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Vol. 32, No. 4

ECONOMIC REVIEW

Reducing Working Hours
by Terry J. Fitzgerald

FEDERAL RESERVE BANK
OF CLEVELAND

Vol. 32, No. 4
http://clevelandfed.org/research/review
Economic Review 1996 Q4

1996 Quarter 4
Earnings, Education,
and Experience

by Peter Rupert, Mark E. Schweitzer,
Eric Severance-Lossin, and Erin Turner

Reducing Working Hours
by Terry J. Fitzgerald

ECONOMIC REVIEW
1996 Quarter 4
Vol. 32, No. 4

Earnings, Education,
and Experience

by Peter Rupert, Mark E. Schweitzer,
Eric Severance-Lossin, and Erin Turner
The value of additional education is typically measured by the increase in
earnings that results. The largest gains are realized on completion of a
degree, whether high school, college, or post-graduate. Failure to correctly
specify an empirical earnings function can lead to substantial bias. In this
article, the authors show that a common misspecification—combining
college graduates with post-graduates—may bias the returns to a college
education upward by as much as 12 percent.

Reducing Working Hours

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by Terry J. Fitzgerald
The hours of U.S. workers have shown little, if any, decline over the past
few decades, while working hours in most other industrialized countries
have fallen substantially. As a result, working hours in the United States
now appear to be among the longest in the industrialized world. In response to these observations, several proposals have been made for shortening U.S. workers’ hours, both to increase their leisure time and to raise
the number of jobs. In this article, the author documents historical trends
in working hours, then examines how reducing weekly hours would affect
employment and output. He finds that a shorter workweek may lead to a
large decline in output with no increase in employment. Although these
results are shown to be sensitive to modeling assumptions, they serve as
a warning to policymakers.

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ISSN 0013-0281

Earnings, Education,
and Experience
by Peter Rupert, Mark E. Schweitzer,
Eric Severance-Lossin, and Erin Turner

Introduction
When the decision to obtain additional education is based on future financial gain, an individual must determine the expected return less the
cost of that education versus the net return to
no further education. This decision is not unlike
other investment decisions requiring a person to
incur a current cost in anticipation of future returns. Typically, economists measure the return
to education using an empirical earnings function based on the specification in Mincer (1974).
Such earnings specifications are also used to
measure wage differences between occupations, races, sexes, and so on. Moreover, the
estimates taken from earnings equations are
often used to guide policy. Unexplained earnings differences across race or sex, for example,
have spurred legislation to correct such “discrimination.” Although the general patterns that
emerge are consistent for a wide variety of
specifications, the individual point estimates are
not. Therefore, proper specification of the earnings equation is extremely important if inferences are to be drawn from the estimates.
For more than 20 years, the Mincer-type
specification has been the workhorse of labor
economists studying the determinants of earn-

Peter Rupert and Mark E. Schweitzer
are economists at the Federal Reserve
Bank of Cleveland. Eric SeveranceLossin was a visiting scholar and
Erin Turner was an intern at the
Cleveland Fed when this manuscript
was completed. The authors thank
Jay Stewart for comments on an earlier draft, and Jennifer Carr for
research assistance.

ings. Not surprisingly, it has also been the object of much scrutiny aimed at uncovering any
shortcomings it may have. In this article, we
examine a standard Mincer empirical earnings
function, concentrating on the return to education as measured by the increase in income resulting from that education. In so doing, we address several issues. The first is determining how
education should enter into a statistical framework, so that the return to years of schooling
can be correctly inferred from the data. The second issue is that of separating the return to education from other effects, such as experience.
In particular, we show that combining into
one category individuals who have attained a
college degree and those who have some postgraduate education leads to an upward bias in
the measured return to a college education.
Furthermore, this problem is exacerbated as the
percentage of the population with more than a
bachelor’s degree increases. Although it is well
known that more and more people are continuing their education past the college level,
earnings specifications that do not separate individuals with graduate course work from those
with only an undergraduate degree are quite
common; therefore, results from such studies
should be used with caution. We also show that

F I G U R E

Log of Real Median Weekly
Earnings, 1993

F I G U R E

Log of Real Median Weekly
Earnings by Educational Level, 1993

cation has also been rising. We reiterate that
failure to control for the latter (that is, combining the effect of undergraduate and postgraduate work) will lead to an overestimate of
the return to a college education. Although this
approach may bias the results only slightly if
data from the 1960s are used (because there
were relatively few post-college graduates
then), the same cannot be said if more recent
data are employed. We find this bias to be in
the neighborhood of 12 percent.
The remainder of the paper is laid out as follows. The first section presents some basic facts
concerning earnings, education, and experience. Section II describes our alternative specifications for earnings. In section III, we present
our empirical results. Section IV concludes.

I. Earnings,
Education, and
Experience:
The Basic Facts
Figure 1 displays the relationship between

NOTE: Data refer to full-time U.S. workforce.
SOURCE: March Current Population Survey, 1994.

specifications using linear “years of education”
may be misleading, because the largest gains in
earnings come in discrete jumps upon the
attainment of a degree, whether high school,
college, or beyond.
Studies measuring the return to education,
such as Juhn, Murphy, and Pierce (1993), show
that the relative earnings of high-school- and
college-educated individuals have become
more disparate over time. This growing divergence arises from two effects. First, the absolute return to a college education has been
increasing. Second, as mentioned above, the
number of people pursuing post-graduate edu-

wages and experience based on the Census
Bureau’s March 1994 Current Population Survey
(CPS), which summarizes 1993 earnings. Initially, wages rise with experience, but then
begin to fall. Because the data are based on a
cross-section, one reason for the profile’s concave shape is that individuals with more experience are generally older and less educated than
younger people. Another reason is that skills
depreciate over an individual’s lifespan. Thus,
we see the same basic shape even within educational levels, although rates of investment
and depreciation may vary across them (see figure 2). We discuss these issues in more detail
below, but it should be clear at this stage that
the effects of experience must be separated
from those of education. Inadequate controls
for experience contaminate the measured
return to education.
Figure 2 shows that, on average, earnings
rise with the level of education. Figure 3 presents this information in a slightly different way,
graphing earnings by education level relative to
those of high school graduates. Several interesting relationships are apparent. First, note that
none of the lines cross, indicating that, on average, higher levels of education lead to higher
earnings. Second, the lines diverge over time,
meaning that the return to a college degree, relative to high school, increases throughout the
years. Part of this effect occurs because the
earnings of high school graduates have been
falling in real terms.

F I G U R E

Log of Real Median Weekly Earnings
by Educational Level as a Share of High
School Graduates’ Earnings, 1963–93

NOTE: Data refer to full-time U.S. workforce.
SOURCE: March Current Population Survey, 1964– 94.

Median (gross) earnings for college graduates (16 years of education) are roughly 60 percent higher than those of high school graduates
(12 years of education), while high school
dropouts earn about 32 percent less than individuals who have a high school diploma.1

II. Specification
Estimates taken from earnings regressions are
often used to formulate statements that may
have substantial policy relevance. Although
potential biases exist in the articles mentioned
below, we do not claim that such biases necessarily affect the studies’ overall conclusions. Nor
do we attempt to measure such biases, since
their extent will depend on correlations with the
education variables. Below, we show how different education specifications may affect sexand race-based earnings estimates.
In a recent paper, Schmitz, Williams, and
Gabriel (1994) examine race and sex differences
in wage distributions using years of education
(linear) as one of their explanatory variables.
They conclude that there are differences in the
distributions and attribute these differences to
“... the impact of differential treatment in the
labor market.” Obviously, any bias in the education specification may affect the measured differences in distributions.
Dooley and Gottschalk (1984) examine
trends in earnings inequality among male cohorts over the 1968–79 period. They show that
earnings differences may be affected by changes
in the size of the labor force. Their preferred

earnings specification uses dummy variables for
education levels, but combines college and
post-college as one group.
Fairlie and Meyer (1996) look at several explanations for the disparity in self-employment
rates across race and ethnic backgrounds. Although they find that higher education leads to
a greater probability of being self-employed,
their specification contains three categories for
education: high school graduate, some college,
and college graduate. If there are racial or ethnic differences in educational attainment, then
their estimates are potentially biased.
Bar-Or et al. (1995) use Canadian data to
measure the return to a university education
from 1971 to 1991. They find that the return
declined during the 1970s and did not rebound
much during the 1980s. Throughout their paper,
they use two groups: university graduates and
those who have completed 11 to 13 years of
education (with no post-secondary schooling).
The standard model relating education,
experience, and earnings is based largely on
the work of Mincer (1974). Optimal investment
in human capital (formal schooling and postschool learning) is based on a maximization
problem that compares the net present value of
earnings for an additional year of schooling, for
example, to that of no additional investment. A
similar maximization problem is undertaken for
post-school investment.
Mincer’s model compares the present value
of s years of schooling to that of s–d years of
schooling. First, calculate the present value of
an individual’s lifetime earnings at the start of
formal education:
n

(1)

Vs = Ys

Σ
t = s +1

1 ,
(1 + r)t

where Ys is the annual earnings of an individual
with s years of schooling, r is the discount rate
the individual uses to discount the future,2 and
n is the length of working life, which, by assumption, is independent of the amount of
schooling. Next, calculate Vs – d to obtain the
present value of s – d years of schooling. Comparing Vs to Vs – d and applying some algebra
leads to3
(2)

yit = α0 + α1EDit ,

■ 1 To examine the net return to education, direct and indirect costs
of acquiring that education must be deducted.
■ 2 Another way of saying this is that r represents the return necessary to delay earning in order to learn.
■ 3 To be correct, the actual derivation is performed using the
continuous-time analogue of equation (1).

where yit is the log of earnings for individual i
at time t, and ED is a measure of education.
Note that in this particular specification, α0, the
constant term, can be interpreted as Y0, α1 = r.
If post-schooling investments are also considered, then optimization would give us a declining rate of investment in human capital over
time. This result follows from the fact that
there is less time to recoup investments in education as age increases; that is, as one gets
older, more time is spent earning and less time
is spent learning.
The conventional empirical method of capturing declining investments over time is to
specify the earnings equation using a quadratic
term in experience:
(3)

yit = α0 + α1EDit + α 2EXit
+ α3EX it2 + γ Zit + ε .

Controls for other relevant factors that may
influence earnings in a systematic way are also
included. The matrix Z in equation (3) represents these other factors and includes such variables as sex and race. ε is assumed to be an
independent and identically distributed error
term reflecting unobservables as well as possible measurement error.
Note that a negative value of α3 gives rise to
a concave shape of the experience–earnings
profile, similar to that in figure 1. This particular
parametric functional form imposes strong
restrictions on how investments decline over
time (more flexible specifications will be examined below). The concave shape arises from the
assumption of linearly declining investments
(either dollar investments or the ratio of investments to earnings). If one assumes (as Mincer
and nearly everyone else does) that experience
is continuous and begins immediately after
completion of schooling, then it can be measured as age minus years of schooling minus the
age at which schooling begins.4 Typically,
experience is defined as age minus education
minus six.
Perhaps more important than the specification of experience is the specification of the
education variable itself. Commonly, this variable is included in an earnings regression in
categorical form. More specifically, it is included as a dummy variable indicating whether
an individual is a high school dropout, has a
high school diploma, has completed some college, or has a bachelor’s degree or more. The
last category is the one typically not considered
in earnings specifications. Another approach is

to include a continuous variable for education,
that is, years of education. However, this specification does not capture the large gains that
occur at discrete points, namely, when a degree
is obtained.
Equation (3) represents the most common
specification used to uncover the factors explaining earnings. Although the estimating
equation arises from optimizing investment
behavior, several issues regarding the form of
the equation do not. Specifically, how should
experience and education enter the equation?
As mentioned above, if one assumes that
post-schooling investment begins immediately
after graduation and is continuous, then investment will decline as one ages. The question
arises as to the form of this drop-off. The most
commonly used is that of linearly declining
investments over time, which leads to the
experience-squared term in equation (3). This
particular specification arises merely by assumption and is not based on any underlying
theory. Obviously, imposing an incorrect functional form can lead to a misspecification of the
model, in turn leading to a bias in the return to
experience and possibly to other variables. Furthermore, this specification does not fit the data
very well. Murphy and Welch (1990) experiment with several forms for experience and
eventually find that a fourth-order polynomial
(quartic) does fit the data reasonably well.
Our strategy for the experience control is to
admit at the outset that we have little a priori
information about its specification, so we allow
it to be an arbitrary smooth function. We apply
the semiparametric procedure of Robinson
(1988) to the data and estimate the parameters
of interest.
A potentially more important issue, however,
is determining how education should enter the
equation. As noted above, many studies include
education as a categorical variable representing
discrete levels of schooling. This specification
produces the result one would expect: More
education leads to higher earnings. However, as
an increasing number of individuals pursue
post-graduate studies, such a specification will
lead to an overestimate of the return to a college education. A similar situation also exists for
persons who did not complete high school.
Early in the survey period, many of these noncompletions were individuals with an elementary education or less, whereas only a few
workers fell into this category in the 1994 CPS.

■ 4 Although actual work experience should be in the equation, data
limitations make it necessary to use potential experience.

T A B LE

Summary Statistics, 1963 and 1993

Variable

1963
Standard
Mean
Deviation

High school dropout 0.42
High school graduate 0.36
Some college
0.10
College graduate
0.07
Post-college graduate 0.03
Years of education
11.10
Real wage and
salary earnings
$23,806
Years of experience 24.10
Black
0.08
White
0.91
Other nonwhite
0.01
Female
0.28

1993
Standard
Mean
Deviation

0.49
0.48
0.30
0.25
0.19
3.20

0.11
0.34
0.28
0.18
0.09
13.40

0.31
0.47
0.45
0.38
0.28
2.60

$35,612
13.60
0.28
0.29
0.09
0.45

$28,957
19.80
0.09
0.86
0.05
0.42

$19,562
11.70
0.28
0.35
0.22
0.49

SOURCE: Authors’ calculations based on the March Current Population Survey,
1964 and 1994.

This would tend to inflate the relative wage
changes of high school dropouts.
Another common specification includes earnings as a linear function of years of education.
However, a large part of the return to education
occurs when a degree is actually earned, so
that a graph of education and earnings would
resemble a step function. Another way of saying this is that the return to stopping one’s formal education as a junior in college is not
much different from the return to stopping as
a sophomore. Below, we quantify these biases
by including a separate term for various education levels.

III. Data and Results
Our data are taken from the March CPS and
consist of full-time workers only. Table 1 presents summary statistics for 1963 and 1993. Note
that the change in educational attainment over
this time span is quite remarkable. In 1963, 42
percent of the full-time workforce consisted of
high school dropouts; by 1993, that figure had
fallen to 11 percent. The fraction of workers
with only a high school diploma also declined
over this period, from 36 to 34 percent. By contrast, the share of the workforce holding a college degree rose substantially, from 7 to 18 percent, and the fraction with some post-graduate
studies shot up from 3 to nearly 9 percent. Note
that the change in measured experience fell by
about four years, from 24.1 to 19.8. This decline

in labor market experience is at least partially
explained by the additional years of schooling,
since experience is measured as age minus
years of education minus six.
In terms of demographics, the share of
blacks in the full-time workforce did not
change much, rising from 8.3 percent in 1963
to 8.8 percent in 1993. However, the fraction of
whites dropped off somewhat, from 91 to 86
percent. The difference is made up by other
nonwhites, whose share grew from slightly less
than 1 to just over 5 percent. Females made up
close to half of the labor force in 1993 (42 percent), up from 28 percent three decades earlier.
To assess the importance of the effect of rising education levels on these estimates, we
next present earnings regression estimates
based on several years of CPS data. Tables 2
through 5 provide results for 1993, 1983, 1973,
and 1963 earnings, respectively. The samenumbered column across years represents the
same specification.
As a point of departure, we report a fairly
standard specification for earnings in column 1.5
We include sex, race, and a quartic (not so
standard) specification for experience. The education control is years of schooling.6 Table 2,
which presents data for 1993, shows that women earn approximately 30 percent less than men
on average, and blacks earn roughly 17 percent
less than whites. Each term of the experience
polynomial enters significantly, and the signs
indicate an “increasing-at-a-decreasing-rate”
experience profile. The years-of-education coefficient implies that each additional year of
schooling adds 11 percent to earnings. However, this specification masks some important
information regarding education and earnings,
mainly because earnings tend to increase substantially with completion of certain levels of
education (high school or college, for example).
The above specification cannot accurately
address the size of the return to a high school
or college education. To do so requires information on the highest degree achieved by an individual. Obtaining this information allows us to
measure the return to specific levels of education. Column 2 of table 2 presents the results
■ 5 In the regressions that follow, we use sampling weights to make
the CPS representative of the population.
■ 6 Beginning with the 1992 survey, the Bureau of Labor Statistics
altered the wording and coding of the CPS to focus on degrees rather than
on years of schooling. Thus, years are not available for partially fulfilled
degrees. We use the means of years for workers falling into these categories
in the 1991 survey as our best estimate for years in which a specific yearsof-education figure is needed. This procedure is consistent with that of
Frazis, Ports, and Stewart (1995), who review the effects of the altered procedure by comparing a sample in which both questions were asked.

T A B L E

Earnings Regression
Estimates, 1993
Variable

(2)

(3)

(4)

(5)

(6)

(7)

4.1594
(0.0164)
Elementary school
—
—
7 to 12 years of education —
—
High school dropout
—
—
1 to 3 years of college
—
—
4 years of college
—
to 1 year of
—
graduate school
2 years of graduate
—
school
—
4 years of college
—
to 2 years of
—
graduate school

(1)

5.4917
(0.0113)
—
—
—
—
–0.3217
(0.0079)
0.1918
(0.0057)
—
—

5.5018
(0.0112)
–0.5506
(0.0166)
–0.2723
(0.0085)
—
—
0.1916
(0.0056)
0.5193
(0.0065)

5.4888
(0.0112)
–0.5527
(0.0167)
–0.2724
(0.0085)
—
—
0.1922
(0.0057)
—
—

5.4745
(0.0113)
—
—
—
—
–0.1954
(0.0092)
0.2318
(0.0056)
0.5592
(0.0065)

5.4905
(0.0112)
–0.5265
(0.0166)
—
—
–0.2241
(0.0092)
0.2080
(0.0056)
0.5355
(0.0065)

—
—
–0.5393
—
—
—
–0.2846
—
0.1866
—
0.5267
—

—
—
0.5892
(0.0058)

0.7311
(0.0083)
—
—

—
—
0.5894
(0.0058)

0.7728
(0.0084)
—
—

0.7476
(0.0083)
—
—

0.7244
—
—
—

Years of education

—
—
0.0812
(0.0022)
–0.0031
(0.0001)
–0.1560
(0.0071)
–0.0793
(0.0111)
–0.2873
(0.0045)
50,828
0.3444

—
—
0.0799
(0.0022)
–0.0030
(0.0001)
–0.1566
(0.0071)
–0.0745
(0.0110)
–0.2869
(0.0045)
50,828
0.3546

—
—
0.0814
(0.0022)
–0.0031
(0.0001)
–0.1600
(0.0071)
–0.0741
(0.0111)
–0.2884
(0.0045)
50,828
0.3476

—
—
0.0771
(0.0023)
–0.0028
(0.0001)
–0.1517
(0.0072)
–0.0905
(0.0112)
–0.2784
(0.0046)
50,828
0.3362

—
—
0.0785
(0.0022)
–0.0029
(0.0001)
–0.1574
(0.0071)
–0.0770
(0.0111)
–0.2841
(0.0045)
50,828
0.3491

—
—
—
—
—
—
–0.1484
—
–0.0710
—
–0.2993
—
50,828
—

Constant

Years of experience
Years of experience2
Black
Other nonwhite
Female
No. of observations
R2

0.1126
(0.0009)
0.0815
(0.0022)
–0.0031
(0.0001)
–0.1700
(0.0071)
–0.0597
(0.0111)
–0.2904
(0.0045)
50,828
0.3464

SOURCE: Authors’ calculations based on the March 1994 Current Population Survey.

from a specification that includes dummy variables for the highest level of schooling achieved,
with high school diploma being the omitted category (so that the interpretation of the education coefficients is relative to having completed
only high school). The education coefficients
clearly reveal the problem with the years-ofeducation specification. Although completing
some college increases earnings somewhat
(about 20 percent over those of a high school
graduate), finishing college or graduate school
boosts that figure to nearly 60 percent. The
years-of-education specification essentially
allows for a smooth line through the data and
hence makes no distinction between completing the third and fourth year of college and
obtaining a bachelor’s degree, for example.

As mentioned above, because more individuals are enrolling in graduate school, including
only “college or more” as a dummy variable
will cause the results of earnings regressions to
suffer from the same problem outlined above
—the return will measure the average of college and post-college. As noted previously, in
1963 only 2.7 percent of those with a college
degree went on to do post-graduate work,
while in 1993 that figure was roughly 9 percent.
The third column in table 2 presents results
from a specification that allows for two additional dummy variables—one for elementary
education only and one for post-graduate work.
These statistics show a large gain to a post-

T A B L E

Earnings Regression
Estimates, 1983
Variable

(1)

(2)

(3)

(4)

(5)

(6)

Constant

4.6163
(0.0147)
—
—
—
—
—
—
—
—
—
—

5.6574
(0.0102)
—
—
—
—
–0.2736
(0.0064)
0.1749
(0.0059)
—
—

5.6623
(0.0102)
–0.4500
(0.0147)
–0.2468
(0.0067)
—
—
0.1753
(0.0058)
0.4110
(0.0061)

5.6536
(0.0102)
–0.4510
(0.0147)
–0.2475
(0.0067)
—
—
0.1755
(0.0058)
—
—

5.6465
(0.0103)
—
—
—
—
–0.1688
(0.0075)
0.2121
(0.0058)
0.4468
(0.0061)

5.6503
(0.0102)
–0.4039
(0.0147)
—
—
–0.1905
(0.0075)
0.1976
(0.0058)
0.4328
(0.0061)

—
—
—
—

—
—
0.4596
(0.0054)

0.5715
(0.0084)
—
—

—
—
0.4602
(0.0054)

0.6096
(0.0085)
—
—

0.5944
(0.0084)
—
—

0.0879
(0.0008)
0.0824
(0.0023)
–0.0035
(0.0002)
–0.1662
(0.0069)
–0.0755
(0.0136)
–0.3828
(0.0043)
50,445
0.3583

—
—
0.0817
(0.0023)
–0.0034
(0.0002)
–0.1648
(0.0070)
–0.0842
(0.0136)
–0.3811
(0.0043)
50,445
0.3562

—
—
0.0807
(0.0023)
–0.0034
(0.0002)
–0.1629
(0.0069)
–0.0853
(0.0135)
–0.3794
(0.0043)
50,445
0.3623

—
—
0.0824
(0.0023)
–0.0035
(0.0002)
–0.1639
(0.0069)
–0.0812
(0.0136)
–0.3820
(0.0043)
50,445
0.3585

—
—
0.0765
(0.0023)
–0.0031
(0.0002)
–0.1737
(0.0070)
–0.0947
(0.0137)
–0.3684
(0.0044)
50,445
0.3437

—
—
0.0786
(0.0023)
–0.0032
(0.0002)
–0.1676
(0.0070)
–0.0869
(0.0136)
–0.3735
(0.0043)
50,445
0.3534

Elementary school
7 to 12 years of education
High school dropout
1 to 3 years of college
4 years of college
to 1 year of
graduate school
2 years of graduate school
4 years of college
to 2 years of
graduate school
Years of education
Years of experience
Years of experience2
Black
Other nonwhite
Female
No. of observations
R2

SOURCE: Authors’ calculations based on the March 1984 Current Population Survey.

graduate degree as compared to a four-year
degree (approximately 20 percentage points).
The measured return to a college education,
however, declined about 12 percent (or about
seven percentage points, from 0.589 to 0.519).
This means that combining post-college graduates with those holding only a bachelor’s degree
leads to a substantial upward bias in the return
to a college education.
Columns 4 to 6 in the tables reflect slight
modifications of the education specification.
For example, column 4 is similar to column 2,
but includes dummy variables for elementary
schooling and 7 to 12 years of education, while
omitting the high school dropout category.
Evidently, these changes make little difference

in the return to college, post-college, race, or
sex coefficients.
The results using the semiparametric experience specification are shown in the last column
of table 2. Because economic theory provides
no particular parametric form for the experience profile, we reran the above regression
allowing that profile to be any smooth function. Estimates for the return to education and
to the various demographic variables shown in
table 2 were obtained using the semiparametric
regression technique of Robinson (1988). This
technique simultaneously solves for discrete,
linear regression parameters and an arbitrary
smooth-kernel regression of a continuous variable by finding the least-squares solution to this

T A B L E

Earnings Regression
Estimates, 1973
Variable

(1)

(2)

(3)

(4)

(5)

(6)

Constant

4.9667
(0.0155)
—
—
—
—
—
—
—
—
—
—

5.8283
(0.0103)
—
—
—
—
–0.2259
(0.0062)
0.1468
(0.0072)
—
—

5.8264
(0.0103)
–0.4063
(0.0130)
–0.2012
(0.0064)
—
—
0.1475
(0.0072)
0.3813
(0.0077)

5.8241
(0.0103)
–0.4068
(0.0130)
–0.2015
(0.0064)
—
—
0.1475
(0.0072)
—
—

5.8000
(0.0105)
—
—
—
—
–0.0954
(0.0071)
0.2012
(0.0071)
0.4315
(0.0077)

5.8061
(0.0104)
–0.3361
(0.0128)
—
—
–0.1223
(0.0071)
0.1838
(0.0071)
0.4158
(0.0077)

—
—
—
—

—
—
0.4025
(0.0069)

0.4646
(0.0117)
—
—

—
—
0.4038
(0.0069)

0.5187
(0.0118)
—
—

0.5014
(0.0117)
—
—

0.0729
(0.0009)
0.0811
(0.0023)
–0.0034
(0.0002)
–0.1888
(0.0079)
–0.0941
(0.0079)
–0.5119
(0.0051)
38,266
0.3837

—
—
0.0805
(0.0023)
–0.0034
(0.0002)
–0.2002
(0.0080)
–0.1134
(0.0203)
–0.5049
(0.0051)
38,266
0.3810

—
—
0.0805
(0.0023)
–0.0034
(0.0002)
–0.1917
(0.0079)
–0.1099
(0.0202)
–0.5058
(0.0051)
38,266
0.3857

—
—
0.0810
(0.0023)
–0.0034
(0.0002)
–0.1921
(0.0079)
–0.1076
(0.0202)
–0.5072
(0.0051)
38,266
0.3851

—
—
0.0763
(0.0024)
–0.0031
(0.0002)
–0.2259
(0.0080)
–0.1172
(0.0206)
–0.4898
(0.0051)
38,266
0.3632

—
—
0.0778
(0.0023)
–0.0032
(0.0002)
–0.2049
(0.0080)
–0.1086
(0.0204)
–0.4969
(0.0051)
38,266
0.3745

SOURCE: Authors’ calculations based on the March 1974 Current Population Survey.

specification. Therefore, the parameters on the
variables of interest (education, race, and sex)
are conditional on the highly flexible experience profile of the nonparametric estimate.
The parameter estimates, although slightly
different in actual magnitude, display almost
the same pattern as the regression based on
the quartic specification. The nonparametric
experience profiles are similar to the column 3
estimates, confirming that the quartic specification does a reasonable job of controlling for
experience. Therefore, for other years we omit
column 7.
Misspecification of either experience or education may affect other variables, but for our

specifications, these changes are quite small.
For example, focusing on the coefficient on
“black” across specifications, using just the
years-of-education specification (column 1 of
table 2), gives a value of –17 percent. However,
allowing dummy variables for educational
achievement and a nonparametric representation of experience (column 7 of table 2)
increases the value on black to –14.8 percent.
Therefore, misspecifying the way experience
and/or education enters has consequences for
the degree of race-based earnings inequality.
Because the educational attainment of the
workforce has changed dramatically over time,

T A B L E

Earnings Regression
Estimates, 1963
Variable

(1)

(2)

(3)

(4)

(5)

(6)

Constant

5.0026
(0.0237)
—
—
—
—
—
—
—
—
—

5.7369
(0.0183)
—
—
—
—
–0.2214
(0.0084)
0.1304
(0.0122)
—
—

5.7328
(0.0182)
–0.3971
(0.0155)
–0.1983
(0.0086)
—
—
0.1303
(0.0121)
0.3059
(0.0129)

5.7328
(0.0182)
–0.3971
(0.0155)
–0.1983
(0.0086)
—
—
0.1303
(0.0121)
—
—

5.6890
(0.0185)
—
—
—
—
–0.0426
(0.0092)
0.0228
(0.0119)
0.3945
(0.0128)

5.6972
(0.0184)
–0.2892
(0.0149)
—
—
–0.0751
(0.0093)
0.1988
(0.0119)
0.3718
(0.0127)

—
—
—
—

—
—
0.3065
(0.0117)

0.3095
(0.0215)
—
—

—
—
0.3068
(0.0116)

0.4030
(0.0217)
—
—

0.3786
(0.0215)
—
—

0.0612
(0.0012)
0.0596
(0.0038)
–0.0022
(0.0002)
–0.3219
(0.0123)
–0.1305
(0.0383)
–0.4962
(0.0077)
18,960
0.3279

—
—
0.0604
(0.0038)
–0.0023
(0.0002)
–0.3517
(0.0123)
–0.1753
(0.0386)
–0.4874
(0.0078)
18,960
0.3182

—
—
0.0606
(0.0038)
–0.0023
(0.0002)
–0.3314
(0.0124)
–0.1574
(0.0384)
–0.4915
(0.0078)
18,960
0.3247

—
—
0.0555
(0.0039)
–0.0020
(0.0003)
–0.3915
(0.0124)
–0.1766
(0.0393)
–0.4663
(0.0079)
18,960
0.2942

—
—
0.0570
(0.0038)
–0.0021
(0.0003)
–0.3544
(0.0125)
–0.1529
(0.0389)
–0.4765
(0.0078)
18,960
0.3080

SOURCE: Authors’ calculations based on the March 1964 Current Population Survey.

we next examine specifications across years.7
Earnings are deflated using the GNP price
deflator for personal consumption. We omit the
specification using semiparametric experience
from the earlier years, since there is little difference between that specification and the one
using a fourth-order polynomial in experience.
Comparing column 1 across years shows that
the return to education (measured by years of
schooling) has been rising over time. In fact,
compared to 1963, the return to an additional
year of schooling has nearly doubled, from 6
percent in 1963 to 11 percent in 1993.
Comparing column 2 across years also
shows a similar pattern for those possessing at
least a college degree. Again, between 1963
and 1993 we see a near doubling of the return

to a college education. The return to completing only one to three years of college did not
change much. However, those who dropped
out of high school fared much worse (compared to high school graduates) in 1993 than
in 1963. In 1963, high school dropouts earned
about 22 percent less than high school graduates; by 1993, they were earning about 32
percent less.
Comparisons using column 3 show that the
gains to finishing at least two years of graduate
school went from about 31 percent above a
high school graduate’s earnings to 73 percent.

■ 7 We chose 10-year intervals simply for convenience; the differences we mention may be slightly affected by business cycle conditions.

On the other hand, the return to a college degree (with up to one year of graduate school)
rose from 31 to 52 percent.
Comparing columns 2 and 3 in 1963 and
1993 clearly shows that the bias has been growing over time. In 1963, combining college with
post-graduate work led to a 31 percent gain in
earnings relative to high school graduates. In
column 3, the return to college grads and those
with at least two years of graduate school was
also about 31 percent more. That is, separating
the various educational groups in 1963 led to
virtually no difference.
The results for 1993 tell a much different
story. The coefficient on the combination of
college and graduate school shows a gain,
compared to high school graduates, of about 59
percent. Separating the different educational
groups, however, reveals that those with some
post-graduate work earned 73 percent more
than high school graduates, while individuals
with only a bachelor’s degree received roughly
52 percent more.
Finally, we turn to an examination of other
estimates that have changed markedly over
time. Specifically, we concentrate on the race
and sex coefficients. In 1963, blacks were paid
roughly one-third less than whites. By 1973,
that gap had narrowed to about 20 percent,
and by 1993, to about 16 percent.
The pattern for females’ earnings is slightly
different. In 1963, women earned about half as
much as men, and that figure did not change
much over the ensuing 10 years. By 1983, however, the male–female earnings differential had
begun to fall, with women making about 38
percent less than men. The gap narrowed again
over the next 10 years, and by 1993, women
were earning about 29 percent less than men.

IV. Conclusion
The general features of individual earnings are
robust to a wide variety of specifications; however, the specific point estimates are not. This
paper investigates two areas where the parameterization of the earnings function can alter
the estimates. In the specification of both education levels and years of experience, the simplest specification could lead to substantial
misestimation of the underlying model that
suggests little about the exact functional form.
Evidently, the return to a college education
has been rising over time. However, part of this
return is due to an increasing number of individuals pursuing post-graduate schooling, a
fact not typically controlled for in the existing
literature. Combining both college and postcollege graduates into one category leads to an
overestimate of the return to college of approximately 12 percent (seven percentage points).
On the other side of the earnings inequality
issue, the relative wages of high school dropouts have been boosted by the rising education
levels of workers within this category.
An experience profile that allows for considerable flatness in later years, after a steep initial
rise, is strongly supported by the data. The simple specification of potential experience and its
square fails to allow earnings to reflect this pattern. Although we favor the estimates derived
using Robinson’s (1988) technique, there
appears to be little difference between these
estimates and those obtained using Murphy
and Welch’s (1990) quartic specification.

References
Bar-Or, Y., J. Burbridge, L. Magee, and A.L.
Robb. “The Wage Premium to a University
Education in Canada,” Journal of Labor Economics, vol. 13, no. 4 (October 1995),
pp. 762–94.
Dooley, M.D., and P. Gottschalk. “Earnings
Inequality among Males in the United
States: Trends and the Effect of Labor Force
Growth,” Journal of Political Economy,
vol. 92, no. 1 (February 1984), pp. 59–89.
Fairlie, R.W., and B.D. Meyer. “Ethnic and
Racial Self-Employment Differences and
Possible Explanations,” Journal of Human
Resources, vol. 31, no. 4 (Fall 1996),
pp. 757 –93.
Frazis, H., M.H. Ports, and J. Stewart. “Comparing Measures of Educational Attainment
in the CPS,” Monthly Labor Review, vol. 118,
no. 9 (September 1995), pp. 40–44.
Juhn, C., K.M. Murphy, and B. Pierce. “Wage
Inequality and the Rise in the Returns to
Skill,” Journal of Political Economy, vol. 101,
no. 3 ( June 1993), pp. 410–42.
Mincer, J. Schooling, Experience, and Earnings. New York: National Bureau of Economic Research, 1974.
Murphy, K.M., and F. Welch. “Empirical Age–
Earnings Profiles,” Journal of Labor Economics, vol. 8, no. 2 (April 1990), pp. 202–29.
Robinson, P.M. “Root- N-Consistent Semiparametric Regression,” Econometrica, vol.
56, no. 4 ( July 1988), pp. 931–54.
Schmitz, S., D.R. Williams, and P.E. Gabriel.
“An Empirical Examination of Racial and
Gender Differences in Wage Distributions,”
Quarterly Review of Economics and Finance,
vol. 34, no. 3 (Fall 1994), pp. 227–39.

Reducing Working Hours
by Terry J. Fitzgerald

Introduction
It has been widely reported that working
hours in the United States have shown little
or no decline over the past few decades, while
they have fallen substantially in most other
industrialized countries—usually below the
U.S. average. For example, one source shows
that German workers have experienced a 27
percent decrease in average annual hours
worked since 1960, compared to a decline of
less than 3 percent in the United States.1
During the same period, the U.S. unemployment rate has risen well above 7 percent several times, reaching as high as 10.8 percent in
1982. In addition, some sectors of the economy, including many manufacturing industries,
have gone through prolonged periods with little or no employment growth. For example,
since 1969, total employment in manufacturing
has fallen by almost 2 million, or roughly 10
percent, while total civilian employment has
increased by almost 50 million.
These observations have led some to conclude that working hours in the United States
are now too long, and that policy steps should
be taken to reduce them. As a result, several
proposals have been put forth. Some of these

Terry J. Fitzgerald is an economist
at the Federal Reserve Bank of
Cleveland. The author thanks Rod
Wiggins for research assistance.

proposals are primarily intended to increase the
time available to workers for personal activities
and leisure. Others are specifically intended to
increase the employment level in some sectors
of the economy, or in the economy as a whole,
by spreading (or sharing) the work across more
people.2 That is, it is believed that if people
worked fewer hours, more workers would be
employed. Although the two goals of increased
leisure and increased employment are distinct,
proposals for attaining both of them share the
same basic approach—reduce the number of
hours that employed people work.
Ironically, while some in the United States
are calling for a reduction in working hours,
several European countries are considering
■ 1 Data are from the Organisation for Economic Co-operation and
Development.
■ 2 For example, former U.S. Senator William Proxmire (1993) proposed reducing the length of the workweek to increase both leisure and
employment. Other proposals with similar objectives have been made by
Shorr (1992) and Rifkin (1995). Examples of government policies intended
to give workers more personal time include the Family and Medical Leave
Act of 1993 and the recently proposed Family Friendly Workplace Act of
1996. An example of a policy intended to increase employment by reducing
weekly hours is the Full Employment Act of 1994, which was introduced in
the House of Representatives but never enacted.

T A B L E

Annual Hours per Worker
in All U.S. Industries
Year

Annual
Hours

1870
1890
1913
1929
1938
1950
1960

2,964
2,789
2,605
2,342
2,062
1,867
1,795

SOURCE: Angus Maddison, Dynamic Forces in Capitalist Development. New
York: Oxford University Press, 1991.

F I G U R E

Average Annual Hours Worked
in All U.S. Industries

SOURCE: Organisation for Economic Co-operation and Development.

Furthermore, a reduction in working hours
would almost certainly lower workers’ total
earnings.4
In this article, I examine the issue of reducing
working hours in the United States. I begin my
analysis by presenting some historical facts that
help explain the appeal of policies to reduce
hours. I then explore a standard labor-demand
model’s predictions about how reducing weekly
working hours would affect employment, output, and productivity. While shedding light on
the potential effects of reducing hours in the
United States, these predictions also provide
information on the possible effects of increasing
hours in European countries.
I find that the impact of a policy which effectively reduces the number of weekly hours per
worker by five depends crucially on the tradeoffs in production between hours per worker,
employment, and output, and on how the policy affects wages. Unless the reduction in hours
is associated with a large increase in the productivity of a fixed number of workers and/or a
substantial decline in weekly wages, the model
used in this paper predicts that the policy will
have little, if any, positive impact on employment and a substantial negative effect on output. This suggests that policymakers and economists should examine these issues carefully
before legislating policies that would affect
working hours.

I. Some Facts about
Working Hours
While it is difficult to obtain economywide

proposals for an increase. It is sometimes argued that the relatively short working hours of
many workers in Europe put firms there at a
competitive disadvantage compared to firms in
the United States and Japan, where working
hours are longer. Proposals for longer weekly
hours and shorter vacations are intended to
increase productivity and thereby boost economic growth and employment.
Key considerations for plans to decrease—or
increase—working hours are the interactions
between hours per worker, employment, productivity, and output, as well as the effect on
workers’ wages. For example, a reduction in
hours per worker may lead to a decline in output because of a fall in labor productivity, possibly due to the difficulty of coordinating production across a larger workforce, and/or because
employment increases are curtailed by the costs
of hiring and training additional workers.3

data on working hours prior to the 1950s, available evidence indicates a substantial decline in
the average annual hours of workers throughout the industrialized world from the late 1800s
through 1960. Table 1 presents data from
Maddison (1991), which show that average
annual hours per worker in the United States
fell steadily over that period, from almost 3,000
in 1870 to about 1,800 in 1960. Other industrialized countries experienced similar declines.
There is evidence, however, that the downward trend in annual working hours has slowed
substantially or stopped in the United States

■ 3 It has been argued that productivity may increase with a reduction
in hours per worker. This possibility will also be considered.
■ 4 Although unions sometimes propose reduced working hours with
no wage decline, a reduction in hours is generally traded off—explicitly or
implicitly—against a wage increase, job security, or some other benefit.

T A B L E

Annual Hours per Worker
in All Industries, 1960–1994
Country

United States
Canada
Finland
Germany
Great Britain
Japan
France
Sweden

Earliest
Observation

1994

2,003.9a
2,025.8b
2,061.3a
2,151.9a
1,945.3c
2,228.0d
1,962.5c
1,802.0a

1,945.3
1,734.6
1,771.4
1,574.6
1,728.2
1,898.0
1,635.2
1,532.2

Percent
Change

–2.9
–14.4
–14.1
–26.8
–11.2
–14.8
–16.7
–15.0

a. Data begin in 1960.
b. Data begin in 1961.
c. Data begin in 1970.
d. Data begin in 1972.
SOURCE: Organisation for Economic Co-operation and Development.

T A B L E

Annual Hours per Worker
in Manufacturing, 1960–1994
Country

United States
Canada
Japan
Denmark
France
Germany
Italy
Netherlands
Norway
Sweden
United Kingdom

1960

1994

Percent
Change

1,939.3
1,932.6
2,477.2
2,080.1
1,994.0
2,096.1
2,045.9
2,109.2
1,945.9
1,853.0
2,134.0

1,993.6
1,898.4
1,959.8
1,573.3
1,637.5
1,541.3
1,803.6
1,598.8
1,548.7
1,627.2
1,825.4

2.8
–1.8
–20.9
–24.4
–17.9
–26.5
–11.8
–24.2
–20.4
–12.2
–14.5

NOTE: The data relate to all employed persons (employees and self-employed
workers) in the United States, Canada, Japan, France, Germany, Norway, and
Sweden, and to all employees (wage and salary earners) in Denmark, Italy, the
Netherlands, and the United Kingdom. Hours are those actually worked, including overtime, and time spent at the workplace waiting, standing by, or taking short rest periods. Hours paid for but not worked, such as paid annual
leave, paid holidays, and paid sick leave, are excluded.
SOURCE: U.S. Department of Labor, Bureau of Labor Statistics, September 1995.

since 1960 (particularly over the past two
decades), while it has continued in most other
industrialized countries. Figure 1 presents
annual data for 1960 through 1995 from the
Organisation for Economic Co-operation and
Development (OECD). Note that the average
annual hours of U.S. workers leveled off in the
1970s and have increased somewhat since the
early 1980s.5 Table 2 shows the decline in

hours between 1960 and 1994 in several countries for which the OECD has data. While hours
declined only 2.9 percent in the United States
over this period, they dropped by about 15 percent in several European countries and Japan,
and by almost 27 percent in Germany.
In addition to comparing trends in working
hours across countries, many casual observers
of these data also compare the level of working hours, despite a warning from the OECD
that such comparisons are not meaningful
because of differences in data collection methods. Comparing levels, one finds that by 1994,
U.S. working hours were the longest of any
country listed in table 2.6 Excluding Japan,
annual U.S. working hours are reported to be
roughly 200 to 400 hours longer than the rest,
or about four to eight hours more per week.7
A similar pattern exists across countries for
workers in the manufacturing sector. Table 3
presents Bureau of Labor Statistics’ data on the
change in average annual hours worked in
manufacturing from 1960 to 1994. It shows that
the hours of manufacturing workers in the
United States actually increased over this 34year period, while declining significantly in
every other country studied except Canada. In
1994, annual hours of U.S. workers exceeded
those of workers in other countries, except
Japan and Canada, by roughly 200 to 400 hours.
Data on weekly U.S. averages, another source
of information about secular trends in working
hours, shed light on how hours trends have
differed across industries. Figure 2 shows post–
World War II data on the average weekly hours
of all workers and all nonagricultural wage and
salary earners. Again, we see that average hours
of all workers trended downward through the
early 1970s and have leveled off and increased
slightly since.8
■ 5 I thank Marianna Pascal of the OECD for providing these data.
■ 6 The OECD has more recent data for several additional countries,
including Australia, Mexico, New Zealand, Norway, Portugal, Spain, and
Switzerland. Of these, only Portugal had a higher reported level of annual
working hours than the United States in 1994.
■ 7 Data from Maddison (1991) show a decline in the annual hours
of U.S. workers from 1960 through 1987, along with an even larger decline
for workers in other industrialized countries. Maddison’s U.S. data are
based on establishment figures for paid weekly hours per job. Data on
average weekly hours at work, collected from the Current Population Survey and shown in figure 2, indicate a much smaller decline in average
weekly hours than do the establishment data. Part of this difference is due
to an increase in moonlighting over this period, which causes the establishment data to overstate the decline in hours per worker.
■ 8 The series for average weekly hours and average annual hours
could exhibit different trends due to changes in vacations, holidays, sick
leave, and other factors that affect the number of weeks worked per year.

T A B L E

Average Weekly Hours of Production
or Nonsupervisory Workers on
Private, Nonagricultural Payrolls

1947
1954
1959
1964
1969
1974
1979
1984
1989
1993
1996

Total

Mining

Construction

Manufacturing

TPUa

Wholesale
Trade

Retail
Trade

FIREb

Services

—
—
—
38.7
37.7
36.5
35.7
35.2
34.6
34.5
34.4

40.8
38.6
40.5
41.9
43.0
41.9
43.0
43.3
43.0
44.3
45.3

38.2
37.1
37.0
37.1
37.8
36.6
37.0
37.7
37.9
38.4
38.9

40.4
39.6
40.3
40.7
40.6
40.0
40.2
40.7
40.9
41.4
41.5

—
—
—
41.1
40.7
40.3
39.9
39.4
38.9
39.6
39.7

41.1
40.5
40.6
40.7
40.2
38.8
38.8
38.5
38.0
38.2
38.3

—
—
—
37.0
34.2
32.7
30.7
29.8
28.9
28.8
28.8

—
—
—
37.3
37.1
36.5
36.2
36.5
35.8
35.8
35.8

—
—
—
36.1
34.7
33.7
32.7
32.6
32.6
32.5
32.4

a. Transportation and public utilities.
b. Finance, insurance, and real estate.
SOURCE: U.S. Department of Labor, Bureau of Labor Statistics.

F I G U R E

Average Weekly Hours at Work

SOURCE: U.S. Department of Labor, Bureau of Labor Statistics.

Interestingly, figure 2 shows relatively little
decline before the 1970s in the average weekly
hours of nonagricultural wage and salary workers. The differences between the trends in these
two series are largely due to a shift in the composition of employment. Since the 1940s, the
fraction of workers who are self-employed or in
agricultural industries has declined substantially.
These are also groups that have traditionally
worked relatively long hours, so that as their
share of employment fell, so did the average
weekly hours of all workers.9

In several industries, the average weekly
hours of wage and salary workers declined little over the past few decades, a fact that has received a great deal of attention. Table 4 shows
the weekly hours of U.S. production and nonsupervisory workers on nonagricultural payrolls
for several industries. Notice that the hours of
workers in goods-producing industries—mining, construction, and manufacturing—have not
only failed to decrease over the past 50 years,
but have actually increased. By contrast, average weekly hours in manufacturing before 1950
fell markedly, from 54.3 hours in 1901 to 38.8
hours in 1948.10 The largest declines in weekly
hours since 1964 occurred in retail trade and the
service industries. (See footnote 7 for a brief discussion of why weekly hours are shown declining steadily in table 4 but not in figure 2.)
To summarize, there is evidence that the
steady decline in annual working hours that
occurred before the 1960s has slowed or
stopped in the United States over the last few
decades, while continuing in virtually all other
industrialized countries. Furthermore, the average weekly hours of workers in several U.S.
■ 9 For example, in 1958, average weekly hours at work was 47.7
for self-employed workers in nonagricultural industries, compared to 39.2
for all wage and salary workers in the same industries. In 1948, the selfemployed and workers in agricultural industries accounted for about
24 percent of total employment. By 1970, that figure had fallen to roughly
11 percent.
■ 10 These numbers are taken from Ehrenberg and Smith (1994).

industries have shown no decline over the past
50 years.11
This evidence has led many U.S. policymakers, union leaders, economists, and social
commentators to advocate policies that would
reduce working hours. One common proposal
is to lower the number of hours people work
each week.12 In the remainder of this article,
I examine the potential effects of reducing
weekly hours per worker so that the annual
hours of full-time, full-year workers in the
United States are more in line with those for
other industrialized countries, as reported in
tables 2 and 3. More specifically, I consider a
five-hour reduction in the workweek, implying
a reduction in annual hours of roughly 200 to
250, depending on the number of weeks actually worked (excluding holidays, vacations, sick
leave, and so forth).

II. A Model
of the Firm
In order to evaluate the implications of reducing
weekly hours, we need a model of how weekly
hours and employment are determined. In this
section, I lay out a simple model in which the
firm chooses both the weekly hours of its workers and the number of workers it employs.13
I then examine the effects of reducing weekly
hours from 40 to 35 within this framework.

The Production
Technology
Output in the model is produced by competitive firms that combine capital and the labor
services of workers. Labor services are assumed
to be a function of the number of workers, n,
and the hours per worker, h. In general, labor
services, L, may be written as
(1)

L = F (h, n),

with labor services typically assumed to be an
increasing function of both arguments. Following Hart (1987), I assume that the labor service
function may be written as
(2)

L = g (h)n θ,

where g(.) is assumed to be positive and strictly
increasing, with g(0) equal to 0.
Output during a week is produced by combining an exogenously given and fixed amount
of capital, k, with the labor services of n em-

ployees working h hours each, and is assumed
to be
(3)

y = f (k)g (h)n θ,

where 0 < θ < 1. Since capital is assumed to
be fixed and exogenous, the exact form of the
function f is unimportant. For a given amount of
capital and number of workers, g (h) determines
total output, and g (h) divided by h determines
average output per hour, or productivity.
I assume that the weekly working hours of
capital at the firm are exogenously given.14 For
simplicity, I assume that the firm is operated
continuously during the week—that is, for 168
hours—and that its workers are distributed
evenly across these hours. The firm’s manager
must decide how many people to employ and
the number of hours per worker.
For example, suppose the manager is told to
hire 16,800 hours of labor, so that 100 people
are working at the firm during each hour.
Among its many options, the firm could employ
210 workers for 80 hours each, 420 workers for
40 hours each, or 840 workers for 20 hours
each. These choices are likely to be associated
with different levels of output. The model is
weekly, and makes no distinction between five
eight-hour days and four 10-hour days.
It is difficult to determine a reasonable specification for the function g (.) from the data. Typically, this function is assumed to be convex at
low values of h, reflecting fixed warm-up or
set-up costs, and concave at high values of h,
reflecting worker fatigue and boredom after
long hours, as well as the decreasing returns
associated with having more people at the firm
each hour. (Recall that people are evenly distributed across the working hours of the firm,
so that an increase in hours per worker implies

■ 11 An important issue, not examined here, is the underlying cause
of cross-country differences in both trends and levels of working hours.
More specifically, one would like to know whether the leveling off of working hours in the United States was associated with efficient production,
distortionary labor market policies and regulations, or some other factor.
■ 12 There have been several proposals to modify the hours and
overtime pay provisions of the Fair Labor Standards Act. These proposals
seek to reduce the “standard” workweek below 40 hours and/or to increase
the overtime premium that firms must pay to employees working more than
the “standard” workweek.
■ 13 This model is similar to the framework used by Hart (1987), who
builds on the work of Ehrenberg (1971), Lewis (1969), and Rosen (1968),
among others.
■ 14 How reduced working hours might affect capital utilization is an
interesting question, but one that this article does not explore.

more people at the firm each hour.) The assumption of decreasing returns to workers also
explains why the exponent on the number of
workers is restricted to be less than one.
Fortunately, for the purposes of this paper
there is no need to specify the entire g function. I will elaborate on this point shortly. What
will be critical is the ratio of g (35) to g (40),
where 40 hours is the equilibrium workweek
before the hours restriction, and 35 is the
restricted number of hours per worker.

The Firm’s
Decision Problem
A basic assumption throughout this paper is that
firms choose hours per worker and the number
of workers so as to maximize profits. In making
these choices, a firm takes as given an increasing weekly wage schedule that depends on the
number of hours a person works. This schedule
is written as
(4)

w (h) ≡ ω h ψ,

where ψ > 0 and ω > 0. The wage schedule is
constant when ψ equals 0, meaning that the
weekly wage is independent of hours, is linear
when ψ equals 1 (implying a constant wage
per hour), and is convex when ψ is greater
than 1 (reflecting an increase in the implied
hourly wage as the number of hours increases).
This wage schedule may also include other
labor costs that vary with hours per worker, and
thus may be thought of more generally as
describing a firm’s variable labor costs, that is,
costs which vary directly with hours per worker.
In addition to variable labor costs, the firm
also faces per worker costs that, roughly speaking, do not vary with changes in hours per
worker. These costs include the time and effort
associated with hiring, training, and firing people, and may include payroll taxes and other
costs that depend on the number of people
employed.15 To capture these per worker costs,
I assume that the total cost associated with
employing each worker for h hours is given by
w (h) plus φ, where the parameter φ represents
per worker costs.
The profit maximization problem faced by a
firm is
(5)

maxh,n f (k)g(h)n θ – [w (h) + φ]n
such that 0 ≤ h ≤ 168, n > 0.

Profits to the firm can be interpreted as the
return to capital.
Necessary conditions for an interior solution
to this problem for h and n are
(6)

f (k)g9(h)n θ = w 9(h)n

(7)

θf (k)g(h)n θ – 1 = w (h) + φ.

Equation (6) states that the marginal benefit of
having all employees work another minute
must equal the marginal cost of having them do
so. Equation (7) says that the marginal product
of hiring an additional worker must be equal to
the marginal cost. Combining (6) and (7), I get
(8)

θg(h)
w (h)+ φ .
=
g9(h)
w 9(h)

Notice that the solution for hours per worker is
independent of employment and is determined
by the shapes of the wage schedules and the
g(.) function. That is, the number of hours per
worker does not depend on the size of the firm
as given by the number of workers. Once h has
been determined, equation (7) can be used to
solve for the number of workers, n.
As mentioned in the preceding subsection,
determining the exact shape of the function
g(.) from the data is difficult and, fortunately,
unnecessary. In the next section, I consider the
implications of restricting hours per worker to
35. I take it as given that the g function is such
that 40 hours per worker is profit maximizing,
and normalize g(40) to 1. I also select a value
for g(35), denoted by γ. For a fixed number of
workers and capital, γ determines how much
lower the output will be at 35 hours per worker
than at 40.
To verify that such a g function exists, given
the model functions and parameter values, I
define the profit function, π(h), as follows:
(9)

π(h) ≡ maxn f (k)g(h)n θ – [w (h) + φ]n
such that n > 0.

If 40 hours per worker is profit maximizing,
then
(10)

π(40) > π(h)

for all 0 < h < 168.

■ 15 A full discussion of employment-related costs to the firm can be
found in Hart (1984).

This profit-maximization condition constrains the shape of the g function. For example, π(40) must be greater than or equal to
π(35). In effect, this condition restricts how
large γ can be. For example, suppose γ were
greater than 1. Then, as long as weekly wages
are lower at 35 hours than at 40, it would not
be profitable for a firm to hire workers for 40
hours, since it could get more output at a lower
cost by hiring the same workers for 35 hours. It
follows that, for reasonable specifications of the
wage function, γ can be no larger than 1 and
will generally need to be somewhat smaller for
(10) to hold.
If π(40) is greater than π(35) for a given value
of γ, then there are many candidate g functions
that satisfy (10) and pass through these two values.16 The exact form of this function is not
important for the purposes of this paper.

A Simple Example
To gain insight into the potential effects of
reducing hours, consider an example. Here, it
is informative to specify a functional form for
the g function. In the case where g(.) is h θ, ψ
is set to 1, and φ is set to 0, the firm’s decision
problem is written
maxh,n f (k)g(hn)θ – ωhn
such that 0 ≤ h ≤ 168, n > 0.
Notice that h and n appear only as h multiplied by n. This implies that for any total
number of hours worked (call it H ), any combination of h and n for which hn = H produces the same profit and the same output.
This example illustrates the intuition that
seems to underlie the arguments of some advocates of work-sharing policies. In this example,
the decomposition of total hours into hours per
worker and the number of workers is irrelevant
for a firm’s productivity or output. Some worksharing advocates implicitly argue that this is a
fairly close approximation of reality. Thus, the
fixed amount of total hours worked can be
reorganized so that more people are working
fewer hours, without having much impact on
output. We will see that this result depends crucially on the assumptions made regarding the
shape of g(.), the wage schedule, and the size
of fixed costs per worker.

III. The Effects of
Reducing Hours
In this section, I examine the effects of reducing weekly hours per worker by five. The
framework has been set up using 40 hours per
week as the solution to the firm’s decision
problem for hours. I consider the effects of
restricting weekly hours per worker to no more
than 35. This restriction translates into an annual
decline of roughly 250 hours for a full-time,
full-year worker, which is in line with the differences between the United States and many
European countries shown in tables 2 and 3.
The experiment amounts to adding the constraint h < 35 to the firm’s decision problem
and comparing the result to the solution of the
problem without this hours constraint.17
After presenting the results for a benchmark
set of parameter values, I explore the sensitivity
of these results to changes in parameter values.
The purpose of these experiments is to give a
sense of the qualitative predictions of a standard labor-demand model and to identify
which parameter values are crucial in determining the quantitative impact of the policy.

Benchmark
Parameter Values
The following parameter values are used as a
benchmark. First, f (k) and g (40) are both normalized to 1. I set the productivity parameter γ,
the value of g (35), equal to 0.875, so that the
12.5 percent reduction in hours per worker
from 40 to 35 leads to a 12.5 percent decline in
g (.). This implies that for a fixed number of
workers and capital, output per hour is unchanged, so that a 12.5 percent decline in hours

■ 16 One rather stark candidate g function is a step function, where
g (h ) = 0 for 0 < h < 35, g (h ) = γ for 35 < h < 40, and g (h ) = 1 for h > 40.
■ 17 In this article, I focus on the effects of actually reducing weekly
hours, rather than examining the effects of a specific policy, such as amending the provisions of the Fair Labor Standards Act, which may or may not
result in a shorter workweek. Much work has been done to examine the effects of changing the Act’s provisions (see, for example, Ehrenberg and
Schumann [1982]). Other studies have analyzed more generally the effects
of policies that attempt to reduce working hours by increasing overtime premiums and/or reducing “standard” weekly work hours (see, for example,
Hart [1987] and Owen [1989]).

T A B L E

Benchmark Results

Effects of a 35-Hour Workweek
(Percent change)
Variable

Table 5 shows the effects of restricting hours
Benchmark Model

Hours per worker
Employment
Total hours worked
Output per hour
Total output
Weekly wages
Profit

–12.5
–1.9
–14.2
0.7
–13.6
–12.5
–13.6

SOURCE: Author’s calculations.

per worker is accompanied by a 12.5 percent
decline in output.18
Next, the value of θ is set to 0.65, which implies that wage payments plus worker fixed
costs equal 65 percent of the value of output.
This is roughly consistent with aggregate U.S.
data on labor’s share of total income, though the
specific percentage varies across industries. I set
φ to 0.05, so that fixed costs per worker equal 5
percent of the wages paid to a 40-hour worker
and roughly 3 percent of total output. Again, this
number varies across industries and depends
greatly on what one includes as fixed costs.19
Finally, we must assign values for the parameters of the wage schedule. The value of ω is
chosen so that w (40) equals 1, which is simply
a normalization. The decline in weekly wages
is determined by the value of ψ. For the baseline experiment, I set ψ to 1.0, which implies
that the hourly wage is constant, so that the
weekly wage falls by 12.5 percent with the
hours restriction.

Hours Restriction
Experiments
Obviously, there is a large degree of uncertainty
in assigning values to some of these parameters, and their values may differ across industries. Therefore, it is important to examine how
changes in parameter values affect the results
of the experiment. After presenting the results
of the hours restriction for the benchmark parameters, I examine how they are affected by
changes in some of these parameter values.

per worker to 35 per week, using the benchmark parameter values. Rather than increasing
employment, as work-sharing advocates would
hope, the restriction causes an employment
decline of 1.9 percent.
The qualitative effect of the hours restriction
on employment can be understood by looking
at the firm’s employment condition as given by
equation (7), which must hold both prior to the
hours restriction (at h = 40) and after the hours
restriction (at h = 35). Holding the value of n
fixed, the benchmark value of γ, that is, g(35),
implies that the marginal product of the last
worker—the left-hand side of (7)—falls by 12.5
percent, matching the decline in h. Although
weekly wages, w (h), also fall by 12.5 percent,
the marginal cost of the last worker (the righthand side) declines by less than 12.5 percent,
since fixed costs per worker, φ, are unchanged.
Given that the marginal cost per worker does
not vary with employment, equality in (7) can
be restored only by decreasing employment so
as to increase the marginal product.
The 1.9 percent employment decline does
result in a 0.7 percent productivity increase,
but this is not nearly enough to offset the 14.2
percent decline in total hours worked. Output
falls by 13.6 percent, as do firm profits.

Sensitivity Analysis
Given the uncertainty in choosing benchmark
parameter values, it is natural to ask how the
results of the experiment change as we vary the
assumptions on 1) the decline in the productivity parameter, γ; 2) the size of per worker costs,
given by φ; and 3) the decline in workers’
weekly wages, determined by ψ. Tables 6
through 8 illustrate how the results vary with
changes in the values of these parameters. To

■ 18 While there are estimates of output elasticity with respect to
hours per worker (see Hamermesh [1993] for a summary), it is unclear that
these estimates are useful when evaluating a major policy-induced decline
in hours per worker. However, the implied value of 1, which is used in the
benchmark case, is within the range of estimates.
■ 19 The 5 percent value used here reflects a back-of-the-envelope
calculation of the costs associated with maintaining job positions (hiring,
training, record keeping, and so forth). This number does not include
employee benefits, some of which are fixed per worker costs. I am implicitly treating employee benefits as being incorporated into the wage schedule. To the extent that 5 percent understates fixed costs, I am biasing the
experiment so that the hours restriction will have more favorable employment and output effects.

T A B L E

Effects of Changes in γ

Variables

0.850

Hours per worker
Employment
Total hours worked
Output per hour
Total output
Weekly wages
Profit

–12.5
–9.7
–21.0
0.7
–20.5
–12.5
–20.5

T A B L E

Value of γ
0.875

0.900

–12.5
–1.9
–14.2
0.7
–13.6
–12.5
–13.6

–12.5
6.3
–7.0
0.7
–6.4
–12.5
–6.4

Effects of Changes in φ
Value of φ
Variables

Hours per worker
Employment
Total hours worked
Output per hour
Total output
Weekly wages
Profit

0.00

0.05

–12.5
0.0
–12.5
0.0
–12.5
–12.5
–12.5

–12.5
–1.9
–14.2
0.7
–13.6
–12.5
–13.6

T A B L E

0.10

–12.5
–3.6
–15.7
1.3
–14.6
–12.5
–12.5

Effects of Changes in ψ
Value of ψ
Variables

Hours per worker
Employment
Total hours worked
Output per hour
Total output
Weekly wages
Profit

0.0

–12.5
–31.7
–40.3
14.3
–31.7
0.0
–31.7

1.0

1.4

–12.5
–1.9
–14.2
0.7
–13.6
–12.5
–13.6

–12.5
13.3
–0.9
–4.3
–5.1
–17.1
–5.1

facilitate comparison with the benchmark experiment, I repeat the benchmark results in the
middle column of every table. Each table
shows how the results are affected by lowering
and raising the value of one of these parameters, leaving the remaining parameters at their
benchmark values.20
Table 6 presents the effects of restricting
hours under different assumptions for the productivity parameter γ. This parameter determines the decline in productivity for a fixed
number of workers associated with the decline
in hours per worker. If employment is held
constant, the parameter values used imply that
output per hour decreases 2.5 percent, is unchanged (the benchmark case), and increases
2.5 percent.
Not surprisingly, the effects of restricting
hours are more favorable for higher values of γ.
The declines in output and employment are
smaller, and, in fact, employment increases for
the highest value of γ. Note that the employment increase, which on its own would lead
output per worker to fall, offsets the increase in
productivity associated with the hours restriction for a fixed number of workers, so that output per hour rises only 0.7 percent.
Table 7 illustrates how the results vary with
different assumptions on the size of fixed costs
per worker. As expected, higher fixed costs imply larger employment and total output losses.
Finally, table 8 shows the effects of the
hours restriction under different assumptions
on the decline in weekly wages, which is determined by the parameter ψ. The results suggest a trade-off between the decline in weekly
wages and the decline in output and employment. If weekly wages are assumed to remain
constant, the drop in employment and output
is massive. If weekly wages are assumed to fall
more than proportionally with hours, then output declines relatively little and employment
increases substantially.21

NOTE: All results show percent change.
SOURCE: Author’s calculations.

■ 20 The qualitative nature of the results is not affected by changes in
the labor share parameter θ over a plausible range.
■ 21 The value of 1.4 for ψ implies that the weekly wage for 48 hours
is 30 percent higher than the weekly wage for 40 hours. This is roughly
the percentage that results when workers are paid 1.5 times their base pay
for the eight hours worked above 40.

IV. Final Remarks
In this paper, I have presented the predictions
of a standard labor-demand model for a policy
that restricts weekly hours to 35. In all of the
experiments, the output of the firm declined,
while employment both increased and decreased, depending on the specific parameter
values used. The key determinants of the policy’s effects were the production trade-offs
between hours per worker, employment, and
output, as well as the magnitude of the wage
decline associated with the policy.
The framework used here abstracts from a
number of potentially important considerations
in determining the effects of reducing hours
per worker. First, wage schedules are given
exogenously, rather than being determined
competitively through the interaction of firms
and workers. Therefore, the experiments have
nothing to say about the impact of the policy
on wages. Second, the model is static, so it
does not address the implications of the policy
for investment and capital accumulation. Third,
the model ignores potentially important labor
supply considerations, such as the effect on
labor force participation and moonlighting.
Fourth, the model abstracts from substantial
differences in the composition of employed
and unemployed people—differences that
may be important in determining the policy’s
impact.22 Finally, I simply assume that a policy
exists which effectively reduces hours per
worker, ignoring the problems of implementation and enforcement.

References
Ehrenberg, R.G. Fringe Benefits and Overtime
Behavior. Lexington, Mass.: Lexington
Books, 1971.
Ehrenberg, R.G., and P.L. Schumann. Longer
Hours or More Jobs?, Cornell Studies in Industrial and Labor Relations, No. 22, New York
State Schools of Industrial and Labor Relations. Ithaca, N.Y.: Cornell University, 1982.
Ehrenberg, R.G., and R.S. Smith. Modern
Labor Economics: Theory and Public Policy,
5th ed. New York: HarperCollins College
Publishers, 1994.

■ 22 See Fitzgerald (1996) for a discussion of this point.

Fitzgerald, T. J. “Reducing Working Hours:
American Workers’ Salvation?” Federal
Reserve Bank of Cleveland, Economic
Commentary, September 1, 1996.
Hamermesh, D.S. Labor Demand. Princeton,
N. J.: Princeton University Press, 1993.
Hart, R.A. The Economics of Non-Wage Labour
Costs. London: Allen & Unwin, 1984.
. Working Time and Employment.
Boston: Allen & Unwin, 1987.
Lewis, H.G. “Employer Interests in Employee
Hours of Work,” University of Chicago, unpublished manuscript, 1969.
Maddison, A. Dynamic Forces in Capitalist
Development. New York: Oxford University
Press, 1991.
Owen, J.D. Reduced Working Hours: Cure for
Unemployment or Economic Burden? Baltimore: Johns Hopkins University Press, 1989.
Proxmire, W. New York Times, November 5,
1993, p. 34-A.
Rifkin, J. The End of Work. New York: G.P.
Putnam’s Sons, 1995.
Rosen, S. “Short-Run Employment Variation
on Class-I Railroads in the U.S., 1947–1963,”
Econometrica, vol. 36, nos. 3– 4 (July/October 1968), pp. 511–29.
Shorr, J. The Overworked American: The Unexpected Decline of Leisure. New York: Basic
Books, 1992.

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