
Also, rising residual wage inequality may be possible even without unmeasured skill differences. One possible explanation of this phenomenon
involves the role of vintage capital. Close examination of the data suggests
that the pace of technological advancement has been accelerating since the
mid-1970s. Yet different firms have adopted new technologies at different
times and at different levels; that is, firms employ technologies of different
vintages. This has important implications for the wage structure. In a model
that includes labor market frictions—meaning that the labor market is not fully
competitive because, for instance, it is costly to switch jobs—workers with the
same skills can be expected to earn different wages. More specifically, their
wages will increase as the productivity of the technology with which they are
working increases. As a result, it is plausible that technological acceleration
may increase wage dispersion within groups, since with more rapid technical
change you have more vintages of technology in operation simultaneously.
19 Acemoglu (2002, 13).

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But what about the drop in real wages of less-skilled workers? In a
world of relatively slow technical change, many skills are easily transferable.
Workers can move from one company to another with little trouble adapting
to the machinery at their new firm. In a world of rapid and accelerating
technological change, however, such moves are more difficult since fewer
skills are transferable. Upon separation—that is, when workers leave a firm—
those workers can expect to suffer wage losses. This scenario is especially
true of workers who have been using the oldest technology, because they find
that the skills they have acquired through experience are even more outdated
than those of workers in similar industries who have been exposed to more
modern technology. Thus, accelerating technological change may help us
explain both the rise in residual inequality and the decline in real wages at the
bottom of the distribution.20
It is important to note, though, that such conclusions are only tentative.
Whereas there seems to be overwhelming evidence and an emerging consensus
about the role of skill-biased technical change on the wage structure, there
remains a good deal of uncertainty about the cause(s) of residual inequality
and the declining real wages of less-skilled workers.

5.

IMPLICATIONS FOR PUBLIC POLICY

What lessons should policymakers draw from our discussion of the causes of
wage inequality in the United States? We might start with a general principle
that is often associated with the medical profession but is applicable to public
policy as well: first, do no harm. There is understandably a great deal of
anxiety among the public about the changing nature of the American economy.
Those forces which create economic growth for us all, also cause disruptions
for some.21 As Joseph Schumpeter famously noted, capitalism is characterized
by “the perennial gale of creative destruction.”22 And to many people, that
gale—at least for the moment—is associated with globalization.
Yet, as we have argued, increased trade with LDCs and immigration from
abroad likely have had little effect on wage inequality, while almost certainly
adding to the strength and vitality of the American economy.23 Efforts to slow
the growth of foreign goods or labor coming to our shores would be costly
to Americans as a whole, as well as to those people who seem to be hurt by
globalization at the present. As Jeffrey Sachs and Howard Shatz have written,
20 This section draws on Violante (2002).
21 Fears about the effect of technical change on the job market—in particular, the belief that

technical innovation is a net destroyer of jobs—is not new. David Ricardo and other classical
economists addressed the issue. See Humphrey (2004).
22 Schumpeter (1942).
23 See Burtless, Lawrence, Litan, and Shapiro (1998) for a discussion of the benefits of open
trade. See Simon (1999) for a discussion of the benefits of liberal immigration policies.

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“U.S. labor market experience . . . teaches that the labor force will respond to
the premium on education by increasing the investment in education, thereby
narrowing the gap in inequality in the future.”24 Insofar as barriers aimed
to slow globalization dampen the incentive to build skills, those barriers will
tend to perpetuate wage inequality.
In addition, we should be wary of proposals to extend the duration of or
expand the generosity of unemployment insurance benefits to those workers
who have lost their jobs due to technical change. Such proposals would tend
to increase the time that displaced workers remain unemployed. Instead, we
ought to encourage those workers to reenter the labor force as quickly as
possible. The problem, of course, is that the jobs that such workers will be
able to secure will likely pay significantly less than their former positions.
“Workers not only lose income when they are unemployed, but many often
suffer a drop in their earnings after finding new jobs. Older workers—who
tend to be less flexible adapting to new production techniques or who lack the
educational background to transfer to well-paid service economy jobs—bear
the greatest losses,” write Lori Kletzer and Robert Litan.25
An alternative way to assist displaced workers may be a simple transfer
program that subsidizes their wages upon reemployment.26 This policy would
boost recipients’ incomes, while allowing them to allocate their financial resources toward the mix of training opportunities and general consumption they
deem most beneficial. Such a program would certainly have problems of its
own, and policymakers would need to implement it in a way that would minimize distortions to labor market conditions as much as possible. As we noted
earlier, in the case of Europe, government involvement in the labor market
often can have undesirable effects.
Perhaps an even more promising option would be to increase public investment in skill acquisition. As we have argued, the principal factor driving
wage inequality is skill-biased technical change. Thus, the most direct and
arguably most effective way to reduce such inequality would be to reduce the
disparity in skills between workers.
What type of skills should we attempt to provide through public investment? The evidence seems increasingly clear that there is a relatively high
level of return on investments in education early in life. As Pedro Carneiro
and James Heckman write, “Skill and ability beget future skill and ability.”27
24 Sachs and Shatz (1996, 239).
25 Kletzer and Litan (2001, 2).
26 Kletzer and Litan outline such a proposal that would work as follows: Once displaced

workers found new jobs, they would receive a subsidy to increase their current lower wage to a
level more closely approximating their former higher wage. The wage subsidy would be available
for only a limited period of time following reemployment and there would be an annual cap on
payments. Ibid., p. 4.
27 Carneiro and Heckman (2003).

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Also, we might expect those investments to yield larger benefits if they are
directed toward broadly generalizable skills. The ability to think critically,
for instance, is crucial to analyzing and adapting to a number of situations. In
contrast, the return on educational investments later in life, especially remedial or compensatory investments, tend to be smaller. This is true for at least
two reasons. First, without a basic level of knowledge on which to build, it
will be difficult for individuals to effectively acquire new skills. Second, by
definition, older workers have less time to recoup the investment in education
than younger workers.
While this may make perfect sense analytically, it still may be difficult
to accept. Such reasoning implies that the people hurting the most now—
those who have been displaced from their jobs—may also have the most trouble building their skills. What should we do to help those people? A good
argument could be made that the government should act as a clearinghouse of
information about job training programs, though we should be cautious about
expanding such training programs given their limited success.28 Similarly, we
should be skeptical about providing greater financial assistance to displaced
workers seeking education at community colleges and four-year institutions.
There is already a wide array of educational subsidies in place, which have
substantially reduced potential credit constraints for low- and middle-income
people.29
Still, increased investment in skill acquisition is a policy option worth
significant consideration. If done properly, it may be an effective tool in
reducing wage inequality and could yield additional benefits to the economy,
such as increasing workers’ productivity.

6.

CONCLUSION

Wage inequality in the United States is large and has been growing during the
past 30 years. The main cause, it appears, is skill-biased technical change.
Those workers with high skill levels have experienced more rapid wage growth
than less-skilled workers, some of whom have seen an actual decline in their
real wages.
This development is cause for concern to many people who fear that a
large share of the workforce no longer has a reasonable chance of achieving
its goals, monetary and otherwise. Such concern is understandable. Indeed,
the evidence suggests that, at present, less-skilled workers face formidable
challenges in the labor market. As a society, we ought to consider investing
more funds in skill development—especially early skill development—to ensure that as many people as possible have the basic tools necessary to succeed.
28 See Kletzer (1998, 131–33).
29 See Carneiro and Heckman (2002).

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Federal Reserve Bank of Richmond Economic Quarterly

But we also need to remember that technical change is not necessarily
skill-biased. There have been significant episodes where technical innovation
appears to have been skill-replacing. From today’s vantage point, it seems
unlikely that we will return to such a world, but developments may lead us
in that direction. Market economies, though highly efficient, often move in
surprising and unpredictable directions.
Perhaps most important, we ought to focus not just on the distributional
effects of technical change—important as they may be—but also on aggregate
well-being. Technical change has fueled much of the economic growth of the
past two centuries and raised living standards to levels once unimaginable.
J. Bradford DeLong has calculated that Real GDP per worker grew from
roughly $13,700 in 1890 to about $65,000 in 2000. That’s nearly a fivefold increase. And as DeLong has noted, that significantly understates our
improvement in living standards. In 1890, people “could not buy modern
entertainment or communications or transportation technologies.” There were
“no modern appliances, no modern buildings, no antibiotics, no air travel.
An income of $13,700 today that must be spent exclusively on commodities
already in use in the late nineteenth century is, for all of us, worth a lot less
than $13,700.”30
It’s useful to consider the alternative to embracing technology. By 1400,
China had invented many of the technologies that triggered the Industrial
Revolution of the eighteenth century, such as moveable-type printing, the
water-powered spinning machine, and the blast furnace. Tight state controls
impeded the spread of those technologies, however, preventing them from
being used to their full potential and inhibiting further innovation.31 We are
not suggesting that others are seriously proposing blocking the development
and distribution of new technologies in the United States as China did centuries
ago. But we do think it is important to understand how powerful a force
technology can be for human well-being—and how counterproductive it can
be to curtail its growth.
Despite the pain that technological change can cause workers in certain
segments of the labor force, we should remember that, on net, technical change
is good for the economy and good for people. We should not discourage or
lament it.

30 DeLong (2000, 14–15).
31 See Landes (1998), especially pp. 51–59.

A. Steelman and J.A. Weinberg: What’s Driving Wage Inequality?

15

REFERENCES
Acemoglu, Daron. 1998. “Why Do New Technologies Complement Skills?
Directed Technical Change and Wage Inequality.” Quarterly Journal of
Economics 113 (November): 1055–89.
. 2002. “Technical Change, Inequality, and the Labor
Market.” Journal of Economic Literature 40 (March): 7–72.
, Philippe Aghion, and Giovanni L. Violante. 2001.
“Deunionization, Technical Change, and Inequality.”
Carnegie-Rochester Conference Series on Public Policy 55 (December):
229–64.
Autor, David H., Lawrence F. Katz, and Melissa S. Kearney. 2004. “Trends
in U.S. Wage Inequality: Re-Assessing the Revisionists.” Manuscript,
MIT Department of Economics (August).
Autor, David H., Lawrence F. Katz, and Alan B. Krueger. 1998. “Computing
Inequality: Have Computers Changed the Labor Market?” Quarterly
Journal of Economics 113 (November): 1169–213.
Autor, David H., Frank Levy, and Richard J. Murnane. 2003. “The Skill
Content of Recent Technological Change: An Empirical Exploration.”
Quarterly Journal of Economics 118 (November): 1279–333.
Borjas, George J., Richard B. Freeman, and Lawrence F. Katz. 1997. “How
Much Do Immigration and Trade Affect Labor Market Outcomes?”
Brookings Papers on Economic Activity (No. 1): 1–67.
Burtless, Gary T., Robert Z. Lawrence, Robert E. Litan, and Robert J.
Shapiro. 1998. Globaphobia: Confronting Fears about Open Trade.
Washington, D.C.: Brookings Institution Press.
Card, David, and John E. DiNardo. 2002. “Skill-Biased Technological
Change and Rising Wage Inequality: Some Problems and Puzzles.”
NBER Working Paper No. 8769 (February).
Card, David, Thomas Lemieux, and W. Craig Riddell. 2003. “Unionization
and Wage Inequality: A Comparative Study of the U.S., the U.K., and
Canada.” NBER Working Paper No. 9473 (January).
Carneiro, Pedro, and James J. Heckman. 2002. “The Evidence on Credit
Constraints in Post-Secondary Schooling.” NBER Working Paper No.
9055 (July).
. 2003. “Human Capital Policy.” NBER Working Paper No.
9495 (February).

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Federal Reserve Bank of Richmond Economic Quarterly

DeLong, J. Bradford. 2000. “Cornucopia: The Pace of Economic Growth in
the Twentieth Century.” NBER Working Paper No. 7602 (March).
´
Eckstein, Zvi, and Eva Nagyp´ l. 2004. “The Evolution of U.S. Earnings
a
Inequality: 1961–2002.” Federal Reserve Bank of Minneapolis
Quarterly Review 28 (December): 10–29.
Goldin, Claudia, and Lawrence F. Katz. 1999. “The Returns to Skill in the
United States across the Twentieth Century.” NBER Working Paper No.
7126 (May).
Goldin, Claudia, and Robert A. Margo. 1992. “The Great Compression: The
Wage Structure in the United States at Mid-Century.” Quarterly Journal
of Economics 107 (February): 1–34.
Henig, Harry, and S. Herbert Unterberger. 1945. “Wage Control in Wartime
and Transition.” American Economic Review 35 (June): 319–36.
Hornstein, Andreas, Per Krusell, and Giovanni L. Violante. 2004. “The
Effects of Technical Change on Labor Market Inequalities.” Federal
Reserve Bank of Richmond Working Paper No. 04-08 (December).
Also: Forthcoming in Handbook of Economic Growth, ed. Philippe
Aghion and Steven Durlauf. Amsterdam: North-Holland.
Humphrey, Thomas M. 2004. “Ricardo Versus Wicksell on Job Losses and
Technological Change.” Federal Reserve Bank of Richmond Economic
Quarterly 90 (Fall): 5–24.
Juhn, Chinhui, Kevin M. Murphy, and Brooks Pierce. 1993. “Wage
Inequality and the Rise in Returns to Skill.” Journal of Political
Economy 101 (June): 410–42.
Kletzer, Lori G. 1998. “Job Displacement.” Journal of Economic
Perspectives 12 (Winter): 115–36.
, and Robert E. Litan. 2001. “A Prescription to Relieve
Worker Anxiety.” Brookings Institution Policy Brief #73 (March).
Krugman, Paul. 1994. “Past and Prospective Causes of High
Unemployment.” Federal Reserve Bank of Kansas City Economic
Review 79 (Fourth Quarter): 23–43.
Landes, David S. 1998. The Wealth and Poverty of Nations: Why Some Are
So Rich and Some So Poor. New York: W.W. Norton.
Lee, David S. 1999. “Wage Inequality in the United States During the 1980s:
Rising Dispersion or Falling Minimum Wage?” Quarterly Journal of
Economics 114 (August): 977–1023.
Lerman, Robert I. 1997. “Reassessing Trends in U.S. Earnings Inequality.”
Monthly Labor Review 120 (December): 17–25.

A. Steelman and J.A. Weinberg: What’s Driving Wage Inequality?

17

Ljungqvist, Lars, and Thomas J. Sargent. 1998. “The European
Unemployment Dilemma.” Journal of Political Economy 106 (June):
514–50.
Mokyr, Joel. 1994. “Technological Change, 1700–1830.” In The Economic
History of Britain Since 1700, Volume I: 1700–1860 (2nd ed.), ed.
Roderick Floud and Donald McCloskey. New York: Cambridge
University Press.
Sachs, Jeffrey D., and Howard J. Shatz. 1996. “U.S. Trade with Developing
Countries and Wage Inequality.” American Economic Review 86 (May):
234–39.
Schumpeter, Joseph. 1942. Capitalism, Socialism, and Democracy. New
York: Harper & Brothers.
Simon, Julian L. 1999. The Economic Consequences of Immigration (2nd
ed.). Ann Arbor, Mich.: University of Michigan Press.
Topel, Robert H. 1997. “Factor Proportions and Relative Wages: The
Supply-Side Determinants of Wage Inequality.” Journal of Economic
Perspectives 11 (Spring): 55–74.
Violante, Giovanni L. 2002. “Technological Acceleration, Skill
Transferability, and the Rise in Residual Inequality.” Quarterly Journal
of Economics 117 (February ): 297–338.

Unemployment and
Vacancy Fluctuations in the
Matching Model:
Inspecting the Mechanism
Andreas Hornstein, Per Krusell, and Giovanni L. Violante

T

he state of the labor market, employment and unemployment, plays
an important role in the deliberations of policymakers, the Federal
Reserve Bank included. Over the last 30 years, economic theory has
led to substantial progress in understanding the mechanics of business cycles.
Much of this progress in macroeconomics has been associated with the use of
calibrated dynamic equilibrium models for the quantitative analysis of aggregate fluctuations (Prescott [1986]). These advances have mainly proceeded
within the Walrasian framework of frictionless markets. For the labor market, this means that while these theories contribute to our understanding of
employment determination, they have nothing to say about unemployment.
Policymakers care about the behavior of unemployment for at least two
reasons. First, even if one is mainly interested in the determination of employment, unemployment might represent a necessary transitional state if frictions
impede the allocation of labor among production opportunities. Second, job
loss and the associated unemployment spell represent a major source of income
risk to individuals.
Over the past two decades, the search and matching framework has
acquired the status of the standard theory of equilibrium unemployment.1
This theory is built on the idea that trade in the labor market is costly and
takes time. Frictions originating from imperfect information, heterogeneity
We wish to thank Kartik Athreya, Sam Malek, Leo Martinez, and Ned Prescott for helpful
comments. The views expressed in this article are those of the authors and not necessarily
those of the Federal Reserve Bank of Richmond or the Federal Reserve System.
1 For a textbook survey, see Pissarides (2000).

Federal Reserve Bank of Richmond Economic Quarterly Volume 91/3 Summer 2005

19

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Federal Reserve Bank of Richmond Economic Quarterly

of firms and workers, and lack of coordination disrupt the ability to form
employment relationships. The quantity of idle inputs in the labor market
(unemployed workers and vacant jobs) is a measure of such disruption. In
its most basic representation, a labor market matching model focuses on the
interaction between unemployment and job creation. Higher productivity increases the return to job creation and thereby increases the rate of job creation.
In turn, a higher rate of job creation makes it easier for unemployed workers
to find jobs and thereby reduces unemployment. This explains the observed
counter-cyclical (pro-cyclical) behavior of unemployment (job creation).
Shimer (2005) goes beyond investigating the qualitative features of the
basic matching model. He follows the research program on dynamic equilibrium models with Walrasian frictionless markets and explores whether or not
a calibrated matching model of the labor market is quantitatively consistent
with observed aggregate fluctuations. He surprisingly concludes that a reasonably calibrated matching model does not generate enough volatility in unemployment and cannot explain the strong procyclicality of the job-finding rate.
In other words, the matching model stops short of reproducing the cyclical
behavior of its two central elements: unemployment and vacancies.2
In this article, we present the basic matching model, also known as the
Mortensen-Pissarides model, in detail and, building on Shimer (2005), we
explain the reasons for the quantitative problems of the model. Essentially,
given the way wages are determined in the (Nash-bargaining) model and the
way Nash bargaining is calibrated, wages respond strongly to changes in productivity so that the incentive for firms to create jobs does not change very
much. We then discuss two possible ways of reconciling a matching model
with the data.
First, as argued by Hall (2005) and Shimer (2004), if wages are essentially
rigid, the model performs much better. We contend that rigid wages per se
are not sufficient; another necessary requirement is a very large labor share—
close to 100 percent of output. Moreover, we show that with rigid wages, the
model has implications for the labor share that seem too extreme: the labor
share becomes perfectly negatively correlated with—and as volatile as—labor
productivity whereas in the data this correlation is −0.5, and the variation of
the share is not nearly as large as that of productivity.
Second, as suggested by Hagedorn and Manovskii (2005), without abandoning Nash bargaining, a different calibration of some key parameters of the
2 We should note that Andolfatto (1996) and Merz (1995) were the first to integrate the
matching approach to the labor market into an otherwise standard Walrasian model and to evaluate
this model quantitatively. Their work, however, was not so much focused on the model’s ability to
match the behavior of unemployment, but on how the introduction of labor market frictions affects
the ability of the otherwise standard Walrasian model to explain movements in employment, hours
worked, and other non-labor-market variables. Andolfatto (1996), however, also pointed out the
model’s inability to generate enough volatility in vacancies.

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

21

model also allows one to raise the volatility of unemployment and vacancies in
the model. For this calibration to work, however, one again needs a very high
wage share. This high share is obtained by “artificially” raising the outside
option of the worker through generous unemployment benefits.3 We tentatively conclude, as do Costain and Reiter (2003), that this parameterization
has implausible implications for the impact of unemployment benefits on the
equilibrium unemployment rate: a 15 percent rise in benefits would double
the unemployment rate.
Why is a very large (very small) wage share (profit share) so important in
order for the model to have a strong amplification mechanism for vacancies and
unemployment? The model has a free-entry condition stating that vacancies
are created until discounted profits equal the cost of entry. If profits are
very small in equilibrium, a positive productivity shock induces a very large
percentage increase in profits, and hence a large number of new vacancies must
be created—through firm entry—thus lowering the rate of finding workers
enough that entry remains an activity with zero net payoff.
We conclude that neither one of the solutions proposed is fully satisfactory,
for two reasons. First, they both have first-order counterfactual implications.
Second, they both assume a very large value for the labor share. It is hard
to assess whether this value is plausible because there is no physical capital
in the baseline matching model. We speculate that the addition of physical
capital, besides providing a natural way of measuring the labor share of
aggregate income, would allow the analysis of another important source of
aggregate fluctuations, investment-specific shocks, which have proved successful in Walrasian models.4
The present article, which can be read both as an introduction to the
matching model of unemployment and as a way of understanding the recent
discussions of the model’s quantitative implications, is organized as follows.
We first quickly describe the data. Next, we describe in Section 2 the basic
model without aggregate shocks. In Section 3, we define and solve for a stationary equilibrium: a steady state. In Section 4, we briefly discuss transition
dynamics within the model without shocks. In Section 5, we derive the qualitative comparative statics for a one-time permanent change of the model’s
parameters. In Section 6, we present the alternative calibration strategies one
could follow to parameterize the matching model, and in Section 7, we show
how the quantitative comparative statics results differ according to the model
3 To be precise, a large wage share is also sufficient for a strong amplification mechanism with
rigid wages. With flexible wages, the large wage share must be achieved by making unemployment
benefits high.
4 See Greenwood, Hercowitz, and Krusell (2000) and Fisher (2003) for a quantitative account
of the role of this type of shock in U.S. business cycles over the postwar period. Costain and
Reiter (2003) illustrate quantitatively that productivity shocks affecting only new jobs improve the
performance of the baseline model.

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Federal Reserve Bank of Richmond Economic Quarterly

Table 1 Aggregate Statistics: 1951:1–2004:4

u
Standard Deviation
Autocorrelation
Correlation with p

0.20
0.94
−0.40

u
Standard Deviation
Autocorrelation
Correlation with p

0.13
0.87
−0.29

HP Smoothing Parameter: 105
v
θ
λw
w
0.23
0.95
0.31

v

0.38
0.95
0.38

0.12
0.91
0.38

0.02
0.95
0.69

s
0.02
0.91
−0.35

HP Smoothing Parameter: 1600
θ
λw
w

0.14
0.90
0.45

0.26
0.89
0.38

NA
NA
NA

0.01
0.81
0.72

s

0.01
0.77
−0.61

p
0.02
0.89
1.00

p
0.01
0.76
1.000

Notes: Data are quarterly, and u is the unemployment rate of the civilian population; v
is the help-wanted advertising index; θ = v/u is labor market tightness; p is output per
employee in the nonfarm business sector; s is the labor share constructed as the ratio of
compensation of employees to output in the nonfarm sector; w is the wage computed as
labor share times labor productivity, i.e., w = s · p. The statistics for the job-finding rate,
λw , are those reported in Shimer (2005) for an HP smoothing parameter of 105 .

calibration. In Section 8, we introduce explicit stochastic aggregate shocks
and discuss how the quantitative comparative statics results for one-time permanent shocks have to be modified to account for persistent but temporary
shocks. Section 9 concludes the article.

1. THE DATA
The focus of the analysis is on fluctuations at the business-cycle frequencies,
and hence low-frequency movements in the data should be filtered out. For
quarterly data, the standard practice (followed by Andolfatto and Merz) is to
use a Hodrick-Prescott (HP) filter with a smoothing parameter set to 1600.
Shimer (2005) chooses a much smoother trend component, corresponding to
an HP smoothing parameter of 105 .
Table 1 summarizes the key labor market facts around which this article
is centered. We report statistics for the detrended log-levels of each series.
When we remove a very smooth trend (smoothing parameter 105 ), we can
summarize the data as follows:
• Unemployment and Vacancies. First, unemployment, u, and vacancies, v, are about 10 times more volatile than labor productivity, p.
Market tightness, θ, defined as the ratio of vacancies to unemployment, is almost 20 times more volatile. Second, market tightness is

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

23

positively correlated with labor productivity. Both unemployment and
vacancies show strong autocorrelation.
• Job-Finding Rates. The job-finding rate, λw , is six times more volatile
than productivity and is pro-cyclical. It is also strongly autocorrelated.
• Wages and Labor Share. Wages and the labor share are roughly as
volatile as labor productivity. The correlation between wages and labor
productivity is high but significantly less than one, and the labor share
is countercyclical.
Using a more volatile trend component (lower smoothing parameter) has
almost no effect on the relative volatilities. For the vast majority of the variables, the percentage standard deviation is reduced roughly by one-third.
Interestingly, the volatility is cut in half for wages and the labor share. Overall,
the autocorrelation of the series is reduced, since some of the persistence is
absorbed by the more variable HP trend. Finally, the correlation structure of
the series with labor productivity is, in general, unchanged except for the labor
share whose negative correlation almost doubles.
We conclude that the choice of smoothing parameter has no impact on the
unemployment and vacancy statistics but does affect the labor share statistics
somewhat.

2. THE MODEL
We now outline and discuss the basic Mortensen-Pissarides matching model
with exogenous separations.5 We choose a formulation in continuous time
in order to simplify some of the derivations. It is useful to first describe the
stationary economy (when aggregate productivity is constant over time) because that model is simple and yet very informative about how the model with
random shocks behaves. Later, we will briefly discuss aggregate fluctuations
with stochastic productivity shocks that are persistent but not permanent.6

Workers and Firms
There is a fixed number of workers in the economy; the model does not consider
variations in the labor force or in the effort or amount of time worked by each
5 The main reference is Pissarides (1985). Mortensen and Pissarides (1994) extend the model
to endogenous separations. Pissarides (2000) contains an excellent survey of the matching models.
See also Rogerson, Shimer, and Wright (2005) for a recent survey.
6 The view that aggregate fluctuations in output and unemployment are due to fluctuations in
productivity is not essential here. For the given environment, one can interpret productivity shocks
as actually representing another source of fluctuations (such as “demand shocks,” e.g., shocks to
preferences).

24

Federal Reserve Bank of Richmond Economic Quarterly

worker. For example, think of workers as being uniformly distributed on the
interval [0,1]—for any point on this interval, there is one worker—though
there is no particular meaning to a worker’s position on the interval.
Workers are all the same from the perspective of both their productivity
and their preferences. Workers are infinitely lived and have linear utility
over consumption of a homogeneous good, meaning that to the extent that
there is uncertainty, workers are risk-neutral. There is constant (exponential)
discounting at rate r. One can therefore think of a worker’s expected present
value of utility as simply the expected present value of income.7
Workers are either employed or unemployed. An employed worker earns
wage income, w, but cannot search. Unemployed workers search for jobs. Let
b > 0 denote the income equivalent of the utility flow that a worker obtains in
the nonworking activity when unemployed, e.g., the monetary value of leisure
plus unemployment benefits net of search costs.8
A firm is a job. The supply of firms (jobs) is potentially infinite. Every
firm is equally productive at any point in time. Firms are risk-neutral and they
discount future income at the same rate as do workers. Production requires
one worker and one firm; firms can really be thought of as another type of
labor input, such as an “entrepreneur.” A firm-worker pair produces p units
of the homogeneous output per unit of time. We assume that the value of
production for a pair always exceeds the value of not working for a worker,
i.e., that p > b > 0.9 There is no cost for a firm to enter the labor market.

The Frictional Labor Market
In a “frictional” labor market, firms and workers do not meet instantaneously.
In addition, firms that want to meet workers have to use resources to post a
vacancy. In particular, a firm has to pay c units of output per unit of time it
posts a “vacancy.” Let the number of idle firms that have an open position
be denoted v(t), and let the number of unemployed workers be u(t). Lack of
coordination, partial information, and heterogeneity of vacancies and workers
are all factors that make trading in the labor market costly.
We do not model these labor market frictions explicitly but use the concept
of a matching function as a reduced form representation of the frictions.10 This
7 Alternatively, one could assume that workers are risk-averse but that they can obtain complete insurance against idiosyncratic income risk. In this case, it would also be optimal for workers
to maximize the expected present value of income.
8 Note that unemployment benefits do not serve an insurance role in this environment since
workers are either risk-neutral or they already obtain complete insurance.
9 This condition is necessary for ruling out a trivial equilibrium with zero employment: if
b > p, no worker would be willing to work even if she could extract the entire value of the
output produced from the firm.
10 The concept of an “aggregate matching function” has been around for some time. In their
survey of the literature on matching functions, Petrolongo and Pissarides (2001) include a short

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

25

formulation specifies that the rate at which new matches, m, are created is
given by a time-invariant function, M, of the number of unemployed workers
searching for a job and the number of vacant positions: m = M(u, v). At this
point, we will assume that M is (1) increasing and strictly concave in each
argument separately and (2) constant returns to scale (CRS) in both arguments.
Thus, matches are more likely when more workers and firms are searching, but
holding constant the size of one of the searching groups, there are decreasing
marginal returns in matching.
New matches are formed according to Poisson processes with arrival rates
λw and λf . Given the rate at which new matches are formed, the rate at which
an unemployed worker meets a firm is simply λw (t) = m(t)/u(t), the total
number of successful matches per worker searching. Similarly, the rate at
which a vacant firm meets a worker is λf (t) = m(t)/v(t). Since the matching
function is CRS, the two meeting rates depend on labor market tightness,
θ (t) = v (t) /u (t) , only:
λw (t) = M [1, θ (t)] and λf (t) = M [1/θ (t) , 1] .

(1)

As the relative number of vacancies increases, the job-finding rate, λw , also
increases, but the worker-finding rate, λf , decreases. We assume that once a
firm and a worker have been matched, they remain matched until “separation”
occurs. Separation occurs according to a Poisson process with exogenous
arrival rate, σ .
If an unemployed worker meets vacant firms according to a Poisson process with arrival rate, λw , then the probability that the worker meets exactly one
vacant firm during a time period, , is λw if the time period is sufficiently
short. Furthermore, the probability that a worker meets two or more vacant
firms during this time period is essentially zero.11 Similarly, the probability
that a vacant firm meets an unemployed worker is λf , and the probability
that a matched firm-worker pair separates is σ . Thus, if we start out with
u (t) unemployed workers and 1 − u (t) employed workers at time t, after a
short time period, , the number of unemployed workers will be
u (t +

)=σ

[1 − u (t)] + [1 − λw (t) ] u (t) .

history of the concept. Lagos (2000) warns against the dangers of such a “reduced-form approach”
to frictions when, for example, evaluating the effects of policies. The underlying reason is that
policies may affect the search behavior of agents and change the shape of the aggregate matching
function.
11 Note that for a Poisson process, the rate λ at which the state changes need not be bounded
above by one. Since we are interested in the limiting case when the time interval, , becomes
arbitrarily small, the probability of a state change, λ , will eventually be less than one for any
fixed and finite λ.

26

Federal Reserve Bank of Richmond Economic Quarterly

Subtracting u (t) from either side of this expression, dividing by , and taking
the limit when the length of the time period goes to zero, we obtain
u(t) = lim
˙

u (t +

) − u (t)

→0

= σ [1 − u(t)] − λw (t)u(t).

(2)

Here u(t) denotes the time derivative (change per unit of time) of u(t): u(t) =
˙
˙
∂u(t)/∂t. This equation captures that the change in unemployment is the flow
into unemployment (the number of employed workers times the rate at which
they separate) minus the flow from unemployment (the number of unemployed
workers times the rate at which they find a job).
The dynamic evolution of unemployment is one of the key concerns in
this model. Notice, however, that the job-finding rate for workers, λw (t) ,
in equation (2) depends on vacancies through labor market tightness, θ (t).
What determines vacancies, v(t)? In order to answer this question, we need
to describe what determines profits for entering firms, which in turn requires
us to discuss what wages workers receive.
With matching frictions, both workers and firms have some bargaining
power since neither party can be replaced instantaneously, as is commonly
assumed in competitive settings. There is a variety of theories that describe
how bargaining allocates output between firms and workers under these circumstances. Below we will determine wages according to the widely used
Nash-bargaining solution. For simplicity, from now on we will mainly consider steady states, situations in which all aggregate variables are stationary
over time. Thus, u(t), v(t), λw (t), and λf (t) are all constant, even though
individual workers and firms face uncertainty in their particular experiences.

3.

STATIONARY EQUILIBRIUM

Values
Denote the net present value of a matched firm J (which in general would
depend on time but in a steady state does not). Given output, p, and the wage,
w, paid to its worker, J must satisfy
rJ = p − w − σ (J − V ),

(3)

where V is the value of the firm when unmatched. This equation is written in
flow form and is interpreted as follows: the flow return of being matched—the
capital value of being matched times the rate of return on that value—equals the
flow profits minus the expected capital loss resulting from match separation—
the rate at which the firm is separated, σ , times the latter capital loss equals
J − V .12
12 This equation is written in flow form but can be derived from a discrete-time formulation
analogous to the derivation of equation (2). Suppose that the value of being vacant is constant

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

27

Similarly, the value of a vacant firm satisfies
rV = −c + λf (J − V ).

(4)

Here, there is a flow loss due to the vacancy posting cost and an expected
capital gain from the chance of meeting a worker.
Turning to the net present value of a matched worker, W , and an unemployed worker, U , we similarly have
rW = w − σ (W − U ), and
rU = b + λw (W − U ).

(5)
(6)

The flow return from not working, b, could be a monetary unemployment
benefit collected from the government, a monetary benefit from working in
an informal market activity, or the monetary equivalent of not working in any
market activity (the value of being at home). We will discuss the role and
interpretation of b more extensively below, because it turns out that it matters
how one thinks of this parameter.

Wage Determination
The values of (un)matched workers and firms depend on the wages—yet to
be determined—paid in a match. Obviously, for a match to be maintained it
must be beneficial for both the worker, W − U ≥ 0, and the firm, J − V ≥ 0.
We define the total surplus of a match, S ≡ (J − V ) + (W − U ), as the sum
of the gain of the firm and worker being in a match relative to not being in
a match. We assume that the wage is set such that the total match surplus is
shared between the worker and firm according to the Nash-bargaining solution
with share parameter β:13
W − U = βS and J − V = (1 − β)S.

(7)

over time from the perspective of a matched firm and that we are looking at one period being
of length . During this period, there is production, and wages are paid, the net amount being
(p − w) since p and w are measured per unit of time. At the end of the period, the match
separates with probability σ and remains intact with probability 1 − σ . So it must be that
J (t) = (p − w) + (1 − σ )e−r J (t + ) + σ e−r V . Here, e−r ≡ δ( ) is a discount factor;
it gives a percentage decline in utility as a function of the length of time, −(dδ( )/d )/δ( ),
which is constant and equal to r. Subtract J (t + )e−r on both sides and divide by . That
−r

)
delivers J (t)−J (t+ ) + (1−e
J (t + ) = p − w − σ e−r (J (t + ) − V ). Take limits as
→ 0.
˙
Then the left-hand side becomes J (t) + rJ (t), the second term coming from an application of
l’Hˆ pital’s rule and the value being a continuous function of time. The right-hand side gives
o
p − w − σ (J (t) − V ). In a steady state, J (t) is constant and equal to J, satisfying the equation
in the text.
13 The Nash-bargaining solution does not describe the outcome of an explicit bargaining process; rather, it describes the unique outcome among the set of all bargaining processes whose
outcomes satisfy certain axioms (Nash [1950]). Also, one can derive the Nash-bargaining solution
as the outcome of a bargaining process where participants make alternating offers until they reach
agreement. For a survey of the bargaining problem, see Osborne and Rubinstein (1990).

28

Federal Reserve Bank of Richmond Economic Quarterly

Summing the value equations for matched pairs and subtracting the values of
unmatched firms and workers, using the Nash-bargaining rule, we therefore
obtain
rS = p − σ S + c − λf (1 − β)S − b − λw βS,

(8)

which implies that
S=

p+c−b
.
r + σ + (1 − β)λf + βλw

(9)

That is, we can express the surplus as a function of the primitives and the
matching rates, which are endogenous and will be determined by the free
entry of firms as shown below. We see that the surplus from being in a match
is
• decreasing in the interest rate (a higher interest rate reduces the present
value of remaining in the match),
• decreasing in the separation rate (a higher separation rate lowers the
expected value of remaining together),
• decreasing in the bargaining share of workers times the rate at which
they meet vacant firms (the higher the chance that unemployed workers
meet vacant firms and the higher the share that workers receive in that
case, the less valuable it is to be matched now), and
• decreasing in the bargaining share of firms times the rate at which vacant
firms meet unemployed workers (the higher the chance that vacant firms
meet unemployed workers and the higher the share that firms receive
in that case, the less valuable it is to be matched now).
To derive a useful expression for the wage, subtract rV from the value
equation for matched firms, (3), and use the Nash-bargaining rule to obtain
r(1 − β)S = p − w − σ (1 − β)S − rV .

(10)

Also, notice that given the surplus sharing rule, (7), and the expressions for
the vacancy and unemployment values, (4) and (6), the surplus in (8) can be
written as
rS = p − σ S − rV − rU.

(11)

Now multiply equation (11) by 1 − β, subtract it from equation (10), and solve
for the wage:
w = β(p − rV ) + (1 − β)rU.

(12)

Thus, the wage is a weighted average of productivity minus the flow value of
a vacancy and the flow value of unemployment with the weights being β and
1 − β, respectively. Intuitively, one can understand this equation as follows:

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

29

w − rU , the flow advantage of being matched for a worker, is just its share, β,
of the overall advantage of being matched for the worker and the firm together,
β(p − rV − rU ).

Firm Entry
There is an infinite supply of firms that can post vacancies, and entry is costless.
Therefore, in an equilibrium with a finite number of firms posting vacancies,
the value of a posted vacancy is zero:
V = 0.

(13)

If V < 0, no firm would enter, and if V > 0, an infinite number of firms
would enter. This means that the number of vacancies, v(t), adjusts at each
point in time so that there are zero profits from entering, given the matching
rate with workers, λf , which depends on u(t) and on v(t).
The free-entry condition (13), together with the definition of the vacancy
value (4) and the surplus sharing rule (7) then determine the surplus value:
c
S=
.
(14)
(1 − β)λf
Moreover, we can use the free-entry condition to simplify the expression for
the surplus in (9); the surplus can now be expressed as
p−b
S=
.
(15)
r + σ + βλw
These two expressions for the surplus can be combined to write
c
p−b
=
.
(16)
r + σ + βλw
(1 − β)λf
This is an equation in one unknown, labor market tightness (θ ), since both
meeting rates (λw and λf ) depend only on the number of vacancies relative to
the unemployment rate (see equation (1)).
We also see that free entry implies that the wage expression (12) simplifies
to
w = βp + (1 − β)rU.

(17)

Equilibrium Unemployment
In a steady state, u(t) = 0, so the evolution for unemployment as given by
˙
equation (2) becomes
σ (1 − u) = λw u.

(18)

Thus, in a steady state, the flow into unemployment—the separation rate in
existing matches times the number of matches—must equal the flow out of
unemployment—the job-finding rate times the number of unemployed.

30

Federal Reserve Bank of Richmond Economic Quarterly

The steady state expression for unemployment can, on the one hand, be
used to express unemployment as a simple function of the separation rate and
the job-finding rate. On the other hand, it can be used to write the job-finding
rate in terms of the unemployment rate and the separation rate. If we know,
for example, that the unemployment rate is 10 percent and that the monthly
separation rate is 5 percent, then the chance of finding a job within a month
must be σ 1−u = 0.05 · 0.9 = 0.45; that is, just under one-half.
u
0.1

Solving the Model
Solving the model is now straightforward. We have derived (16) and (18)
in two unknowns, θ and u. Furthermore we can solve the two equations
sequentially. First, from (1) it follows that λw (λf ) is increasing (decreasing)
in θ . This, in turn, implies that the left-hand side (LHS) of (16) is decreasing
in θ and that the right-hand side (RHS) is increasing in θ . Thus, if a solution,
θ , to (16) exists, it is unique. Second, conditional on θ , we can solve (18) for
the equilibrium unemployment rate.
One can show that a solution to (16) exists if we assume that the matching
function satisfies the Inada conditions.14 We assume a particular functional
form for the matching function that meets these conditions and that is the most
common one in the literature, the Cobb-Douglas (CD) matching function,
M(u, v) = Auα v 1−α .

(19)

The CD matching function has convenient properties in terms of how the
matching rates change with changes in labor market tightness,
λw = Aθ 1−α and λf = Aθ −α .

(20)

Independent of the level of unemployment, if the labor market tightness increases by 1 percent, the rate at which a worker (firm) finds a firm (worker)
goes up (down) by 1 − α (α) percent. 15
Using the CD matching function, our equilibrium condition, (16), becomes
p−b
c
=
.
(21)
1−α
(1 − β)Aθ −α
r + σ + βAθ
For θ = 0, the LHS of (21) is finite and positive, and the RHS is zero. As θ
becomes arbitrarily large, the LHS converges to zero and the RHS becomes
arbitrarily large. Thus there exists a positive θ that solves (21). The unem-

∞.

14 Let f (θ ) = M (θ , 1). Then the Inada conditions are f (0) = 0, f (∞) = ∞, and f (0) =

15 Shimer (2005) argues that the constant elasticity CD matching function describes the data
for the U.S. labor market well. See also Section 7 on calibration.

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

31

ployment rate then can be solved for in a second step, using (18), as
σ
u=
.
(22)
σ + Aθ 1−α
We obtain the wage by using the definitions of the matching rates, (20),
and substituting the expressions for rU and the value of S, (6), and (15) in
wage equation (17):
βc
w = βp + (1 − β) b +
θ = β(p + cθ ) + (1 − β)b.
(23)
1−β

A Digression: The Frictionless Model
We now show that as search frictions become small, the equilibrium of the
economy with matching frictions converges to the equilibrium of the corresponding economy without matching frictions. Search frictions can become
small either because the cost of searching for vacant firms, c, becomes small
or because the efficiency of the matching process, A, improves.
The frictionless economy is identical to the one outlined so far, except
that matching between vacant firms and unemployed workers is instantaneous
and costless. The resource allocation problem in the frictionless economy,
which can be studied from the perspective of a benevolent social planner, is
trivial. There will always be the same number of firms as workers operating because there is no cost in creating vacancies, and the matching process
is instantaneous. Leaving workers idle would therefore be inefficient since
p > b. There are no vacancies since matching is instantaneous. There is a
competitive equilibrium that supports this allocation given some wage rates,
w(t), specified at all points in time. It is clear that for these wages, w(t) must
equal p for all t because workers are in short supply, and firms are not. That
is, firm entry bids down profits to zero, and workers obtain the entire output.
Now suppose that the vacancy-posting costs become arbitrarily small:
c → 0. Then for any finite θ, the LHS of (21) is strictly positive, but the RHS
converges to zero. Therefore, it must be that θ → ∞. To find the wage, some
care must be taken, since the wage expression contains cθ , i.e., 0 · ∞. Since
workers meet firms at an ever-increasing rate, λw → ∞, the unemployment
rate becomes arbitrarily small, u → 0, and from equation (9) it follows that
the surplus from being in a match becomes arbitrarily small: S → 0. Then
simply inspect (10), which implies that w → p, as expected: workers obtain
the whole production value.
The same kind of result is obtained if the matching efficiency becomes
arbitrarily large, A → ∞. Now, however, there will be no vacancies, and θ
will remain finite. To see this formally, multiply (21) with Aθ −α , divide the
numerator and denominator of the LHS by A, and take the limit as A → ∞:
p−b
c
=
.
βθ ∞
1−β

32

Federal Reserve Bank of Richmond Economic Quarterly

Since θ ∞ = limA→∞ θ (A) is finite, the limits of both λf and λw are infinite.
Thus from equation (9) it follows that the limit of the surplus is zero; from
(22) it follows that the limit of the unemployment rate is zero; and from (10)
it follows that the limit of the wage again must equal p. Since θ ∞ is positive
and finite, v∞ must equal 0 since u∞ equals 0. There is no unemployment,
and there are no vacancies.

4. TRANSITION DYNAMICS
So far, we have discussed how the key endogenous variables—unemployment,
vacancies, job-finding rates, and wages—are determined in steady state. But
how does the economy behave out of a steady state? To answer this question,
one needs to find out what the economy’s state variables are. A state variable
is a variable that is predetermined at time t and that matters to outcomes. Here,
unemployment is clearly a state variable, because it is a variable that moves
slowly over time according to (2). In fact, it is the only state variable. No
other variable is predetermined. This means that, in general, allocations at t
depend on u(t) but not on anything else.
So what is a dynamic equilibrium path of the economy if it starts with
an arbitrary u(0) at time zero? It turns out that the equilibrium is very easy
to characterize. All variables except u(t) and v(t) will be constant over time
from the very beginning.16 To show that this is indeed an equilibrium, simply
assume that θ is constant from the beginning of time and equal to its steady
state value and then verify that all equilibrium conditions are satisfied. Since
θ is constant, all job-finding rates—λw (t) and λf (t)—will be constant and
equal to their steady state values because they depend on θ and on nothing
else. Since the λs are the only determinants of the values J , V , W , and U , the
solution for the values will be the same as the steady state solution. It then
also follows that the wage must be the steady state wage. To find u(t) and
v(t), we conclude that u(t) will simply follow
u(t) = σ [1 − u(t)] − λw u(t),
˙

(24)

which differs from (2) only in that λw is now constant. Once we have solved for
u(t), we can find the path for v(t) residually from v(t) = θ u(t). Moreover,
note that if u(0) is above the steady state, u, the RHS of equation (24) is
negative, which means that u(0) is negative. Unemployment falls, and as
˙
long as it is still above u, it continues falling until it reaches (converges to) u.
Similarly, if it starts below u, it rises monotonically over time toward u.17
16 Pissarides (1985; 2000, Chapter 1) shows that this is the unique equilibrium path.
17 Formally, the solution for u(t) is the solution to the linear differential equation (24): u(t) =

σ
u + e−(σ +λw )t (u(0) − u), where u = σ +λ .
w

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

33

The fundamental insight here is that there are no frictions involved in firm
entry, but there are frictions in movement of workers in and out of jobs.18
Therefore, u(t) is restricted to follow a differential equation which is “slowmoving,” whereas v(t) does not have to satisfy such an equation. It can jump
instantaneously to whatever is has to be so that θ is equal to its steady state
value from the beginning of time.

5.

COMPARATIVE STATICS

We now analyze how different parameters influence the endogenous variables.
In particular, how does unemployment respond to changes in productivity?
Here, we emphasize that these are steady state comparisons. We find the longrun effect of the permanent change in the parameter. For most variables—all
except u(t) and v(t)—the impact of a permanent change in the parameter is
instantaneous because θ immediately moves to its new, long-run value (see
the discussion in the previous section). Of course, in the section below where
some of the primitives are stochastic, their changes need not be permanent,
and slightly different results apply.
For example, if we are looking at a 1 percent permanent increase in productivity, p, the comparative statics analysis in this section will correctly
describe the effect on θ both in the long and in the short run, whereas the
effect on unemployment recorded here only pertains to how it will change in
the long run. The short-run effect on unemployment of a permanent change
in a parameter is straightforward to derive, nevertheless: It simply involves
tracing out the new dynamics implied by the linear differential equation (24)
evaluated at the new permanent value for λw (which instantaneously adopts
its new value because θ does). In particular, one sees from the differential
equation that an increase in θ will increase λw and thus increase the speed of
adjustment to the new steady state rate of unemployment.
We are mainly interested in how the economy responds to changes in p,
but we will also record the responses to b, σ , and c. We compute elasticities,
i.e., we use percentage changes and ask by what percent θ and u will change
when p, b, σ , and, c change by 1 percent. We derive the relevant expressions
by employing standard comparative statics differentiation of (21) and (22).
Using x to denote d log(x) = dx/x, it is straightforward to derive
ˆ
18 The speed of movements from unemployment into employment is regulated by the hiring
rate, λw , which, in turn, depends on the endogenous market tightness, θ . Separations instead are
exogenous, and, hence, the speed of movements from employment to unemployment is simply
determined by the parameter, σ .

34

ˆ
θ=

Federal Reserve Bank of Richmond Economic Quarterly

b ˆ
σ
r + σ + βλw
p
p−
ˆ
b−
σ − c , and
ˆ
ˆ
α (r + σ ) + βλw p − b
p−b
r + σ + βλw
(25)
ˆ
u = (1 − u) σ − (1 − α) θ .
ˆ
ˆ

(26)

The Effect of an Increase in Productivity
From equation (25), we see that an increase in p of 1 percent leads to more
than a 1 percent increase in θ since α < 1, and p > b > 0. Intuitively,
p increases the value of matches, and given that firms capture some of the
benefits of this increase in value, there will be an increase in the number of
firms per worker seeking to match. The larger the fraction of the surplus going
to the firm (β small), the more vacancies and market tightness will respond to
a change in labor productivity. We also see that to the extent that b is close to
p, the effect can be large, since p/(p − b) can be arbitrarily large. Why is this
effect larger the closer b is to p? When (p − b) 0, the profit from creating
vacancies is small, and θ 0. Hence, even a small change in p induces very
large changes in firms’ profits and market tightness, θ , in percentage terms,
through the free-entry condition (21).
ˆ
Because the job-finding rate, λw , equals Aθ 1−α , we obtain that λw =
ˆ , so the effect of p on θ is higher than that on job-finding rates by
(1 − α)θ
a constant factor, 1/(1 − α). If we look at the effect on unemployment, note
from (26) that a 1 percent increase in θ lowers unemployment by (1−u)(1−α)
percent.

The Effects of Changing b, σ , and c
Changes in income when unemployed, b, have a very similar effect to productivity changes, p, but with an opposite sign. Increasing b, in particular,
lowers θ significantly if b is near p, but it has very little effect on θ if b is
close to zero. An increase in the match separation rate, σ , decreases labor
market tightness. More frequent separations reduce the expected profits from
creating a vacancy, and, thus, θ falls. The effects on labor market tightness
of higher vacancy-posting costs, c, are negative as well. A 1 percent increase
in the vacancy cost lowers the labor market tightness (by less than 1 percent)
because it requires firms’finding rates to go up in order to preserve zero profits,
and, hence, there must be fewer vacant firms relative to unemployed workers.
There is less than a one-for-one decrease because the surplus, once matched,
increases as well, as is clear from equations (14) and (15).

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

35

The effects on the job-finding rate of all the above changes in primitives are
ˆ
all one minus α times the effect on θ. Similarly, the effects on unemployment
ˆ
are −(1 − u)(1 − α) times those on θ, with the exception of a change in σ
because from (22), the total effect on unemployment of a rise in σ by 1 percent
is twofold. The first effect is an indirect decrease through the impact on θ (a
higher σ leads to a higher θ ), which lowers unemployment. The second effect
is a direct increase of unemployment due to the higher rate at which matches
separate. The total effect cannot be signed without more detailed assumptions;
for example, if α ≥ 1/2, the net effect is to increase unemployment.

An Additional Friction: Rigid Wages
In the model just described, productivity changes arguably have such a small
impact on labor market tightness and unemployment that they cannot account
for the observed fluctuations in the data. Hall (2005) and Shimer (2004)
suggest that one way to address this shortcoming is to change the wage-setting
assumption. We now describe a very simple model that captures this idea.
The values for workers and entrepreneurs continue to be defined by equations (3), (4), (5), and (6). Now, assume that wages are fixed at some exogenous
level, w, such that the implied capital values for entrepreneurs and workers
¯
satisfy J > 0 and W > U . Hall (2005) justifies this assumption on wage
determination as a possible sustainable outcome of a bargaining game. The
new equilibrium zero-profit condition from a vacancy creation is
p−w
¯
c
c
=
=
.
r +σ
λf
Aθ −α

(27)

It follows that the impact of a change in labor productivity on market tightness
is given by
ˆ
θ=

p
p.
ˆ
α (p − w)
¯

(28)

Comparing this last expression to that in equation (25), we see that the rigidwage model gives a stronger response. In particular, independent of b, if the
average wage, w, is large as a fraction of output (i.e., if the labor share is large),
¯
then market tightness will be very sensitive to small changes in productivity.
The effect on unemployment, given the changes in θ , is the same whether
or not wages are rigid, as given by equation (26). Finally, a comparison of
equations (21) and (27), reveals that by choosing a value for the worker’s
bargaining power, β, close to zero in the model with Nash bargaining, one
achieves essentially rigid wages, since w is then almost the same as b.

36

Federal Reserve Bank of Richmond Economic Quarterly

Table 2 Parameters and Steady States for Calibrations
Common across Calibrations
r = 0.012, α = 0.72, p = 1,
A = 1.35, λ = 1.35, θ = 1, u = 0.07
Specific to Calibrations
β
b
w/p
b/w
ηwp

6.

Shimer
0.72
0.40
0.98
0.41
1.00

Hagedorn & Manovskii
0.05
0.95
0.97
0.98
0.50

Hall
NA
0.40
0.98
0.41
0.00

CALIBRATION

In the previous section on comparative statics we demonstrated how steady
states change when primitives change. In particular, we have analyzed qualitatively how a permanent productivity change affects labor market tightness
(recall that the effect is the same in the short as well as in the long run) and
how it influences unemployment in the long run. However, what are the magnitudes of these effects? In order to answer this question we need to assign
values to the parameters, and we will do this using “calibration.” We will,
to the extent possible, select parameter values based on long-run or microeconomic data. Hence, we will not necessarily select those parameters that
give the best fit for the time series of vacancies and unemployment, since we
restrict the parameters to match other facts.
The parameters of the model are seven: β, b, p, σ , c, A, and α. The steady
state equations that one can use for the calibration are three: (21), (22), and
(23). Some aspects of the calibration are relatively uncontroversial, but as
we will see below, some other aspects are not. Therefore, we organize our
discussion in two parts. We first describe how to assign values to the subset of
parameters that allows relatively little choice. We then discuss the remaining
parameters and show how, depending on what data one uses to calibrate these,
different parameter selections may be reasonable. We also explain why this is
a crucial issue—the effect of productivity changes for vacancies, and unemployment may differ greatly across calibrations. We summarize the different
calibration procedures in Table 2.

Basic Calibration. . .
In this section, we follow the calibration in Shimer (2005). We think of a unit
of time as representing one quarter. Therefore, it is natural to select r = 0.012,

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

37

given that the annual real interest rates have been around 5 percent. We choose
the separation rate, σ = 0.10, based on the observation that jobs last about
two and a half years on average.19
Job-finding rates in the data are estimated by Shimer to be 0.45 per month.
Thus, a target for λw of 1.35 per quarter seems reasonable. Notice from
equations (25), (26), and (28) that the response of labor market tightness and
the unemployment rate to changes in productivity and other parameters does
not depend on the worker-finding rate, λf . We therefore follow Shimer and
simply normalize labor market tightness, θ = 1, so that the worker-finding
rate is equal to the job-finding rate.20
Next, consider the elasticity of the matching function: what should α be?
Shimer plots the logarithm of job-finding rates against log(v/u) and observes
something close to a straight line with a slope coefficient of about 0.28, which
the theory’s formulation, λw = Aθ 1−α , says it should be. Therefore, we set
α = 0.72. Since we have set θ equal to one and λw equal to Aθ 1−α , it follows
that A = 1.35. From the condition determining steady state unemployment,
(22), we now obtain that 0.1(1.35 − u) = u, so that u is 6.9 percent, which is
roughly consistent with the data. Notice also that the system of equilibrium
conditions is homogeneous of degree one in c, p, and b. Therefore, we
normalize p = 1 in steady state.
It remains to select c, b, and β. We have two equations left: the wage
equation, (23), and the free-entry equilibrium condition, (21), which is the one
that solves for θ in terms of primitives. We can think of this latter equation as
residually determining c once b and β have been selected. Two more aspects
of the data therefore need to be used in order to pin down b and β.

. . . but what are b and β ?
We now turn to the more contentious part of the calibration.

Completing Shimer’s Calibration

It is common to regard b as being the monetary compensation for the unemployed. The OECD (1996) computes average “replacement rates” across
countries, i.e., the ratio of benefits to average wages, and concludes that,
whereas typical European replacement rates can be up to 0.70, replacement
19 For a Poisson process with arrival rate σ , the average time to the arrival of the state

change is 1/σ . Thus, the average time from forming a match to separation is 1/σ = 10 quarters.
20 Alternatively, we could have followed Hall (2005) and set the monthly worker-finding rate
to one so that λf = 3, implying that θ = 1/3. The value chosen for θ does not influence our
results.

38

Federal Reserve Bank of Richmond Economic Quarterly

rates are at most 0.20 in the United States.21 Shimer (2005) sets b equal to 0.4,
which is even beyond this upper bound for the replacement rate since it turns
out that the wage is close to one in his calibration. One reason why b should
be higher than 0.2 is that it also includes the value of leisure associated with
unemployment. We will discuss some alternative ways to calibrate b below.
Regarding β, it is common to appeal to the Hosios condition for an efficient
search.22 This condition says that in an economy like the present one, firm
entry is socially efficient when the surplus sharing parameter, β, is equal to
the elasticity parameter of the matching function, α. Thus, Shimer (2005)
assumes that β = α. This is one possible choice, though it is not clear why
one should necessarily regard the real-world search outcome as efficient. In
conclusion, if β = 0.72 and b = 0.4, from the free-entry condition we obtain
c = 0.324, and the calibration in Shimer (2005) is completed. Note that
Shimer does not use the wage equation in his calibration.

Alternative: Use the Wage Equation

Let us now look at an alternative way of calibrating the model that exploits the
wage equation. Hagedorn and Manovskii (2005) point to two observations
that arguably can be used to replace those used by Shimer to calibrate b and
β.
First, they argue that one can look at the size of profits in the data. Referring to empirical studies, Hagedorn and Manovskii argue that the profit share,
which they identify as (p − w)/p in the model, is about 0.03.23 That is, this
calibration strategy is equivalent to selecting a wage share a few percentage
points below one. Second, they argue that one can look at how much wages respond to productivity. Using microeconomic data, Hagedorn and Manovskii
conclude that a 1 percent productivity increase raises wages by half a per21 In the United States, unemployment insurance replaces around 60 percent of past earnings,
but in the data, unemployed workers earn much less than the average wage.
22 See Hosios (1990). Free entry of firms involves an externality since individual vacant firms
do not take into account that variations in the vacancy rate affect the rate at which they meet
unemployed workers and the rate at which unemployed workers meet them.
23 A pure aggregate profit measure should probably take the cost of vacancies into account,
and, as such, it should be computed somewhat differently:

((1 − u)(p − w) − vc)/(p(1 − u)) = 1 − (w/p) − θ (c/p)(u/(1 − u)).
If this expression equals 0.03, one obtains a smaller wage share, but since c must be less than
one for zero profits to be feasible, w/p cannot be below 0.97 − 1 · 1 · 0.05/0.95 ∼ 0.92. Thus,
both computations lead to a wage share close to one.

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

39

cent.24 We now show how one can use these two observations to determine b
and β.
The wage share. The wage income share in the model is obtained by
dividing the wage equation (23) by productivity:
w
cθ
=β 1+
p
p

b
+ (1 − β) .
p

(29)

Rearranging the equilibrium condition (21) yields
cθ
(1 − β) λw
=
p
r + σ + βλw

1−

b
.
p

(30)

It is informative to calculate the wage share implied by Shimer’s calculations.
Now, given Shimer’s preferred parameter values,
cθ
1−β
≈
p
β

1−

b
p

since (r + σ ) is small relative to λw . Therefore, with this expression inserted
into (29), we conclude that
w
≈ 1,
p
meaning that calibration of the wage share to 0.97 will not by itself be a large
departure from Shimer’s parameterization. Indeed, Shimer obtains a wage
share of w/p = 0.973.
However, there are several different choices of the pair (b/p, β) that can
achieve this value of the labor share. To see this, combine equations (29) and
(30) by eliminating cθ/p:
w
(r + σ ) [β + (1 − β) b/p] + βλw
=
.
(31)
p
(r + σ ) + βλw
Shimer chooses a relatively large value of β, which makes the wage share in
(31) close to one without imposing constraints on b/p. Alternatively, β can
be set close to zero, in which case a value for b/p needs to be around one.
Recall that with b close to p, the dynamic properties of the model change
dramatically. The model has a much stronger amplification mechanism, but
how can one justify this choice of β?
The wage elasticity with respect to productivity. We differentiate (31) in order to derive a relation between ηθp ≡ d log θ /d log p, the percentage change
in θ in response to a 1 percent increase in p, and ηwp ≡ d log w/d log p (the
24 When we regress the cyclical component of wages on labor productivity (see Table 1 for
a description of the data), we obtain an elasticity of 0.57 with the low smoothing parameter and
0.72 with Shimer’s smoothing parameter. The first number is higher than, but not too distant from,
Hagerdorn and Manovskii’s preferred estimate of 0.5. In particular, it is not statistically different
from 0.5.

40

Federal Reserve Bank of Richmond Economic Quarterly

corresponding measure for how wages respond to productivity). We obtain
ηwp =

β 1 + (cθ /p) ηθp
.
w/p

(32)

When r + σ is small relative to βλw , as in Shimer’s calibration, the elasticity
of labor market tightness with respect to productivity satisfies
ηθp ≈

1
,
1 − b/p

demonstrating that the wage elasticity must be
ηwp ≈

1
w/p

(it must be close to one if the labor share is near one). That is, Shimer’s
calibration generates a one-for-one wage increase in response to productivity,
measured in percentage terms, which is twice as large as the estimates cited
by Hagedorn and Manovskii.
To obtain such a low elasticity, one needs to decrease β, so that r + σ
is no longer small relative to βλw , and this is how Hagedorn and Manovskii
accomplish the task. A combination of (32) and the exact expression for ηθp
from (25) allows us, after some simplifications, to solve for ηwp as
ηwp =

β
w/p

α(r + σ ) + λw
.
α(r + σ ) + βλw

(33)

It is now easy to see that using the baseline (uncontroversial) calibration together with w/p ≈ 1 and β = 0.13 takes us to a number for ηwp that is closer
to one-half.25 Notice also that when β is close to zero, the approximation
that ηθp ≈ p/(p − b) is no longer so good; rather, ηθp is significantly higher
than p/(p − b), thus further strengthening the amplification of shocks in the
model.
Put differently, if we restrict the model so that it generates a weaker response of wages to productivity, then expression (33) tells us that β has to be
significantly smaller. And as we saw before, that (together with a wage share
sufficiently close to one) totally changes the dynamics of this model.
How does the calibration influence the amplification from productivity to
unemployment? As seen in (26), the transmission from θ to u depends only
on α and on u itself, so there is little disagreement here. The contentious
parts of the calibration do not influence this channel. That is, the differences
in the amplification of unemployment between the alternative calibrations are
25 Again, we need to remind the reader that our wage elasticity is defined for a one-time
permanent change of productivity. Hagedorn and Manovskii (2005) base their analysis on an economy with recurrent and persistent, but not permanent, shocks. Therefore, our calibration results
for various parameters can differ somewhat.

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

41

inherited from the differences in how these calibrations amplify labor market
tightness.
Some Further Remarks on Calibration

What is the value of the labor share? Apparently, relatively minor differences
in how close the wage share is to one make a significant difference in the
results. It seems to us, however, that wage shares are very difficult to calibrate
properly without having the other major input in the model, namely capital.
Of course, some search/matching models do allow an explicit role for capital.
Pissarides (2000), for example, discusses a matching model where firms, once
they have matched, rent capital in a frictionless market for capital. Thus, a
neoclassical (or other) production function can be used, and the wage share
can be calibrated to the ratio of wage income to total income using the national
income accounts. The relevant wage income share, however, is then net of
capital income, and the same applies to the definition of output. Alternatively,
in Hornstein, Krusell, and Violante (2005), we assume that capital is purchased
in competitive markets but that an entrepreneur has to purchase capital first in
order to be able to search for a worker—in order to qualify as a “vacant firm.”
It is an open question as to whether models with capital will also embody a
sensitivity of the amplification mechanism to the calibration of the labor share.
What is the value for the wage elasticity? If one insists that wages are less
responsive to the cycle than what is implied by Shimer’s calibration, then there
is more amplification from productivity shocks, and the model’s implications
are closer to the data. Hall (2005) maintains an even more extreme assumption
that wages are entirely rigid; this is why we considered a version of the model
with rigid wages. Going back to equation (28), we see that a rather extreme
outcome is produced, provided that we still calibrate so that the wage share
is close to one. Now inelastic wages and a high wage share interact to boost
the amplification mechanism. However, the model has the counterfactual
implication that the labor share, w/p, is perfectly negatively correlated with
output while only mildly countercyclical in the data.
What is the value for the elasticity of unemployment to benefits? Finally,
a possible third clue for calibrating this model can be obtained if one has
information about how the economy responds to changes in unemployment
compensation.26 Of course, the absence of controlled experiments makes it
difficult to ascertain the magnitude of such effects. The upshot, however, is
that if the response of θ to p is large (because b is close to p), then the response
of an increase in unemployment compensation would be a very sharp decrease
in θ (and increase in unemployment). In particular, as explained in Section
5, the elasticity of the exit rate from unemployment with respect to b equals
26 This way of assessing matching models was proposed in Costain and Reiter (2003).

42

Federal Reserve Bank of Richmond Economic Quarterly

(1 − α) times ηθb . Given α = 0.72, the Hagedorn-Manovskii calibration
implies that this elasticity equals −6.3 (see Table 3). Thus, a 10 percent rise
in unemployment benefits would increase expected unemployment duration
(1/λw ) by roughly 60 percent.
The existing estimates of the elasticity of unemployment duration with
respect to the generosity of benefits, which are based on “quasi-natural” experiments, are much smaller. Bover, Arellano, and Bentolila (2002) find for
Spain that not receiving benefits increases the hazard rate at most by 10 percent, implying a local elasticity of 0.1. For Canada, Fortin, Lacroix, and Drolet
(2004) exploit a change in the legislation that led to a rise in benefits by 145
percent for singles below age 30 and estimate an elasticity of the hazard rate
around 0.3. For Slovenia, van Ours and Vodopivec (2004) conclude that the
1998 reform which cut benefits by 50 percent was associated with a rise in the
unemployment hazard by 30 percent at most, implying an elasticity of 0.6.
Finally, an earlier survey by Atkinson and Micklewright (1991) argues that
reasonable estimates lie between 0.1 and 1.0.
In sum, these estimates mean that the elasticity implied by the HagedornManovskii parametrization is between six and sixty times larger than the available estimates.

7.

QUANTITATIVE RESULTS FOR THE DIFFERENT
CALIBRATIONS

In this section, we show that the three alternative calibrations discussed in
Section 6 have very different quantitative implications for the comparative
statics discussed in Section 5. Note that, although the values for certain key
parameters—β and b in particular—are different, the steady state values of the
key aggregate variables are the same across parameterizations. The reason,
as explained, is that certain parameters are not uniquely identified in steady
state.

Implications for θ , λw , and u
Table 3 summarizes the results for the preferred calibrations of Shimer, Hagedorn and Manovskii, and Hall. Recall that Hall’s parameterization has a
constant wage.
With Shimer’s calibration, the model has a very poor amplification mechanism.27 A 1 percent permanent rise in productivity leads only to a 1.7 percent
27 Though Table 3 contains information about the comparative statics of separation rates, we
focus the discussion on the effects of productivity. Shimer (2005) shows that in terms of equation
(1), most unemployment volatility in the U.S. economy is accounted for by variations in job
creation (the job-finding rate), as opposed to job destruction (the job-separation rate). Furthermore,

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

43

Table 3 Steady State Elasticities
Response of
to change in
Shimer
Hagedorn &
Manovskii
Hall

p

θ
b

σ

p

λw
b

σ

p

u
b

σ

1.72 −0.69 −0.07

0.48 −0.19 −0.02

−0.45

0.18

0.95

23.72 −22.51 −0.08
81.70
0.00 −8.17

6.64 −6.30 −0.02
22.88 0.00 −2.29

−6.18
−21.30

5.87
0.00

0.95
3.06

rise in market tightness, a response that is below that in the data by a factor of
16. Similarly, unemployment and the job-finding rate move very little in the
wake of a productivity change. Shimer attributes the failure of the model to the
fact that, with Nash bargaining, the wage is too closely linked to productivity
and absorbs too large a fraction of the productivity fluctuations. As a result,
profits do not rise enough to give firms the incentive to create many additional
vacancies.
Hall’s calibration imposes a constant wage.28 The consequences of this
assumption are striking: Market tightness and unemployment respond almost
50 times more than in Shimer’s baseline model. Since wages are fixed, a rise in
productivity translates entirely into profits. Firms post many more vacancies,
which also boost the volatility of the job-finding rate, λw .
Hagedorn and Manovskii’s calibration, finally, leads to the best results for
the volatility of market tightness and for the job-finding rate with respect to
productivity shocks: A 1 percent productivity increase leads to a 20 percent
increase of market tightness and a 7 percent increase of the job-finding rate.
The main problem, however, is that this calibration induces what seems to be
excessive sensitivity of u to unemployment benefits b. The elasticity is about
six—almost 20 times larger than the number resulting from Shimer’s calibration. To interpret what this magnitude means, consider a policy experiment
where unemployment benefits are raised by 15 percent; the unemployment
rate would then double under Hagedorn and Manovskii’s calibration.29
as Table 3 demonstrates, variations in the job-separation rate have a negligible effect on the jobfinding rate.
28 For the calibration of Hall’s sticky-wage model, we match the wage income share and the
unemployment benefits from the Shimer calibration. In all other respects, the calibration is the
same as for the Shimer calibration.
29 The fact that the Hagedorn and Manovskii parameters are chosen such that wages do
not respond strongly to changes in productivity implies that wages respond strongly to changes
in benefits. For the Hall calibration, wages are simply assumed to be fixed, which imposes no
additional restrictions on calibration. Thus, even though wages are less responsive than under
Hagedorn and Manovskii, changes in b have no impact on the equilibrium. When wages are
fixed exogenously, the level of benefits is irrelevant.

44

Federal Reserve Bank of Richmond Economic Quarterly

Quantitative Implications for the Cyclicality
of the Labor Share
From equation (32), it is straightforward to rewrite the elasticity of wages, w,
and the labor share, s, with respect to a productivity shock, p, as
cθ /p
β
p+β
ˆ
ηθp , and
s
s
s = w − p,
ˆ
ˆ
ˆ

w =
ˆ

where ηθp denotes the elasticity of θ with respect to p.
For Hall’s calibration, the implications are immediate—the model has
the counterfactual implication that the volatility of wages is zero and that
the correlation between the labor share and labor productivity is minus one.
With Shimer’s calibration, w ≈ 1.15, and, hence, wages respond one-forˆ
one to labor productivity, absorbing most of their impact, as explained above.
Compared to the data, wages are too volatile. The labor share is essentially
acyclical, in contrast with the data. Thus, the baseline calibration of the
matching model with a low b also fails along these two dimensions.
Hagedorn and Manovskii’s parameter choice is constructed to match w =
ˆ
0.5, and therefore s = −0.5. Under this parameterization, the model is quite
ˆ
successful in matching the elasticity of the labor share, since in the data, the
labor share is about as volatile as labor productivity and is countercyclical.
Here, it is evident that the choice made by Hagedorn and Manovskii of setting
β near zero is useful since one can reconcile a large value for ηθp with small
fluctuations in the wage and a countercyclical labor share.

8. THE MATCHING MODEL WITH AGGREGATE RISK
In the comparative statics exercise above we have studied how long-run outcomes in our model economy respond to one-time permanent changes in
parameters. Yet we want to evaluate how well the model matches the business
cycle facts of the labor market, and the business cycle is arguably better
described by recurrent stochastic changes to parameters. For this reason we
now modify the model and include stochastic productivity shocks that are
persistent but not permanent.
One might conjecture that the difference between the effects of one-time
permanent shocks and persistent—but not permanent—shocks will be smaller,
the more persistent the shocks are. In this case the difference between the
comparative statics exercise and the analysis of the explicit stochastic model
might be small since labor productivity is quite persistent. The autocorrelation
coefficient is around 0.8 (see Table 1). It turns out that the difference between
the two approaches is noticeable, but it does not overturn the basic conclusion
from the comparative statics analysis. If the calibration is such that wages

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

45

respond strongly to changes in productivity, then productivity shocks cannot
account for the volatility of the labor market.
The modified model can be analyzed in almost closed form—again
because free entry makes vacancies adjust immediately to any shock. Thus,
as before, unemployment is a state variable, but it will only influence its own
dynamics (and, residually, that of vacancies), whereas all other variables will
depend only on the exogenous stochastic shocks in the economy. Again, the
argument that backs this logic up proceeds by construction: specify an equilibrium of this sort, and show that it satisfies all the equilibrium conditions.
We will focus on a simple case in which the economy switches between
a low-productivity state, p1 = p (1 − μ), and a high-productivity state, p2 =
p (1 + μ), with μ > 0. The switching takes place according to a Poisson
process with arrival rate τ .30 The capital values of (un)matched firms and
workers, (3) to (6), are easily modified to incorporate the dependence on the
aggregate state of the economy:
rJi
rVi
rWi
rUi

= pi − wi − σ (Ji − Vi ) + τ (J−i − Ji ) ,
= −c + λf (θ i ) (Ji − Vi ) + τ (V−i − Vi ) ,
= wi − σ (Wi − Ui ) + τ (W−i − Wi ) , and
= b + λw (θ i ) (Wi − Ui ) + τ (U−i − Ui ) ,

(34)
(35)
(36)
(37)

for i = 1, 2, where −i denotes 1 if i = 2 and vice versa. Each value equation
now includes an additional capital gain/loss term associated with a change
in the aggregate state. We continue to assume that wages are determined
to implement the Nash-bargaining solution for the state-contingent surplus,
Si = Ji − Vi + Wi − Ui , and that there is free entry: Vi = 0.
We now apply the surplus value definition and the free-entry condition to
equations (34) to (37) in the same way as for the steady state analysis in the
previous sections. The equilibrium can then be characterized by the following
equations:
c
c
= pi − rUi + τ
, and (38)
(r + σ + τ )
(1 − β) λf (θ i )
(1 − β) λf (θ −i )
βλw (θ i ) c
(39)
+ τ U−i ,
(r + τ ) Ui = b +
(1 − β) λf (θ i )
for i = 1, 2. The idea is to see how an increase in μ from zero—when
μ = 0, we are formally in the previous model without aggregate shocks—
will influence labor market tightness: If p goes up by 1 percent, that is, μ
increases by 0.01, by how many percentage points does θ 1 go down and θ 2
go up? And how does the answer depend on τ ? We will find answers with
two different methods. First we will use a local approximation around μ = 0,
30 The model can easily be extended to include a large but finite number of exogenous
aggregate states.

46

Federal Reserve Bank of Richmond Economic Quarterly

which allows us to derive an elasticity analytically. Then we will look at a
particular value of τ > 0 and compute exact values for θ 1 and θ 2 .

Local Approximations
For a local approximation at a point where the two states are identical (μ = 0),
the equilibrium is symmetric such that θ 1 goes down by the same percentage
amount by which θ 2 goes up. For this case, we can show explicitly how the
equilibrium elasticity depends on the persistence parameter, τ . We solve for
the elasticity in two steps.
First, taking the total derivative of expression (38) with respect to a change
in productivity, μ yields
αc
ηi = (1 − β)
λf,i

αc
η−i ,
λf,−i
(40)
where ηi ≡ (∂θ i /∂μ) (1/θ i ) denotes the elasticity of tightness in state i with
respect to a change in productivity. Since we consider only a small productivity
difference across states, we approximate the terms in curly brackets by the nonstate-contingent steady state values for μ = 0. Furthermore, since everything
is symmetric, the solution is such that
(r + σ + τ )

(−1)i p −

∂rUi
∂μ

+ τ

η = η2 > 0 > η1 = −η.

(41)

Inspecting the results, it is easy to see that keeping the effect of productivity on
the flow value of unemployment constant, the absolute value of the elasticity is
higher, the lower τ is. The response of labor market tightness to productivity
is stronger, the more persistent the shock is. However, higher productivity
also raises the flow value of unemployment, which hurts firms, and this effect
goes in the opposite direction.
In order to understand the latter effect, we need to solve expression (39)
for the flow return on unemployment as a function of labor market tightness:
rUi = b +

β
(r + τ ) θ i + τ θ −i
c
for i = 1, 2.
1−β
r + 2τ

We see here that if there is no discounting (r = 0), productivity would not
affect the flow value of unemployment since it would raise θ 2 and lower θ 1 , but
the two effects are symmetric and cancel each other out. However, discounting
results in a larger weight on the current aggregate state. To analyze the effect
in detail, take the total derivative with respect to the change in productivity,

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

47

Table 4 Elasticity of Tightness with Respect to Productivity, ηθ p ;
Local Approximation
τ
Average Duration (in years)
Shimer
Hagedorn & Manovskii
Hall

0.00
∞
1.72
23.67
81.70

0.01
25.00
3.94
29.28
69.32

0.02
12.50
5.42
28.24
60.20

0.05
5.00
7.04
22.12
43.16

0.10
2.50
6.47
15.49
29.33

0.50
0.50
2.23
4.42
8.23

μ, to deliver31
(r + τ ) ηi + τ η−i
β
∂rUi
= cθ
for i = 1, 2.
(42)
∂μ
1−β
r + 2τ
Again using symmetry (41) in (42) we obtain
∂rU2
∂rU1
β
r
=−
= cθ
η.
(43)
∂μ
∂μ
1 − β r + 2τ
It is apparent that with discounting (r > 0), the elasticity of the flow return
on unemployment is positively influenced by productivity (it goes up in state
two relative to state one), and as shocks become more persistent (as τ falls),
the effect is stronger (for a given value of η). We also see that changes in the
persistence parameter have a bigger impact on how the flow unemployment
value responds to productivity when the persistence parameter is large: τ appears in the denominator so that when it is large, the effects are close to zero.
Intuitively, when there is almost no persistence, the flow value of unemployment almost does not react to productivity because it is so short-lived, and
small changes in persistence become unimportant too.
Inserting expression (43) into (40) and using symmetry again, one obtains
the following expression for the elasticity of labor market tightness:
(r + σ + 2τ )

αc
r
+ θβ
λf
r + 2τ

η=

(1 − β) p
.
c

(44)

In Table 4, we display the elasticity of labor market tightness with respect
to labor productivity for our three different calibrations and how the elasticity
depends on the persistence of the aggregate state. For the purpose of business
cycle analysis, an average duration of the state between 2.5 (τ = 0.1) and 5
years (τ = 0.05) appears to be appropriate. We see that for business-cycle
durations the results differ from the τ = 0 case, which reproduces the numbers from the comparative statics analysis for a one-time permanent shock. In
particular, for less-than-permanent shocks, the different calibrations produce
31 We have again approximated the state-contingent values of θ with the non-state-contingent
i
steady state value, θ.

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Federal Reserve Bank of Richmond Economic Quarterly

Table 5 Elasticity of Tightness with Respect to Productivity; Exact
Solution for μ = 0.005 and τ = 0.05
1 to 2
Shimer
Hagedorn & Manovskii
Hall

2 to 1

7.30
24.98
54.52

−6.80
−19.93
−35.28

results that are more similar. The amplification under Shimer’s calibration increases relative to the amplification under the alternative calibrations/models.
It remains true that with the Shimer calibration labor productivity fluctuations cannot account for the volatility of labor market tightness, whereas the
Hagedorn and Manovskii and Hall calibrations come close. Recall that in the
U.S. economy labor market, tightness is about 20 times as volatile as labor
productivity (see Table 1). For an arrival rate consistent with the persistence
of business cycles, τ ∈ [0.05, 0.1], labor market tightness for the Shimer calibration is only seven times more volatile than productivity, whereas for the
Hagedorn and Manovskii calibrations, tightness is 20 times more volatile than
productivity. It is 30 to 40 times as volatile for the Hall calibration.
We also confirm the theoretical analysis above regarding the effects of
persistence. The table reveals that the elasticity of labor market tightness with
respect to changes in productivity is not necessarily monotone with respect
to the arrival rate of the aggregate state change. On the one hand, the more
persistent shocks are, the more a productivity increase influences the present
value revenue of the firm. As a consequence, more firms enter and labor
market tightness goes up. However, as persistence increases, so do the costs
of the firms—they are determined by the workers’ outside options—and this
effect works in the opposite direction. Moreover, as shown above, this latter
effect is a particularly important one when persistence is large but a relatively
unimportant one when shocks are very short-lived. Thus, as Table 4 shows, the
response of labor market tightness to productivity first increases as persistence
goes up and then decreases when shocks become close to permanent, and the
effect on workers’ outside options dominates.

Exact Solution
In Table 5 we display exact results for a case in which a switch from the
low productivity to the high productivity represents a 1 percent change in
productivity. For Shimer’s calibration, this results in a 7.3 percent increase or
a 6.8 percent reduction of labor market tightness. The approximation in Table
4 for τ = 0.05 is roughly the average of the elasticities reported in Table 5;
thus, the accuracy of the approximations is reasonable.

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment
9.

49

CONCLUSION: WHERE NEXT?

We have reviewed recent literature that assesses the ability of the search/
matching model of the labor market to match some key characteristics of labor
markets, namely, the large fluctuations in vacancies and in unemployment. We
have, in particular, discussed what features of a calibration seem necessary
for matching the data within the context of the standard model or of one
augmented with an assumption that real wages are rigid. In this discussion,
we have tentatively concluded that there is no wholly satisfactory calibration of
the basic setup or a simple alteration thereof that allows the key characteristics
of the data to be roughly reproduced. On the one hand, one can assume that
the value of being at home is almost as large as that of having a job, but that
seems somewhat implausible on a priori grounds, and it implies that there
must also be strong sensitivity of unemployment to unemployment benefits,
which arguably we do not observe. On the other hand, one can assume rigid
wages, but we show that rigid wages necessitate a wage share close to one in
order to be powerful in creating large fluctuations in labor market variables,
and this route moreover produces an excessively volatile labor share.
It is an open question as to where one might go next. In our view, it
seems important to first examine a model with capital, because the results we
report above are very sensitive to the value of the labor share. In a model with
capital, there is no ambiguity about how one should interpret the labor share.
Moreover, a model with capital offers another natural source of fluctuations in
vacancies and unemployment, namely, fluctuations in the price of investment
goods. Such fluctuations will directly influence the incentives for firms to
enter/open new vacancies, and, hence, seem a promising avenue for further
inquiry.

REFERENCES
Andolfatto, David. 1996. “Business Cycles and Labor Market Search.”
American Economic Review 86 (1): 112–32.
Atkinson, Anthony B., and John Micklewright. 1991. “Unemployment
Compensation and Labor Market Transitions: A Critical Review.”
Journal of Economic Literature 29 (4): 1679–1727.
Bover, Olympia, Manuel Arellano, and Samuel Bentolila. 2002.
“Unemployment Duration, Benefit Duration and the Business Cycle.”
Economic Journal, Royal Economic Society 112 (127): 223–65.
Costain, James S. and Michael Reiter. 2003. “Business Cycles,

50

Federal Reserve Bank of Richmond Economic Quarterly
Unemployment Insurance, and the Calibration of Matching Models.”
CESifo Working Paper 1008.

Fisher, Jonas D.M. 2003. “Technology Shocks Matter.” Federal Reserve
Bank of Chicago Working Paper 2002-14, rev. 2003.
Fortin, Bernard, Guy Lacroix, and Simon Drolet. 2004. “Welfare Benefits
and the Duration of Welfare Spells: Evidence from a Natural Experiment
in Canada.” Journal of Public Economics 88 (7–8): 1495–1520.
Greenwood, Jeremy, Zvi Hercowitz, and Per Krusell. 2000. “The Role of
Investment-Specific Technological Change in the Business Cycle.”
European Economic Review 44 (1): 91–115.
Hagedorn, Marcus, and Iourii Manovskii. 2005. “The Cyclical Behavior of
Equilibrium Unemployment and Vacancies Revisited.” Mimeo,
University of Pennsylvania.
Hall, Robert E. 2005. “Employment Fluctuations with Equilibrium Wage
Stickiness.” American Economic Review 95 (March): 50–65.
Hornstein, Andreas, Giovanni L. Violante, and Per Krusell. Forthcoming.
“The Replacement Problem in Frictional Economies: A Near
Equivalence Result.” Journal of the European Economic Association.
Hosios, Arthur J. 1990. “On the Efficiency of Matching and Related Models
of Search and Unemployment.” Review of Economic Studies 57(2):
279–98.
Lagos, Ricardo. 2000. “An Alternative Approach to Search Frictions.”
Journal of Political Economy 108 (October ): 851–73.
Merz, Monika. 1995. “Search in the Labor Market and the Real Business
Cycle.” Journal of Monetary Economics 36 (2): 269–300.
Mortensen, Dale T., and Christopher A. Pissarides. 1994. “Job Creation and
Job Destruction in the Theory of Unemployment.” Review of Economic
Studies 61 (3): 397–416.
Nash, John F. 1950. “The Bargaining Problem.” Econometrica 18 (2):
155–62.
Organisation for Economic Co-operation and Development. 1996. OECD
Employment Outlook. OECD: Paris.
Osborne, Martin J., and Ariel Rubinstein. 1990. Bargaining and Markets.
San Diego: Academic Press.
Petrongolo, Barbara, and Christopher A. Pissarides. 2001. “Looking into the
Black Box: A Survey of the Matching Function.” Journal of Economic
Literature 39 (2): 390–431.

A. Hornstein, P. Krusell, and G. L. Violante: Models of Unemployment

51

Pissarides, Christopher A. 1985. “Short Run Equilibrium Dynamics of
Unemployment, Vacancies, and Real Wages.” American Economic
Review 75 (4): 676–90.
. 2000. Equilibrium Unemployment Theory, 2nd edition.
Cambridge: MIT Press.
Prescott, Edward C. 1986. “Theory Ahead of Business Cycle Measurement.”
Federal Reserve Bank of Minneapolis Quarterly Review 10 (Fall): 9–22.
Rogerson, Richard, Robert Shimer, and Randall Wright. Forthcoming.
“Search-Theoretic Models of the Labor Market.” Journal of Economic
Literature.
Shimer, Robert (2004). “The Consequences of Rigid Wages in Search
Models.” Journal of the European Economic Association (Papers and
Proceedings) 2 (May–April), 469–79.
. 2005. “The Cyclical Behavior of Equilibrium
Unemployment and Vacancies.” American Economic Review 95
(March): 24–49.
van Ours, Jan C., and Milan Vodopivec. 2004. “How Changes in Benefits
Entitlement Affect Job-Finding: Lessons from the Slovenian
‘Experiment.’” Institute for the Study of Labor Discussion Paper 1181.

Oil Prices and Consumer
Spending
Yash P. Mehra and Jon D. Petersen

A

lthough a large body of empirical research indicates that oil price
increases have a significant negative effect on real GDP growth, considerable debate exists about both the strength and stability of the
relation between oil prices and GDP. In particular, some analysts contend that
the estimated linear relations between oil prices and several macroeconomic
variables appear much weaker since the 1980s (Hooker 1996).1
The evidence of a weakening effect of an oil price change on the macroeconomy in data since the 1980s happens to coincide with another change in
the nature of oil price movements: Before 1981, most big oil price movements
were positive. Since then, however, oil prices have moved significantly in both
directions, reflecting the influences of endogenous macrodevelopments on oil
prices. The choppy nature of oil price movements since the 1980s has led some
analysts to argue that evidence indicating that oil price changes do not have
much of an effect on real GDP is spurious and that the evidence arises from
the use of endogenous oil price series. Hamilton (2003), in fact, posits that the
relation between oil price changes and real GDP growth is nonlinear, namely,
that oil price increases matter but oil price declines do not. Furthermore,
oil price increases that occur after a period of stable oil prices matter more
than those increases that simply reverse earlier declines. He shows that if
the true relation is nonlinear and asymmetric as described above, then the
standard linear regression that relates real growth to oil price changes would
The authors thank Hubert Janicki, Bob Hetzel, Pierre Sarte, and John Weinberg for many
helpful comments. The views expressed are those of the authors and do not necessarily represent the views of the Federal Reserve Bank of Richmond or the Federal Reserve System.
All errors are our own.

1 Hooker (1996) reports evidence that oil price changes no longer predict many U.S. macroeconomic indicator variables in data after 1973 and that the estimated linear relations between oil
price increases and real economic activity indicator variables do appear weaker since the 1980s.
Hooker (2002) also reports evidence of weakening of the link between oil prices and inflation
since the 1980s.

Federal Reserve Bank of Richmond Economic Quarterly Volume 91/3 Summer 2005

53

54

Federal Reserve Bank of Richmond Economic Quarterly

spuriously appear unstable over a sample period spanning those two subperiods of different oil price movements.
In order to capture the above-noted hypothesized nonlinear response of
GDP growth to oil price changes, Hamilton has proposed a nonlinear transformation of oil price changes. In particular, he uses a filter that weeds out
oil price drops and measures increases relative to a reference level, yielding
what he calls “net oil price increases.”2 This nonlinear filter, when applied to
oil price changes, is supposed to weed out short-term endogenous fluctuations
in oil prices, leaving big oil price increases that may reflect the effect of exogenous disruptions to oil supplies. He then shows that the estimated linear
relation between net oil price increases and real growth is strong and depicts
no evidence of parameter instability over the period 1949 to 2001.3
In discussing why oil price shocks have an asymmetric effect on real
GDP growth, Hamilton, among others, has emphasized both the “demandside” and “allocative” channels of influence that oil price shocks have on the
real economy. On the demand side, a big disruption in energy supplies has
the potential to temporarily disrupt purchases of large-ticket consumption and
investment goods that are energy-intensive because it raises uncertainty about
both the future price and availability of energy, as in Bernanke (1983).4 Both
households and firms may find it optimal to postpone purchases until they
have a better idea of where energy prices are headed after an oil price shock,
leading to potential changes in the mix of consumption and investment goods
they demand. This postponement and/or shift in the mix of demand may have
a nonlinear effect on the economy working through the so-called “allocative”
channels that become operative when it is costly to reallocate capital and labor
between sectors affected differently by oil price changes. In particular, both
2 Quite simply, his series of net oil price increases is defined as the percentage change from
the highest oil price change over the past four, eight, or twelve quarters, if positive, and zero
otherwise. This procedure yields net oil price increases measured relative to past one-, two-, and
three-year peaks.
3 Worth noting is that Hamilton (1996, 2003) was not the first to provide evidence of an
asymmetric response to oil price increases and oil price declines. Mork (1989) provided evidence
indicating that oil price increases had a negative effect on real GNP growth whereas oil price
declines did not. However, Hamilton’s (2003) paper is the first “rigorous” statistical test of nonlinearity, using flexible functional forms.
4 The basic argument is that oil price uncertainty may be as important of a determinant of
economic activity as the level of oil prices. In case of investment, Bernanke (1983) shows it
is optimal for firms to postpone irreversible investment expenditures when they face an increased
uncertainty about the future price of oil. When the firm is faced with a choice between adding
energy-efficient or energy-inefficient capital, increased uncertainty raises the option value associated
with waiting to invest, leading to reduced investment. Hamilton (2003, 366) makes a similar
argument for the postponement of purchases of consumer goods which are intensive in the use of
energy.

Y. P. Mehra and J. D. Petersen: Oil Prices and Consumer Spending

55

oil price increases and decreases may have a negative effect on GDP growth
if oil price effects work primarily through allocative channels.5
Of course, oil price increases may affect aggregate spending through other
widely known channels. For instance, because oil price increases lead to
income transfers from countries that are net importers of oil, such as the
United States, to oil-exporting countries, it is plausible for the oil-importing
countries to exhibit a reduction in spending. Since an increase in the price of
oil would lead to an increase in the overall price level, real money balances
held by firms and households would be reduced through familiar monetary
channels including the Federal Reserve’s counter-inflationary monetary policy
response.6 These income-transfer and real-balance channels, however, imply
a symmetric relation between oil price changes and GDP growth.
The asymmetric effect of oil price changes on GDP growth may arise if we
consider oil price effects generated through all three channels described above
because oil price effects, working through allocative channels, are asymmetric
with respect to oil price changes. However, that is not the case for oil price
effects working through other channels. Thus, an oil price increase is likely
to depress GDP because all three channels (income-transfer, real-balance, and
allocative) work to depress aggregate demand in the short run. In contrast,
an oil price decline may not stimulate GDP because the positive effect of
lower oil prices on aggregate demand generated through the real-balance and
income-transfer channels is offset by the negative effect on demand generated
through the so-called allocative channels. Another potential contributory factor is the asymmetric response of monetary policy to oil prices—the Federal
Reserve tightening policy in response to oil price increases but not pursuing
expansionary policies in the face of oil price declines.
This article investigates how much of the negative effect of an oil price
increase on real GDP growth works through the consumption channel. As
noted above, many analysts have emphasized that big spikes in oil prices affect
real growth because they may lead consumers to postpone purchases of largeticket, energy-guzzling consumption goods. Of course, oil price increases
may affect consumer spending, working through other widely known incometransfer and real-balance channels. Another issue investigated here is whether
the asymmetric relation between oil prices and real GDP growth found in data
holds at the consumption level.
The empirical methodology used to identify the effect of an oil price
increase on consumer spending is straightforward: We test for the direct effect
of an oil price change on spending that is beyond what can be accounted for by
5 Hamilton (1988) provides a theoretical model in which oil price increases and declines may

adversely affect real economic activity because of the high cost of reallocating labor or capital
among sectors affected differently by oil price changes.
6 A good review of these channels appears in Mork (1994).

56

Federal Reserve Bank of Richmond Economic Quarterly

Figure 1 Quarterly Changes in Oil Prices
Panel A: BEA Prices

25
20
15
10
5
0
-5
-10
-15
-20
-25
1959

1963

1967

1971

1975

1979

1983

1987

1991

1995

1999

2003

Panel B: PPI Prices

60
40
20
0
-20
-40
-60
1959

1963

1967

1971

1975

1979

1983

1987

1991

1995

1999

2003

Notes: The BEA oil price series is an index of gas and oil, normalized to 100 in 1982,
and deflated. The PPI oil price series is an index of crude oil, normalized to 100 in 1982,
deflated, and not seasonally adjusted. The quarterly changes represent the first difference
of the log of the prices, multiplied by 100.

other economic determinants of spending, such as households’ labor income
and net worth. We alternatively measure oil price shocks as “positive oil price
increases” (Mork 1989) or “net oil price increases” (Hamilton 1996, 2003).
The sample period studied is 1959:Q1 to 2004:Q2.
The empirical work presented here finds evidence of a nonlinear relation between oil price changes and growth in real consumer spending: Oil
price increases have a negative effect on spending whereas oil price declines
have no effect. The estimated negative effect of an oil price increase on
consumer spending is large if oil price increases are measured as net increases, suggesting oil price increases that occur after a period of stable oil
prices matter more than those increases that simply reverse earlier declines.
Furthermore, the estimated negative effect on spending is also large if consumer spending is broadly defined to include spending on durable goods,
suggesting the possible negative influence of oil price increases on the purchase
of big-ticket consumption goods. Finally, the estimated oil price coefficients in

Y. P. Mehra and J. D. Petersen: Oil Prices and Consumer Spending

57

the consumption equation do not show parameter instability during the 1980s,
the period when oil prices moved widely for the first time in both directions.
This article is organized as follows. Section 1 examines the behavior
of two oil price series to highlight the choppy nature of oil price changes
since 1981 and to derive estimates of oil shocks as defined in Hamilton (1996,
2003). Section 2 presents the aggregate empirical consumer spending equation
that underlies the empirical work here and reviews theory about how oil price
shocks may affect the macroeconomy. Section 3 presents the empirical results,
and Section 4 contains concluding observations.

1. A PRELIMINARY REVIEW OF OIL PRICE CHANGES AND
NET OIL PRICE INCREASES
In this section we first examine the behavior of two oil price series and then review the rationale behind the construction of net oil price increases as measures
of oil price shocks, as in Hamilton (1996, 2003). The first series, prepared
by the Bureau of Economic Analysis (BEA), measures gas and oil prices paid
by consumers. The second series is the Producer Price Index (PPI) for crude
petroleum prepared by the Bureau of Labor Statistics (BLS). In estimating the
impact of oil price increases on real GDP growth, analysts have commonly
focused on the oil price series for crude petroleum. We, however, focus on the
consumer oil price series because changes in consumer spending are likely to
be correlated with changes in oil prices actually faced by consumers rather
than with changes in the producer price of crude petroleum.
Figure 1 plots the first differences of logs of these two oil price indexes.
(The reported differences are multiplied by 100.) This figure highlights one
key change in the time-series behavior of oil price changes over 1959 to 2004:
Before 1981, big oil price movements were mostly positive. Since then,
however, oil prices have moved widely in both directions. Hamilton argues
that this change in the time-series behavior of oil price changes reflects the
growing influence of endogenous macroeconomic developments on oil prices,
namely that oil prices during the 1980s had been influenced dramatically by
demand conditions. As a result of the increased endogenous nature of oil price
movements, the estimated linear relation between oil price changes and real
GDP growth appears unstable over the sample period that includes pre- and
post-1980s oil price changes.
Hamilton proposes a nonlinear transformation of oil price changes in order
to uncover the relation between the exogenous oil price movements and GDP
growth. As indicated at the outset, he uses a filter that leaves out oil price
declines and measures increases relative to a reference level, yielding what
he calls net oil price increases. Briefly, a net oil price increase series is the
percentage change from the highest oil price reached over the past four, eight,
or twelve quarters, if positive, and zero otherwise.

58

Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 Using BEA’s Oil Price Index
Panel A: Changes in Oil Prices
16
14
12
10
8
6
4
2
0
1959

1963

1967

1971

1975 1979 1983

1987

1991

1995

1999

2003

1996

2000

2004

1997

2001

2005

Panel B: Net Oil Price Changes (1-year Horizon)
16
14
12
10
8
6
4
2
0
1960

1964

1968

1972

1976 1980 1984

1988

1992

Panel C: Net Oil Price Changes (2-year Horizon)
16
14
12
10
8
6
4
2
0
1961

1965

1969

1973

1977 1981 1985

1989

1993

Notes: The oil price index is for the BEA’s index of gas and oil, and it is deflated. The
net oil price increase is the maximum of (a) zero and (b) the difference between the log
level of the oil price index for quarter t and the maximum value for the level achieved
during the previous four (Panel B) or eight (Panel C) quarters.

Y. P. Mehra and J. D. Petersen: Oil Prices and Consumer Spending

59

Figure 2 plots oil price increases using the consumer oil price series.
Panel A of Figure 2 plots only quarterly increases, whereas Panels B and C
plot net oil price increases measured relative to past one- and two-year peaks,
respectively. If we compare Panels A, B, and C, we may note that the use
of a nonlinear filter results in weeding out certain increases in oil prices that
were simply corrections to earlier declines. For example, the big spike in oil
prices observed during the first quarter of 2003 does not show up in the net
oil price increases measured relative to two-year peaks because it followed
the big decline of oil prices in 2001. If we focus on net oil price increases
measured over two-year peaks, we get relatively few episodes of oil price
spikes, occurring in 1973–1974, 1979–1980, 1990, 1999–2000, and 2004.
Hamilton argues that these oil price spikes can be attributed to disruptions in
oil supplies associated with military conflicts and, hence, exogenous to the
U.S. economy, with one exception.7 The most recent spike in oil prices may
be attributed mainly to the surge in world oil demand (Hamilton 2004).
Figure 3 plots net oil price increases using both oil price series. Two
observations stand out. The first is that the net oil price increase series for crude
petroleum gives qualitatively similar inferences about the nature of oil price
movements as does the consumer price series for gas and oil. However, net oil
price increases measured using the consumer oil price series are significantly
smaller than those derived using the producer price of crude petroleum. The
empirical work presented below uses the net oil price increases created using
the consumer oil price series.

2.

EMPIRICAL AGGREGATE CONSUMER SPENDING
EQUATIONS

The empirical strategy used to identify the consumption effect on an oil price
increase is to look for the direct impact of a “net oil price increase” on
consumer spending beyond that which can be accounted for by other economic determinants of consumption. We use as control variables economic
determinants suggested by the empirical “life-cycle” aggregate consumption
equations estimated in Mehra (2001). The empirical work in Mehra (2001)
identifies income and wealth as the major economic determinants of consumer
spending, and the “life-cycle” aggregate consumption equations provide sensible estimates of income and wealth elasticities, besides predicting reasonably
well the short-term behavior of consumer spending. In particular, the empirical short-term consumption equation used here is based on the following
consumption equations:
7 The dates of military conflicts that led to declines in world production of oil are November

1973 (Arab-Israel War), November 1978 (Iranian Revolution), October 1980 (Iran-Iraq War), and
August 1990 (Persian Gulf War). See Hamilton (2003, 390).

60

Federal Reserve Bank of Richmond Economic Quarterly

Figure 3 Comparison of Oil Price Increases
Panel A: Increases in Oil Prices
45
40
35

BEA

30

PPI

25
20
15
10
5
0
1959

1963

1967

1971

1975 1979 1983 1987 1991 1995
Panel B: Net Oil Price Increases (1-year Horizon)

1999

2003

2000

2004

2001

2005

35
30

BEA

25

PPI

20
15
10
5
0
1960

1964

1968

1972

1976

1980

1984

1988

1992

1996

Panel C: Net Oil Price Increases (2-year Horizon)
35
30
BEA
25
PPI
20
15
10
5
0
1961

1965

1969

1973

1977

1981

1985

1989

1993

1997

Notes: The oil price series are identical to those of Figures 1 and 2.

Y. P. Mehra and J. D. Petersen: Oil Prices and Consumer Spending

p

e
Ct = a0 + a1 Yt + a2 Yt+k + a3 Wt , and

p

p

Ct = b0 + b1 Ct−1 − Ct−1 + b2 Ct +

k
s=1

b3s Ct−s + μt ,

61

(1)

(2)

p

where Ct is planned current consumption, Ct is actual current consumption,
Yt is actual current-period labor income, Wt is actual current-period wealth,
e
and Yt+k is average anticipated future labor income over the earning span (k)
of the working-age population.
Equation 1 simply states that aggregate planned consumption depends
upon the anticipated value of lifetime resources, which equals current and
anticipated future labor income and current value of financial assets. This
equation identifies income and wealth as the main economic determinants of
aggregate planned consumption.
Equation 2 allows for the possibility that actual consumption in a given period may not equal planned consumption, reflecting the presence of adjustment
lags and/or habit persistence. In this specification, changes in current-period
consumption depend upon changes in current-period planned consumption,
the gap between last period’s planned and actual consumption, and lagged
actual consumption. The disturbance term μ in (2) captures the short-run influences of unanticipated shocks to actual consumer spending. If we substitute
(1) into (2), we get the short-run dynamic consumption equation (3):

Ct

p

e
= b0 + b1 (Ct−1 − Ct−1 ) + b2 (a1 Yt + a2 Yt+k + a3 Wt )

+

k
s=1

b3s Ct−s + μt .

(3)

The key feature of equation (3) is that changes in current-period consumption depend upon changes in income and wealth variables, besides depending upon the last period’s gap between the level of actual and planned
consumption.
We estimate the “direct” influence of oil price changes on consumer spending by including lagged values of net oil price increases in the short-term
consumption equation (3). As another control variable, we also include lagged
values of changes in the nominal federal funds rate in order to capture the
possible additional influence of changes in short-term interest rates on consumer spending. The inclusion of a short-term nominal interest rate in the
consumption equation also controls for the potential influence of oil price

62

Federal Reserve Bank of Richmond Economic Quarterly

increases on spending that work through the monetary policy channel, arising
as a result of the Federal Reserve’s monetary policy response to oil shocks.8
The empirical work below makes two additional assumptions. The first is
that expected future labor income is simply proportional to expected current
labor income. The second assumption is that current-period values of income
and wealth variables are not observed, and, hence, planned consumption depends upon their known past values. Under these assumptions, the estimated
short-consumption equation is
Ct

p

= β 0 + β 1 (Ct−1 − Ct−1 ) + β 2 Yt−1 + β 3 Wt−1
+

6
s=1

β 4s Ct−s +

3
s=1

β 5s Oil Pr icest−s +

(4)

3
s=1

β 6s F Rt−s ,

where
p

C t = α 0 + α 1 Yt + α 2 W t .
In the empirical, short-term consumption equation (4), changes in current
consumer spending depend on lagged values of changes in income, net worth,
the short-term nominal interest rate, and oil prices, besides depending on
lagged changes in consumption and the gap between the level of actual and
planned consumption.

3.

OIL PRICE EFFECT CHANNELS AND
THE REDUCED-FORM EMPIRICAL EVIDENCE

In this section, we review theory on how oil price increases may affect the
real economy and discuss its implications for interpreting the evidence of a
relation between oil price changes and consumer spending found using the
aggregate consumer spending equation (4).
How do oil prices, in theory, affect the macroeconomy? A simple answer is that previous research does not offer any dominant theoretical mechanism.9 Researchers have emphasized several different theoretical mechanisms
through which oil may affect the macroeconomy. One of those mechanisms
focuses on the inflation effect of oil price increases and its associated consequences that work through the so-called real-balance and monetary policy
8 A debate exists about whether the contractionary consequences of oil price shocks are due
to oil price shocks themselves or to the monetary policy that responds to them. The evidence so
far is not very conclusive. See, for example, Leduc and Sill (2004) who investigate this question
in a calibrated general equilibrium model in which oil use is tied to capital utilization. Their
findings suggest that while the monetary policy rule in place can contribute to the magnitude of
the negative output response to an oil-price shock, the “direct” effect of the oil-price increase is
the more important factor.
9 See Hooker (2002), Hamilton (2003), and references cited in both.

Y. P. Mehra and J. D. Petersen: Oil Prices and Consumer Spending

63

channels. The real-balance channel posits that oil price increases lead to
inflation, lowering real money balances held by the households and firms
in the economy and thereby depressing aggregate demand through familiar
monetary channels. The monetary policy channel becomes operative if the
Federal Reserve tightens policy in response to inflation induced by oil prices,
which may exacerbate further the negative output effect associated with oil
shocks.
Another theory of how oil may affect the macroeconomy arises out of
viewing an oil price as an import price. In particular, oil price increases
lead to income transfers from countries that are net importers of oil, such as
the United States, to oil-exporting countries. The first-round effect of this
reduction in income is to cause economic agents in oil-importing countries to
reduce their spending, leading to reduced aggregate demand. 10
Some other channels through which oil may affect the macroeconomy
arise when oil is modeled as another input in the production function. If oil
and capital are complements in the production process, then oil price increases
lead to a decline in the economy’s productive capacity as agents respond to
higher oil prices by reducing their utilization of both oil and capital. In this
case, oil price increases lead to negative transitional output growth as the
economy moves to a new steady-state equilibrium growth path. To the extent
oil price increases raise uncertainty about both its future price and availability,
oil price increases may also lead to the postponement of purchases of largeticket consumption and investment goods, as in Bernanke (1983).11 Hence,
oil price increases have the potential to affect real growth by reducing both
potential output and aggregate demand.
Another theoretical mechanism that links oil to the macroeconomy has
emphasized the allocative effects of oil price shocks (Hamilton 1988, 2003).
An oil price increase is likely to reduce demand for some goods but possibly
raise demand for some others. For example, demand for inputs is likely to fall
in sectors that use energy but likely to increase in sectors that produce energy.
If it is costly to reallocate capital or labor between sectors affected differently
by an oil price increase, then aggregate employment and output will decline
in the short run. In this framework, an oil price decrease may also lower
demand for some goods (demand for inputs used in energy-producing sector)
and, hence, may be contractionary if labor or capital could not be moved to
favorably affected sectors.
10 The second-round effects arise from, among others, the recycling of income transfers, which
is increased income of oil-exporting countries that leads to increased demand for products of the
oil-importing countries, thereby offsetting the initial fall in aggregate demand. A recent empirical
study, however, finds that among most oil importing countries, including the United States, oil price
increases have a negative effect on economic activity (Jimenez-Rodriguez and Sanchez 2004).
11 See footnote 4.

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Federal Reserve Bank of Richmond Economic Quarterly

The discussion above implies that oil price increases may, in theory, affect real growth through several different channels, as emphasized by different
researchers. This review then raises another question: Does the empirical evidence reported in previous research support any dominant theoretical mechanism? The answer to this question again appears to be “no” because most
of the empirical evidence is based on estimated reduced-form regressions that
relate changes in GDP growth to changes in oil prices, controlling for the
influences of some other variables on real growth such as lagged real GDP
growth, short-term interest rate, import price inflation, etc. As is well known,
the evidence based on reduced-form regressions indicating that oil price increases have a significant effect on the macroeconomy may be consistent with
several different theoretical mechanisms.
However, analysts who have reported the empirical evidence of the nonlinear and asymmetric relation between oil prices changes and real GDP growth
assert that such evidence does appear to favor mechanisms in which oil shocks
affect real GDP through the so-called uncertainty and allocative channels, as
in Hamilton (2003). The main reason for the emphasis on allocative channels is that other channels, such as income-transfer and real-balance, imply
a symmetric relationship between oil price changes and GDP growth. The
asymmetry may arise because oil price effects that work through allocative
channels differ from those that work through other channels already mentioned. Thus, an oil price increase is likely to depress GDP because all three
channels described above (income-transfer, real-balance, and allocative) work
to depress aggregate demand. In contrast, an oil price decline may not stimulate GDP because the positive effect of lower oil prices on aggregate demand
generated through the real-balance and income-transfer channels is offset by
the negative effect on demand generated through the so-called allocative channels. Another factor that may augment the asymmetric response of oil prices to
GDP is the asymmetric response of monetary policy to oil prices—the Federal
Reserve tightening policy in response to oil price increases but not pursuing
expansionary policies in face of oil price declines.12
Given the considerations noted above, we investigate whether oil price
increases directly affect consumer spending and whether the nonlinear and
asymmetric relation between oil prices and real GDP found in previous research hold at the consumption level.
12 Some analysts have argued that during the 1980s and 1990s the Federal Reserve followed
an “opportunistic” disinflation policy in the sense that if actual inflation declined due to some
shocks, the Federal Reserve lowered its inflation target and adjusted policy to maintain the lower
inflation rate. Since oil price shocks have been an important source of movements in inflation,
the Federal Reserve following an opportunistic disinflation policy may not follow an expansionary
policy if actual inflation falls below its short-term target in response to an oil price decrease. In
that regime, a relatively tight policy offsets the expansionary effect of an oil price decrease on
the real economy. The quantitative importance of this oil-price policy interaction channel remains
a subject of future research.

Y. P. Mehra and J. D. Petersen: Oil Prices and Consumer Spending
4.

65

EMPIRICAL RESULTS

In this section, we present and discuss the evidence regarding the effect of oil
price changes on consumer spending, using estimated reduced-form consumer
spending equations as shown in (4). The consumption equations are estimated
using quarterly data over 1962:Q1 to 2004:Q2 and measurement of variables
as in Mehra (2001).13

Estimates of Oil Price Effects
Table 1 reports coefficients from the short-term consumption equation (4)
estimated using total consumer spending and three different measures of oil
price changes: quarterly oil price changes, positive increases in oil price,
and net oil price increases. We report the sum of coefficients that appear
on the oil price variable and the t-value for a test of the null hypothesis that
the sum of oil price coefficients is zero. Since the consumption equation is
estimated including lagged consumption, the cumulative response of spending
to an oil price increase is likely to differ from its short-term response. Hence,
we also report the cumulative size of the coefficient that appears on the oil
price variable, which is just the short-term oil price coefficient divided by
one minus the sum of estimated coefficients on lagged consumption. We
also report estimated coefficients on other control variables that appear in
the short-term consumption equation, including lagged consumption, labor
income, household net worth, and the short-term interest rate.
The columns labeled (1) through (5) in Table 1 contain coefficients from
the short-term consumption equation estimated using different measures of oil
price changes. The estimates with quarterly oil price changes are in column
(1), those with positive oil price changes are in column (2), and those with net
oil price increases measured relative to one-, two-, and three-year peaks are in
columns (3), (4), and (5), respectively. If we focus on the oil price coefficient,
the estimated coefficient on the oil price variable has a negative sign and is
statistically different from zero only when oil price changes are measured either as oil price increases or net oil price increases (compare t-values on the
oil price change variable in different columns of Table 1). The estimated coefficient on the quarterly oil price change variable is small and not statistically
different from zero. The small t-value of the null hypothesis that the estimated
coefficient on oil price declines when added into the short-term consumption
equation containing oil price increases, given in column (2), suggests that oil
13 Consumption is measured as per capita consumption of durables, nondurables, and services
in 2000 dollars (C). Labor income is measured as per capita disposable labor income, in 2000
dollars (Y ). Household wealth is measured as per capita household net worth in 2000 dollars. The
short-term interest rate is the nominal federal funds rate. The oil price series measures gas and
oil prices paid by consumers, prepared by the BEA.

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Table 1 Empirical Aggregate Consumer Spending Equations

ct

p

= β 0 + β 1 ct−1 − ct−1 + β 2 yt−1 + β 3 wt−1 +
6

β 4s ct−s +

s=1

3
s=1

β 5s oilpricest−s +

3

β 6s F Rt−s

s=1

p

where ct = f0 + f1 yt + f2 wt + f3 T Rt
Independent
Variables
ct−s
yt−1
w1
F Rt−s
p
ct−1 − ct−1
oilt−s
P oilt−s
NP oilt−s
1-year
2-year
3-year
Adj.R 2
SER
Cumulative oil
price coefficient

(1)
0.660
0.110
0.050
−0.003
−0.130
−0.100

(2)

(3)

(4)

(5)

(4.6) 0.560 (4.2) 0.580 (4.5) 0.540 (4.2) 0.530 (4.0)
(2.4) 0.120 (2.5) 0.100 (2.1) 0.100 (2.0) 0.100 (2.1)
(2.5) 0.050 (2.9) 0.040 (2.6) 0.040 (2.6) 0.040 (2.3)
(4.5) −0.003 (4.3) −0.003 (4.3) −0.003 (4.1) −0.003 (4.1)
(3.3) −0.120 (3.0) −0.120 (3.1) −0.130 (3.3) −0.130 (3.2)
(0.4)
−0.030 (1.6)
−0.050 (1.8)

0.3600
0.0055
−0.0200

0.3800
0.0054
−0.0800

0.3700
0.0054
−0.1200

−0.070 (2.1)
0.3800
0.0053
−0.1600

−0.070 (2.1)
0.3800
0.0053
−0.1600

Notes: The coefficients (t-values in parentheses) reported above are ordinary least squares
estimates of the short-term consumption equation. c is change in real consumer spending, y is change in labor income, w is change in net worth, F R is change in the
nominal federal funds rate, cp is planned consumption, oil is change in oil prices,
P oil is positive changes in oil prices, N P oil is net oil price increases measured relative to one-, two-, and three-year peaks, Adj.R 2 is the adjusted R-squared, and SER is
the standard error of regression.
The coefficient reported on ct−s is the sum of coefficients that appear on six lagged
values of consumer spending and the coefficient on the oil price variable is the sum of
coefficients that appear on three lagged values of the oil price variable. The cumulative
oil price coefficient is the coefficient on lagged oil divided by one minus the coefficient
on lagged consumption. The effective sample period is 1961:Q1 to 2004:Q2.

price declines have no effect on consumer spending. Together these estimates
suggest only oil price increases have a negative effect on consumer spending,
implying the presence of an asymmetric relation between oil price changes
and consumer spending.
The estimated size of the cumulative oil price response coefficient is −0.08
when oil price changes are measured as oil price increases and ranges between
−0.12 to −0.16 when oil price changes are measured as net oil price increases.

Y. P. Mehra and J. D. Petersen: Oil Prices and Consumer Spending

67

Those estimates imply that a 10 percent increase in oil prices is associated
with the level of consumer spending at the end of six quarters being anywhere
between 0.80 percent to 1.60 percent lower than what it otherwise would
be. This effect includes the direct effect of the net oil price increase and the
indirect effect that comes through lagged consumption. Given that consumer
spending is two-thirds of GDP, the above estimates imply that a 10 percent
increase in the price of oil working through the consumption channel will be
associated with the level of GDP that is anywhere between one-half to one
percentage point lower than what it otherwise would be. In Hamilton (2003),
a 10 percent increase in the price of oil is associated with the level of GDP
that is 1.4 percent lower than what it otherwise would be, which is above
the estimated range, suggesting oil price increases may also affect real GDP
working through investment and other components of aggregate demand.
It is worth pointing out that estimated coefficients on other variables such
as household labor income, net wealth, and changes in the short-term nominal
interest rate have theoretically correct signs and are statistically different from
zero (see t-values for those variables in different columns in Table 1). Furthermore, the estimated coefficient on the so-called error-correction variable,
which measures the effect on current spending of last period’s gap between
actual and planned spending, as in (4), is correctly negatively signed and
statistically different from zero.
Table 2 presents some robustness analysis of oil price effects with respect to few changes in the specification of the aggregate consumer spending equation. The estimates of oil price effects discussed above are derived
using consumer spending that includes spending on durable goods because oil
price shocks are hypothesized to affect spending on big-ticket consumer goods
that are intensive in the use of energy. But since oil price increases may affect
consumer spending by working through other channels, we also estimate the
short-term consumption equations that include spending only on nondurable
goods and services. Furthermore, we also estimate the aggregate consumer
spending equation without controlling for the direct effect of changes in the
short-term nominal interest rate on spending. Many analysts have argued that
the negative effect of oil price shocks observed on real GDP growth may be
due not to oil price shocks themselves but to the monetary policy response to
them. Although this issue can not be examined in a rigorous manner using
reduced-form spending equations, we offer some preliminary evidence by examining whether the magnitude of oil price effects on consumer spending is
sensitive to the exclusion of the interest rate variable.
Table 2 reports estimates of the cumulative oil price coefficient found
using consumer spending on nondurable goods and services with and without
the interest rate. It also includes results of total consumer spending. Three
observations stand out: The first is that the estimated negative effect of an oil
price increase on consumer spending is large if spending is broadly defined to

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Federal Reserve Bank of Richmond Economic Quarterly

Table 2 Sensitivity Analysis
Cumulative Oil Price Coefficient
Measures of Consumer Spending
Consumer spending including durables
with F Rt−s
without F Rt−s
Consumer spending without durables
with F Rt−s
without F Rt−s

P oil

1-year

−0.08*
−0.09*

−0.12*
−0.13*

−0.16*
−0.18*

−0.16*
−0.17*

−0.03
−0.04

−0.05
−0.06

−0.09*
−0.09*

−0.08*
−0.09*

N P oil
2-year

3-year

Notes: See notes in Table 1.
* significant at the 0.05 level

include spending on durable goods (compare the size of the oil price coefficient
estimated using alternative measures of spending with and without spending on
durables, as shown in Table 2). The second observation is that the magnitude
of the oil price effect on spending estimated here is not overly sensitive to
the exclusion of the interest rate variable from the short-term consumption
equation. The third point to note is that the estimated negative effect on
spending of net oil price increases is larger than that of positive increases
in oil prices, suggesting those increases that occur after a period of stable
oil prices affect spending more than oil price increases that simply reverse
earlier declines (compare the relative magnitude of the oil price coefficient on
oil price increases and net oil price increases, as shown in Table 2). Together
these results are consistent with the view that oil price increases affect spending
by influencing spending on durable goods and that oil price increases have a
direct effect on spending that is beyond what could occur through the monetary
policy response to oil prices.

Stability of Oil Price Coefficients
Hamilton (2003) has argued that if we focus on exogenous oil price increases,
then the estimated linear relation between exogenous oil price shocks and real
GDP growth remains stable. We follow Hamilton in measuring exogenous oil
price shocks as net oil price increases believed to be associated with major
disruptions to world oil supplies. We now examine whether such a result
holds at the consumption level. As indicated before, oil prices have swung
widely in both directions since 1981. Hence, we investigate whether oil price
coefficients in the aggregate consumer spending equation (4) have changed
since 1981.

Y. P. Mehra and J. D. Petersen: Oil Prices and Consumer Spending

69

We implement the test of stability of oil price coefficients using a dummy
variable approach with the break date around 1981. We also implement the
stability test treating the break date unknown in the 1980s. In particular,
consider the following aggregate consumption equation:
Ct

= β0 +

3

β 1s OilPricest−s +

s=1

+β 2s Xt−s + ε t ,

3
s=1

d1s ( OilPrices∗ DU )t−s
(5)

where DU is a dummy variable, defined as unity over the period since the break
date and zero otherwise; X is the set of other control variables including lagged
values of consumer spending, labor income, household net worth, and changes
in the nominal interest rate, as in (4). In (5), the test of the null hypothesis of
stable oil price coefficients against the alternative that they have changed at
date t1 is that all slope dummy coefficients are zero, i.e., d1s = 0, s = 1, 2, 3.
Under this null hypothesis, the standard F statistic Ft1 would have a chi-squared
distribution with three degrees of freedom, χ 2 (3), asymptotically.14
We calculate the value of the statistic for every possible value of the break
date between 1981:Q1 to 1990:Q4, using oil price increases and net oil price
increases as alternative measures of oil price changes. Panel A in Figure 4
plots the p-value from this test as a function of the break date t1 using oil price
increases, whereas panels B through D do so using net oil price increases. As
can be seen, the p-value from this test is above the 0.05 p-value for all the break
dates and for all measures of oil price increases. These test results suggest
that the nonlinear relations between oil price changes and growth in consumer
spending do not depict any parameter instability during the 1980s.15

5.

CONCLUDING OBSERVATIONS

This article reports empirical evidence indicating that oil price increases have
a negative effect on consumer spending whereas oil price declines do not. Furthermore, oil price increases that occur after a period of stable oil prices matter
more than oil price increases that reverse earlier declines. This finding of a
14 The aggregate consumption equations have been estimated allowing for the presence of
a heteroscedastic disturbance term, and, hence, the standard F statistic has a chi-squared, not F,
distribution.
15 The inference regarding stability of oil price coefficients does not change if we were to
treat the break date from 1981:Q1 to 1990:Q4 as unknown and compare the largest value of the
F statistic over possible break dates with the 5 percent critical value, as in Andrews (1993). The
largest value of the F statistic is 4.7 when oil price changes are measured as oil price increases,
which is below the 5 percent critical value of 9.29 given in Andrews (1993, Table 1, using π =
0.48, p = 3 restrictions). The largest F takes values 6.1, 5.2, and 4.9 for net oil price increases
measured relative to one-, two-, and three-year peaks, respectively. For these alternative measures
of oil price changes, the largest F remains below the 5 percent critical value, suggesting that oil
price coefficients do not depict any parameter instability during the 1980s.

70

Federal Reserve Bank of Richmond Economic Quarterly

Figure 4 Chow Test for Stability of Oil Price Coefficients
Panel A: Oil Price Increases
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1980

1981

1982

1983

1984

1985

1986

1987

1988

1989 1990

Panel B: Net Oil Price Increases (1-year)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1989

1990

1989

1990

Panel C: Net Oil Price Increases (2-Year)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1980

1981

1982

1983

1984

1985

1986

1987

1988

Panel D: Net Oil Price Increases (3-Year)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1980

1981

1982

1983

1984

1985

1986

1987

1988

Notes: Each figure plots the p-value of a Chow test where the null hypothesis is that
oil price coefficients are stable against an alternative that they have changed at the given
date. The dashed lines indicate a p-value of 0.05.

Y. P. Mehra and J. D. Petersen: Oil Prices and Consumer Spending

71

nonlinear and asymmetric relation between oil price changes and consumer
spending is in line with what other analysts have found existing between oil
price changes and aggregate real economic activity such as real GDP growth.
The results reported here also indicate that oil price increases have a
stronger effect on consumer spending if spending is broadly defined to include spending on durables, suggesting oil price increases may be affecting
consumer spending by affecting demand for consumer durable goods. However, oil price increases may be affecting consumer spending by working
through other channels as well because oil price increases continue to have a
significant effect if spending includes only nondurables and services.
The evidence indicating that oil price decreases have no effect on consumer
spending is derived using reduced-form consumer spending equations and,
hence, may be consistent with several different theoretical mechanisms. One
explanation of why an oil price decrease does not have a significant effect on
spending is that the positive effect of an oil price decrease generated through
the real-balance and income-transfer channels offsets the negative effect on
spending generated through allocative channels. Furthermore, if the Federal
Reserve does not lower the funds rate in response to oil price declines but
raises it in response to oil price increases, we may also find that oil price
decreases have no significant effect on spending whereas oil price increases
do. Without help from a structural model, we cannot determine which of these
two mechanisms is dominant in generating the asymmetry found in data.
The empirical work here focuses on the effect of “exogenous” oil price
increases (measured by net oil price increases) on consumer spending, namely,
oil price increases caused by exogenous events such as those resulting from
disruptions to oil supplies caused by military conflicts. However, increases in
oil prices that are due to a rising world demand for oil may not necessarily raise
uncertainty about future energy supplies and prices and thus may not adversely
affect demand for durable consumption goods, as emphasized in this literature.
To the extent that oil price increases affect spending by working through other
channels, however, oil price increases, even if due to rising world oil demand,
could still adversely affect consumer spending in the short run.

REFERENCES
Andrews, Donald W. K. 1993. “Tests for Parameter Instability and Structural
Change with Unknown Change Point.” Econometrica 16 (4): 821–56.
Bernanke, B.S. 1983. “Irreversibility, Uncertainty and Cyclical Investment.”
Quarterly Journal of Economics 97 (1): 86–106.

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Federal Reserve Bank of Richmond Economic Quarterly

Hamilton, James D. 2004. “Causes and Consequences of the Oil Shock of
2004.” Available at: http://weber.ucsd.edu/˜jhamilto/Oil Aug04.htm
(accessed 20 May 2005).
. 2003. “What is an Oil Shock?” Journal of Econometrics
113 (2): 363–98.
. 1996. “This is What Happened to the Oil
Price-Macroeconomy Relationship.” Journal of Monetary Economics 38
(2): 215–20.
. 1988. “A Neoclassical Model of Unemployment and the
Business Cycle.” Journal of Political Economy 96 (3): 593–617.
Hooker, M. A. 1996a. “What Happened to the Oil Price-Macroeconomy
Relationship?” Journal of Monetary Economics 38 (2): 195–213.
. 1996b. “This is What Happened to the Oil
Price-Macroeconomy Relationship: Reply.” Journal of Monetary
Economics 38 (2): 221–22.
. 2002. “Are Oil Shocks Inflationary? Asymmetric and
Nonlinear Specifications versus Changes in Regime.” Journal of Money,
Credit and Banking 34 (2): 541–61.
Leduc, Sylvain, and Keith Sill. 2004. “A Quantitative Analysis of Oil-Price
Shocks, Systematic Monetary Policy, and Economic Downturns.”
Journal of Monetary Economics 51 (4): 781–808.
Limenez-Rodriguez, Rebeca, and Marcelo Sanchez. 2004. “Oil Price Shocks
and Real GDP Growth.” European Central Bank Working Paper No. 362.
Mehra, Yash P. 2001. “The Wealth Effect in Empirical Life-Cycle Aggregate
Consumption Equations.” Federal Reserve Bank of Richmond Economic
Quarterly 87 (2): 45–68.
Mork, Knut A. 1989. “Oil and the Macroeconomy When Prices Go Up and
Down: An Extension of Hamilton’s Results.” Journal of Political
Economy 97 (3): 740–44.
. 1994. “Business Cycles and the Oil Market.” Energy
Journal 15 (4): 15–38.