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Journal of Business & Economic Statistics

ISSN: 0735-0015 (Print) 1537-2707 (Online) Journal homepage: http://www.tandfonline.com/loi/ubes20

Educational Attainment and the Cyclical Sensitivity
of Employment
Philip N Jefferson
To cite this article: Philip N Jefferson (2008) Educational Attainment and the Cyclical
Sensitivity of Employment, Journal of Business & Economic Statistics, 26:4, 526-535, DOI:
10.1198/073500108000000060
To link to this article: http://dx.doi.org/10.1198/073500108000000060

Published online: 01 Jan 2012.

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Date: 12 January 2016, At: 22:51

Educational Attainment and the Cyclical
Sensitivity of Employment
Philip N. J EFFERSON
Economics Department, Swarthmore College, Swarthmore, PA 19081 (pjeffer1@swarthmore.edu )
This article examines whether there are educational premiums on the quantity side of the labor market.
We document four findings: (1) Trend employment patterns shifted for most educational levels post-1977;
(2) the lower the level of educational attainment, the more volatile the employment ratio; (3) the volatility
of employment for female high school dropouts increased over time even as the economy became less
volatile; and (4) since 1984, the responses of skilled and unskilled employment to the business cycle have
become more alike. This latter finding is consistent with a reduced degree of capital–skill complementarity
during this period.

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KEY WORDS: Capital–skill complementarity; Gender; Volatility.

1. INTRODUCTION
It is widely recognized that the level of educational attainment is an important determinant of labor market outcomes.
With respect to labor market returns, wages and earnings rise
with the level of educational attainment. Although there are
reasons to exercise caution in interpreting this correlation, Card
(1999) concluded that the weight of the empirical evidence appears to be consistent with the hypothesis that the direction of
causation runs from education to wages. Positive and economically significant labor market returns to education are central
to the alignment of individual incentives for further educational
attainment and the design of social policy; however, it is the attachment to work that permits the realization of the return to education, and this attachment varies by levels of education over
the course of the business cycle.
The purpose of this article is to study the cyclical variation in
the employment-to-population ratio by educational attainment
and gender. There are three motivations for the article. The first
is the view that the combination of positive returns to education and the attachment to work contributes to the proliferation
of social cohesion. Second, building on the work of Krusell,
Ohanian, Rios-Rull, and Violante (2000), Castro and CoenPirani (2008) showed that dissecting aggregate hours by skill
levels reveals complex cyclical behavior. Our results contribute
to this emerging literature by examining the extent to which
employment (as opposed to average hours) and gender are central to this story. Insight in this regard is of particular interest

given the well-documented reduction in the volatility in GDP
since the mid-1980s. Third, as indicated by Autor, Katz, and
Kearney (2006) and Lemieux (2006), there has been some debate over the evolution of the skill premium in the United States
over the past 40 years. This suggests that further examination of
the quantity side of labor market can deepen our understanding
of controversial labor market outcomes. There are a number of
questions of interest in this regard: Are there educational premiums on the quantity side of the labor market? How large are
they? How have they changed over time? What are their cyclical features? Using data on the employment-to-population ratio
(or, simply, the employment ratio) by educational attainment
and gender for 1968–2005 and two subsamples, 1968–1983 and
1984–2005, this article provides quantitative answers to these
questions.

We document four central empirical findings: (1) Trend employment ratio patterns shifted for most educational levels during the post-1977 period; (2) the lower the level of educational
attainment, the more volatile the employment ratio; (3) the
volatility of the employment ratio for women who did not finish high school increased over time even as the economy became less volatile; and (4) since 1984, the responses of skilled
and unskilled employment to the business cycle have become
more alike. In the context of the economic model presented,
this latter finding is consistent with a reduced degree of capital–
skill complementarity during this period. Our view is that

these facts and others reported herein place important restrictions on economic theory. As suggested by Jefferson (2005),
they also can inform the monetary and fiscal policy making
process.
The article is organized as follows. In Section 2 we present an
overview of the employment data. This includes quantification
of its trend behavior and its cyclical volatility. In Section 3 we
provide an interpretation of the contemporaneous relationship
between the educational employment ratio and output that is
grounded in production and preference parameters. We also test
hypotheses generated by the economic model. Because gender
differences can have implications for labor market outcomes,
we estimate the sensitivity of the educational employment ratio
to GDP by gender in Section 4. Finally, we report our conclusions in Section 5.
2. AN OVERVIEW OF THE DATA
The underlying raw data used in this study are employmentto-population ratios by educational attainment. Data on employment by educational attainment are available from the Bureau of Labor Statistics. Currently, data for four levels of educational attainment are reported for the civilian population age 25
and older. Because of changes in educational attainment classifications, these data are available only since 1992; for example,
since 1992, a clear distinction is made between attaining a BA
degree and attending college for 4 years. Clearly, the latter does

526

© 2008 American Statistical Association
Journal of Business & Economic Statistics
October 2008, Vol. 26, No. 4
DOI 10.1198/073500108000000060

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Jefferson: Educational Attainment and the Cyclical Sensitivity

not imply the former. To extend the time span of study, we follow the recommendation of Jaeger (1997) for reconciling old
and new Current Population Survey (CPS) education questions
using the March CPS. We apply Jaeger’s consistent categorical
recoding scheme to the March CPS microdata for 1967–2005.
We use the scheme to establish four educational categories that
can be made consistent across the old and new questions: less
than high school diploma (Dropouts); completed 12 years of
schooling, no college (12th Grade); some college and/or associate’s degree (Some College); and bachelor’s degree or better
(College). Jaeger emphasized that the old CPS education question did not provide information about receipt of a high school
diploma; hence his suggested use of the category name 12th

Grade. Next, we determine whether people are employed, unemployed, or not in the labor force. Then we sum up the number
of people employed in each educational category in March of
each year and divide by the population with that level of education. Thus the frequency of the employment data is Marchannual.
2.1 Trend Behavior
Figure 1 shows how the employment-to-population ratio
(hereinafter, simply the employment ratio) by educational attainment has evolved over the full sample, 1967–2005. Figure 1 suggests a diversity of trend behavior over the sample period. In particular, the employment ratio of dropouts declined
precipitously over most of the sample, and that of those with
some college rose slightly throughout the sample, with that for
those with a BA or better and those with a 12th grade education
falling somewhere in between. On balance, their ratios appear
to be relatively flat.
To better characterize the evolution of the employment ratios
over the full sample, we consider three sample splits: pooled
gender (men and women), women only, and men only. Furthermore, we provide summary statistics that are consistent with
alternative views about the stochastic properties of the trends
driving the data shown in Figure 1.

Figure 1. Employment ratio by educational attainment ( ,
Dropouts; , 12th Grade; , Some College; , College).

527

2.1.1 Pooled-Gender Sample. Table 1 presents three types
of information for each measure of the educational employment
ratio: sample moments of the growth rate, the least squares
trend coefficient, and the stability of the least squares trend coefficient. The stability of the least squares trend coefficient is assessed using the maximum Lagrange multiplier test statistic of
Andrews (1993) and the asymptotic p value of Hansen (1997).
Also reported are dates associated with the lowest p value for
the test statistic and estimates of the least squares trend coefficient before and after that date.
Several facts emerge from the top part of Table 1. First, a
higher level of educational attainment is not associated with a
higher average rate of employment ratio growth; in particular,
the employment ratio growth rate of the Some College group is
greater than that for the College group. Second, a higher level of
educational attainment is associated with a less-volatile rate of
employment ratio growth. Third, from the perspective of deterministic trends, there is some evidence of parameter instability
across levels of educational attainment; that is, the null hypothesis of no break in the least squares trend coefficient over the
interior of the sample (1972–2000) is rejected at conventional
significance levels for three of the four employment ratios. The
years of the indicated breaks range from the mid-1990s to 2000.

Fourth, the postbreak least squares trend coefficients indicate
that there have been significant reversals of fortune for each educational group.
Overall, these statistical findings are consistent with the visual impression left by Figure 1. They are suggestive of structural change in the labor market that cuts across educational
attainment categories although to varying degrees. For example, the roaring economy of the late 1990s and early 2000 was
the backdrop for both a shift in the Some College trend coefficient that is consistent with a relative decline in the employment
prospects of those with that level of education and an improvement in the Dropouts trend coefficient that represents a reprieve
for a group that faced declining employment for more than 21/2 decades.
2.1.2 By-Gender Sample. Because there are important
differences across gender in labor market outcomes due to several factors, including rates of labor force participation, occupational choice, child-bearing and rearing, and (hopefully fading)
discrimination, it is useful to examine sample splits by gender. Table 1 reports summary statistics on employment ratios
by gender and educational attainment.
The average employment ratio growth rate is positive for
women in all educational groups. There is no ordering with respect to educational attainment. The average growth rate for the
Some College group is the greatest for any educational group
without regard to gender. By definition, the Some College group
comprises individuals who, for various reasons, did not complete their college education. If some of those same reasons influence their work or labor force participation decisions, then
perhaps it is not unreasonable to expect that the employment
growth rate for this group would be higher than that for other
groups. The results on the volatility of the employment ratio
growth rates indicate a lack of an education/volatility ordering,

as was found in the pooled sample. The volatility of the employment growth rate for the Dropouts group is especially large relative to that of the other educational groups for women. In terms
of deterministic trends, there is evidence that the full sample

528

Journal of Business & Economic Statistics, October 2008

Table 1. Employment ratio by educational attainment and gender, 1967–2005
Growth rate
mean

Growth rate
standard deviation

Least squares
trend

Test

Break

Before

After

Pooled-gender
Dropouts

−.50

2.63

−.14

1.55

.18

1.18

−.03

.81

26.437
[.000]
4.614
[.291]
13.919
[.004]
19.845
[.000]

1996

12th Grade

−.582
(.123)
−.073
(.027)
.227
(.032)
.053
(.028)

−1.256
(.105)
−.023
(.024)
.318
(.019)
.138
(.018)

.660
(.130)
−1.304
(.304)
−.775
(.248)
−.718
(.145)

Women
Dropouts

.09

3.39

12th Grade

.44

1.87

1.19

1.90

.77

1.49

−.097
(.098)
.548
(.067)
1.254
(.098)
.906
(.079)

23.029
[.000]
17.082
[.001]
23.717
[.000]
22.915
[.000]

−.559
(.089)
.725
(.046)
1.717
(.081)
1.254
(.058)

−.283
(.221)
−1.676
(.180)
−.388
(.076)
−.703
(.087)

Men
Dropouts

−.74

2.62

12th Grade

−.74

1.62

Some College

−.46

1.20

College

−.37

.78

−.898
(.139)
−.739
(.037)
−.431
(.020)
−.329
(.011)

26.083
[.000]
21.210
[.000]
11.560
[.013]
6.984
[.104]

−1.704
(.088)
−.965
(.038)
−.646
(.044)
−.401
(.042)

.781
(.123)
−.599
(.112)
−.415
(.048)
−.362
(.016)

Some College

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College

Some College
College

2000
2000
2000

1997
2000
1996
1997

1995
1994
1987
1977

NOTE: Growth rate is the first difference of the logarithm multiplied by 100. Least squares trend is the coefficient on the trend term in an OLS regression of the logarithm of the
employment-to-population ratio on a constant and a deterministic time trend. Standard errors are in parentheses. Test is the maximum Lagrange multiplier statistic, with asymptotic p
value in brackets. The null hypothesis tested is that there is no break in the least squares trend over the interior 74% of the sample period. Break is the year with the lowest p value for the
test statistic. Before and After report the least squares trend coefficient before and after the break date with the lowest p value, respectively.

trends mask a break for each level of educational attainment.
The timing of these breaks are roughly consistent with those
for the pooled-gender sample; however, the shifts in employment ratio trends for women are dramatic. For the 12th Grade
group, trend employment ratio growth falls by over 2.4% post2000. The Some College and College groups fare little better,
experiencing postbreak falls in trend employment ratio growth
of 2.1% and 2.0%. In the late 1990s, an improvement in the
trend employment ratio is seen for women who failed to complete 12th grade (Dropouts).
The average employment ratio growth rate is negative for
men in all educational groups. Apart from the fact that the rate
of decline is the same for the 12th Grade and Dropout groups,
the lower the level of education, the greater the decline in the
average employment ratio growth rate. In contrast to the female sample split, however, there is an education/volatility ordering for men. The volatility of employment ratio growth rates
declines as the level of educational attainment rises. Such an
ordering is consistent with a view that employment security is
a potential return to education that should induce risk-averse
individuals to want to accumulate more education other things
equal. The results for the deterministic trends indicate that the
late-1980s and mid-1990s was a period of shifting trends for
male employment. Notable in this regard is the change in fortune for Dropouts beginning in 1995. That they stopped losing

ground represents a relative gain compared with other educational groups. For those in the Some College group, a slight
improvement (a movement toward zero) in their trend employment ratio growth is seen as early as 1987.
In summary, the by-gender split suggests that the pooledgender sample masks some differences with respect to gender
in the trend behavior of the employment ratio. In particular, the
behavior of the average growth rates, growth rate volatilities,
and timing of trend breaks in the educational employment ratios all appear to be sensitive to gender.
2.2 Cyclical Volatility
Long-term trends in employment and educational attainment
are likely to be heavily influenced by structural factors, such
as population dynamics, educational access, and household formation trends. These factors are commonly considered to lie
outside the realm of monetary and fiscal policies that affect
overall economic activity at the higher frequencies. It is the
connection between employment and economic activity at the
business cycle frequency that motivates and informs policy deliberations. Therefore, our statistical analysis focuses on transformations of the raw data described earlier. These transformations result from application of the approximate bandpass
filter of Baxter and King (1999). This filter extracts the cyclical

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Jefferson: Educational Attainment and the Cyclical Sensitivity

529

Figure 2. Cyclical employment ratio by educational attainment (with NBER-dated recessions): (a) Dropouts; (b) 12th Grade; (c) Some
College; (d) College.

component of each variable. Intuitively, these cyclical components can be considered the difference between the variable and
an estimate of the variable’s underlying stochastic trend. More
formally, the filter uses a two-sided 3-year moving average of
the data and passes over periodicities from 2 to 8 years. Baxter
and King recommended the two-sided 3-year moving average
as a standard. This filter puts the data in a form better suited for
an independent study of cyclical behavior. Figure 2 shows the
cyclical components of the employment ratio by educational attainment for the pooled-gender data. The units of the bandpassfiltered series are percent deviations from (a possibly stochastic) trend path. A striking feature of Figure 2 is the apparent
differences in volatility across different educational levels. To
examine the issues at hand more closely, we split the full sample
period into pre-1984 and post-1984 subperiods. McConnell and
Perez-Quiros (2000) and Kim and Nelson (1999) found that the
volatility of real GDP was attenuated significantly in the latter
period. Castro and Coen-Pirani (2008) found that the volatility
of aggregate hours for skilled workers actually increased during
the latter period. Thus this sample split is of intrinsic relevance
to us.
Table 2 quantifies the volatility of the educational employment ratios. The results can be summarized as follows. Over
the full sample (1968–2005), there is a clear volatility ordering

Table 2. Volatility of cyclical components
1968–2005

1968–1983

1984–2005

GDP

1.41

1.96

.87

Pooled-gender
Dropouts
12th Grade
Some College
College

1.51
1.09
.82
.49

1.80
1.40
1.00
.57

1.31
.84
.67
.43

Women
Dropouts
12th Grade
Some College
College

2.06
1.17
1.09
.77

1.67
1.55
1.31
1.03

2.37
.84
.92
.51

Men
Dropouts
12th Grade
Some College
College

1.53
1.14
.84
.55

1.91
1.39
1.00
.60

1.23
.96
.72
.52

NOTE: Row heading indicates employment-to-population ratio by the given level of educational attainment. Standard deviations of cyclical components. Units are percent deviation from trend.

530

Journal of Business & Economic Statistics, October 2008

in the pooled-gender sample. The lower the educational level,
the higher the cyclical volatility of the employment ratio. The
only exception to this ordering is Women post-1984. Reading
across the columns of the table, we see that all of the employment ratios except that for female Dropouts exhibit a reduction
in volatility as occurred with GDP. The degree of the reduction
in volatility varies across employment ratios, however. This implies that significant shifts in relative volatilities may have occurred over time.

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3. CAPITAL–SKILL COMPLEMENTARITY
AND EMPLOYMENT
In this section we quantify the sensitivity of the educational
employment ratio to output using a reduced-form equation built
up from an elementary supply-and-demand model. Our purpose is to provide an interpretation of the contemporaneous comovement between educational employment ratios and output
that is grounded in production and preference parameters. The
model provides a perspective on why we might expect the employment ratio sensitivities to differ across educational groups.
3.1 Production and Labor Demand
We begin by specifying an aggregate production function that
relates output, (Y) to capital (K) skilled labor employment (S),
and unskilled labor employment (Ni ):
Yt = At [µuσt + (1 − µ)xtσ ]1/σ ,

(1)

η 1/η
ρ
ρ 1/ρ
and xt = [λKt + (1 − λ)St ] , A is
where ut = [ αi Nit ]
total factor productivity; and µ, λ, and αi are share parameters.
Finally, the parameters ρ, η, and σ (all ≤ 1) are the determinants of the elasticity of substitution between capital and skilled
labor, the elasticity of substitution between different types of
unskilled labor, and the elasticity of substitution between unskilled labor (or capital) and skilled labor. Equation (1) is the
production function introduced by Krusell et al. (2000) with a
slight modification. In their specification unskilled labor is homogeneous and capital is differentiated. Here unskilled labor
is differentiated and capital is homogeneous. Skilled labor is
workers with a college degree or better, whereas unskilled labor
is workers with one of three different educational levels denoted
by i: Dropouts (i = 1), 12th Grade (i = 2), and Some College
(i = 3). The classification of workers as skilled or unskilled is
crucial in this production function. The skilled are complementary with capital, whereas the unskilled are not necessarily so.
Our purpose for using this production function is to derive labor demand functions for workers of different educational levels. Toward that end, efficient utilization of labor requires that
each type of labor be hired up until its marginal product is equal
to its real wage. For unskilled labor, this implies that
σ −η

µαi Aσt Yt1−σ ut

η−1

Nit

= wuit

(2)

for i = 1, 2, 3, where wuit is the real wage for unskilled workers
of education level i. For skilled labor, this implies that
σ −ρ ρ−1
St

(1 − µ)(1 − λ)Aσt Yt1−σ xt

where wst is the real wage for skilled workers.

= wst ,

(3)

Equations (2) and (3) are not the direct targets of our empirical strategy. This is fortunate because, as Lemieux (2006)
pointed out, calculating accurate skill-based wages from the
March CPS is far from straightforward. Rather, when combined
with a labor supply schedule, they produce tractable reducedform relationships between educational employment and output
that can be taken to the data.
3.2 Labor Supply
We next turn to a representation of individual behavior. For
simplicity, we assume that educational attainment is the only
distinguishing characteristic among individuals. We use a variant of the utility function that Romer (2006) used to articulate
the essential features of several canonical macroeconomic models, ranging from the imperfect information model of Lucas
(1972) to a model of imperfect competition and price setting,
Uit = Cit −

θt γi
L ,
γi it

(4)

where C is consumption and L is employment. In our application, i = 1, 2, 3, 4 represents the four levels of educational attainment (i = 4 denotes College). We also allow θt = 1. θ can
be interpreted as a preference shock that can affect the marginal disutility of work; that is, it permits shifts in labor supply.
The educational level–specific parameter γi > 1 determines the
elasticity of labor supply with respect to the real wage for individuals with educational attainment i.
Efficient resource allocation requires that
γ −1

θt Liti

= wuit

(5)

for unskilled labor, where i = 1, 2, 3, and
γ −1

θt L4t4

= wst

(6)

for skilled labor. In equilibrium, we have Lit = Nit for i = 1, 2, 3
and L4t = St .
3.3 Reduced Forms and Their Interpretation
The structure imposed on technology and preferences lays
the groundwork for estimation of reduced-form equations between the employment ratio and output. An advantage of this
structure is that it suggests what may underlie differences in
sensitivities of the educational employment ratio to output. Substituting (5) into (2) yields the reduced form for the unskilled,
γ −η

Niti

σ −η −1
θt

= µαi Aσt Yt1−σ ut

(7)

for i = 1, 2, 3. Substituting (6) into (3) yields the reduced form
for the skilled,
γ −ρ

St 4

σ −ρ −1
θt .

= (1 − µ)(1 − λ)Aσt Yt1−σ xt

(8)

Because our focus is on the relationship between the educational employment ratio and output at the cyclical frequency,
we need to recast (7) and (8) in terms of the employment-topopulation ratio and then in terms of cyclical components. We
illustrate how this can be done using (8) and then apply the
same methodology to (7). Let πit denote the population with
educational level i at time t. The skilled employment ratio,

Jefferson: Educational Attainment and the Cyclical Sensitivity

531

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st = St /π4t , can be incorporated into the model by dividing both
γ −ρ
sides of (8) by π4t4 , yielding
 σ −ρ 
xt
γ4 −ρ
σ 1−σ
(9)
st
= [(1 − µ)(1 − λ)At Yt ]
γ −ρ .
θt π4t4
The right side of (9) has two components, as indicated by
the brackets. Some intuition on these components may be expressed. Consider the second component, which captures the
affect of changes in participation on the employment ratio. To
see this, suppose that a cyclical rise in physical capital occurred. If physical capital and skilled labor are complements,
σ −ρ
σ − ρ > 0, then xt
would rise and the skilled employment
ratio would rise. Ceteris paribus, this could occur only if the
number of skilled not working (the number out of the labor
force) decreased. Alternatively, suppose that either a positive
shock to the disutility of labor (an increase in θt ) or a rise in the
skilled population occurred. Either one of these disturbances
would reduce the skilled employment ratio. In this sense, the
second component in brackets is an index that provides information on variation in the participation rate of the skilled labor
force. Next, consider the first component, which captures the
influence of output and productivity. Ceteris paribus, a positive
shock to output will stimulate the demand for skilled workers,
thereby increasing the skilled employment ratio. Thus the first
component in brackets captures the impact of the employment
rate on the skilled employment ratio.
With these intuitions in hand, we can ease notation by denoting the second term in brackets in (9) as P4t and rewriting (9)
as
γ −ρ

st 4

= (1 − µ)(1 − λ)Aσt Yt1−σ P4t .

(10)

Next, we recast this equation in terms of cyclical components. Following Castro and Coen-Pirani (2008), for any variable zt , define its cyclical component zct as
zct =

zt
,
zTt

(11)

where zTt is the trend component. For each variable in (10),
rewrite zt as zct zTt . This yields
(sct sTt )γ4 −ρ = (1 − µ)(1 − λ)(Act ATt )σ (Ytc YtT )1−σ (Pc4t PT4t ).
(12)
When zct = 1, we must have
(sTt )γ4 −ρ
T
(At )σ (YtT )1−σ (PT4t )

= (1 − µ)(1 − λ).

(13)

We impose this restriction. Therefore, substituting (13) into
(12) yields
(sct )γ4 −ρ = (Act )σ (Ytc )1−σ (Pc4t ),
which is a relationship between cyclical components only. Taking logs of the previous equation yields






1−σ
1
σ
c
c
c
s̃t =
Ãc , (14)
Ỹ +
P̃ +
γ4 − ρ t
γ4 − ρ 4t
γ4 − ρ t
where a tilde above a variable denotes its natural logarithm.

Performing parallel operations on the equations for unskilled
workers yields
(ncit )γi −η = (Act )σ (Ytc )1−σ (Pcit )
for i = 1, 2, 3 and where nit = Nit /πit . Taking logs in this case
yields






1−σ
1
σ
c
c
c
Ãc
ñit =
(15)
Ỹ +
P̃ +
γi − η t
γi − η it
γi − η t
for i = 1, 2, 3.
The coefficients on output in (14) and (15) suggest that, all
other things being equal, the sensitivity of the educational employment ratio to output is determined by technological and
preference parameters. Because ρ, η, σ ≤ 1 and γi > 1 for
i = 1, 2, 3, 4, these coefficients should not be negative. But because of differences in the degree of complementarity with capital and the responsiveness of labor supply to wages, these sensitivities need not be equal across levels of educational attainment.
3.4 Estimation and Hypothesis Testing
Equations (14) and (15) are almost in a form that can be taken
to the data. But each equation includes a technology shock and a
theoretically defined participation index that are unobservable.
This poses a challenge for identifying impact of output on the
educational employment ratio. Our empirical strategy is to control for the participation index using data on actual participation and use instrumental variables to control for the correlation between innovations in technology and output. The resulting equations to be estimated have the educational employment
ratio as a dependent variable. The regressands are instrumented
output and the participation rate. The error term is a composite
of the productivity shock and approximation error associated
with using actual participation in place of the theoretical participation concept.
Two hypotheses are of particular interest in reference to (14)
and (15): whether the employment ratio output sensitivities (the
coefficient on Ỹtc ) are homogeneous across educational attainment levels, and whether changes in the degree of capital–skill
complementarity can be detected by shifts in the relationship
between sensitivity coefficients over time. We formally test
these hypotheses in this section.
The basic method used to estimate (14) and (15) is 2SLS. We
deploy the growth rate of real oil prices lagged 2 and 5 years as
instruments for cyclical output, Ỹtc . This deployment assumes
that changes in real oil prices lagged 2 and 5 years ago are not
correlated with current innovations in technology, and yet these
same changes influence current output. An argument for the former assumption is that innovations in technology are likely to
be significantly driven by research and development processes
that come to fruition intermittently. We know of no reason why
the timing of such innovations would be systematically related
to changes in oil prices in the intermediate past. An argument
for the latter assumption is related to lags in the adjustment of
installed capital in response to changing input prices. Changing
input prices may trigger the desire to replace installed capital.
Because it may be costly to adjust the capital stock quickly, or
the installed capital may not be at the end of its productive life,

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532

Journal of Business & Economic Statistics, October 2008

firms may delay replacement even though the capital is now less
efficient. During the interval between the period of the change
in the real price of oil and the time at which all firms in the
economy have had time to adjust their capital stock, the economy can be influenced by changes in the real price of oil. That
this time interval could be between 2 and 5 years does not seem
unreasonable. This second assumption is testable. In the Appendix we report the F-statistic from the first-stage regression
of 2SLS.
Table 3 reports the results from estimating equations (14)
and (15) for the pooled-gender sample. There appears to be
an ordering of the impact sensitivities according to educational
attainment; the lower the level of educational attainment, the
more sensitive the employment ratio to output at the cyclical frequency. An interpretation of the GDP coefficient in the
Dropouts employment ratio equation for the 1968–2005 sample
is that, all other things being equal, if GDP rises by 1% above
its trend level, then the Dropouts employment ratio responds by
increasing by approximately .7% on average. The coefficient
on GDP for the other levels of educational attainment can be
interpreted analogously. Figure 3 shows the fitted relationship
between the educational employment ratios and output. A striking feature of Figure 3 is the reduced volatility of the economy,
as evidenced by the contrast between (b) and (c). The tempermentality of the economy before 1984 is transmitted to the ed-

Table 3. GDP coefficients
Dropouts

12th Grade

Some College

College

1968–2005
.724∗
(.141)

.604∗
(.100)

.371∗
(.072)

.188∗
(.038)

1968–1983
.795∗
(.241)

.548∗
(.148)

.428∗
(.074)

.144∗
(.035)

1984–2005
.667∗
(.199)

.537∗
(.092)

.349∗
(.080)

.269∗
(.064)

NOTE: Pooled-gender sample. The dependent variable is the cyclical employment-topopulation ratio of the group at column head. Standard errors are in parentheses.
∗ significant at the 5% level.

ucational employment ratios, and the quiescence of the economy since 1984 also is transmitted to the ratios. The Appendix
presents results using a limited-information maximum likelihood estimator that may be compared with the 2SLS estimates
reported in Table 3.
To test whether the employment ratio output sensitivities are
homogeneous across educational attainment levels, we impose
the restriction that the coefficient on Ỹtc is the same across equations in (14) and (15). Then we test this restriction using the

Figure 3. Employment sensitivity and educational attainment: (a) 1968–2005; (b) 1968–1983; (c) 1984–2005.

Jefferson: Educational Attainment and the Cyclical Sensitivity

533

Table 4. Equality of GDP coefficients across equations

D-statistic

1968–2005

1968–1983

1984–2005

5.243
[.155]

6.679
[.083]

3.952
[.267]

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NOTE: Pooled-gender sample. The null hypothesis is that there is no difference between
the coefficients across equations. The Newey–West D-statistic (Newey and West 1987) is
distributed as χ 2 (r), where r = 3 is the number of restrictions. p values are in brackets.

pooled-gender data from the full sample (1968–2005) using
generalized methods of moments (GMM). The null hypothesis is that there is no difference between the coefficients across
equations. The results of this test are shown in the first column
of Table 4. The p value of the test indicates that the size of the
test would have to be increased to about 16% to reject the null
hypothesis. This is somewhat larger than a more conventional
level, say 10%, but given our sample size, it hardly seems unreasonable. The Appendix reports the results of tests of the validity
of the GMM overidentifying restrictions.
To test whether changes in the degree of capital–skill complementarity can be detected by shifts in the relationship between sensitivity coefficients over time, we do exactly the same
test as for our first hypothesis for each time-based subsample.
The logic of this test is as follows. The reduction in the volatility
of GDP is common to all of the educational employment ratio
equations. Now assume that preferences are stable, so that it is
reasonable to assert that labor supply elasticities do not shift
in response to the reduction in GDP volatility. This assumption is consistent with the approach often taken in the wage
structure literature that holds that the slope of the relative labor
supply curve constant while studying variation in the skill premium (see, e.g., Acemoglu 2002; Katz and Autor 1999). Thus
a detected change in the relationship between sensitivity coefficients between the two time periods would have to be due to a
shift in the technological parameters. If that change is in the direction of making the GDP coefficients more alike, this implies
that skilled labor has become more like unskilled labor, due to
a reduction in the degree of capital skill complementarity (i.e.,
an increase in ρ), as Castro and Coen-Pirani (2008) found, an
increase in unskilled labor type complementarities (a decrease
in η), or a combination of both.
A prediction that follows from this logic is that the sensitivity
coefficients should differ more greatly in the earlier subsample
than in the later subssample. The results of this test are shown
in the second and third columns of Table 4. There is much more
evidence against the null hypothesis in the earlier subsample
compared with the later subsample. This suggests that since
1984, skilled labor has become more like unskilled labor. Our
model is consistent with the view that this erosion of distinction
is due in part to a reduction in the degree of capital–skill complementarity. The particular time subsample split examined is
motivated by the broader macroeconomic literature cited earlier
on the moderation of the volatility of GDP. We are not claiming that the possible reduction in capital–skill complementarity
started precisely in 1984; rather, we suggest that a hypothesis
that the reduction began around that time or has endured during most of the post-1984 period is not inconsistent with our
results.

4. REDUCED–FORM ESTIMATES FOR
BY–GENDER SAMPLES
The model in Section 3 was specific to differences in education attainment without regard to gender. As our earlier analysis
indicated, however, gender differences can have implications
for labor market outcomes. Therefore, in this section we estimate the response of educational employment ratios to GDP
by gender using specifications that are formally identical to
those of the previous section. Table 5 reports the findings. For
women, the employment ratios for Dropouts and those with a
12th Grade education are relatively sensitive to GDP. Employment ratios for women with an education level of some college or more are relatively insulated from the cyclical variation
in GDP. For men, before 1984, the employment ratio for those
with at least a college degree was insulated from the cycle. Post1984, there has been a dramatic change in this sensitivity coefficient. Looking across genders, generally, the employment ratio
of men is more sensitive to cyclical variation in GDP than that
of women regardless of the level of educational attainment.
5. CONCLUSIONS
The bulk of the literature on the return to education focuses
on the price side of the labor market. This is understandable because wage differentials are an important source of overall economic inequality. But labor market quantities, arguably, are just
as important. Only through actual employment can any of the
much-discussed price returns be realized. Are there educational
premiums on the quantity side of the labor market? Using data
on the employment-to-population ratio (or simply employment
ratio) by educational attainment and gender for 1968–2005
and two subsamples, 1968–1983 and 1984–2005, this article
has provided quantitative answers to this and related questions.
Four central empirical findings are documented: (1) Trend employment ratio patterns shifted for most educational levels during the post-1977 period; (2) the lower the educational level, the
higher the cyclical volatility of employment; (3) the volatility of
Table 5. GDP coefficients

1968–2005
Women
Men
1968–1983
Women
Men
1984–2005
Women
Men

Dropouts

12th Grade

Some College

College

.481∗
(.163)
.765∗
(.120)

.421∗
(.085)
.761∗
(.140)

.293∗
(.071)
.539∗
(.136)

.150∗
(.031)
.266∗
(.064)

.578∗
(.178)
.946∗
(.234)

.466∗
(.119)
.758∗
(.193)

.348∗
(.084)
.526∗
(.117)

.146∗
(.068)
.114∗
(.055)

.408∗
(.237)
.595∗
(.171)

.295∗
(.091)
.742∗
(.160)

.162
(.119)
.459∗
(.147)

.162∗
(.044)
.332∗
(.087)

NOTE: By-gender samples. The dependent variable is the cyclical employment-topopulation ratio of the group at column and row head. Standard errors are in parentheses.
∗ Significant at the 5% level.

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Journal of Business & Economic Statistics, October 2008

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the employment ratio for women who did not finish high school
increased even as the economy became less volatile; and (4) the
lower the level of educational attainment, the more sensitive
is employment to output at the cyclical frequency. Strikingly,
however, we find that in the post-1984 period an erosion occurred in the distinction associated with attainment of a college
degree. This erosion was particularly acute for men. In the context of the economic model presented herein, this finding is consistent the reduced degree of capital–skill complementarity during this time period. To the extent that facts about employment
trends and cycles provide a foundation for improving the labor
market experiences and outcomes for those most sensitive to
aggregate economic conditions, inform the monetary and fiscal
policy making process, and stimulate the development of economic theory, these findings suggest to us that further research
on nonprice returns to educational attainment is warranted.
ACKNOWLEDGMENTS
The author thanks Seth Carpenter, Barbara Craig, Bart Hobijn, Kenneth Kuttner, and seminar participants at Weslyan University, Oberlin College, and Swarthmore College for helpful
comments and Rebecca Sela for excellent research assistance.
Additional thanks go to the editor, an associate editor, and two
referees for their clarifying feedback and patient guidance. The
author alone is responsible for any remaining errors. This research was supported by a Swarthmore College Faculty Research Grant and a Eugene Lang Faculty Fellowship.
APPENDIX: SUPPORTING HYPOTHESIS TESTS
Table A.1 reports the F-statistic from the first stage regression of cyclical real GDP on a constant and the growth rate
of real oil prices lagged 2 and 5 years. The p values for the
F-statistics permit rejection of the null hypothesis at reasonable
significance levels.
The value of the F-statistics in Table A.1 indicate that our
instruments are not as strong as recommended by Stock and
Yogo (2005). Therefore, in Table A.2, we present results using
a limited-information maximum likelihood (LIML) estimator
that may be compared with the 2SLS estimates reported in Table 3. The LIML estimator and confidence intervals were calculated using the conditional likelihood ratio (CLR) approach
of Moreira (2003). An advantage of this estimator is that it does
not require strong instruments. The CLR test p values are based
on these of Andrews, Moreira, and Stock (2006). Andrews et al.
(2007) showed that this CLR test is almost uniformly most powerful among similar tests. The 2SLS and LIML point estimates
generally are in close agreement. The CLR 95% confidence intervals are somewhat wider than the 2SLS confidence intervals.
These results suggest that bias is not a significant issue with
2SLS in this particular application, but that the precision of the
2SLS estimator may be somewhat overestimated.
Table A.3 reports the results of tests of the null hypothesis
that the overidentifying restrictions are true when the GDP coefficient is unconstrained across equations in the GMM estimation.
[Received March 2005. Revised October 2007.]

Table A.1. GDP and real oil prices

F-statistic

1968–2005

1968–1983

1984–2005

4.535
[.018]

2.586
[.113]

5.916
[.010]

NOTE: F-statistic from the first stage regression of cyclical real GDP on a constant and
the growth rate of real oil prices lagged 2 and 5 years. p values are in brackets.

Table A.2. LIML GDP coefficients
Dropouts

12th Grade

Some College

College

1968–2005
.724
[.021]
(.19, 1.58)

.608
[.004]
(.32, 1.27)

.370
[.028]
(.08, .63)

.189
[.010]
(.07, .42)

1968–1983
.796
[.183]
(–, –)

.559
[.078]
(–, –)

.430
[.009]
(.18, .74)

.144
[.134]
(−.35, 1.01)

1984–2005
.666
[.127]
(−.38, 1.61)

.536
[.0114]
(.16, .97)

.343
[.125]
(−.17, .73)

.269
[.022]
(.06, .67)

NOTE: Pooled-gender sample. The dependent variable is the cyclical employment-topopulation ratio of the group at column head. Limited information maximum likelihood
(LIML) point estimates. Conditional likelihood ratio (CLR) test p values are in brackets.
CLR 95% confidence intervals, where available, are in parentheses.

Table A.3. Tests of overidentifying restrictions

J-statistic

1968–2005

1968–1983

1984–2005

2.633
[.621]

1.281
[.864]

1.410
[.842]

NOTE: Pooled-gender sample. The null hypothesis is that the overidentifying restrictions are true when the GDP coefficient is unconstrained across equations in the GMM
estimation. The J-statistic of Hansen (1982) is distributed χ 2 (j), where j = 4 is the number of restrictions. p values are in brackets.

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