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Entrepreneurship and the Policy Environment
Yannis Georgellis and Howard J. Wall
This paper uses a panel approach to examine the effect that the government-policy environment
has on the level of entrepreneurship. Specifically, the authors investigate whether marginal income
tax rates and bankruptcy exemptions influence rates of entrepreneurship. Whereas previous work
in the literature finds that both policies are positively related to entrepreneurship, these results
show non-monotonic relationships: a U-shaped relationship between marginal tax rates and entrepreneurship and an S-shaped relationship between bankruptcy exemptions and entrepreneurship.
Federal Reserve Bank of St. Louis Review, March/April 2006, 88(2), pp. 95-111.

ntrepreneurship is thought to be an
important factor in cultivating innovation, employment, and economic
growth. Because the benefits flowing
from entrepreneurship are not necessarily captured by the entrepreneurs themselves, but can
be realized more generally, the case is often made
that the level of entrepreneurship is below its
social optimum and deserves some attention from
policymakers. Despite the recognized importance
of entrepreneurship, however, there has been relatively little empirical analysis of the role played
by the government-policy environment.
Previous research on self-employment and
entrepreneurship has examined the roles of various demographic, human capital, and financial
considerations in a person’s decision to become
an entrepreneur. Typically, studies have indicated
the importance of (i) the earnings differential
between entrepreneurship and paid employment
(Rees and Shah, 1986; Gill, 1988; and Hamilton,
2000); (ii) liquidity constraints (Evans and
Jovanovic, 1989; Evans and Leighton, 1989; HoltzEakin, Joulfaian, and Rosen, 1994a,b; and Black

and Strahan, 2002); (iii) satisfaction differentials
(Taylor, 1996; Blanchflower and Oswald, 1998;
and Blanchflower, 2000); (iv) macroeconomic conditions (Taylor, 1996; Parker, 1996; and Cowling
and Mitchell, 1997); and (v) intergenerational
human capital transfers (Dunn and Holtz-Eakin,
2000; and Hout and Rosen, 2000).1
Empirical studies that have considered the
effects of the policy environment on entrepreneurship have focused on personal income tax rates,
with the expectation that higher tax rates should
suppress entrepreneurship. Nearly all studies,
however, have found a positive relationship,
whether it is between tax rates and aggregate rates
of entrepreneurship (Long, 1982a; Evans and
Leighton, 1989; Blau, 1987; Parker, 1996; Robson,
1998; and Bruce and Mohsin, 2003) or between
tax rates and the likelihood that an individual
will be an entrepreneur (Long, 1982b; Schuetze,
2000; and Fan and White, 2003).
The divergence between expectations and
results with regard to the effects of the personal
1

Le (1999) provides a fairly comprehensive survey of the empirical
literature.

Yannis Georgellis is a senior lecturer in the department of economics and finance at Brunel University, Uxbridge, United Kingdom. Howard J.
Wall is an assistant vice president at the Federal Reserve Bank of St. Louis. The authors acknowledge the comments and suggestions of Kate
Antonovics, Mark Partridge, Mike Dueker, and seminar participants at the Southern Illinois University at Carbondale and the annual conference
of the Western Economic Association International, Seattle, June 29–July 3, 2002. Paige Skiba provided research assistance.

© 2006, The Federal Reserve Bank of St. Louis. Articles may be reprinted, reproduced, published, distributed, displayed, and transmitted in
their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses, and other derivative works may be made
only with prior written permission of the Federal Reserve Bank of St. Louis.

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income tax is usually attributed to the perception
that, because of the nature of a tax system that
relies on self-reporting, being an entrepreneur
allows for relatively greater opportunities for tax
evasion.2 Cullen and Gordon (2002), however,
argue that, because entrepreneurs decide whether
or not to incorporate their business, and because
personal income tax rates are higher than corporate rates, the tax system provides a net subsidy
to risk-taking. This net subsidy arises because an
entrepreneur facing losses would prefer to face
personal income tax rates so that the deduction
of the losses against other income would have
greater tax-reducing value. All else equal, an
increase in personal income tax rates makes this
option more valuable, thereby increasing the
likelihood that someone would choose to become
an entrepreneur.
Other studies have begun to look at the question of taxes and entrepreneurship using morecomplicated indicators of the tax system. Robson
and Wren (1999) separate the effects of average and
marginal tax rates, suggesting that the former
represents the incentive for tax evasion while
the latter represents the disincentive.3 Bruce
(2000) looks at the differential tax treatment of
self-employment and wage-and-salary earnings,
finding that marginal and average tax rates on
self-employment earnings are negatively related
to the probability of becoming self-employed.
Gentry and Hubbard (2000) find that the more
progressive a tax system is, the less likely it is
that an individual will enter self-employment.
Bruce, Deskins, and Mohsin (2004) look at statelevel differences in a variety of tax policies,
including rates of sales taxes and personal and
corporate income taxes, along with whether states
allow combined reporting and limited liability
corporations.
A recently opened line of inquiry into the
effects of the policy environment on entrepre-

neurship has raised the question of whether or
not bankruptcy laws affect the number of entrepreneurs (Berkowitz and White, 2004; Fan and White,
2003; and White, 2001). Briefly, U.S. bankruptcy
laws allow individuals filing for personal bankruptcy to exempt some of their assets and income
from distribution to their creditors. The exemptions, which differ a great deal across states, can
include some or all of the value of a person’s home
(the homestead exemption), pension holdings,
and an assortment of other assets.4
The direct effect of these exemptions is to
provide a sort of wealth insurance in the event
that an entrepreneurial venture fails. Thus, through
this wealth-insurance effect, higher exemption
levels should lead to more entrepreneurs. Less
direct than the wealth-insurance effect is a creditaccess effect, which works in the opposite direction. It arises because banks and other credit
providers adjust their actions in response to
changes in bankruptcy exemptions. As a result,
the higher the exemption level, the less credit
will be available at a given interest rate.5 These
two opposing effects of bankruptcy exemptions
on entrepreneurship mean that the sign of the total
effect is ambiguous in general. However, Fan and
White (2003) find that the wealth-insurance effect
dominates the credit-access effect for all levels
of the exemption. In fact, they find that homeowners in states with an unlimited homestead
exemption are 35 percent more likely to be selfemployed than equivalent homeowners in states
with low exemption levels.
In an attempt to resolve the discrepancies in
estimating the effects of taxes and to enhance the
modeling of bankruptcy exemptions, we estimate
the effects of government policies on entrepreneurship in a different way. Specifically, following
Georgellis and Wall (2000a), we create a state-level
panel dataset that pools observations over space
and time.6 This allows us to look at the effects of

Robson and Wren (1999) is an exception that finds a negative
relationship between tax rates and entrepreneurship. The authors
also have a theoretical model of tax evasion and the entrepreneurial
decision.

For detailed discussions of U.S. personal bankruptcy laws and the
incentives they create, see White (1998), Fay, Hurst, and White
(2002), Gropp, Scholz, and White (1997), and Dye (1986).

Their theoretical model separates the tax effects into pure marginal
and pure average tax changes, roughly analogous to substitution
and income effects. Unfortunately, the tax rates they use in their
empirical analysis are simply the average and marginal tax rates,
each of which has income and substitution effects.

Berkowitz and White (2004) show how small, unincorporated
businesses face lower credit access and higher interest rates in
states with higher exemption levels.

See also Wall (2004), Bruce, Deskins, and Mohsin (2004), and Black
and Strahan (2002).

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Georgellis and Wall

changes in policies over time while exploiting
the large differences across states in levels of
entrepreneurship, bankruptcy exemptions, and
tax rates. The advantages of this approach over
aggregate time-series studies—which have only
one observation per time period—are that we can
include a large number of control variables, use
more-general specifications of policy variables,
and control for trends more effectively. Another
advantage, which we outline in greater detail
below, is that it allows us to create a continuous
variable for the homestead exemption, rather
than having to group different exemption levels
together into dummy variables, as is necessary
when using individual-level panels.
Using the panel approach, we find a U-shaped
relationship between marginal tax rates and
entrepreneurship. At low tax rates the relationship is negative, and at high rates it is positive.
Also, we find an S-shaped relationship between
the homestead exemption and entrepreneurship.
Specifically, an increase in the homestead exemption from very low or very high levels acts to
reduce the number of entrepreneurs, while an
increase in the middle range acts to increase the
number of entrepreneurs.

ship is usually calculated with the labor force or
total employment in the denominator. We prefer
to use the working-age population (ages 18-64)
because, unlike the size of the labor force or the
number employed, it is not likely to move with
the number of entrepreneurs as people move
between employment states. This distinction also
recognizes the fact that entrepreneurs are drawn
from the entire working-age population, not just
those currently employed or in the labor force.
Figure 1 illustrates the cross-state differences
in the levels and growth of entrepreneurship
during our sample period, 1991-98. In general,
states in the western half of the country had the
highest levels of entrepreneurship. The eastern
part of the country contained all of the regions
with the lowest rates of entrepreneurship: the
Great Lakes, the Upper South, and the Deep South.
In the East, only New England states were in the
top two quartiles of entrepreneurship. As Figure 1B
shows, all states saw increases in their rates of
entrepreneurship between 1991 and 1998, and
there was some convergence. Southern states,
New York, and some of the lagging western states
had the highest growth in entrepreneurship.

EMPIRICAL MODEL
SPATIAL AND TEMPORAL TRENDS
IN U.S. ENTREPRENEURSHIP
We define the rate of entrepreneurship as the
proportion of the working-age population that is
classified as nonfarm proprietors. As with most of
the literature, we exclude farm proprietors on the
grounds that the decision to become a farm proprietor depends on different factors than the decision
to become a nonfarm proprietor; also, farmers
operate under their own set of bankruptcy laws.
Proprietors’ employment is the number of
people who are employed in their own business,
regardless of whether that business is incorporated. Various other definitions of entrepreneurship have been used in the literature, such as the
nonfarm self-employed, which excludes farmers
and the incorporated.7 The rate of entrepreneur7

Bruce and Holtz-Eakin (2001) examine a variety of measures and
conclude that it makes little difference which is used.

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Following Georgellis and Wall (2000a), we
estimate state rates of entrepreneurship with the
following regression equation, using t to denote
the time period and i to denote the state:
(1)

E it = α i + τ t + β ′X it + θ ′Zit + γ ′G it + ε it .

In the above expression, αi is a state-specific
component that is constant over time and τt is a
year-specific component that is common to all
states. The vectors Zit and Xit measure, respectively, lagged business conditions and lagged
average demographic characteristics in state i in
year t. Government policy variables are included
in the vector Git, and εit is the error term.
The demographic variables included in Xit
capture the spatial and temporal differences in
age, gender, and racial compositions of state
employment. As outlined in Georgellis and Wall
(2000b), rates of self-employment differ a great
deal across these categories. We therefore include
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Figure 1A
Average Rates of Entrepreneurship, 1991-98

16.6 to 20.2 (11)
14.5 to 16.6 (13)
12.2 to 14.5 (12)
10.5 to 12.2 (14)

Figure 1B
Changes in Rates of Entrepreneurship, 1991-98

1.95 to 2.89 (13)
1.51 to 1.95 (10)
1.27 to 1.51 (12)
0.58 to 1.27 (15)

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age variables that measure differences in employment shares of broad age categories. Also, because
men are nearly twice as likely as women to be
self-employed, we include the female share of a
state’s employment. Finally, Xit includes the black,
Native American, Asian and Pacific Islander, and
Hispanic employment shares. Large variations
in self-employment across these groups might
explain state-level differences in entrepreneurship. For example, the self-employment rate for
blacks is only about one-third of that for whites
and Asians.
Here and in the previous section we discuss
these variables in terms of the supply of potential
entrepreneurs. However, one should be careful
about the interpretation of the estimated coefficients because these demographic groups might
also differ in their demand for the products that
are more likely to be produced by entrepreneurs.
For example, as Georgellis and Wall (2000b)
report, over 10 percent of self-employed women
in 1997 were in the child-care business, while
virtually no men were. This indicates that a state
with a higher-than-average female employment
share might have a higher-than-average supply
of child-care providers. On the other hand, such
a state also has a higher-than-average number of
women demanding child-care services.
The vector of business conditions, Zit, includes
measures of a state’s economy that affect the
profitability of entrepreneurship. These include
the state’s unemployment rate, per capita real
income, per capita real wealth (as proxied by dividends, interest, and rent), relative proprietor’s
wage, and industry employment shares. As with
our demographic variables, the interpretation of
the roles of these variables is not entirely clear
because each can simultaneously indicate the
demand for entrepreneurs’ services and the supply
of entrepreneurs. For example, while we include
the unemployment rate as a measure of the health
of a state’s economy, Parker (1996), among others,
includes it as an indicator of the number of people
with limited opportunities for wage-and-salary
employment who might be pushed into selfemployment.
As Georgellis and Wall (2000a) demonstrate,
the specification of our control variables—the
F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

elements of Xit and Zit—is potentially important.
The authors show, for example, that the relationship between the rates of self-employment and
unemployment in Britain is hill-shaped. Indeed,
the best fit in the present context would allow
for nonlinear relationships. Nonetheless, our
present purpose is to estimate the effects of taxes
and the homestead exemption, and a simple linear
specification for the control variables makes little
difference in this regard. Therefore, for parsimony,
we use a linear specification for these control
variables.
Presently, the variables of most interest are
those measuring marginal tax rates and the homestead exemption. For the former, we use the maximum marginal tax rates (state plus federal) as
generated by the National Bureau of Economic
Research’s TAXSIM model (see Table 1 for the
state maximum marginal tax rates in 1990 and
1997, the first and last years of data used in our
study). Of the tax rate measures used in the literature, this one best fits our needs. For one, it is the
measure used in the paper most comparable to
ours—Fan and White (2003). But, more importantly, it is exogenous, unlike the average marginal
tax rate also generated by TAXSIM. Although very
few people will actually face the maximum marginal tax rate, there should be a very strong correlation between the marginal tax rates that the
average person faces and the maximum rate.
We constructed our homestead exemption
variable to take into account several state-level
differences in bankruptcy law and to provide a
measure of the percentage of the value of the
average person’s home that is exempt from bankruptcy proceedings. First, as noted above and as
summarized by Table 1, there are large differences
in the exemption level across states: In 1997, five
states did not allow any homestead exemption,
whereas seven had an unlimited exemption. Also,
some states allow for the federal exemption to be
substituted at the filer’s discretion, and some
states allow married filers to double the exemption level. We also take into account differences
in the average house prices and the likelihood
that a filer owns rather than rents.
Our homestead exemption variable starts by
taking the state exemption level or, if the state
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Table 1
State Homestead Exemptions and Maximum Marginal Tax Rates
Maximum marginal tax rates (%)
State

1990

1997

Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Hawaii
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
Federal

3.65
0
6.51
7
9.3
4.76
0
7.7
0
5.66
9
8.2
3
3.4
7.39
5.15
4.39
4.14
8.5
5
5.95
4.6
8
4.75
4.39
8.59
6.4
0
0
3.5
7.83
7.88
7
3.77
6.9
6.72
8.12
2.1
6.04
7
0
0
0
6.26
6.54
5.75
0
6.5
6.93
0

3.12
0
4.8
7
9.78
5.36
4.5
6.9
0
5.83
9
8.2
3
3.4
6.36
6.45
6
3.75
8.5
6
5.95
4.4
8.86
4.85
6
6.83
7
0
0
6.37
8.4
6.85
8.08
5.25
7.2
6.05
9
2.8
9.66
7.3
0
0
0
5.72
8.85
5.75
0
6.5
6.93
0

100

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Homestead exemptions ($)
1990
5,000
54,000
100,000
No limit
7,500
20,000
0
0
No limit
5,000
30,000
30,000
7,500
7,500
No limit
No limit
5,000
15,000
7,500
0
100,000
3,500
No limit
30,000
8,000
40,000
10,000
90,000
5,000
0
20,000
10,000
7,500
80,000
5,000
No limit
15,000
0
0
5,000
No limit
5,000
No limit
8,000
30,000
5,000
30,000
7,500
40,000
10,000
7,500

1997
5,000
54,000
100,000
No limit
15,000
30,000
75,000
0
No limit
5,000
30,000
50,000
7,500
7,500
No limit
No limit
5,000
15,000
12,500
0
100,000
3,500
200,000
75,000
8,000
40,000
10,000
125,000
30,000
0
30,000
10,000
10,000
80,000
5,000
No limit
25,000
0
0
5,000
No limit
5,000
No limit
8,000
30,000
5,000
30,000
15,000
40,000
10,000
15,000

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allows the federal option, the maximum of the
state and federal exemption levels. If this is greater
than the average house price in the state, we use
the average house price instead, which is a more
accurate representation of the exemption that the
average person would get. We then multiply this
by the state’s homeownership rate and, if the state
allows married householders to double the exemption, we also multiply it by 1 plus the state’s share
of households in which both spouses reside
together. The result of this divided by the average
house price yields our homestead exemption rate.
Note that the sources for all of the data used
to construct our variables are given in the data
appendix, as are the summary statistics for all of
the independent variables described above. We
should also note that our two most important independent variables—the homestead exemption rate
and the maximum marginal tax rate—are uncorrelated, with a correlation coefficient of –0.01.
As we mention above, one of the main benefits
of our panel approach is that the relative abundance of observations means that we can easily
allow for nonlinearities. This is important because,
for each of our government policy variables, there
are opposing effects, meaning that the relationships might be non-monotonic. This is easiest to
see with tax rates, for which the standard negative
labor-effort effect is countered by the positive taxevasion effect. Assuming a non-trivial cost to being
caught evading taxes, at low tax rates the incentive
to evade taxes will not be terribly strong because
the net expected benefits are not very high. Conversely, under very high tax rates, the benefit of
evading taxes is much higher.
In preliminary analyses, we found that a cubic
specification fits the homestead exemption rate
well, whereas a quadratic specification fits the
tax variable well. Thus, our baseline model, which
we report and discuss in detail below, uses a
quadratic tax variable and a cubic homestead
exemption variable. In the section following our
discussion of the baseline results, we discuss
alternative specifications, the final of which justifies the cubic specification for the homestead
exemption rate.
F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

EMPIRICAL RESULTS
Our dependent variable is the rate of entrepreneurship, as defined above, for 1991-98, and
our independent variables are all lagged by one
year. To allow for the most general error structure
given our data constraints, we estimate (1) using
feasible generalized least squares (FGLS). This
allows for state-specific heteroskedastic errors,
although, because of a relatively short panel, we
still need to assume that errors are uncorrelated
across states (Beck and Katz, 1995). We also allow
for each state’s errors to follow their own AR(1)
process.
Table 2 summarizes our results. As discussed
above, we attach little importance to the coefficients on our demographic and business conditions variables, but simply note that omitting
them would have a statistically significant effect
on the results. More importantly, our estimation
indicated that the marginal tax rate and the
homestead exemption rate are both related nonmonotonically to the rate of entrepreneurship.
Our estimates of the effects of marginal tax
rates on entrepreneurship indicate that at tax
rates at the low end of our observed rates—28 to
35 percent—an increase in the tax rate will reduce
the number of entrepreneurs (see Figure 2). Beyond
this range, higher marginal taxes will increase the
number of entrepreneurs indirectly as, presumably,
the tax-evasion incentives become large enough
to begin outweighing the possible penalties.
The cubic relationship between the homestead
exemption rate and entrepreneurship is illustrated
by Figure 3. At very low and very high exemption
rates—between 0 and 20 percent and above 60
percent—an increase in the homestead exemption
leads to a decrease in the rate of entrepreneurship,
suggesting that the credit-access effect dominates.
At the mid-range of exemption rates—between
20 and 60 percent—an increase in the homestead
exemption rate leads to an increase in the rate of
entrepreneurship, suggesting that the wealthinsurance effect dominates. Note, though, that
only rates between 50 and 72 percent lead to a
higher rate of entrepreneurship than there would
be with no homestead exemption at all.
The year dummies are also interesting and
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Table 2
Baseline FGLS Results
Dependent variable:
state rate of entrepreneurship = (nonfarm proprietors’ employment)/(working-age population)
Coefficient

Standard error

t-Statistic

–0.092

0.056

–1.66

Policies
Maximum marginal tax rate
Maximum marginal tax rate squared
Homestead exemption rate
Homestead exemption rate squared
Homestead exemption rate cubed

1.3 e–3

0.7 e–3

1.75

–0.118

0.024

–4.93

0.004

0.001

4.77

–3.3

e–5

0.7

e–5

–4.69

Demographics
Adult share aged 45-65

0.173

0.054

3.22

Adult share aged 65+

0.034

0.078

0.44

Female share
Black share
Native American share

0.080

0.020

4.06

–0.146

0.086

–1.70

0.175

0.407

0.43

Asian and Pacific Islander share

–0.111

0.180

–0.62

Hispanic share

–0.067

0.066

–1.01

Business conditions
Unemployment rate

0.106

0.025

–1.1 e–4

Real per capita wealth

0.310

0.229

1.35

Relative proprietor’s wage

0.342

0.399

0.86

Yes

—

Industry shares

0.9 e–4

4.26

Real per capita income

–1.23

Year dummies
1992

–0.221

0.055

–4.01

1993

–0.106

0.090

–1.18

1994

0.207

0.119

1.73

1995

0.606

0.152

3.98

1996

1.038

0.183

5.67

1997

1.153

0.219

5.25

1998

1.224

0.255

4.81

Yes

—

State fixed effects
Constant

–22.442

Log-likelihood

119.659

–0.19

–6.291

Number of observations

400

Estimated covariances

Estimated autocorrelations

NOTE: The estimation corrects for state-specific heteroskedasticity and autocorrelation. Omitted reference variables are as follows:
adult share aged 18-44, white share of employment, government share of employment, and 1991.

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Figure 2
Entrepreneurship and Marginal Taxes
Difference from Zero-Tax Entrepreneurship Rate
–1.52
–1.54
–1.56
–1.58
–1.60
–1.62
–1.64
–1.66
31
36
41
State Plus Federal Maximum Marginal Income Tax Rate

Figure 3
Entrepreneurship and the Homestead Exemption
Difference from No-Exemption Entrepreneurship Rate
0.4
0.2
0
0

–0.2
–0.4
–0.6
–0.8
–1
–1.2

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Homestead Exemption Rate

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Figure 4
Estimated State Fixed Effects

–2.4 to 2.7 (11)
–4.1 to –2.4 (13)
–5.4 to –4.1 (12)
–9.5 to –5.4 (14)

suggest an underlying trend in entrepreneurship
not captured by demographics, business conditions, or government policies. The estimated
coefficient on the 1998 dummy indicates that
state rates of entrepreneurship would have risen,
on average, by 1.2 percentage points from 1991
to 1998 had all of the variables we include in our
estimation remained at their initial levels.
Figure 4 plots the estimated fixed effects
across the states, illustrating the extent to which
differences in entrepreneurship are determined
by differences in the variables included in our
regression. Most noticeably, comparing Figures
1A and 4, we see that not all states with low levels
of entrepreneurship also have low estimated fixed
effects. In particular, states in the Great Lakes,
Upper South, and Deep South regions have low
levels of entrepreneurship, typically falling in the
lowest quartile. However, the fixed effects for the
Deep South states are not in the lowest quartile,
while those for the Great Lakes and Upper South
states are. This indicates that the relatively low
levels of entrepreneurship in the Deep South are
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due to relatively inhospitable business conditions,
demographic factors, or government policies. On
the other hand, the low levels of entrepreneurship
in the Great Lakes and Upper South are attributable to fixed factors, which Georgellis and Wall
(2000a) suggest might include cultural, historical,
or sociological factors that suppress entrepreneurship. At the other extreme are states in New
England and the West, which have high levels of
entrepreneurship and high estimated fixed effects.
These conditions suggest that one of the reasons
for the high levels of entrepreneurship is that
these states contain the cultural, historical, and
sociological makeup to pursue and succeed in
entrepreneurship.

ALTERNATIVE ESTIMATES
Our baseline model uses specific functional
forms for the policy variables and generalized
least-squares estimation to allow for state-specific
autocorrelation and cross-sectionally uncorrelated
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Georgellis and Wall

Table 3
Alternative FGLS Results
Dependent variable:
state rate of entrepreneurship = (nonfarm proprietors’ employment)/(working-age population)

Maximum marginal tax rate
Maximum marginal tax rate squared
Homestead exemption rate

III

0.008*
(0.004)

–0.096*
(0.055)

0.066
(0.084)

–0.134*
(0.065)

–0.129*
(0.065)

–0.119*
(0.053)

1.4 e–3*
(0.7 e–3)

0.001
(0.001)

0.002*
(0.001)

–0.010
(0.009)

–0.158*
(0.029)

–0.116*
(0.023)

–0.115*
(0.023)

—

9.8 e–5
(9.9 e–5)

0.006*
(0.001)

0.004*
(0.001)

—

–3.2 e–5*
(0.7 e–5)

—

—
–0.003
(0.004)

Homestead exemption rate squared

—

Homestead exemption rate cubed

—

–4.9 e–5*
(0.9 e–5)

–3.2 e–5*
(0.7 e–5)

Second octile of homestead exemption rate

—

–0.285*
(0.087)

Third octile of homestead exemption rate

—

–0.391*
(0.095)

Fourth octile of homestead exemption rate

—

–0.477*
(0.199)

Fifth octile of homestead exemption rate

—

–0.445*
(0.126)

Sixth octile of homestead exemption rate

—

0.146
(0.165)

Seventh octile of homestead exemption rate

—

0.382*
(0.233)

Eighth octile of homestead exemption rate

—

0.259*
(0.232)

Demographics, business conditions,
year and state effects

Yes

Heteroskedasticity
Autocorrelation
Log-likelihood

Yes

State

None

Common

State

–26.46

0.514

–7.56

–4.49

–114.92

–26.55

NOTE: Standard errors are in parentheses; * indicates statistical significance at the 10 percent level.
Alternative I: baseline model with restriction that higher-order effects of policy variables are zero.
Alternative II: baseline model with restriction that third-order effect of homestead exemption is zero.
Alternative III: baseline model with assumption that errors are homoskedastic.
Alternative IV: baseline model with assumption that errors are not autocorrelated.
Alternative V: baseline model with assumption that autocorrelation is common across states.
Alternative VI: baseline model with home exemption rate octiles and state-specific heteroskedasticity and autocorrelation.

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heteroskedasticity. To check the consequence of
these choices on our estimation of the effects of
our policy variables, we present the results of six
alternatives.8 These alternative results, which
either use a different specification of the policy
variables or place stronger restrictions on the
error terms, are reported in Table 3 and illustrated
by Figures 5 and 6.
Alternative I restricts the coefficients on the
squared and cubed terms of the policy variables
to zero. Estimation under these restrictions yields
a positive and statistically significant effect for
the marginal tax rate on entrepreneurship and a
negative but statistically insignificant effect for
the homestead exemption rate. Alternative II
restricts the coefficient on the cubed term of the
homestead exemption rate to zero while using the
same quadratic functional form for the marginal
tax rate as in the baseline model. The estimated
relationship between the maximum marginal tax
rate and entrepreneurship under this restriction
differs very little from the baseline results. On the
other hand, as previously stated, the estimated
coefficients on the homestead exemption rate
are both statistically no different from zero. The
results from these two alternative specifications
indicate that the choices we have made about the
specification of the policy variables are important
for our conclusions. Likelihood ratio tests reject
the null hypotheses that the restrictions that these
alternatives place on the higher-order terms do
not have a statistically significant effect on the
estimation. Therefore, the least-restrictive baseline model is preferred statistically to the two
alternatives.
Three other alternatives place stronger restrictions on the error terms than does the baseline
model: In alternative III they are assumed to be
homoskedastic, in alternative IV they are not
autocorrelated, and in alternative V their autocorrelation is common across states. As Figure 5
illustrates, none of these restrictions has an effect
on the estimated U-shape for the relationship
between marginal tax rates and the rate of entrepreneurship, although the coefficients in alter8

Wall (2004) demonstrates how not allowing for autocorrelation and
heteroskedasticity, in particular, has severe consequences for the
state-level panel of entrepreneurship in Black and Strahan (2002).

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native III are not statistically significant. The
important differences are that the estimated relationship is flatter with alternative III and steeper
with alternatives IV and V.
For the relationship between the homestead
exemption rate and the rate of entrepreneurship,
only the estimates from alternative III differ in
any non-trivial way. All three alternatives yield
an S-shaped relationship, although the estimated
relationship is everywhere steeper with alternative III than with the baseline model. Another
important difference is that alternative III suggests
that all homestead exemption rates above 42 percent will yield more entrepreneurship than would
a zero exemption, whereas the baseline model
suggests that this is true only for homestead
exemption rates between 50 and 72 percent.
Alternative VI replaces the continuous homestead exemption variables with dummy variables
for discrete ranges of the homestead exemption
rate. Because this model removes any general
assumption regarding functional form, it allows
us to verify the general shape of the cubic relationship of our baseline model. We split the observed
homestead exemption rates into octiles, each with
50 observations, and estimate the model with the
first octile omitted to avoid perfect collinearity.
As summarized by Table 3, for all but one of the
octiles of the homestead exemption rate, the rate
of entrepreneurship is statistically different from
what it would be under the first octile. Further, as
illustrated by Figure 6, these results confirm the
general S-shape to the relationship between the
homestead exemption rate and the rate of entrepreneurship. Note also that this specification
has little effect on the estimated relationship
between the rate of entrepreneurship and the
maximum marginal tax rate.

CONCLUDING REMARKS
This paper uses the panel approach of
Georgellis and Wall (2000a) to estimate the effects
of personal income tax rates and bankruptcy
exemptions on entrepreneurship. Using data for
all 50 states of the United States for 1991-98, we
find non-monotonic relationships. Specifically,
at low initial tax levels, an increase in marginal
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Georgellis and Wall

Figure 5
Alternative Estimates: Maximum Marginal Tax Rate
Alternative I

Baseline

Alternative

–1.5

0.4

Baseline
–1.5

–1.6

0.3

–1.6

0.2

–1.7

–1.7
28

Alternative II

–1.6

–1.7
28

Maximum Marginal Tax Rate

Alternative III

Baseline
–1.5

Alternative
–1.1

Baseline
–1.5

–1.2

–1.6

–1.3

–1.7

–1.7
31

Alternative V

Alternative

Alternative IV

Alternative
–2.25

Maximum Marginal Tax Rate

–1.7
31

–2.45
28

–1.6

–2.35

Maximum Marginal Tax Rate

Baseline
–1.5

Maximum Marginal Tax Rate

–1.6

Alternative
–1.5

Maximum Marginal Tax Rate

–2.15

Baseline
–1.5

–2.25

–1.6

–2.35

–1.7

Alternative VI

Alternative
–1.9

–2

–2.1
28

Maximum Marginal Tax Rate

NOTE: Alternative I: baseline model with restriction that higher-order effects of policy variables are zero; Alternative II: baseline model
with restriction that third-order effect of homestead exemption is zero; Alternative III: baseline model with assumption that errors
are homoskedastic; Alternative IV: baseline model with assumption that errors are not autocorrelated; Alternative V: baseline model
with assumption that autocorrelation is common across states; Alternative VI: baseline model with home exemption rate octiles and
state-specific heteroskedasticity and autocorrelation.

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Figure 6
Alternative Estimates: Homestead Exemption Rate
Alternative I

1.0

0.6

0.6
0.2
–0.2 0

Alternative II

1.0

0.2
10

–0.2 0

–0.6

–1.0

–1.4

Homestead Exemption Rate

Alternative III

1.0

0.6

0.2

0.2
10

Alternative IV

1.0

0.6

–0.2 0

–0.6

–1.0

–1.4

–1.4
Homestead Exemption Rate

Homestead Exemption Rate

Alternative V

1.0

0.6

0.2

0.2
10

Alternative VI

1.0

0.6

–0.2 0

–1.4
Homestead Exemption Rate

–0.2 0

–0.2

–0.6

–1.0

–1.4

–1.4
Homestead Exemption Rate

Homestead Exemption Rate

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tax rates reduces the number of entrepreneurs,
although at higher initial tax levels it will do the
opposite. We also find that at very low and very
high initial levels, an increase in the homestead
exemption will reduce the number of entrepreneurs. In the mid-range of homestead exemption
rates, there is a positive relationship between the
exemption level and entrepreneurship. Further,
only for relatively high homestead exemption rates
will the level of entrepreneurship be higher than
if there were no homestead exemption at all.

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DATA APPENDIX
Data series

Source

Nonfarm proprietors’ employment

Regional Economic Information System, Bureau of Economic
Analysis, Table CA25

Unemployment rate

Bureau of Labor Statistics

Dividends, interest, and rent

Regional Economic Information System, Bureau of Economic
Analysis, Table CA05

Per capita gross state product

Bureau of Economic Analysis

Average nonfarm proprietors’ income;
average wage and salary disbursements

Regional Economic Information System, Bureau of Economic
Analysis, Table CA30

Industry employment shares

Establishment Survey, Bureau of Labor Statistics

Age, race, and sex employment shares

Bureau of Labor Statistics

Maximum marginal tax rates

TAXSIM, National Bureau of Economic Research

Homestead bankruptcy exemptions

Elias, Renaur, and Leonard, How to File for Chapter 11 Bankruptcy,
various editions

Median house price

Derived using median house price from 1990 Census and the
Home Price Index from the Office of Federal Housing
Enterprise Oversight

Home ownership rate

Bureau of the Census

Share of households with householder
and spouse

Bureau of the Census, derived from 1990 and 2000 Census
assuming constant state-level rates of change

Table A1
Summary Statistics
Mean

Standard deviation

Rate of entrepreneurship

14.51

2.90

Maximum marginal tax rate

38.37

4.14

Homestead exemption rate

28.71

24.75

Adult share aged 45-65

26.52

1.56

Adult share aged 65+

17.12

2.56

Female share of employment

46.07

1.32

Black share of employment

9.90

9.34

Native American share of employment

1.66

2.94

Asian and Pacific Islander share of employment

3.11

8.73

Hispanic share of employment

5.91

7.87

Unemployment rate

5.72

1.49

Real per capita income

$20,862

$3,746

Real per capita wealth

4.08

0.83

Relative proprietor’s wage

0.74

0.11

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F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

Human Capital Growth in a Cross Section of
U.S. Metropolitan Areas
Christopher H. Wheeler
Growth of human capital, defined as the change in the fraction of a metropolitan area’s labor
force with a bachelor’s degree, is typically viewed as generating a number of desirable outcomes,
including economic growth. Yet, in spite of its importance, few empirical studies have explored
why some economies accumulate more human capital than others. This paper attempts to do so
using a sample of more than 200 metropolitan areas in the United States over the years 1980, 1990,
and 2000. The results reveal two consistently significant correlates of human capital growth:
population and the existing stock of college-educated labor. Given that population growth and
human capital growth are both positively associated with education, these results suggest that the
geographic distributions of population and human capital should have become more concentrated
in recent decades. That is, larger, more-educated metropolitan areas should have exhibited the
fastest rates of increase in both population and education and thus “pulled away” from smaller,
less-educated metropolitan areas. The evidence largely supports this conclusion.
Federal Reserve Bank of St. Louis Review, March/April 2006, 88(2), pp. 113-32.

uman capital is now commonly
held to be one of the fundamental
drivers of economic growth. To be
sure, the notion that the skills possessed by an economy’s workforce promote technological advancement and productivity growth
is an intuitively appealing one. Yet, there is also
a fair amount of empirical evidence that supports
this notion. In particular, a sizable literature in
the past two decades has established a strong
statistical association between human capital
(usually captured by educational attainment) and
the growth of employment, productivity, and
income. Moreover, this relationship holds with
striking regularity at different levels of geographic
aggregation, including countries (Barro, 1991),
U.S. states (Barro and Sala-i-Martin, 1992), and
cities and metropolitan areas (Glaeser,
Scheinkman, and Shleifer, 1995; Glaeser and
Saiz, 2003; and Simon and Nardinelli, 2002).

Economic growth, however, is only one
benefit that has been associated with human
capital. A variety of studies also suggest that
greater educational attainment within local
economies (e.g., states or cities) may tend to be
accompanied by lower rates of crime (Lochner
and Moretti, 2004), greater civic involvement
(Dee, 2004; Milligan, Moretti, and Oreopoulos,
2004), and less political corruption (Glaeser and
Saks, 2004). Clearly, because these are desirable
outcomes, identifying the determinants of human
capital growth is a worthwhile undertaking. Unfortunately, while a host of theoretical models have
done so,1 surprisingly little empirical research
has followed suit. Most existing studies have
focused on what human capital produces rather
than why some economies accumulate more of
1

See Barro and Sala-i-Martin (1995) for a survey of human capital–
based models of growth.

Christopher H. Wheeler is a senior economist at the Federal Reserve Bank of St. Louis. Elizabeth La Jeunesse provided research assistance.

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Wheeler

it than others.2 As such, our understanding of
human capital accumulation remains limited.
This paper looks at the growth of human
capital in a sample of more than 200 U.S. metropolitan areas identified in the decennial U.S.
Census over the years 1980, 1990, and 2000.
Defining human capital accumulation as the
change in the fraction of a metropolitan area’s
employed labor force with a bachelor’s degree or
more, I find that metropolitan areas with larger
populations and higher fractions of their workers
with a bachelor’s degree tend to accumulate
human capital at faster rates than less-populous,
less-educated metropolitan areas. The results
suggest that a 1-standard-deviation increase in
either total resident population or the fraction
of workers with a four-year college degree (in the
cross section of metropolitan areas) tends to be
associated with a 0.4- to 0.7-percentage-point rise
in the share of college graduates in the workforce
over the next decade. These estimated magnitudes,
it should be noted, are not meant to be interpreted
as causal, but simply to quantify the strength of
the observed associations between these two variables and the accumulation of highly educated
workers. Although some evidence suggests that
certain measures of industrial composition and
observable city-level amenities (e.g., restaurants
and universities) are also associated with changes
in the college fraction, none are as robustly correlated as population and the existing level of
human capital.
These findings are intriguing, as they seem
to suggest that the geographic distribution of
human capital across the cities of the United
States should have grown more concentrated
(or unequal) between 1980 and 2000. After all,
because human capital accumulation tends to be
positively associated with the current level of
human capital, the gap between initially higheducation cities and low-education cities ought
2

There are two notable exceptions: Moretti (2004) offers a short
analysis of the determinants of changing college attainment rates
among U.S. metro areas, similar to what I do here. Glaeser and Saiz
(2003) examine whether educational attainment responds to economic growth. With both of these papers, however, the primary
issue under consideration is not the determinants of human capital
growth. Consequently, their analyses are much more cursory with
respect to this issue than my analysis here.

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to have widened in recent decades. The evidence
strongly supports this conclusion. Various measures that characterize the degree of spread in the
distribution of metropolitan area–level college
attainment show rising dispersion between 1980
and 2000.
In addition, because previous research has
established a positive link between population
growth and education (e.g., Glaeser, Scheinkman,
and Shleifer, 1995), one would expect to find a
similar pattern of “divergence” in population
levels across U.S. metropolitan areas in recent
decades. That is, if more-populous cities accumulate highly educated workers more quickly
than less-populous ones, then they should also
gain population faster too. Rising educational
attainment fuels population growth, which, in
turn, spurs human capital accumulation and so
on. This conclusion is also largely borne out in
the data. The distribution of the logarithm of
population became more concentrated within
particularly large metropolitan areas between
1980 and 2000.
Although one might surmise that rising concentrations of population and education in the
largest and most-educated cities have also led to
a greater concentration of income, the evidence
on this issue is somewhat mixed. In particular,
while the data show that the distribution of metropolitan area–level average log hourly wages grew
wider between 1980 and 1990, they also show
that it narrowed slightly between 1990 and 2000.
Growing concentrations of population and collegeeducated workers in the metropolitan areas of
greatest size and abundance of human capital,
then, have not been accompanied by substantial
increases in the degree of inter-city (average)
earnings inequality.

DATA
The data used in the analysis are taken primarily from the 5 percent public use samples of
the 1980, 1990, and 2000 U.S. Census as reported
by the Integrated Public Use Microdata Series
(Ruggles et al., 2004). These data files include a
variety of personal characteristics, including age,
education, and earnings, for samples of more
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Wheeler

than 11 million individuals in each year, as well
as information about each individual’s place of
residence. These data are used to construct a time
series of metro area–level characteristics, including human capital.
In principle, “human capital” could be defined
in many different ways: e.g., time spent on a
particular job, time spent working on all jobs,
numbers of different jobs held, educational attainment, some measure of “innate” ability or productivity. This paper takes a standard approach by
using educational attainment, which can be justified by noting that (i) schooling has been shown
to have a significant causal influence on individual
productivity, at least as quantified by earnings
(Card, 1999), and (ii) it tends to be strongly correlated with a variety of outcomes commonly
theorized to be tied to “human capital,” including
economic growth. For these reasons, education is
treated as a suitable metric for human capital. More
specifically, I use the fraction of a metro area’s
employed labor force with a bachelor’s degree or
more because previous work on economic growth
and education externalities in cities has found
this particular quantity to capture variation in
educational attainment reasonably well.3
Formally, metro areas in the analysis represent
either metropolitan statistical areas (MSAs), New
England county metropolitan areas (NECMAs),
or consolidated metropolitan statistical areas
(CMSAs) in the event that an MSA or NECMA
belongs to a CMSA.4 A total of 210 of these local
markets are identified in the 1980 data, 206 in
1990, and 245 in 2000. Only 188 appear in all
three Census years.
Additional characteristics describing metro
areas are derived from the USA Counties CD-ROM
(U.S. Bureau of the Census, 1999) and from County
Business Patterns (CBP) files for the years 1980,
1990, and 2000. The former dataset provides
information about county-level population and
land area, which is used to generate population
and population density figures at the metro-area
3

See, for example, Black and Henderson (1999) and Moretti (2004).

Throughout the paper, I use the terms “metropolitan area” and
“city” interchangeably for expositional purposes. In all cases,
“local markets” refers to MSAs, NECMAs, or CMSAs.

F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

level.5 The latter reports the numbers of various
types of private sector establishments (e.g., restaurants and bars), which are used to characterize the
amenity value of a metro area. Further details
about the data appear in the appendix.

EMPIRICAL FINDINGS
Human Capital and Urban Agglomeration
Within the United States, human capital has
typically been concentrated in metro areas. Among
workers in the Census samples used here, 86.1
percent of all college graduates resided in a metro
area in 1980. By 2000, this figure had risen to 89.9
percent. In contrast, approximately 78 percent of
workers with only a high school diploma were
metro dwellers in either year.
Why are highly educated workers drawn to
cities? Numerous characteristics, of course, distinguish metro areas from non-metro areas and,
thus, could offer some semblance of an answer.
Besides larger and better-educated populations,
urban agglomerations also tend to possess greater
numbers of industries that highly educated
workers may find particularly appropriate or
appealing given their skills (e.g., professional
and technical services). Metro areas also tend to
offer a greater array of amenities (e.g., restaurants
and museums), which may serve to attract and
maintain a pool of highly educated labor (see
Glaeser, Kolko, and Saiz, 2001).
Economically, the estimated returns to education do tend to be particularly high in metro areas.
Consider, for instance, the results from a regression of log hourly earnings on five educational
attainment indicators (no high school, some high
school, a high school diploma only, some college
or an associate’s degree, a bachelor’s degree or
more), eight indicators representing years of potential work experience,6 a metro residence dummy,
5

County-level population data for the year 2000 are derived from
the population estimates program of the U.S. Census Bureau at
www.census.gov/popest/estimates.php. In all years, land area
from 1990 is used to compute density.

These indicators represent 6-10 years of experience, 11-15 years,
16-20 years, 21-25 years, 26-30 years, 31-35 years, 36-40 years,
and 41 or more years.

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and interactions between metro residence and
each of the education and experience variables.7
To keep the analysis simple, I have limited the
sample of workers used for this regression to white
males between the ages of 18 and 65. I have also
performed the estimation separately for the 1980
and 2000 samples to account for any changes in
the coefficient values over time.8
The resulting coefficient estimates, which for
the sake of conciseness have been limited to the
education variables, appear in Table 1. The raw
coefficients on the five educational attainment
dummies in the first five rows of results can be
interpreted as the average log wages (conditional
on all of the other covariates in the model) for
workers in these education groups who reside
outside of a metro area. The average log wages for
workers inside metro areas is then given by the
sum of these raw coefficients and the corresponding interaction listed in the remaining rows of
the table.
With this interpretation in mind, it is evident
that, although college graduates earn more than
workers with less schooling, the premium associated with a college degree is particularly high
within metro areas. In non-urban areas in 1980,
for example, college-educated workers earned
approximately 30 percent more than workers with
only a high school diploma.9 Within metro areas,
that differential was 45 percent. By the year 2000,
the college premium had risen to 49 percent outside of metro areas, 75 percent within them. In
terms of raw (conditional) wage levels, college
graduates earned an average of $10.48 per hour
outside of metro areas in 1980, $12.26 within
them.10 By 2000, these figures stood at, respectively, $10.80 and $13.40, implying a 20-year
7

The regressions also include dummies for marital status, disability
status, veteran status, and foreign-born status.

The 5 percent sample for 1990 does not report metropolitan status
for all individuals in the sample. Hence, estimating the regression
for this year is not possible.

Percentages are derived from the estimates in Table 1 by exponentiating the log wage differential and subtracting 1. A 26-log-point
differential between college and high school graduates in non-metro
areas in 1980, for example, corresponds to roughly 30 percent.

These estimates are based on exponentiating the coefficients in
Table 1.

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growth rate of roughly 3 percent in rural areas,
but 9.3 percent in urban areas.
These figures, of course, should not be interpreted causally. That is, a highly educated
worker’s metropolitan status does not necessarily
cause him to earn more than if he were situated
in a smaller labor market. On the contrary, the
results may reflect, at least in part, a selection
mechanism by which the most productive, highly
educated workers have chosen to live in cities.
Still, these results seem to suggest that there are
strong economic incentives for highly educated
workers to reside in urban areas.
To gain a better sense of which factors (e.g.,
metro area size, existing human capital, education
premia, industrial composition) may underlie
human capital accumulation, I now turn to the
analysis of a cross section of metro areas. The
underlying goal is to exploit the variation exhibited across cities with respect to their education,
size, and other characteristics to draw inferences
about which features are most strongly associated
with the growth of human capital.

Correlates of Human Capital
Accumulation: Baseline Results
As noted previously, the Census data used in
this article identify more than 200 metro areas in
each of the three years (1980, 1990, 2000) considered. Using this sample, I estimate the following
simple regression in which the change in metro
area i’s college fraction during decade t, ΔColli,t ,
is specified as
(1)

ΔColli ,t = μ + δt + β X i ,t + ε i ,t ,

where μ is a constant, δt is a decade-specific fixed
effect, Xi,t is a set of characteristics describing the
metro area at the beginning of the decade, and εi,t
is a stochastic element, assumed to be uncorrelated across metro areas but potentially correlated
within them (i.e., εi,t and εi,s may show some nonzero association). This equation is meant to be
analogous to those used in empirical studies of
economic growth in which a measure of growth
is regressed on a set of initial characteristics
(e.g., Barro, 1991, and Glaeser, Sheinkman, and
Shleifer, 1995).
F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

Wheeler

Table 1
Education Premia by Metropolitan Status
Variable

1980

2000

No high school

1.84 (0.004)

1.73 (0.006)

Some high school

1.96 (0.003)

1.81 (0.005)

High school

2.09 (0.003)

1.98 (0.004)

Some college

2.15 (0.003)

2.11 (0.004)

College or more

2.35 (0.003)

2.38 (0.004)

No high school–metro

0.013 (0.004)

–0.014 (0.007)

Some high school–metro

0.031 (0.004)

0.035 (0.005)

High school–metro

0.046 (0.003)

0.053 (0.004)

Some college–metro

0.081 (0.004)

0.107 (0.004)

College–metro

0.156 (0.004)

0.215 (0.004)

NOTE: Coefficients are from regressions of log hourly wages on education indicators and their interactions with a metropolitan status
dummy; 1,850,727 observations for the year 1980; 2,135,811 observations for the year 2000; standard errors appear in parentheses.

Among the characteristics considered in the
vector Xi,t are the following: (i) an estimate of a
metro area’s return to a college degree,11 (ii) its
level of human capital (given by the fraction of
college-educated workers in the labor force), (iii)
its raw size (given by the logarithms of population
and population density), and (iv) its broad industrial composition (measured by shares of total
employment accounted for by each of 20 industries). Summary statistics for each of these regressors appear in Table 2.12
Results are given in Table 3. The first column,
labeled I, reports the resulting coefficients when
each covariate is entered into the regression separately. In all instances, estimation of equation
(1) also includes a set of three region dummies to
account for any exogenous differences in the rate
11

Metro-area college degree returns are derived from city-year–specific
regressions of log hourly wages on five education indicators, eight
experience indicators, and dummies for marital status, disability
status, veteran status, and foreign-born status. The coefficient on
the college completion dummy is used to estimate the return to a
college degree.

Because they are easier to interpret, Table 2 lists summary statistics
for population and population density levels rather than logarithms.
In the regression analysis, I use these variables in log form, which
is reasonably standard in the empirical literature on cities.

A list of the state-level composition of the four U.S. Census regions
appears in the appendix.

F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

of human capital accumulation in different parts
of the country.13
Based on the estimates, many of these regressors do turn out to be significantly associated with
the growth of the college fraction, at least in a
simple, univariate sense. Metro areas with initially
larger populations, higher levels of population
density, and larger fractions of workers with a
bachelor’s degree or more all see their college
attainment rates rise by more over the following
decade than smaller, less-dense, less-educated
metro areas. In addition, greater fractions of
employment accounted for by industries such as
agriculture, mining, and manufacturing (either
durable or nondurable) tend to correlate negatively
with human capital accumulation, whereas a
strong presence of industries such as finance,
insurance, real estate, and business and repair
services are positively associated with the change
in the college attainment rate. Given that the former set of industries tends to employ fewer highly
educated workers than the latter set of industries
(see Table 4), these associations are rather intuitive. The estimated city-specific return to a college
degree, while positive, is not statistically important. Greater discussion of this last regressor is
provided below.
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Wheeler

Table 2
Metropolitan Area Summary Statistics
Variable

Mean

Estimated return

2.47

Population

888,590.6

Density

578.3

Standard deviation
0.115
1,912,186
1,178.4

Minimum
2.05
100,376
6.01

Maximum
2.84
19,397,717
16,258.1

College fraction

0.218

0.065

0.09

0.455

Fraction agriculture, forestry, fisheries

0.007

0.006

0.001

0.063

Fraction mining

0.006

0.016

0.148

Fraction construction

0.068

0.017

0.033

0.19

Fraction nondurable manufacturing

0.077

0.047

0.014

0.365

Fraction durable manufacturing

0.123

0.072

0.009

0.453

Fraction transportation

0.045

0.014

0.018

0.152

Fraction communications

0.015

0.006

0.004

0.052

Fraction utilities

0.015

0.007

0.003

0.075

Fraction wholesale trade

0.044

0.013

0.015

0.126

Fraction retail trade

0.163

0.022

0.096

0.24

Fraction finance, insurance, real estate

0.061

0.021

0.027

0.24

Fraction business and repair services

0.051

0.018

0.016

0.149

Fraction private household services

0.005

0.003

0.02

Fraction personal services

0.024

0.015

0.012

0.23

Fraction entertainment and recreation services

0.012

0.003

0.139

Fraction medical services

0.091

0.024

0.04

0.292

Fraction educational services

0.105

0.031

0.052

0.27

Fraction social services

0.013

0.004

0.005

0.034

Fraction other professional services

0.02

0.009

0.004

0.088

Fraction public administration

0.055

0.031

0.015

0.255

NOTE: Summary statistics are taken over 661 city-year observations.

The next two columns of results, II and III,
report the coefficients from two different specifications of (1) in which various combinations of
these covariates appear. The longer of these (III)
suggests that, unlike what is reported above, very
few of the initial industry shares are significantly
associated with human capital accumulation.
Indeed, comparing the results from columns I
and III, only one industry share enters significantly
in both cases: finance, insurance, real estate.
Industrial composition, therefore, seems largely
unimportant for explaining the growth of human
capital, at least once we have conditioned on
initial education, size, and returns.
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Among the remaining covariates, only two
show consistently positive and significant associations with human capital accumulation: log
population and the initial college fraction. Both
of these regressors produce significant coefficients
in all three reported specifications. Log density,
by contrast, becomes insignificant when industry
shares are included, and the initial return to a
college degree enters negatively (and significantly)
in specifications II and III. This latter result may
simply reflect the inverse association between
various measures of urban growth (e.g., population
and average earnings) and initial wages, which
is a common finding in the urban economics litF E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

Wheeler

Table 3
Human Capital Accumulation Regression Results
Variable (initial value)

III

Estimated return

0.018 (0.011)

Log population

0.006* (0.001)

–0.02* (0.006)
0.003* (0.001)

–0.03* (0.014)
0.004* (0.002)

Log density

0.007* (0.001)

0.003* (0.001)

0.002 (0.002)

College fraction

0.16* (0.015)

0.12* (0.02)

0.11* (0.04)

Fraction agriculture, forestry, fisheries

–0.38* (0.13)

—

Fraction mining

–0.13* (0.03)

—

Fraction construction

–0.002 (0.07)

—

0.18* (0.09)

Fraction nondurable manufacturing

–0.06* (0.02)

—

0.02 (0.04)

Fraction durable manufacturing

–0.03* (0.017)

—

0.03 (0.04)

0.07 (0.08)

—

0.01 (0.08)

Fraction transportation
Fraction communications
Fraction utilities
Fraction wholesale trade

0.003 (0.17)
–0.01 (0.06)

0.94* (0.19)

—

0.02 (0.23)

–0.29* (0.15)

—

–0.08 (0.15)

0.01 (0.09)

—

–0.06 (0.1)

–0.13* (0.06)

—

–0.01 (0.05)

Fraction finance, insurance, real estate

0.36* (0.06)

—

Fraction business and repair services

0.36* (0.11)

—

–0.15 (0.1)

–0.56 (0.42)

—

–0.3 (0.4)

0.02 (0.05)

—

Fraction retail trade

Fraction private household services
Fraction personal services

0.19* (0.07)

0.06 (0.08)

Fraction entertainment and recreation services

0.04 (0.08)

—

0.004 (0.1)

Fraction medical services

0.03 (0.05)

—

0.03 (0.06)

–0.0005 (0.05)

—

–0.04 (0.06)

0.76* (0.43)

—

0.25 (0.4)

Fraction educational services
Fraction social services
Fraction other professional services

0.83* (0.24)

—

0.1 (0.2)

Fraction public administration

0.09* (0.03)

—

0.04 (0.05)

NOTE: The dependent variable is the change in college fraction for 1980-90 and 1990-2000. Region indicators and a dummy for the
1980-90 decade appear in all regressions. Column I reports coefficients from separate regressions for each regressor. Columns II and III
report coefficients from regressions that include all regressors for which estimates are reported. Heteroskedasticity-consistent standard
errors, adjusted for correlation within metro areas, appear in parentheses; * denotes significance at the 10 percent level or better.

erature (e.g., Glaeser, Scheinkman, and Shleifer,
1995). Higher returns to a college degree, not
surprisingly, tend to be associated with higher average wages overall in these data. As growth slows,
human capital accumulation tends to slow as
well.14
How significant are the estimated associations
14

The positive coefficient on the initial estimated college return in
specification I may therefore emanate from omitted-variable bias.
As shown previously, returns to a college degree tend to be higher
in metro areas, suggesting a positive association with population
and the college attainment rate. Not including these two variables

F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

between, on the one hand, initial log population
and the college completion rate and, on the other,
the subsequent change in the college completion
fraction? Based on the point estimates from the
longest specification in Table 3, a 1-standarddeviation increase in log population (in the cross
section) corresponds to a 0.43-percentage-point
rise in the college attainment rate over the next
decade. A 1-standard-deviation increase in the
in specification I may therefore bias a truly negative coefficient
on initial returns upward.

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Table 4
College Attainment by Major Industry
Industry

1980

1990

2000

Agriculture, forestry, fisheries

0.154

0.16

0.154

Mining

0.138

0.179

0.141

Construction

0.072

0.094

0.089

Nondurable manufacturing

0.112

0.153

0.196

Durable manufacturing

0.111

0.158

0.183

Transportation

0.09

0.123

0.144

Communications

0.146

0.231

0.328

Utilities

0.123

0.181

0.194

Wholesale trade

0.152

0.199

0.212

Retail trade

0.092

0.116

0.136

Finance, insurance, real estate

0.227

0.306

0.364

Business and repair services

0.2

0.255

0.33

Private household services

0.033

0.052

0.068

Personal services

0.067

0.105

0.12

Entertainment and recreation services

0.194

0.226

0.259

Medical services

0.219

0.289

0.33

Educational services

0.546

0.55

0.562

Social services

0.359

0.41

0.467

Other professional services

0.467

0.53

0.537

Public administration

0.252

0.298

0.352

NOTE: Fractions of each industry’s total employment with a bachelor’s degree or higher.

initial fraction of workers with a bachelor’s degree
or more has a somewhat larger implied association: a 0.72-percentage-point rise in the college
attainment rate over the next 10 years.15 Although
they may seem small compared with average
college completion rates near 22 percent for the
metro areas in the sample, these magnitudes are
far from negligible. In particular, they represent
between 20 and 34 percent of the cross-sectional
standard deviation of the 10-year change in the
college fraction in these data, which is approximately 2.1 percentage points.
15

The cross-sectional standard deviations for log population and
the college completion rate are roughly 1.08 and 0.065. In terms
of population levels, 1 standard deviation corresponds to roughly
680,000 residents.

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Robustness
In this section, I consider a few simple alterations to the statistical analysis to assess the
robustness of the results. The first seeks to
account for the influence of certain amenities
(e.g., restaurants, theaters, museums) on human
capital accumulation. As noted previously,
Glaeser, Kolko, and Saiz (2001) have demonstrated
that cities have significant consumption aspects
that seem to influence the willingness of individuals to live in dense urban environments. If the
highly educated have an especially strong preference for these characteristics, amenities may
play an important part in human capital accumulation that the analysis above misses. Indeed, it
may not be a city’s population or initial level of
F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

Wheeler

educational attainment that are important for
explaining the growth of a city’s college share,
but its array of urban amenities. Population or
education may simply be proxies for these types
of characteristics. To explore this possibility, I
consider the influence of the following eight
amenities: eating and drinking establishments;
movie theaters; elementary and secondary schools;
live entertainment venues; museums, botanical
gardens, and zoos; colleges and universities;
hospitals; and commercial sports clubs (which
includes professional athletics teams).16 Initial
values of these quantities, the first four of which
are expressed in per capita terms, are added to
equation (1).
Because the number of colleges and universities may not adequately capture the full extent
of the college community in a metro area, I also
include the total number of workers employed in
these institutions. This variable should help to
discern whether a metro area has, say, a particularly large university rather than a small college.
In addition, although the number of elementary
and secondary schools per capita is intended to
serve as a rough proxy for the quality of a city’s
education system, it is a highly imperfect measure. As an additional proxy for school quality, I
include in the regression the fraction of children
between the ages of 3 and 17 who are enrolled in
public school. In theory, cities with good school
systems should have relatively large fractions of
their school-aged children enrolled in public
education. Cities with ineffective and undesirable
public school systems, after all, should be characterized by higher proportions of their children
attending private schools.
The second alteration takes a different
approach to controlling for the influence of industrial composition. While initial shares of a metro
area’s employment across a broad array of sectors
may offer some explanatory power with respect
to human capital accumulation, how they change
over time may be more relevant. That is, it may
not be the initial share of employment in a city’s
durable manufacturing sector that affects its

college fraction, but the change in the fraction
accounted for by that sector. Again, as demonstrated in Table 4, there are substantial differences
in college attainment across the 20 industries considered. Therefore, one might expect that rising
shares of employment in, say, retail trade, which
employs relatively few college-educated workers,
would have a negative influence on a city’s overall
level of education; whereas, a rise in the fraction
of workers employed in educational services,
which employs primarily college-educated labor,
would accomplish just the opposite. To address
this potential misspecification of the regression,
I include contemporaneous changes in each sector’s employment share in (1) and drop the initial
levels.
Although this approach likely introduces a
simultaneity issue into the estimation (i.e.,
changes in employment shares may be influenced
by contemporaneous changes in the fraction of
college-educated workers in the local population),
it should be stressed that the objects of primary
interest in this second alteration are the coefficients on log population and the initial college
fraction, not those on the changes in each industry
share (which, accordingly, may be biased). The
idea behind this regression, quite simply, is to
see whether initial size and education are still
significantly correlated with subsequent changes
in human capital even after removing all of the
variation in human capital accumulation associated with changes in a metro area’s industrial base.
Results appear in Table 5. As before, I report
coefficient estimates from three different specifications to gauge the sensitivity of the findings to
variations in the model. The first column, labeled
I, reports coefficients from the regression of the
change in the college attainment rate on the initial
estimated return earned by college graduates, log
population, log density, the initial college fraction,
and initial quantities of the 10 amenities listed
above.17 Interestingly, five of these amenities
enter significantly. Eating and drinking places
per capita, live entertainment venues per capita,
and numbers of colleges and universities all enter
17

Many of these variables were identified by Glaeser, Kolko, and
Saiz (2001) as being significantly related to population growth.

F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

Results were similar when the 20 initial industry shares were
included. Because reporting all of these additional coefficients
would have been excessive, I have omitted them from the regression.

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Table 5
Robustness Checks
Variable

Initial estimated return

–0.015 (0.011)

–0.028* (0.01)

III
–0.027* (0.01)

Initial log population

0.005* (0.002)

0.004* (0.002)

Initial log density

0.002 (0.001)

0.0006 (0.002)

–0.0001 (0.001)

Initial college fraction

0.1* (0.02)

0.13* (0.02)

0.11* (0.02)

Initial eating and drinking places per capita

11.6* (3.8)

—

6.6* (4)

Initial movie theaters per capita

56.6 (72.1)

—

47.7 (72.4)

Initial live entertainment venues per capita

47.7* (23.4)

—

Initial elementary and secondary schools per capita

59.5 (53.3)

Initial museums, botanical gardens, zoos

–0.0003* (0.0001)

—

0.0005* (0.0001)

—

0.0003* (0.0001)

–0.0003* (0.00007)

—

–0.0002* (0.0001)

0.0001 (0.0003)

—

Initial colleges and universities
Initial employment in colleges and universities
Initial hospitals
Initial commercial sports clubs
Initial fraction students in public school

0.0008 (0.002)

–0.009 (0.03)

Δ Fraction mining

—

Δ Fraction construction

—

25.7 (24.9)
64.9 (54.5)
–0.0002 (0.0001)
–0.00004 (0.002)

—
0.37* (0.22)
–0.01 (0.22)

0.0002 (0.0002)
–0.02 (0.03)
0.32 (0.23)
–0.05 (0.24)

Δ Fraction nondurable manufacturing

—

0.03 (0.22)

–0.0003 (0.24)

Δ Fraction durable manufacturing

—

0.06 (0.22)

0.014 (0.23)

Δ Fraction transportation

—

0.05 (0.24)

Δ Fraction communications

—

–0.29 (0.29)

0.08 (0.26)
–0.27 (0.3)

Δ Fraction utilities

—

0.09 (0.28)

0.07 (0.29)

Δ Fraction wholesale trade

—

0.24 (0.25)

0.21 (0.26)

Δ Fraction retail trade

—

0.05 (0.22)

0.04 (0.24)

Δ Fraction finance, insurance, real estate

—

0.56* (0.25)

0.51* (0.26)

Δ Fraction business and repair services

—

0.56* (0.26)

0.53* (0.27)

Δ Fraction private household services

—

–0.04 (0.5)

Δ Fraction personal services

—

–0.11 (0.21)

Δ Fraction entertainment and recreation services

—

0.007 (0.24)

–0.06 (0.26)

Δ Fraction medical services

—

0.28 (0.24)

0.25 (0.25)

Δ Fraction educational services

—

0.48* (0.23)

0.41 (0.25)

Δ Fraction social services

—

0.93* (0.38)

0.8* (0.4)

Δ Fraction other professional services

—

0.63* (0.36)

0.57 (0.37)

Δ Fraction public administration

—

–0.02 (023)

0.04 (0.53)
–0.11 (0.22)

–0.06 (0.25)

NOTE: The dependent variable is the change in college fraction for 1980-90 and 1990-2000. Region indicators and a dummy for the
1980-90 decade appear in all regressions. Employment in colleges and universities is expressed in 10,000s. Heteroskedasticity-consistent
standard errors, adjusted for correlation within metro areas, appear in parentheses; * denotes significance at the 10 percent level or
better.

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positively; the number of museums, botanical
gardens, and zoos and the number of hospitals
both enter negatively.18 In spite of this result,
however, the coefficients on log population and
the college fraction do not change appreciably
from what was reported above.
The second column of results drops these 10
amenities and adds changes in 19 of the 20 industry employment shares to determine whether
specifying industrial composition in 10-year
differences rather than initial levels makes any
difference in the remaining coefficient estimates.19
Compared with the specification of industry mix
in initial levels, a greater number of industries
now produce significant associations, and many
of these are quite reasonable, at least intuitively.
An increase in the importance of finance, insurance, and real estate, as well as social and business
and repair services, for example, should be associated with increases in the fraction of workers
with a bachelor’s degree or more. These sectors,
after all, tend to employ relatively large proportions of college-educated labor. This conclusion
is indeed borne out regardless of whether the 10
amenities listed above are included in the regression (column III) or not (column II).
At the same time, inclusion of changes in
industrial composition has very little impact on
the estimated initial population and college fraction coefficients. Both remain statistically significant, and the magnitudes are very similar to those
reported in all previous specifications. Such a
finding seems to reinforce the conclusion that,
even after accounting for a city’s industrial composition, a city’s initial scale and education are
strongly associated with the rate at which it
accumulates highly educated workers.
Of course, characterizing the industrial composition of a metro area by using a set of 20 broad
sectors is less than ideal. There is a fair amount
of heterogeneity inherent in each industry; hence,
this classification scheme may miss important
18

The number of hospitals may be associated with the growth in the
numbers of relatively old workers who tend to possess less education than younger workers.

Because changes in all 20 industry shares (by definition) sum to 0,
I drop the change in the employment share of agriculture, forestry,
and fisheries.

F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

differences in the types of employers present in
each metro area. For example, the types of employers belonging to the nondurable manufacturing
sector in one city (e.g., drugs or chemicals) may
be quite different from those in another (e.g., textiles or food processing). These differences may
be important in explaining the growth of human
capital, but would be missed by the present
analysis. More seriously, these unmeasured differences may very well be directly correlated
with either population or the college fraction. In
such an instance, the coefficients reported thus
far for these two regressors would be upwardly
biased.20
I attempt to address this matter by looking,
instead, at a collection of more than 200 industries,
representing sectors at a mostly three-digit (standard industrial classification) level, although
some two- and four-digit industries, as well as
combinations of two-, three- and four-digit industries, also appear.21 These are the most detailed
industrial categories available in the decennial
Census files.
Unfortunately, because adding more than 200
industry shares to the estimation of (1) is not
practically feasible, I use the following approach:
First, I create a “predicted” college attainment
fraction, PColli,t , for each metro area, i, in each
year t, as follows:
(2)

PColli ,t =

N i ,t

∑ Shares,i,tColls,t ,

s =1

where Shares,i,t is the share of sector s in metro
20

For example, one city may attract human capital because it has a
strong presence of nondurable manufacturing, which hires mostly
highly educated workers (e.g., drugs and chemicals), whereas
another may attract less human capital because it has a strong
presence of nondurable manufacturing, which hires primarily
less-educated workers (e.g., textiles and food processing). The
presence of high- and low-human capital nondurable manufacturers
will therefore be directly related to each city’s initial stock of
human capital, but the association between industrial composition
and human capital accumulation (which is significant in this
example) will be picked up by the initial stock of human capital.

Specifically, there are 223 industries in the 1980 data, 221 in the
1990 data, and 214 in the 2000 data. These are identified using
consistent codes established using the correspondence provided
by the U.S. Bureau of the Census. Tobacco and crude petroleum
and natural gas are examples of two-digit industries; drugs, electric
light and power, and grocery stores are examples of three-digit
industries; jewelry stores and retail florists are examples of fourdigit industries.

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Table 6
Residual College Fraction Regressions
Variable (initial value)

Estimated return

–0.026* (0.01)

–0.024* (0.01)

Log population

0.003* (0.001)

0.004* (0.002)

Log density

0.001 (0.001)

0.0006 (0.001)

College fraction

0.08* (0.02)

0.065* (0.02)

Eating and drinking places per capita

—

5.8* (3.3)

Movie theaters per capita

—

44.3 (65.2)

Live entertainment venues per capita

—

Elementary and secondary schools per capita

55.7* (21.1)
38.6 (45.4)

Museums, botanical gardens, zoos

—

–0.0003* (0.0001)

Colleges and universities

—

0.0004* (0.0001)

Employment in colleges and universities

—

Hospitals

—

Commercial sports clubs

—

Fraction students in public school

—

0.0002 (0.002)
–0.0002* (0.00006)
0.0001 (0.0002)
–0.02 (0.03)

NOTE: The dependent variable is the change in the difference between a city’s college fraction and its predicted college fraction based
on its detailed industrial composition. Region indicators and a dummy for the 1980-90 decade appear in all regressions. Employment
in colleges and universities is expressed in 10,000s. Heteroskedasticity-consistent standard errors, adjusted for correlation within metro
areas, appear in parentheses; * denotes significance at the 10 percent level or better.

area i’s total employment in year t, Colls,t is the
college completion fraction for sector s in year t
(calculated using aggregate data for the United
States), and Ni,t is the number of sectors in metro
area i in year t. Second, I compute a “residual”
college fraction given by (Colli,t – PColli,t ), which
measures the difference between a city’s actual
college-completion fraction and the fraction that
would result if its industries resembled the
national average. I interpret this difference as the
part of a city’s college-attainment fraction that is
not explained by its detailed industry composition. I then consider regressions of the form
(3)

(

)

Δ Colli ,t − PColli ,t = μ + δt + β X i ,t + ε i ,t ,

where two specifications of the regressors Xi,t are
considered: One controls for the estimated college
return, log population, log density, and the college
fraction, all in initial levels; the other further adds
initial values of the 10 amenities discussed above.
The resulting estimates appear in Table 6.
In general, they demonstrate very little change
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from what has already been reported. Among the
amenities, the same five variables (eating and
drinking places per capita; live entertainment
venues per capita; numbers of museums, botanical
gardens, and zoos; numbers of colleges and universities; and numbers of hospitals) all enter
significantly and with the same signs as before.
Additionally, the initial college-return produces
a significantly negative coefficient, while the
logarithm of population and the initial fraction
of college-educated workers in total employment
generate significantly positive coefficients.
With these latter two regressors, it is worth
noting that the coefficients are now somewhat
smaller than what is reported in Tables 3 and 5.
For example, in Table 6, log population produces
coefficients between 0.003 and 0.004 rather than
between 0.003 and 0.006 previously, whereas
the initial college completion rate generates a
coefficient ranging from 0.065 to 0.08 rather than
from 0.1 to 0.16. These decreases are consistent
with the idea mentioned previously that using
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Table 7
Growth Regressions
Dependent variable

Specification

Initial
college fraction

Initial
log population

Initial average
log hourly wage

Population growth

0.28* (0.13)

—

Average hourly wage growth

—

0.011* (0.005)

—

III

0.41* (0.14)

0.02* (0.006)

–0.33* (0.08)

0.26* (0.04)

—

–0.11* (0.035)

—

III

0.42* (0.05)

0.02* (0.003)

–0.39* (0.05)

NOTE: Regressions of metro area–level population growth and average hourly wage growth on initial values of the college fraction,
log population, and average log hourly wages. Region indicators and a dummy for the 1980-90 decade appear in all regressions.
Heteroskedasticity-consistent standard errors, adjusted for correlation within metro areas, appear in parentheses; * denotes significance
at the 10 percent level or better.

20 broad industry shares leads to upwardly biased
coefficients on the initial college fraction and log
population. Still, the evidence is remarkably
consistent with respect to the influence of these
two variables. Regardless of how the statistical
model is specified, initial population and education are significant predictors of human capital
accumulation.

Human Capital, Growth, and Divergence
The finding that more-populous and -educated
cities tend to experience the largest increases in
human capital has an intriguing implication with
respect to the geographic distributions of population and college-educated labor. Specifically, it
suggests that the distributions of these two quantities should have been characterized by increasing
concentration over the 1980-2000 period. Human
capital accumulation, after all, tends to be faster
in cities with larger initial fractions of highly
educated workers. This mechanism should then
lead to a growing gap between the education levels
across cities over time as the top end of the distribution pulls away (or “diverges”) from the bottom.
Because previous work has shown that moreeducated cities also tend to see faster population
growth (e.g., Glaeser, Scheinkman, Shleifer, 1995),
I arrive at a similar implication with respect to
the distribution of population. This section examF E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

ines whether there has been this type of “divergence” in the distribution of these two quantities.
Before doing so, I attempt to establish some
basic results relating the growth of two quantities—
population and average hourly wages—to education. While the former is of greater interest in
this particular exercise, the latter more closely
resembles the object of interest in most studies
of economic growth (i.e., per capita income).
Results from the regression of each quantity’s 10year growth rate on the initial level of human
capital appear in the specifications labeled I in
Table 7.22 Not surprisingly, each shows a significantly positive association with initial education.
Here, the magnitudes indicate that a 1-standarddeviation (i.e., a 6.5-percentage-point) increase
in a city’s college attainment rate tends to be
accompanied by a 1.8-percentage-point rise in
its rate of population growth and a 1.7-percentagepoint rise in its rate of average wage growth over
the next 10 years. These figures represent, respectively, 16 and 20 percent of the cross-sectional
standard deviations in these two growth series.
These associations, therefore, seem to be both
statistically and economically important.
To explore whether there has been divergence
across city-level human capital, population, and
22

As with all of the other regressions, these include three region
dummies and an indicator for the 1980-90 decade.

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average wages, I consider two approaches. The
first looks for so-called β-convergence, the test for
which involves a simple regression of the growth
of a quantity on its initial level.23 A negative
coefficient on the initial level of a variable would
indicate a tendency for that quantity to converge
to a common level across metro areas. After all, a
negative coefficient would indicate that cities with
low levels of human capital, for example, would
experience faster human capital growth than cities
with high levels. This process should generate a
less-concentrated distribution of human capital
over time as the bottom of the distribution catches
up with the top. The second approach looks for
σ-convergence, which is based on how the crosssectional dispersion of a particular quantity
changes over time. Decreasing dispersion (i.e.,
falling concentration) would be indicative of
σ-convergence.24
One common criticism of these statistical
approaches, particularly tests for β-convergence,
pertains to the appropriateness of pooling a set
of extremely heterogeneous economies in the
same regression (see Durlauf and Quah, 1999).
While this point is certainly valid when considering studies of countries, which tend to vary
substantially in terms of various fundamental
characteristics including how their economies
function (e.g., Japan and Nigeria), it is less likely
to be a significant issue when comparing the
experiences of metro areas within the same country (e.g., Seattle and Atlanta).
The β-convergence results for metro-area college attainment are already well-established in
the findings shown thus far. The strong positive
association between the initial level of a city’s
college fraction and its subsequent change over
the next decade indicates divergence in this variable. Results for the logarithm of population and
the average log hourly wage appear in the specifications labeled II in Table 7.
23

Again, all regressions also include three region dummies and a
time effect to pick up differences in growth across decades. The
β in β-convergence refers to the coefficient on the initial level of a
variable in a growth regression.
The σ in σ-convergence refers to the standard deviation. Barro
and Sala-i-Martin (1995) provide an overview of the statistical
techniques commonly used in studies of convergence/divergence.

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The population series also shows divergence
which, intuitively, is precisely what one would
expect in light of the results shown to this point.
Larger populations tend to be associated with
more rapid human capital accumulation, which
raises education levels. This, in turn, leads to faster
population growth. Hence, one would expect to
see a positive association between initial population and its subsequent rate of growth. Interestingly, however, the positive association between
initial population and its subsequent growth also
holds after conditioning on the initial college
fraction and the initial average log hourly wage.
This result is reported in specification III. The
direct association between population and population growth, therefore, does not seem to be
driven entirely by education. There is some aspect
of metro area size that, independent of education,
draws additional population.
Average hourly wages, by contrast, show evidence of convergence rather than divergence. That
is, higher average wages tend to be followed by
slower rates of wage growth over the next decade.
This finding, too, is sensible given the evidence
already presented. Recall that higher wages tend
to be accompanied by slower subsequent human
capital accumulation. The significantly negative
coefficients on the initial college return in the
regression results presented above demonstrate
this point clearly. Slower human capital accumulation, then, implies slower growth of average
hourly wages. Thus, one would expect to see a
negative association between initial average wages
and future wage growth. This relationship turns
out to hold whether initial education and log
population are accounted for or not (compare
specifications II and III).
To look at σ-convergence, I need a measure
that characterizes the degree of spread in the distributions of human capital, log population, and
the average log hourly wage.25 In an effort to keep
the analysis broad, I consider several possible
25

For this exercise, I use population and average wages in logarithmic
form because the distributions of their levels will tend to show
increasing dispersion even if growth is unrelated to the initial
level. For example, the gap between the populations of two cities,
one with population of 100, the other with a population of 1000,
will grow wider if both cities grow by the same percentage (and
possibly if the smaller city grows by a larger percentage).

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Table 8
Features of the Education, Population, and Average Hourly Wage Distributions
Variable
College fraction

Statistic

Average log hourly wage

1990

2000

Mean

0.178

0.219

0.253

10th percentile

0.122

0.148

0.17

25th percentile

0.15

0.18

0.206

50th percentile

0.175

0.216

0.248

75th percentile

0.203

0.25

0.284

90th percentile

0.238

0.296

0.339

Standard deviation

0.043

0.054

0.064

90-10 difference

0.116

0.148

0.168

90-50 difference

0.063

0.08

0.091

50-10 difference

0.053

0.068

0.077

75-25 difference
Log population

1980

0.053

0.069

0.078

Mean

12.96

13.06

13.19

10th percentile

11.76

11.79

11.91

25th percentile

12.07

12.17

12.36

50th percentile

12.77

12.88

13.01

75th percentile

13.61

13.71

13.9

90th percentile

14.37

14.62

14.76

Standard deviation

1.057

1.075

1.092

90-10 difference

2.61

2.83

2.86

90-50 difference

1.6

1.74

1.75

50-10 difference

1.09

1.1

75-25 difference

1.54

Mean

2.46

2.45

2.5

10th percentile

2.33

2.32

2.43

25th percentile

2.39

2.38

2.5

50th percentile

2.46

2.45

2.55

75th percentile

2.51

2.61

90th percentile

2.58

2.68

Standard deviation

0.098

0.109

0.105

90-10 difference

0.24

0.26

0.25

90-50 difference

0.12

0.14

0.13

50-10 difference

0.13

0.12

75-25 difference

0.12

0.13

0.11

NOTE: Statistics are based on 188 metro areas for the college fraction and average log hourly wage and 187 metro areas for log
population.

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measures: the standard deviation and a host of
inter-quantile differences (e.g., the difference
between the 90th percentile and the 10th). One
important consideration in looking at these distributional features is maintaining a consistent
sample of metro areas. The sample of metro areas
identified by the Census does change from one
year to the next. As a consequence, there may be
changes in the degree of spread in the distribution
of these variables that stem from changes in the
composition of the sample rather than an actual
convergence or divergence mechanism. In computing these distributional features, then, I confine the sample to those 188 metro areas that
appear in all three years.
The resulting estimates appear in Table 8.
Looking at the distribution of college attainment
rates, it is evident that, although there has been an
increase in the fraction of workers with a bachelor’s degree or more at all points of the distribution, that increase has been larger at the top than
at the bottom. The 90th percentile, for example,
rose by more than 10 percentage points between
1980 and 2000, increasing from 0.238 to 0.339.
The corresponding increases for the median and
10th percentiles over this period were 7.3 and
4.8 percentage points. Accordingly, each of the
four listed percentile gaps (90-10, 90-50, 50-10,
75-25) grew wider over time. Rising dispersion
can also be inferred from the evolution of the standard deviation, which started at 0.043 in 1980,
rose to 0.054 in 1990, and stood at 0.064 by 2000.
Evidently, human capital became more unevenly
distributed during this time frame.26
The logarithm of population, the distributional features of which appear just below the
human capital results in Table 8, reveals a similar
trend. On average, metro areas in the United States
experienced population gains between 1980 and
2000, and these gains were registered at all five
quantiles of the distribution. Again, however,
the gains tended to be somewhat larger at the top
of the distribution than at the bottom. With the
exception of the inter-quartile difference (75-25),
which did not change between 1980 and 2000,
26

Moretti (2004) documents a similar rise in the degree of human
capital “inequality” across U.S. metro areas.

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all other quantile differentials increased in both
decades. Increasing dispersion in the logarithm
of population also shows up in the standard
deviations, which increased from 1.057 in 1980
to 1.075 in 1990 to 1.092 in 2000. Log population,
therefore, also shows evidence of both types of
divergence.
These results are particularly striking because
they stand somewhat at odds with what conventional economic analysis might suggest. Indeed,
as cities grow in population, they tend to become
more congested, which, in turn, raises costs
(financial and otherwise) to both workers and
employers. These “agglomeration diseconomies”
should, therefore, work to slow subsequent rates
of population growth as firms and workers seek
less-congested labor markets. Similarly, as the
fraction of workers with a bachelor’s degree rises,
the relative return received by college-educated
workers (all else equal) should decline because
the supply of such workers has risen relative to
demand. This is a standard diminishing marginal
productivity argument whereby the return
received by a factor of production (e.g., collegeeducated labor) declines as it is used more intensively relative to all other inputs. A lower return
paid to college-educated labor, of course, should
reduce the rate at which workers with a bachelor’s
degree move into an area. Empirically, however,
there seems to be little support for these theoretical ideas in the data.
Recall that average hourly wages show a very
different pattern. Regressions of wage growth on
initial wage levels reveal a significantly negative
relationship between the two. One might expect,
therefore, to see a decrease in the degree of dispersion in the distribution of city-level average
log wages. The estimated dispersion measures in
Table 8, however, show only a decrease between
1990 and 2000, when the standard deviation and
all four quantile differences narrowed. During
the 1980s, all but the 50-10 difference increased.
These results demonstrate an important difference
between β- and σ-convergence. Although a negative association between the initial level of a
variable and its subsequent growth rate may certainly reduce the degree of variance in a distribution, it may also increase it. Durlauf and Quah
F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

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(1999), for example, show how β-convergence
may generate a wider distribution if economies
with low levels of a variable overshoot economies
with high levels. Distributional dynamics of this
sort may help to explain these results.
Another possible explanation may relate to
the influence of population and the college fraction, which, as shown in Table 7, tend to be positively related to wage growth over the next decade.
As these two variables have diverged, they may
have led to a divergence in wage levels during the
1980s if their influence outweighed the natural
tendency for wage levels to converge. Assuming
that this natural tendency was stronger during the
1990s, of course, the cross-sectional dispersion
in average log wages would have declined.27

CONCLUDING DISCUSSION
This paper has explored the issue of human
capital accumulation across a set of U.S. metro
areas. Among the more prominent findings is that
cities with larger populations and larger fractions
of workers with college degrees tend to see faster
growth in their stocks of human capital. Because
human capital also tends to be positively associated with population growth, this process has led
to a divergence of both human capital and population in the United States between 1980 and 2000.
Hence, the largest and most-educated cities in
the country have tended to accumulate population and human capital faster than smaller and
less-educated cities.
The divergence of human capital and population has not, interestingly, generated much divergence with respect to average wage levels across
cities. Although the amount of dispersion in the
distribution of metro area–level average wages
did grow larger between 1980 and 2000, this
growth occurred during the decade of the 1980s.
Dispersion in wage levels actually declined somewhat between 1990 and 2000. This result could
27

A similar argument relating to the relative strengths of the college
attainment rate, population, and average wage levels could be
made in explaining the divergence patterns of human capital and
log population. In those cases, evidently, the mechanisms leading
to divergence were stronger than any effects that wage levels might
have had.

F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

be related to the mechanism described above in
which the increasing concentration of workers
with college degrees may depress the returns
they receive.
If true, however, why would college-educated
workers continue to flock to labor markets with
large populations and stocks of highly educated
workers? Glaeser (1999) suggests that workers
with a college degree may seek to surround themselves with other college graduates because they
are able to learn from one another. Highly educated
workers, according to this line of reasoning, are
especially committed to the acquisition of productive skills. Since previous work suggests that
there may be productive externalities associated
with the presence of college-educated individuals
(e.g., Moretti, 2004), the positive association
between initial college attainment rates and subsequent changes in these rates may reflect the
desire of highly educated workers to reside in
environments that facilitate learning.
Peri (2002) echoes this view, suggesting that,
if skill acquisition is an important reason for the
concentration of human capital in cities, we should
expect to see large numbers of “young” collegeeducated workers in cities. Young workers, after
all, are more likely than their older counterparts
to seek learning opportunities because they are
in the early stages of their careers and, therefore,
know relatively little. The evidence he reports is
certainly consistent with this idea. Between 1970
and 1990, the ratio of college-educated workers
with fewer than 20 years of work experience to
those with more than 20 years rose from 1.5 to
2.12 within the metro areas of the United States.
Populous cities may also help facilitate the
job search process for highly educated married
couples. Costa and Kahn (2000) suggest that
“power couples” (i.e., those in which both partners
have a bachelor’s degree or more) have increasingly
moved into large metro areas over the past several
decades because cities are more likely to offer job
opportunities for both spouses. Large cities, therefore, may provide a solution to the occupational
co-location problem.
An additional possibility that deserves to be
mentioned involves the amenity value of collegeeducated workers themselves. That is, while the
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college-educated may be enticed to locate in cities
with a large presence of certain types of establishments (say, eating and drinking places), they might
also want to be around other college-educated
workers because they desire homogeneity in their
social interactions. So, even though concentrations
of highly educated workers may be associated
with diminishing returns and lower earnings (at
least, all else equal), college graduates may still
want to surround themselves with other highly
educated workers because they find them to be
desirable neighbors. Of course, a strong presence
of college-educated workers may also be associated
with characteristics that have not been accounted
for directly here (e.g., low crime, greater civic
engagement, good schools), but which are especially desirable to these types of workers.
Whatever the reason, divergence in the distribution of human capital may, over longer time
horizons, begin to lead to divergence in earnings
and productivity across cities and regions.
Although there is only limited evidence of that
having occurred between 1980 and 2000, it may
occur to a greater extent in future decades. In
particular, if technologies respond to the supply
of skills (e.g., as suggested by Acemoglu, 1998),
cities with large stocks of college-educated labor
may increasingly use technologies that complement these types of workers. This trend may further reinforce the divergence of human capital by
encouraging highly educated workers to congregate in the most educated cities as well as lead to
greater productivity differentials between cities
with small stocks of human capital and those with
large stocks.

REFERENCES
Acemoglu, Daron. “Why Do New Technologies
Complement Skills? Directed Technical Change and
Wage Inequality.” Quarterly Journal of Economics,
November 1998, 113(4), pp. 1055-89.
Barro, Robert J. “Economic Growth in a Cross Section
of Countries.” Quarterly Journal of Economics,
May 1991, 106(2), pp. 407-43.
Barro, Robert J. and Sala-i-Martin, Xavier.
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“Convergence.” Journal of Political Economy, April
1992, 100(2), pp. 223-51.
Barro, Robert J. and Sala-i-Martin, Xavier. Economic
Growth. New York: McGraw-Hill, 1995.
Black, Duncan and Henderson, Vernon. “A Theory of
Urban Growth.” Journal of Political Economy,
April 1999, 107(2), pp. 252-84.
Card, David. “The Causal Effect of Education on
Earnings,” in Orley Ashenfelter and David Card, eds.,
Handbook of Labor Economics. Volume 3A.
Amsterdam: Elsevier, 1999, pp. 1801-63.
Costa, Dora L. and Kahn, Matthew E. “Power Couples:
Changes in the Locational Choice of the College
Educated, 1940-1990.” Quarterly Journal of
Economics, November 2000, 115(4), pp. 1287-315.
Dee, Thomas S. “Are There Civic Returns to
Education?” Journal of Public Economics, August
2004, 88(9-10), pp. 1697-720.
Durlauf, Steven N. and Quah, Danny T. “The New
Empirics of Economic Growth,” in John B. Taylor
and Michael Woodford, eds., Handbook of
Macroeconomics. Volume 1A. Amsterdam: Elsevier,
1999, pp. 234-308.
Glaeser, Edward L. “Learning in Cities.” Journal of
Urban Economics, September 1999, 46(2), pp.
254-77.
Glaeser, Edward L.; Kolko, Jed and Saiz, Albert.
“Consumer City.” Journal of Economic Geography,
January 2001, 1(1), pp. 27-50.
Glaeser, Edward L. and Saiz, Albert. “The Rise of the
Skilled City.” Discussion Paper No. 2025, Harvard
Institute of Economic Research, 2003.
Glaeser, Edward L. and Saks, Raven E. “Corruption
in America.” Discussion Paper No. 2043, Harvard
Institute of Economic Research, 2004.
Glaeser, Edward L.; Scheinkman, José A. and Shleifer,
Andrei. “Economic Growth in a Cross-Section of
Cities.” Journal of Monetary Economics, December
1995, 36(1), pp. 117-43.
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Wheeler

Lochner, Lance and Moretti, Enrico. “The Effect of
Education on Crime: Evidence from Prison
Inmates, Arrests, and Self-Reports.” American
Economic Review, March 2004, 94(1), pp. 155-89.
Milligan, Kevin; Moretti, Enrico and Oreopoulos,
Philip. “Does Education Improve Citizenship?
Evidence from the United States and the United
Kingdom.” Journal of Public Economics, August
2004, 88(9-10), pp. 1667-95.
Moretti, Enrico. “Human Capital Externalities in
Cities,” in J. Vernon Henderson and JacquesFrancois Thisse, eds., Handbook of Regional and
Urban Economics. Volume 4. New York: Elsevier,
2004, pp. 2243-91.
Park, Jin Heum. “Estimation of Sheepskin Effects
and Returns to Schooling Using the Old and the
New CPS Measures of Educational Attainment.”
Princeton Industrial Relations Section Working
Paper No. 338, Princeton University, 1994.

Peri, Giovanni. “Young Workers, Learning, and
Agglomerations.” Journal of Urban Economics,
November 2002, 52(3), pp. 582-607.
Ruggles, Steven; Sobek, Matthew; Alexander, Trent;
Fitch, Catherine A.; Goeken, Ronald; Hall, Patricia
Kelly; King, Miriam and Ronnander, Chad.
Integrated Public Use Microdata Series: Version 3.0
[machine-readable database]. Minneapolis, MN:
Minnesota Population Center, 2004.
Simon, Curtis J. and Nardinelli, Clark. “Human
Capital and the Rise of American Cities, 1900-1990.”
Regional Science and Urban Economics, January
2002, 32(1), pp. 59-96.
U.S. Bureau of the Census. USA Counties 1998, on
CD-ROM [machine readable data file]. Washington,
DC: U.S. Bureau of the Census, 1999.

APPENDIX
Census Data
The data are taken from the 1980, 1990, and 2000 5 percent samples of the Integrated Public Use
Microdata Series (IPUMS) described by Ruggles et al. (2004). Specifically, I use the 1980 5 percent state
sample, the 1990 5 percent state sample, and the 2000 5 percent sample. These files have roughly 11.3
million, 12.5 million, and 14 million observations, respectively.
To calculate educational attainment distributions among each metropolitan area’s labor force, I focus
on the working age population (i.e., those who are between the ages of 18 and 65) who report positive
wage and salary earnings and are not in school at the time the Census was taken. In estimating the
returns to various levels of formal schooling, I further limit the analysis to white males who earn between
$1 and $250 per hour. This trimming procedure is designed to eliminate the influence of outlier observations, which occasionally appear due to the computation of hourly earnings as the ratio of annual wage
and salary earnings to the product of weeks worked and usual hours per week. All dollar figures are
converted to real terms (year 2000 dollars) using the personal consumption expenditure chain type
price index.
Potential experience is calculated as the maximum of (age minus years of education minus 6) and 0.
Because years of education is not reported for all individuals in the 1990 and 2000 Census, where
educational attainment is sometimes reported as a range, I have imputed years of schooling completed
using Table 5 of Park (1994).
As noted in the text, metro areas are defined as metropolitan statistical areas (MSAs), New England
county metropolitan areas (NECMAs), or consolidated metropolitan statistical areas (CMSAs) if an
MSA or NECMA belongs to a CMSA. Although somewhat large when considering local labor markets
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(e.g., New York– northern New Jersey–Long Island), CMSAs greatly facilitate the construction of geographic areas that have reasonably consistent geographic boundaries. Due to changes in geographic
definitions, residents of one MSA within a CMSA in a particular year are sometimes categorized as
residing in a different MSA (within the same CMSA) in another year. Aggregating to the CMSA level
eliminates any problems arising from this type of definitional change.
Across the 210 metro areas identified in the 1980 Census, the average number of individual level
observations used to construct the college attainment and industry share statistics is 14,484.1 (minimum
= 1,557, maximum = 315,128). Among the 206 metro areas identified in the 1990 data, the average is
15,863.4 (minimum = 1,426, maximum = 329,632). In the 245 metro areas from the 2000 Census, the
mean is 16,526.4 (minimum = 1,426, maximum = 371,278). When confining the sample to white males
only for the college return regressions, the mean numbers of observations (minimum, maximum) per
metro area are 6,928.1 (666, 144,886) for 1980, 7,275.7 (670, 144,698) for 1990, and 6,600.7 (516, 134,898)
for 2000.
A complete list of the detailed industries appears in the IPUMS documentation at www.ipums.org.
These can be found in the link to the industry codes for 1980. The 1990 and 2000 codes are translated
into equivalent 1980 codes using the programs that accompany this paper.

Additional Data Details
Metro-area population density is calculated as a weighted average of county-level densities, where
the weights are given by population shares. This measure is intended to give a better sense of the average
density per square mile faced by a typical city dweller than average density (metro area population to
metro area land area), which may be misleading, particularly among cities in the western United States,
which encompass extremely large, but sparsely populated counties.

U.S. Census Regions
Midwest: Illinois, Indiana, Iowa, Kansas, Michigan, Minnesota, Missouri, Nebraska, North Dakota,
Ohio, South Dakota, Wisconsin
Northeast: Connecticut, Maine, Massachusetts, New Hampshire, New Jersey, New York, Pennsylvania,
Rhode Island, Vermont
South: Alabama, Arkansas, Delaware, District of Columbia, Florida, Georgia, Kentucky, Louisiana,
Maryland, Mississippi, North Carolina, Oklahoma, South Carolina, Tennessee, Texas, Virginia,
West Virginia
West: Alaska, Arizona, California, Colorado, Hawaii, Idaho, Montana, Nevada, New Mexico, Oregon,
Utah, Washington, Wyoming

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Macroeconomic News and Real Interest Rates
Kevin L. Kliesen and Frank A. Schmid
Economic news affects the perceptions of investors, forecasters, and policymakers about the
strength or weakness of the economy. These expectations are updated on the basis of regularly
occurring surprises in macroeconomic announcement data. The response of asset prices to positive
or negative announcement surprises has been a regular feature of the literature for more than 20
years. In this vein, the authors evaluate the responses of the yield of 10-year Treasury inflationindexed securities to nearly three dozen macroeconomic announcements. They find that the real
long-term rate of interest responds positively to surprises in a handful of key macroeconomic
indicators, including labor productivity growth. Also, the authors find no support for the proposition that the Federal Reserve has information about its actions or the state of the real economy
that is not in the pubic domain and, hence, not already priced in the real long-term interest rate.
Federal Reserve Bank of St. Louis Review, March/April 2006, 88(2), pp. 133-43.

ederal Reserve officials often make
remarks and offer their thoughts in
public forums. Recent comments by
Bill Poole and Janet Yellen, of the
Federal Reserve Banks of St. Louis and San
Francisco, respectively, have added to the discussion of the role of economic data in monetary
policy:
“I think there has been an effort to emphasize
that increasingly, the policy decisions will
be data-driven, driven by incoming
information…”1
“Uncertainties and risks that could complicate
things considerably were evident even before
the havoc unleashed by Hurricane Katrina, so
our approach during this phase must be particularly dependent on information from
incoming data.”2

USA Today (2005).

Yellen (2005).

Their comments suggest that key information
is contained in the evolving flow of these data
that informs policymakers’ assessments of the
strength of the economy and perhaps also affects
the future stance of policy.
Moreover, studies with macroeconomic
announcement data suggest that surprises in the
data can influence such things as the market price
of Treasury securities or inflation expectations.
We focus our analysis on the relationship between
surprise data announcements and the yield on
Treasury inflation-indexed securities (TIIS, a
measure of the real interest rate) from January
1997 through June 2003. Consider this example:
Suppose the Federal Reserve and financial market
participants view the monthly jobs number within
the employment report released by the Bureau of
Labor Statistics as a reliable indicator of the nearterm strength of the economy. In this case, a positive (negative) surprise would signal to the Fed
and the markets that the economy was growing

Kevin L. Kliesen is an associate economist at the Federal Reserve Bank of St. Louis, and Frank A. Schmid is a senior economist at the National
Council on Compensation Insurance. This article was written while Schmid was affiliated with the Federal Reserve Bank of St. Louis. The
authors thank Hui Guo and Jeremy Piger for comments and suggestions. Jason Higbee provided research assistance.

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at a quicker (slower)-than-expected pace. Under
these circumstances, the demand for investment
goods would be expected to increase (decrease)
and the real interest rate would have to rise (fall)
to clear the market.
There are many other examples of news that
might affect real long-term interest rates (such as
a surprise increase in labor productivity growth
or in the government budget deficit). But it is not
our intention here to test the theory that budget
deficits cause higher interest rates or to model the
real rate of interest in a macroeconomic setting.
Rather, we simply test whether there is a core set
of economic variables that traders in the TIIS
market respond to more than others. Along these
lines, other potential influences on the TIIS market
are actions and commentary by Federal Reserve
officials. Accordingly, we also test whether TIIS
investors re-price the real long-term interest
rate in response to surprises in monetary policy
actions.
We look at the data from January 31, 1997,
through June 30, 2003, and ask whether the real
long-term rate of interest responds to a sample of
35 surprise economic announcements from that
period, as well as to the surprises in the federal
funds interest rate target. We measure the real
long-term rate of interest of on-the-run (that is,
most recently issued) 10-year TIIS. We gauge
surprises in macroeconomic announcements by
the difference between the expected value and
the actual released value of the data series. The
former is the median forecast among a sample of
forecasters and market participants. Except for
the growth of real GDP, the GDP price index, and
nonfarm labor productivity (there are forecasts
for the preliminary and revised growth rates),
the latter is the first-reported value for the series.
Our analysis suggests that participants in the
TIIS market respond to the announcements for
seven economic data series in a statistically significant manner: business inventories, the employment cost index, the preliminary GDP estimate,
initial jobless claims, new home sales, nonfarm
payroll employment, and the preliminary estimate
of nonfarm labor productivity. Finally, we fail to
reject the hypothesis that uncertainty surrounding the real long-term interest rate is unaffected
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by Federal Reserve communication and surprises
in monetary policy actions. Taking into consideration both those results in our analysis, we find
no support for the proposition that the Federal
Reserve has information about its own actions or
the state of the real economy that is not in the
pubic domain and, hence, priced in the real longterm interest rate.

RELATED LITERATURE
The studies most closely related to our work
are Calomiris et al. (2003), Gürkaynak, Sack,
and Swanson (2003), and Kohn and Sack (2003).
Calomiris et al. study the response of the real
interest rate, as measured by the market yield of
the 10-year TIIS, to surprises in 19 macroeconomic
data releases, among them the monthly federal
budget deficit/surplus reported by the U.S.
Treasury Department. Surprises in labor productivity or monetary policy announcements are
not included in the regression. Calomiris et al.
find that surprises in the federal budget surplus
cause no statistically significant change in the
real interest rate. Gürkaynak, Sack, and Swanson
(2003) analyze the response of the forward real
interest rate to surprises in macroeconomic data
releases and in Federal Reserve monetary policy
actions—that is, changes to the targeted federal
funds rate set by the Federal Open Market
Committee (FOMC). Their forward rates are
derived from the yields of 10-year TIIS.3 The
authors fail to reject the hypothesis that the “longterm equilibrium real rate of interest” is unaffected
by surprises in these productivity and federal
budget numbers. In a separate regression,
Gürkaynak, Sack, and Swanson (2003) study
the impact on the same dependent variable of
surprises in announced changes of the targeted
3

The studied pair of 1-year forward rates applies to the 12-month
time window between the maturity dates of the on-the-run 10-year
TIIS and the 10-year TIIS issued 12 months earlier. Prior to July
2002, and starting in 1997, 10-year TIIS were issued only once per
year, in January. This implies that the authors analyze changes to
the 1-year real interest rate that is expected to prevail at the beginning of a 12-month time window that begins, on average, 8.5 years
from the time of the data release. The analyzed time period runs
from January 1997 through July 2002 and covers 39 macroeconomic
data series.

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Kliesen and Schmid

federal funds rate; again, the authors do not reject
the null hypothesis of no influence.4 Faust et al.
(2006) estimate a Kalman filter approach in
gauging the surprise effect of macroeconomic
announcements to the U.S. dollar exchange rate
and to nominal (short- and long-term) interest
rates. These authors find that the surprises in such
announcements for a wide variety of macroeconomic variables have a statistically significant
effect on the dollar and interest rates.
Kohn and Sack (2003) study the effect of
Federal Reserve communication on financial
variables using daily observations for the period
January 3, 1989, through April 7, 2003. In their
analysis, Fed communication comprises statements released by the FOMC and, since June 1996,
Congressional testimonies and speeches delivered
by the Chairman of the Federal Reserve. Kohn and
Sack make no attempt to gauge the influence on
the level of Treasury yields; rather, the authors
measure the effect of Fed communication on
Treasury yield volatility. Kohn and Sack investigate the effect that Federal Reserve communication has on various financial variables, such as
the yields (to maturity) of the nominal 2-year and
10-year Treasury notes. Kohn and Sack find that
statements of the FOMC and testimonies of the
Chairman of the Federal Reserve have a statistically significant impact on the variance of 2-year
and 10-year Treasury note yields; no such influence was found for the Chairman’s speeches. We
build on Kohn and Sack when studying the effect
of Federal Reserve communication on the (conditional) variance of the yield of the 10-year TIIS
or, put differently, on the uncertainty that surrounds the real long-term rate of interest.

is determined by the series of macroeconomic data
releases provided by Money Market Services
(MMS). The dataset comprises median polled
forecast values for 38 macroeconomic data series,
along with the sample standard deviations of
these forecast values. The MMS survey is conducted every Friday morning among senior economists and bond traders with major commercial
banks, brokerage houses, and some consulting
firms, mostly in the greater New York, Chicago,
and San Francisco areas. Among these 38 variables in the survey, there are three items—CPI,
PPI, and retail sales—for which there also exists
a “core” measure. Although the comprehensive
versions of the CPI and the PPI include food and
energy items, the respective core measures do not.
For retail sales, the narrowly defined concept
excludes motor vehicles and parts. In the regression analysis, we use the core concepts only; this
leaves us with 35 macroeconomic variables.5
We relate daily changes in the real long-term
rate of interest to the surprise component in
macroeconomic data releases. Like Gürkaynak,
Sack, and Swanson (2003), we define the surprise
component as the difference between the actual
and the median forecast values; but unlike these
authors (and unlike Calomiris et al.), we normalize these surprises by the sample standard deviation of the individual forecasts, which we take to
be a measure of forecaster uncertainty surrounding these expectations. In the literature, normalizing announcement surprises, though common,
is not universal.6 We also control for the surprise
component in changes (or the absence thereof) of
the targeted federal funds rate, which we measure
as suggested by Kuttner (2001) and discussed by
Watson (2002). For each scheduled and unsched-

THE DATA

We find no statistically significant difference, for any of our statistical analyses, between the core and the comprehensive measures.

Fleming and Remolona (1997, 1999) calculate the surprise component by normalizing the difference between the actual and the
forecast values by the mean absolute difference observed for the
respective variable during the sample period. Balduzzi, Elton,
and Green (2001) normalize the difference between the actual and
the forecast values by the standard deviation of this difference
during the sample period. Gürkaynak, Sack, and Swanson (2005)
normalize the announcement surprise by its standard error. Faust
et al. (2006) simply use a non-normalized forecast error (surprise)
in their analysis of intraday exchange rate and nominal interest
rate data.

Our analysis covers the period from January 31,
1997, through June 30, 2003. The starting date of
this sample period is determined by the availability of the 10-year TIIS yield; the ending date
4

These findings of surprises in macroeconomic data releases and
monetary policy actions on real interest rates are included only in
the Gürkaynak, Sack, and Swanson working paper (2003) but not
in the published version (Gürkaynak, Sack, and Swanson, 2005).

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uled FOMC meeting, we scaled up by 30/(k +1)
the change of the price of the federal funds futures
contract for the current month on the day of the
FOMC meeting, t, where t + k denotes the last
calendar day of the month.7 (Note that this variable is not on the same scale as the surprise component in the macroeconomic data releases.) In a
sensitivity analysis, we use an alternative measure of the surprise component in monetary policy
actions; this alternative measure, devised by Poole
and Rasche (2000), rests on price changes of
federal funds futures contracts also.8 Finally, we
control for Federal Reserve communication and
actions. Our concept of Federal Reserve communication comprises (i) the Fed Chairman’s semiannual testimony to Congress (formerly known as
Humphrey-Hawkins testimony) and (ii) speeches
and other testimonies of the Fed Chairman.
In announcement studies, the timing of the
data releases can sometimes be an issue. This is
particularly true if intraday observations are used.
In this paper, there are two potential timing issues,
neither of which is likely to significantly influence
the results because we do not use intraday prices.
First, most data releases occur in the morning at
8:30 and 10:00 eastern standard time. However,
there are some releases that occur in the afternoon,
such as consumer credit and the budget surplus/
deficit, and some that have an irregular release
time (auto and truck sales). This is also the case
with Fed speeches and testimonies, which can
occur when markets are open or closed. A second
potential issue are data releases and speeches
that occur on holidays or when the markets are
closed. Data releases on days when the markets
were closed were moved to the next trading day
(the day on which this information was priced
in the marketplace). We also moved Federal
Reserve communication to the next trading day
if this communication occurred after hours (that
is, after the real interest rate had been recorded)
7

Following Gürkaynak, Sack, and Swanson (2003), we use the
(unscaled) change in the price of the federal funds futures contract due to expire in the following month if the FOMC meeting
took place within the last seven calendar days of the month.

See Gürkaynak, Sack, and Swanson (2002) for a discussion of
how measures of market expectations are measured in relation to
monetary policy actions.

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or on days on which there was no trading. Thus,
in some cases, U.S. markets will have a shorter
time period in which to react to the announcement surprise, while in other cases they will have
a longer time period.
Table 1 shows the frequency of the macroeconomic announcements during the period of
analysis (January 1997 through June 2003). The
number in parentheses—the number of data
releases during the analyzed time period—differs
because of missing values in the recorded real
interest rate. For example, there are 77 observations (surprises) for most monthly variables, such
as business inventories. Of the 77 observations
for business inventories, 68 were used. Note that
Table 1 also includes two monetary policy variables and one Fed communication variable. We
also report matches for scheduled and unscheduled FOMC meetings—the federal funds target
variable, the surprise component of which was
calculated as outlined above—and the two Federal
Reserve communication variables defined above.
The only weekly series in the dataset, initial jobless claims, has the highest frequency. The nextto-highest frequency is observed for testimonies
other than semiannual testimony to Congress,
followed by monthly data releases, FOMC actions
(federal funds target), quarterly data releases,
and the Chairman’s semiannual testimonies to
Congress. An exception is nonfarm productivity,
which entered the MMS dataset during the analyzed time period. The first surveyed number
refers to the first quarter of 1999.
Table 2, center column, offers a frequency
distribution for the coincidence of surprises in
macroeconomic data releases (MMS survey) and
monetary policy actions. For instance, in the
sample period of 1,527 trading days, there are
445 trading days on which there were no surprises
in data releases or monetary actions, possibly
because no data were released or no action taken.
There are 600 trading days (39 percent) with
more than one surprise and 268 trading days (18
percent) with more than two surprises. Table 2
(right column) offers a frequency distribution
with Federal Reserve communication included.
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Table 1
Number of Total Macroeconomic Announcements and Monetary Policy Variables that
Correspond with Daily Inflation Compensation Observations
Data series
Auto sales
Business inventories
Capacity utilization
Civilian unemployment rate
Construction spending
Consumer confidence
Consumer credit
Consumer price index (CPI-U)
CPI excluding food and energy (CPI-U, “core”)
Durable goods orders
Employment cost index (Q)
Existing home sales
Factory orders
Federal funds target: unscheduled FOMC meeting
Federal funds target: scheduled FOMC meeting
GDP price index (advance) (Q)
GDP price index (preliminary) (Q)
GDP price index (final) (Q)
Goods and services trade balance (surplus)
Chairman’s speeches and testimonies
Hourly earnings
Housing starts
Industrial production
Initial jobless claims (W)
Leading indicators
Purchasing managers index (PMI)
New home sales
Nonfarm payrolls
Nonfarm productivity (preliminary)
Nonfarm productivity (revised)
Personal consumption expenditures
Personal income
Producer price index (PPI)
PPI excluding food and energy (“core”)
Real GDP (advance) (Q)
Real GDP (final) (Q)
Real GDP (preliminary) (Q)
Retail sales
Retail sales excluding autos (“core”)
Treasury budget (surplus)
Truck sales

Total (actual used)
77 (68)
77 (67)
77 (67)
77 (67)
77 (72)
77 (69)
77 (72)
77 (74)
77 (74)
77 (69)
25 (25)
61 (56)
77 (72)
4 (4)
52 (50)
26 (26)
26 (22)
26 (23)
77 (74)
145 (137)
74 (63)
77 (73)
77 (67)
334 (306)
78 (73)
77 (65)
78 (74)
77 (66)
17 (16)
17 (17)
78 (62)
78 (62)
77 (67)
77 (67)
26 (26)
26 (22)
26 (23)
77 (72)
77 (72)
77 (71)
77 (68)

NOTE: Variables not included in the dataset of macroeconomic data releases are italicized. Monthly series if not indicated otherwise
(Q: quarterly; W: weekly). Numbers in parentheses indicate actual number of observations used in the analysis; this number differs
from total because of missing observations for the measures of inflation compensation due to holidays or unreported values.

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Table 2
Frequency Distribution of Concurrence in Surprises
Number of surprises
per trading day

MMS survey and
federal funds target

MMS survey, federal funds target,
and Federal Reserve communication

445

410

482

478

332

343

147

159

9
Total

1,527

EMPIRICAL APPROACH AND
FINDINGS
The empirical approach rests on the following regression equation:
35

(1)

rt − rt −1 = α + β . D + ∑

k =1

. xtk + γ . fft + εt ,

where rt – rt–1 is the change in the real interest rate
from trading day t –1 to trading day t; D is an indicator variable that is equal to 1 if all explanatory
variables are equal to 0 (and is equal to 0 otherwise); xtk is the surprise component in the macroeconomic data release; fft is the surprise component
in the Federal Reserve action (the federal funds
target variable); and εt is an error term.9
The change in the real long-term interest rate
is measured by the daily change in the on-the-run
10-year TIIS yield. Although the Treasury has in
the past issued 5- and 20-year and a small number
of 30-year TIIS, we focus solely on the 10-year
yield because that is the maturity that has been
continuously issued since 1997. Figure 1 shows

a kernel estimate of the distribution of this
dependent variable (thick line), along with a frequency distribution (candlesticks) and a normal
distribution (blue line) based on the sample
moments. The change in the real interest rate
exhibits statistically significant excess kurtosis
(5.164) and mild but statistically significant skewness (0.401).10
Table 3 shows the results of regression equation (1). The table shows traditional t values and—
because of the excess kurtosis of the dependent
variable—significance levels obtained from distribution free bootstrap t intervals (see Efron and
Tibshirani, 1993). The empirical results reported
in the table suggest that there are seven economic
announcements that matter: business inventories,
the employment cost index, the annualized rate
of growth of the GDP price index (preliminary
estimate), initial jobless claims, new home sales,
nonfarm payroll employment, and the preliminary
estimate of nonfarm labor productivity. With the
exception of new home sales, each of the coefficients has the predicted sign. That is, stronger10

The intercept indicator variable, D, eliminates the influence of
certain observations on the observed mean of the dependent variable—specifically, those observations for which none of the
explanatory variables contains information pertinent to the measured inflation compensation.

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Excess kurtosis means that, compared with the normal distribution,
there is excess probability mass in the center of the distribution.
We use a Gaussian kernel along with an (under the null of normal
distribution) optimal bandwidth of (4/3) 0.2 . σ̂ . T –0.2, where T is
the number of sample observations and σ̂ is the sample standard
deviation (Silverman, 1986).

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Table 3
On-the-Run 10-year TIIS Yield and Data Surprises
Explanatory variable

Coefficient

Auto sales
Business inventories
Capacity utilization
Civilian unemployment rate
Construction spending
Consumer confidence
Consumer credit
Consumer price index (CPI-U, “core”)
Durable goods orders
Employment cost index
Existing home sales
Factory orders
Federal funds target
GDP price index (advance)
GDP price index (preliminary)
GDP price index (final)
Goods and services trade balance (surplus)
Hourly earnings
Housing starts
Industrial production
Initial jobless claims
Leading indicators
Purchasing managers index (PMI)
New home sales
Nonfarm payrolls
Nonfarm productivity (preliminary)
Nonfarm productivity (revised)
Personal consumption expenditures
Personal income
Producer price index (PPI, “core”)
Real GDP (advance)
Real GDP (preliminary)
Real GDP (final)
Retail sales, excluding motor vehicles and parts (“core”)
Treasury budget (surplus)
Truck sales
Intercept indicator variable (D)
Intercept

–2.715
–4.176
1.476
–2.471
–7.883
1.184
1.425
–3.002
4.171
4.972
1.921
–1.467
7.257
6.833
1.748
–1.595
–1.039
–8.496
3.213
4.051
–2.009
9.660
2.855
–2.990
3.840
5.764
–3.469
–3.529
–2.310
–9.685
1.695
–3.731
–5.376
–2.279
–2.545
2.776
1.724
–1.342

. 10–3
. 10–3
. 10–4
. 10–3
. 10–4
. 10–3
. 10–3
. 10–3
. 10–4
. 10–3
. 10–4
. 10–4
. 10–2
. 10–4
. 10–3
. 10–3
. 10–3
. 10–4
. 10–4
. 10–3
. 10–3
. 10–3
. 10–3
. 10–3
. 10–3
. 10–3
. 10–3
. 10–3
. 10–3
. 10–5
. 10–3
. 10–3
. 10–3
. 10–4
. 10–3
. 10–3
. 10–3
. 10–3

F-statistic (1)
F-statistic (2)
R2
R2 adj.
Ljung-Box statistic
Rao’s score test
Number of nonzero observations

2.147***
2.216***
0.051
0.027
3.323
13.63***
1,082

Number of observations

1,527

t-Statistic
–0.948
–2.114**
0.056
–1.587
–0.486
0.730
1.210
–1.245
0.379
1.978**
0.237
–0.051
1.075
0.388
2.456**
–0.880
–0.530
–0.520
0.165
1.028
–3.103***
1.395
1.226
–1.739*
3.057***
2.263**
–0.818
–0.848
–0.773
–0.050
0.690
–1.282
–1.498
–0.094
–0.958
0.847
1.062
–1.212

Bootstrap
**

***

*
***
*

NOTE: ***/**/* Indicates significance at the 1/5/10 percent levels, respectively (t-tests are two-tailed). F-statistics and t-statistics are
Newey and West (1987) corrected. Federal funds target is not included in the MMS survey. F statistic (1): all MMS survey variables and
federal funds target; F-statistic (2): all MMS survey variables. The number of nonzero observations indicates the number of trading
days where there was a surprise in a macroeconomic data release or a monetary policy action priced in the market.

F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

MARCH/APRIL 2006

139

Kliesen and Schmid

Table 4
Instrumental-Variables Approach
Explanatory variable

Coefficient

t-Statistic

Bootstrap

Federal funds target (GSS)

1.281 . 10–1

1.517

Not significant

Federal funds target (PR)

1.185 . 10–1

1.538

Not significant

NOTE: Neither regression coefficient is statistically significant (t-tests are two-tailed; t-statistics are Newey and West (1987) corrected).
GSS and PR indicate the federal funds market measure for monetary policy surprises as suggested by Gürkaynak, Sack, and Swanson
(2002) and Poole and Rasche (2000), respectively.

Figure 1
Distribution of Daily Changes in the Real
Long-Term Interest Rate
Probability Density
25.0
22.5
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5
0.0
–0.10

–0.05

–0.00

0.05

0.10

0.15

0.20

Change in 10-Year TIIS Yield

than-expected economic growth raises the real
rate of interest. Recall that the announcement
surprises have been normalized by the sample
standard deviation of the individual forecasts
(measured over the entire sample). If strongerthan-expected economic growth arises from a
productivity shock, then that growth raises the
desired capital stock; the real rate of interest must
rise to restore the goods-market equilibrium.
Indeed, our results show that we can reject the
null hypothesis that surprises in productivity
growth have no impact on the real long-term rate
of interest.
140

MARCH/APRIL 2006

Two other potentially interesting results from
Table 3 are worth mentioning. First, our results
suggest that surprise changes in the federal budget
deficit (surplus) have no discernable impact on
market participants who buy and sell 10-year TIIS.
Second, a surprise increase in inflation (growth
of the GDP price index) is expected to raise the
real long-term interest rate. The latter result is
perhaps puzzling given that the long-term real
interest rate is thought to be determined by real
factors (capital formation, productivity growth,
population, etc.). The R2 in Table 3 is about 5
percent, which implies that surprises in macroeconomic announcements explain only 5 percent
of the variation of the dependent variable around
its mean, the remainder being noise. Overall, the
results from Table 3 suggest that the real long-term
interest rate can change in response to surprise
increases in some macroeconomic data releases,
but that other factors appear to be more economically significant.
The results in Table 3 also allow us to speculate about the hypothesized linkage between the
effects of surprise changes in the federal funds
target rate. We find that surprises in changes of
the targeted federal funds rate have no discernable
impact on the real rate of interest. This finding
squares with Weiss (2006), who finds no measurable effect of the federal funds rate (as derived
from futures contracts) on the 10-year TIIS yield.
Poole, Rasche, and Thornton (2002) argue that
monetary policy surprises as gauged by changes
in federal funds futures prices are measured with
error. This is because federal funds futures prices
not only change in response to monetary policy
actions, but also respond to other information
F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

Kliesen and Schmid

Table 5
Uncertainty about Real Interest Rates
Explanatory variable

Coefficient

t-Statistic

Bootstrap

Panel A: GSS measure of federal funds target surprises
Federal Reserve communication
Federal funds target
Intercept indicator variable (D)
Intercept
Number of nonzero observations
Number of observations

–2.217 . 10–4

–0.493

4.209 . 10–3

0.689

–4.828 . 10–4

–1.056

1.243 . 10–3

2.774***

180
1,527

Panel B: PR measure of federal funds target surprises
Federal Reserve communication
Federal funds target
Intercept indicator variable (D)
Intercept
Number of nonzero observations
Number of observations

–1.139 . 10–4

–0.265

5.118 . 10–3

0.653

–3.759 . 10–4

–0.859

1.137 . 10–3

2.657***

182
1,527

NOTE: ***/**/* Indicates significance at the 1/5/10 percent levels, respectively (t-tests are two-tailed). GSS and PR indicate the federal
funds market measure for monetary policy surprises as suggested by Gürkaynak, Sack, and Swanson (2002) and Poole and Rasche (2000),
respectively. The variable Federal Reserve Communication equals 1 on trading days on which the Chairman of the Federal Reserve’s
semiannual testimony to Congress (formerly known as Humphrey-Hawkins Testimony) or speeches and other testimonies of the Fed
Chairman were priced in the market. The number of nonzero observations indicates the number of trading days where there was a
surprise in a macroeconomic data release or a monetary policy action priced in the market.

pertinent to the future path of the federal funds
rate. Because of the measurement error introduced
by such ambient price changes of federal funds
futures contracts, the regression coefficient of
the federal funds target variable is biased toward
0. We account for this error-in-variable problem
with an instrumental variables approach. We use
as an instrument for the federal funds target an
indicator equal to 1 if the federal funds target
exceeds its median positive value, equal to –1 if
it falls short of its median negative value, and
equal to 0 otherwise.11
Table 4 shows the regression results of the
instrumental variables approach applied to equation (1). We use two alternative definitions of the
surprise component of monetary policy actions
(the federal funds target variable). First, we provide
results for the concept that we used above—the
11

For details on this error-in-variable approach, see Greene (2003).

F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

measure suggested by Gürkaynak, Sack, and
Swanson (2003), which is denoted federal funds
target (GSS) in the table. Second, we present
results for the surprise measure devised by Poole
and Rasche (2000); this measure is denoted federal
funds target (PR) in the table. Unlike the GSS
measure, which rests on the scaled price change of
the current month’s federal funds futures contract
(unless the monetary policy surprise happens
within the last seven days of the month), the PR
measure always uses the price change of the next
month’s federal funds futures contract. For the GSS
measure, the regression coefficient for the federal
funds target variable is indeed larger (in absolute
value) than it is without the error-in-variable correction (shown in Table 3) but remains statistically
insignificant. But, for the PR measure, the regression coefficient for the federal funds target variable
is smaller (in absolute value) than it is without
the error-in-variable correction (not shown); it
remains statistically insignificant as well.
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Kliesen and Schmid

We have been unable to establish evidence
that monetary policy actions of the Federal
Reserve affect the real long-term rate of interest.
But the Federal Reserve has another channel of
influence—communication. As discussed above,
the surprise component in Federal Reserve communication is next to impossible to ascertain. Yet,
following Kohn and Sack (2003), we can analyze
the effect of Federal Reserve communication on
the (conditional) variance of the dependent variable; this variance may be viewed as a measure
of uncertainty that surrounds the future path of
real short-term interest rates. Note that, if Federal
Reserve communication and surprises in monetary policy actions affect the uncertainty surrounding the real rate of interest, then the error
term of the regression equation (1) is heteroskedastic; Rao’s score test on heteroskedasticity
indeed rejects the null hypothesis that there is
no such heteroskedasticity.12
We study the impact of Federal Reserve communication and surprises in monetary policy
action on real interest rate uncertainty by analyzing the squared residuals from regression equation (1)—as shown in Table 3—in an estimation
approach suggested by Amemiya (1977, 1978).
We regress these squared residuals on (i) the
(absolute value of the) federal funds target variable, an indicator variable that is equal to 1 on
days when Federal Reserve communication was
priced in the market and 0 otherwise and (ii) the
previously introduced intercept indicator variable
(D). The regression results, presented in Table 5,
indicate that neither Federal Reserve communication nor monetary policy surprises influence
the conditional variance of the real rate of interest.
Hence, we do not reject the hypothesis that neither
surprises in Federal Reserve monetary policy
action nor Federal Reserve communication affect
the uncertainty surrounding the real long-term
interest rate.

Treasury inflation-indexed securities—respond
to surprise announcements of macroeconomic
data. Our findings are consistent with economic
theory, which suggests that stronger-than-expected
growth, perhaps caused by surprises in productivity growth, affects the real long-term interest
rate. In the case of nonfarm productivity growth,
the greater the surprise in the released nonfarm
productivity growth number, the greater the
accompanying increase in the real long-term rate
of interest. We found no evidence that surprise
increases in the monthly federal budget deficit
increase the real rate of interest. Further, we find
no evidence supporting the proposition that
Federal Reserve communication or surprises in
monetary policy actions—as gauged by changes in
the targeted federal funds rate—influence the
expected value or variance of the real long-term
interest rate.

CONCLUSION

Efron, Bradley and Tibshirani, Robert J. Introduction to
the Bootstrap. New York: Chapman and Hall, 1993.

The results in this paper suggest that real
interest rates—as measured by market yields on
12

For Rao’s score test, see Amemiya (1985).

142

MARCH/APRIL 2006

REFERENCES
Amemiya, Takeshi. “A Note on a Heteroscedastic
Model.” Journal of Econometrics, November 1977,
6(3), pp. 365-70.
Amemiya, Takeshi. “Corrigenda.” Journal of
Econometrics, October 1978, 8(2), p. 275.
Amemiya, Takeshi. Advanced Econometrics.
Cambridge, MA: Harvard University Press, 1985.
Balduzzi, Pierluigi; Elton, Edwin J. and Green, T.
Clifton. “Economic News and Bond Prices: Evidence
from the U.S. Treasury Department.” Journal of
Financial and Quantitative Analysis, December
2001, 36(4), pp. 523-43.
Calomiris, Charles; Engen, Eric; Hassett, Kevin A.
and Hubbard, R. Glenn. “Do Budget Deficits
Announcements Move Interest Rates?” Unpublished
manuscript, December 22, 2003.

Faust, Jon; Rogers, John H.; Wang, Shing-Yi B. and
Wright, Jonathan H. “The High-Frequency Response
of Exchange Rates and Interest Rates to MacroF E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

Kliesen and Schmid

economic Announcements.” Journal of Monetary
Economics (forthcoming, 2006).
Fleming, Michael J. and Remolona, Eli M. “What
Moves the Bond Market?” Federal Reserve Bank of
New York Economic Policy Review, December
1997, 3(4), pp. 31-50.
Fleming, Michael J. and Remolona, Eli M. “What
Moves Bond Prices?” Journal of Portfolio
Management, Summer 1999, 25(4), pp. 28-38.
Greene, William H. Econometric Analysis. 5th ed.
Upper Saddle River: Prentice Hall, 2003.
Gürkaynak, Refet S.; Sack, Brian P. and Swanson,
Eric T. “Market-Based Measures of Monetary Policy
Expectations.” Working Paper, Division of Monetary
Affairs, Board of Governors of the Federal Reserve
System, August 1, 2002; www.federalreserve.gov/
pubs/feds/2002/200240/200240pap.pdf.
Gürkaynak, Refet S.; Sack, Brian P. and Swanson,
Eric T. “The Excess Sensitivity of Long-Term Interest
Rates: Evidence and Implications for Macroeconomic
Models.” Working paper, Division of Monetary
Affairs, Board of Governors of the Federal Reserve
System, April 4, 2003; www.clevelandfed.org/
CentralBankInstitute/conf2003/august/
sensitivity_apr4.pdf.
Gürkaynak, Refet S.; Sack, Brian P. and Swanson,
Eric T. “The Sensitivity of Long-Term Interest Rates
to Economic News: Evidence and Implications for
Macroeconomic Models.” American Economic
Review, March 2005, 95(1), pp. 425-36.
Kohn, Donald L. and Sack, Brian P. “Central Bank
Talk: Does it Matter and Why?” Paper presented at
the Macroeconomics, Monetary Policy, and Financial
Stability Conference in Honor of Charles Freedman,
Bank of Canada, Ottawa, Canada, June 20, 2003;
www.federalreserve.gov/boarddocs/speeches/
2003/20030620/paper.pdf.

F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

Kuttner, Kenneth N. “Monetary Policy Surprises and
Interest Rates: Evidence from the Fed Funds Futures
Market.” Journal of Monetary Economics, June 2001,
47(3), pp. 523-44.
Newey, Whitney K. and West, Kenneth D. “A Simple,
Positive Semi-definite, Heteroskedasticity and
Autocorrelation Consistent Covariance Matrix.”
Econometrica, May 1987, 55(3), pp. 703-808.
Poole, William and Rasche, Robert H. “Perfecting the
Market’s Knowledge of Monetary Policy.” Journal
of Financial Services Research, December 2000,
18(2/3), pp. 255-98.
Poole, William; Rasche, Robert H. and Thornton,
Daniel L. “Market Anticipations of Monetary
Policy Actions.” Federal Reserve Bank of St. Louis
Review, July/August 2002, 84(4), pp. 65-93.
Silverman, Bernard W. Density Estimation for
Statistics and Data Analysis. London: Chapman
and Hall/CRC Press, 1986.
USA Today. “Poole Sees Stable Economy Ahead,”
Money Section, February 22, 2005.
Watson, Mark W. “Commentary.” Federal Reserve
Bank of St. Louis Review, July/August 2002, 84(4),
pp. 95-97.
Weiss, Laurence. “Inflation Indexed Bonds and
Monetary Theory.” Economic Theory, 2006, 27(1),
pp. 271-75.
Yellen, Janet. “Views on the Economy and Implications
for Monetary Policy.” Remarks delivered at the San
Diego Community Leaders Luncheon, September 8,
2005.

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2006

F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

Using Cyclical Regimes of Output Growth to
Predict Jobless Recoveries
Michael J. Dueker
Gaps between output and employment growth are often attributed to transitional phases by which
the economy adjusts to shifts in the rate of trend productivity growth. Nevertheless, cyclical factors
can also drive a wedge between output and employment growth. This article shows that one
measure of cyclical dynamics—the expected output loss associated with a recession—helps predict
the gap between output and employment growth in the coming four quarters. This measure of the
output loss associated with a recession can take unexpected twists and turns as the recovery unfolds.
The empirical results in this paper support the proposition that a weaker-than-expected rebound
in the economy can partially mute employment growth for a time relative to output growth.
Federal Reserve Bank of St. Louis Review, March/April 2006, 88(2), pp. 145-53.

“

n like a lamb, out like a lamb” is a common
refrain one hears about business recessions.
The assertion is that the robustness of the
recovery is proportional to the severity of
the contraction phase of a cyclical downturn
(Wynne and Balke, 1992). If this is true, a socalled jobless recovery might be considered part
and parcel of a mild recession. But, beware the
Ides of March because this argument misses the
point that a jobless recovery is a big event—the
cost of a business cycle downturn rises substantially if the economy does not enjoy a snapback phase of above-trend growth following a
contraction in output.
The degree to which people expect that a
contraction in output will not be undone in the
future can be measured as the expected output
loss associated with an economic downturn. In
this article, I develop a measure of expected output
loss from recession. In some recessions, the timing
and relative magnitude of expected output loss
closely mirrors the widely used Hodrick-Prescott
measure of the output gap. In the recoveries from
the past two recessions—both of which were

labeled jobless recoveries—the expected permanent output loss looks much worse than the output gap, in terms of both magnitude and duration.
This article demonstrates that one can use this
output loss measure as a predictor of the extent to
which output growth will outpace employment
growth at least six months ahead.
This article provides empirical evidence that
cyclical forces significantly influence the gap
between output and employment growth, in addition to the effects that shifts in trend productivity
generate. Wen (2005) uses a rational expectations
model to show that firms optimally hoard labor
in anticipation of stronger demand for their goods.
If the economy’s rebound from a recession is
weaker than anticipated, firms might find that
they had been holding too much labor, resulting
in a period of muted employment growth.

MEASURING EXPECTED OUTPUT
LOSS FROM A RECESSION
A key part of this article’s perspective on the
consequences of recessions is that the snap-back,

Michael J. Dueker is an assistant vice president and an economist at the Federal Reserve Bank of St. Louis. Andrew Alberts provided research
assistance.

F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

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145

Dueker

high-growth phase the economy experiences following a recession has a random duration. In
many recessions, the snap-back phase lasts long
enough such that the output loss associated with
the recession is 1 percent or less. From this vantage
point, a so-called jobless recovery occurs when
the snap-back phase lasts an unexpectedly short
time or is skipped altogether. In general, labor
productivity continues its upward trend during
the recession, so by the end of the recession the
effective, productivity-adjusted labor input is high
relative to output. This ratio can return to its equilibrium value either through above-normal growth
in output or below-normal growth in employment.
In a jobless recovery, the latter predominates,
although the reasons for this outcome are not
always clear.
This article assumes that each recovery from
a recession is the result of stochastic transitions
between output growth states. Simply not enough
data exist at this point to parameterize these
transitions as functions of novel labor market
patterns. Gordon (1993) and Schreft and Singh
(2003, p. 65), in contrast, offer a structural change
perspective on jobless recoveries. The latter
authors posit that changes in the labor market may
contribute to a greater tendency toward jobless
recoveries going forward. They suggest that “justin-time employment lets firms wait to see that a
recovery is robust before hiring, yet still expand
production on short notice by hiring temps and
using overtime.’’ Aaronson, Rissman, and Sullivan
(2004) concur that just-in-time hiring practices
played an important role in the recovery from
the 2001 recession.
To build an empirical model of jobless recoveries, I use a model of output growth in which
the expected output loss associated with a recession could undergo sizable changes between the
start and the end of the recovery.1 To do this, I
estimate a four-state Markov switching model,
with four distinct growth states for real gross
domestic product (GDP). Real GDP growth is
denoted y and the growth states are μi:
1

Engemann and Owyang (2006) also present an empirical model of
jobless recoveries.

146

MARCH/APRIL

2006

y t = μSt + et

(1)

et ∼ N (0,σ 2 )
St = i, i = 1,..., 4

μ1 < μ2 < μ3 < μ4 .
In this set-up, the fourth state has the highest
growth rate and, therefore, will represent the
snap-back growth. A jobless recovery will be one
where state 4 is either skipped or is shorter than
in other recoveries.

Related Empirical Models of
Asymmetric Cycles
The four-state Markov switching model of
GDP growth falls within a large class of models
of asymmetric business cycles. For a model of
output growth, asymmetry implies that the fluctuations above and below the unconditional mean
growth rate are not mirror images. Sichel (1993)
described particular attributes that the asymmetry
might have, including asymmetries in steepness
and deepness. McQueen and Thorley (1993) added
asymmetry in sharpness. Clements and Krolzig
(2003) noted that a two-state Markov switching
model cannot imply an asymmetry in steepness.
The four-state Markov switching model will generally display all three types of asymmetry.
Sichel (1994) suggested that the rebuilding
of inventories implied three states in U.S. economic activity: normal growth, recession, and a
snap-back phase of high growth following a recession, as inventories were restocked. Kim, Morley,
and Piger (2005) effectively add to a two-state
Markov switching model a third state whose timing and length are deterministic functions of the
preceding recession state. Van Dijk and Franses
(1999) similarly extend two-state threshold autoregressive models so that they have multiple
regimes but in a framework where predetermined
transition variables determine the regime, leaving
no room for contemporaneous surprises regarding
the regime. This framework, however, does not
reflect the public perception that jobless recoveries
are unpleasant surprises. For this reason, I use a
four-state Markov switching model where all
transitions between regimes are stochastic.
F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

Dueker

Estimates of the Four-State Markov
Switching Model
The transition probabilities for the Markov
states are
(2) Prob(St = i St −1 = j ) = pij ,i = 1,...4; j = 1,..., 4.
This leads to a matrix of transition probabilities
that enter the likelihood function, lt, which is
expressed as a prediction-error decomposition:
(3)

⎛

⎞

∑ lt = ∑ ln ⎜⎝ ∑ Prob(St = i y t −1 ) f ( y t St = i )⎟⎠ .
t

The results of estimating the model for quarterly
U.S. chain-weighted real GDP growth from 1958:Q1
to 2005:Q3 are shown below. The estimated
growth states (expressed as annual rates) and
their unconditional probabilities are as follows:

μi , i = 1,..., 4 =
⎛ −4.0% 0.072 State 1 : recession
⎞
⎜ 1.7% 0.366 State 2 : slow growth
⎟
⎜
⎟.
nary growth ⎟
⎜ 3.6% 0.326 State 3 : ordin
⎜ 7.6% 0.236 State 4 : snap-back growth⎟
⎝
⎠
Figure 1 plots GDP growth against the
probability-weighted fitted value, using the
smoothed-state probabilities. It is remarkable that,
using either the filtered or smoothed probabilities,
the weighted average of the four growth states
explains enough of the dynamics in GDP growth
that the residuals show no significant serial correlation. In fact, after 1994 the degree of serial correlation in the residuals is even lower than for the
full sample, despite the model finding fewer transitions in the growth states. In contrast, in a twostate model—e.g., Hamilton (1989)—it is necessary
to model GDP growth as an autoregressive process
to remove the serial correlation. Figure 2 shows
the smoothed probabilities of the snap-back, highgrowth state. The recoveries from the 1990-91 and
2001 recessions were the times when this snapback phase was largely absent.
The transition probability matrix has entries
such that Prob(St = i St −1 = j ) = pij appear in row i
and column j:
F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

⎛ 0.267300
⎜ 0.607963
⎜
⎜ 0.0156676
⎜ 0.109070
⎝

0.133134 9.18590e − 08 0.0163723⎞
0.612537 0.0533640 0.342089 ⎟
⎟.
0.0249191 0.946636
0.0302375⎟
0.229411 2.22045e − 16 0.611301 ⎟⎠

Note that standard errors are not reported for
these maximum-likelihood parameter estimates
because the estimated information matrix is not
positive definite, given that several transition
probabilities lie near the boundary of the parameter space, i.e., zero.
The transition probability matrix shows that
the probability that the economy will shift from
either the recession state or the low-growth state
straight to the ordinary growth state without passing through the fast, snap-back growth state 4 is
low (p41 = 0.109). Also, there is a good chance that
the economy could bounce back and forth more
than once between the low-growth state 2 and the
snap-back growth state 4 before entering the relatively persistent ordinary growth state 3 (p21 =
0.608 and p12 = 0.133). It is quite likely, according
to this transition matrix, that the economy will
spend a nontrivial period of time in the snap-back
growth state following a recession. In fact, the
unconditional probability of the economy being
in the snap-back growth state is almost 24 percent.
Based on this model, one would expect that much
of the output loss from a recession would be
undone by the snap-back state. The fact that there
is no transition from the persistent ordinary growth
state 3 to the snap-back growth state 4 (p43 is
essentially zero) means that a recovery will remain
“jobless” if the ordinary growth state takes hold
before much snap-back growth has taken place.
Given the accrued output loss to date from a
recession and the filtered probabilities of the
current state, one can use this Markov switching
model to calculate, at each quarter following the
onset of the recession, an expected value of the
output loss associated with that recession. Figure 3
illustrates a hypothetical example, based on the
parameter estimates from the four-state Markov
switching model. In this example, we calculate
the expected output loss from a recession that
started four quarters ago. In the four quarters that
have already ensued, the first quarter was in the
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147

Dueker

Figure 1
GDP Growth and Fitted Value from Four-State Markov Model Using Smoothed State Probabilities
Quarterly Growth Rate
4

–1
–2

Actual
Fitted

–3
1960:Q1

1966:Q1

1972:Q1

1978:Q1

1984:Q1

1990:Q1

1996:Q1

2002:Q1

Figure 2
Smoothed Probability of Fast-Growth State 4
Probability
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1960:Q1

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2006

1972:Q1

1978:Q1

1984:Q1

1990:Q1

1996:Q1

2002:Q1

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Figure 3
Path of Expected Output Four Quarters After the Onset of a Hypothetical Recession
115

110

105

100

Output with Constant Growth Rate
Expected Output

95
1

recessionary state 1, the next two were in the
slow-growth state 2, and the fourth was in the
snap-back state 4. From that point, the model is
simulated many times (4,000) to arrive at an
expected path for the level of output. I compare
this path with a reference path in which output
grew at a constant rate equal to the model-implied
unconditional growth rate (0.83 percent per quarter) for the entire time. Provided that the length
of the simulated path is long enough so that the
probabilities of the four growth states converge
to their unconditional probabilities and the
implied growth rate becomes fixed at its unconditional value (0.83), the ending point of the simulation will provide a measure of the long-run or
“permanent” output loss associated with the
recession. With the transition probabilities estimated here, a simulation length of 40 quarters is
more than sufficient to converge to the unconditional probabilities. Thus, in this example plotted
in Figure 3, the expected long-run output loss from
the hypothetical recession is about 0.7 percent,
with the expectation taken four quarters after the
onset of the hypothetical recession.
Using the unconditional, constant-growth path
described above as a reference path, we can calculate this measure of expected long-run output
F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

loss at each quarter following the onset of each
recession in our sample. Throughout the recession
itself, the expected output loss will become larger
because, for every quarter that the economy
remains in recession, the probability that the
economy will remain in recession for an aboveaverage length of time increases. As with any duration, the right tail of the distribution is inevitably
longer than the left tail, since there is no way that
today’s situation can last for an arbitrarily shorterthan-expected time, but it can last for an arbitrarily
longer-than-expected time. As the economy begins
to recover from the recession, however, the
expected output loss associated with the recession
recedes in accordance with the number of quarters
spent in the snap-back growth state.
Figure 4 plots the average across all U.S.
recessions since 1960 of the expected long-run
output loss as a function of quarters since the onset
of recession. Across all recessions, the snap-back
growth state occurs for enough quarters to undo
most of the output loss associated with the preceding recession. Across all recessions, after 18
quarters, the expected long-run output loss is
about 1 percent. In this light, we can see why the
past two jobless recoveries—following the 1990-91
and the 2001 recessions—disappointed the public.
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Figure 4
Expected Effect on Output from Recession, Calculated at Each Quarter from Recession Onset
Percent
0

–1

–2

–3

–4
Average
2001 Recession

–5

1990-91 Recession
–6

Figure 5
Expected Long-Run Effect on Output from Recession and HP Output Gap
Percent
4

–2

–4

–6

Effect of Recession
HP Output Gap

–8
1960:Q1

150

1966:Q1

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1972:Q1

1978:Q1

1984:Q1

1990:Q1

1996:Q1

2002:Q1

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Dueker

Since neither recession lasted an unusually long
time, the path of expected output loss was fairly
typical, or even slightly milder than normal, during the actual recessions. Yet, the failure to spend
a considerable length of time in the snap-back
phase following the recession—especially in the
aftermath of the 1990-91 recession—meant that
the usual diminution of expected output loss failed
to materialize. Figure 4 shows that the expected
output losses associated with the 1990-91 and
2001 recessions were well above the typical 1
percent—4.5 and 2.6 percent, respectively—15
quarters after recession onset.
Figure 5 plots the expected output loss following each recession since 1960 alongside the widely
used Hodrick-Prescott measure of the output gap.
Note that the short 1980 recession, in which the
recovery melded with the start of another recession
in 1981, is excluded from the output loss calculations. Also, the expected output loss converges
to a constant after about 15 quarters. At that point,
the output loss from the recession essentially has
been realized and is no longer an expected value.
Nor are expectations of the future related to the
value of the output loss measure at this point, so
those observations beyond 15 quarters are dummied out of the expected output loss measure in
Figure 5.
Figure 5 shows that the correspondence
between the expected output loss and the HodrickPrescott output gap is fairly close for the 1960-61,
1969-70, and 1981-82 recessions. In contrast, the
expected output loss measure makes the 1974-75,
1990-91, and 2001 recessions look worse than the
output gap does. In the case of the 1974-75 recession, the economy did spend time in the snap-back
growth state, as seen in Figure 1. It did not spend
enough time in that state, however, to overcome
the large output loss accrued during the recession.
Figure 1 shows a contrasting picture for the jobless recoveries after the 1990-91 and 2001 recessions, when the economy spent minimal time in
the snap-back growth state. For this reason, the
output loss from the past two recessions was
quite large in relation to the maximum size that
the output gap attained.
F E D E R A L R E S E R V E B A N K O F S T. LO U I S R E V I E W

PREDICTING CYCLICAL GAPS
BETWEEN OUTPUT AND
EMPLOYMENT GROWTH
One well-known disadvantage of HodrickPrescott filtering is that the two-sided nature of
the filter makes filtered data inappropriate for use
in prediction models. The filtered value at time t
is a function of future values of the data. The
expected output loss measure, in contrast, was
constructed from unsmoothed regime probabilities, using information only through time t. Thus,
the only sense in which the expected output loss
measure is constructed from future information
is through the full-sample parameter estimates.
This parameter channel, however, is a very weak
source of future information in comparison with
a two-sided filter. Consequently, I examine how
well the expected output loss measure can be
used to predict the effect that business cycle
dynamics will have on the gap between output
and employment growth.
To test the importance of such a cyclical
channel in the determination of the gap between
output and employment growth, I regressed the
gap between quarterly GDP growth and employment growth (the log change in aggregate payroll
employment):
(4)

Δy t − Δnt = μ + γ i ELosst −1 + εt ,

where y is the log of GDP, n is the log of employment, and ELoss is the expected output loss from
recession. The coefficient on γi is significant for
lag lengths from i = 1 through 4 quarters. Table 1
presents the estimates of γi , i = 1,…,4 and shows
that the expected output loss is a significant predictor of the gap between output and employment
growth at each horizon up to four quarters. I then
estimated the same equation for the four-quarter
moving average of the gap, allowing for three
moving-average terms to account for the serial
correlation induced by the overlapping data. This
specification answers the question of whether the
expected output loss is a significant predictor of
the gap between output and employment growth
in the coming year:
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Figure 6
Expected Long-Run Effect on Output from Recession (Lagged One Year) and Moving Average of
Gap Between Output and Employment Growth
Percent
6
4

2
0

–2

–4
Effect of Recession

–6

Moving Average (Annualized) of Gap
–8
1960:Q1

1966:Q1

1972:Q1

1978:Q1

1984:Q1

1990:Q1

1996:Q1

2002:Q1

1 4 ∑ ⎡⎣ Δy t − j − Δnt − j ⎤⎦ =

Table 1

j =0

Using Expected Output Loss from Recession
to Explain the Gap Between Output and
Employment Growth

(5)

Parameter

Not surprisingly, given the period-by-period
results, the estimated value of Γ is also a significant predictor of the gap between output and
employment growth in the following year. Table 1
includes the estimates of Γ and the moving-average
coefficients θk,k = 1,…,3.
The reason for the significant Γ coefficient in
the moving-average specification from equation
(6) becomes clear in a plot of the expected output
loss from recession with the moving average of
the gap between output and employment growth
in the subsequent four quarters. Figure 6 plots
these two variables together. Figure 6 shows the
tendency for one to be the negative image of the
other, and this relationship has held throughout
the sample, not only for the two most recent jobless recoveries.

Value

Standard error

Period-by-period specifications—equation (4)

γ1

–0.100

(0.023)

γ2

–0.085

(0.023)

γ3

–0.071

(0.023)

γ4

–0.054

(0.023)

Moving-average specification—equation (5)
Γ

–0.038

(0.012)

θ1

0.998

(0.043)

θ2

0.933

(0.049)

θ3

0.851

(0.041)

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μ + ΓELosst − 4 +

∑ θ k εt − k + νt .

k =1

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Dueker

SUMMARY AND CONCLUSION
This article uses a four-state Markov switching
model of U.S. GDP growth to derive a novel
measure of the time path of expected output loss
associated with each recession since 1960. A key
feature that distinguishes this model of snap-back
growth is that the occurrence and length of the
snap-back state are allowed to be random. Thus,
the expected output loss from a recession is still
evolving after the recession has ended, in accordance with the strength of the recovery. One key
feature of the estimated Markov model is that once
the economy enters the ordinary growth state, it
cannot return directly to the snap-back state. Thus,
once a strong recovery has been skipped or has
ended early, the expected output loss from the
preceding recession is essentially known, and
not just an expected value, at that point.
For many recessions, especially 1960, 1969,
and 1981, the expected long-run output loss
measure corresponds closely with the HodrickPrescott measure of the output gap. For the recessions where the long-run output loss was larger
than average, such as 1974, 1990, and 2001, the
expected output loss measure makes those downturns look more severe in comparison with the
output gap measure. The constructed measure of
the expected output loss associated with a recession is a significant predictor of the gap between
output and employment growth in the coming
four quarters, which could help policymakers
identify jobless recoveries as they unfold.

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