Does School Quality Matter? Returns to Education and the Characteristics of
Public Schools in the United States
David Card; Alan B. Krueger
The Journal of Political Economy, Vol. 100, No. 1. (Feb., 1992), pp. 1-40.
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Does School Quality Matter? Returns to
Education and the Characteristics of Public
Schools in the United States
David Card and Alan B. Krueger
Princetor1 Ur~iversity
This paper estimates the effects of school quality-measured by the
pupillteacher ratio, average term length, and relative teacher payon
the rate of return to education for men born between 1920 and
1949. Using earnings data from the 1980 census, we find that men
who were educated in states with higher-quality schools have a
higher return to additional years of schooling. Rates of return are
also higher for individuals from states with better-educated teachers
and with a higher fraction of female teachers. Holding constant
school quality measures, however, we find no evidence that parental
income or education affects average state-level rates of return.
Beginning with the highly influential Coleman report (Coleman et al.
1966), researchers have found little, if any, association between the
quality of schools and student achievement on standardized tests (see
Hanushek [I9861for a recent survey). On the basis of these findings,
it is now widely argued that increases in public school funding have
few important benefits for students. This conclusion, although politically
popular, contradicts two other strands of evidence on the quality
of schooling. On one hand, the small number of studies that have
directly correlated school quality and earnings have found a significantly
positive relationship between them (Welch 1966; Morgan and
We are grateful to Michael Boozer and Dean Hyslop for outstanding research assistance.
We have also benefited from the comments of Richard Freeman, Claudia Goldin,
Jean Grossman, James Heckman, Lawrence Katz, Robert Margo, Sherwin Rosen, an
anonymous referee, and seminar participants at several institutions. Financial support
from the Princeton Industrial Relations Section is gratefully acknowledged.
[Journal of Pohtccal Economy, 1992, vol. 100, no. I] 

O 1992 by The University of Chicago. All rights reserved. 0022-3808/92/0001-0003$01.50 

2 JOURNAL OF POLITICAL ECONOMY
Sirageldin 1968;Johnson and Stafford 1973; Wachtel 1976; Rizzuto
and Wachtel 1980). On the other hand, much of the gain in blackwhite
relative earnings over the past century has been attributed to
growth in the relative quality of black schooling (Welch 1967, 1973a,
19736; Freeman 1976; Smith and Welch 1989).
There are several possible explanations for the conflicting evidence.
Studies of earnings and school quality typically focus on the
correlation between school characteristics (suchas per capita expenditure)
and the average earnings of students educated in a school district.
One can easily argue that family background variables affect
both education expenditures and labor market earnings. In this case,
the correlation of school quality and earnings is potentially spurious.
From the opposite perspective, one can argue that test scores are an
imperfect measure of school performance. Indeed, although earnings
and test scores are correlated, they are by no means identical.'
Factors that affect subsequent labor market achievement may have a
much smaller impact on test scores. Furthermore, the relation between
school quality and test scores at the eighth or twelfth grade
fails to capture any effects of school quality on subsequent learning.
This paper presents an extensive analysis of the relation between
earnings and school quality for cohorts of men born between 1920
and 1949. We use the relatively large samples available from the 1980
census to estimate rates of return to education by state of birth and
cohort. We then relate rates of return to schooling to objective measures
of school quality, including pupillteacher ratios, relative wages
of teachers, and the length of the school term.2
Our procedures overcome at least some of the objections to earlier
studies of earnings and school quality. First, our statistical models
include unrestricted state of birth effects and therefore control for
any differences in the mean earnings of men born in different states.
To the extent that differences in family characteristics raise or lower
earnings for all levels of schooling attainment, our estimated rates of
return are purged of any effects of differential family background.
Second, we control for systematic differences in the returns to education
associated with an individual's current region of residence. We
thereby eliminate relative supply or demand effects that raise or
lower the returns to education in different parts of the country. Finally,
in much of our analysis we incorporate permanent state-specific
For example, the addition of test score information to the earnings models reported
by Griliches and Mason (1972,table 3) improves the explanatory power of their models
by less than one-half of a percentage point.
Our approach is conceptually similar to that of Behrman and Birdsall (1983), who
relate the returns to schooling among young Brazilian men to the average years of
education of teachers in each individual's region of residence.
3RETURNS TO EDUCATION
effects in the return to education and use only the within-state variation
among consecutive cohorts to identify the effects of school quality
on the returns to education.
Our results indicate that there is substantial variation in the rate of
return to education across individuals born in different states and at
different times. Much of this variation is associated with differences
in the quality of schooling. We find that rates of return are higher
for individuals who attended schools with lower pupillteacher ratios
and higher relative teacher salaries. For example, our estimates suggest
that a decrease in the pupillteacher ratio by five students is associated
with a 0.4-percentage-point increase in the rate of return to
schooling. Similarly, a 10 percent increase in teachers' pay is associated
with a 0.1-percentage-point increase in the rate of return to
schooling. We also find that returns are linked to higher education
among teachers. Controlling for measures of school quality, however,
we find no evidence that returns to education are related to the income
or schooling levels of the parents' generation.
Our main focus is on the relation between school quality and the
rate of return to education. Changes in the slope of the earningsschooling
relation, however, do not necessarily raise average earnings.
For example, the earnings gains of better-educated workers may
come at the expense of the less educated. On the other hand, changes
in the quality of schooling may affect the average level of education
as well as the marginal return to added years of schooling. To address
these issues we present some simple "reduced-form" evidence on the
relationship between school quality and the mean levels of education
and earnings. Controlling for any permanent differences across individuals
born in different states, we find significant positive effects of
school quality on both the average years of schooling and mean earnings
of students. The reduced-form results suggest that increases in
school quality affect subsequent earnings by increasing the number
of years of completed education and by increasing the return to each
year of schooling.
I. 	 An Empirical Framework for Modeling
Returns to Schooling
Our goal is to relate the returns to education earned by individuals
educated in different states to the characteristics of the public school
system during the time they attended school. To fix ideas it is useful
to assume that individuals attend school in their state of birth and
to ignore private schooling. (The effects of these simplifications are
explored below.) Let yii, represent the logarithm of weekly earnings
for individual i, born in statej in cohort c and currently living in state
4 JOURNAL OF POLITICAL ECONOMY
k of region r, and let Eqk,represent the years of education completed
by individual i. Suppose that earnings are determined by an equation
of the form
where 9, represents a (cohort-specific) fixed effect for each state of
birth, kkcrepresents a (cohort-specific)fixed effect for each state of
residence, Xgkcrepresents a set of measured covariates (years of labor
market experience, marital status, and an indicator for whether i lives
in a standard metropolitan statistical area [SMSA]), and eijk,represents
a stochastic error term. Equation (1) assumes a linear specification
of the return to education, consisting of two components: a cohort
and state of birth effect (y,,) and a cohort and region of residence
effect (P,).~ These components allow observed rates of return to
schooling to vary because of differences in the return to education
across different regional labor markets (i.e.,variation in p,,) and because
of differences in the rate of return to education earned by
individuals in a given state of birth and cohort group in any labor
market (i.e., variation in yt).
Notice that when we include interactions between state of birth
dummies and education and another set of interactions between region
of residence dummies and education, the state of birth-specific
contribution to the return to education is identified by individuals
who are educated in one state and move to another region. It is the
shift in the return to education attributable to schooling in a particular state
that we seek to explain by differences in school quality across states and over
tzme.
Specifically, we hypothesize that the state of birth components in
the return to education depend on the quality of the public schools,
and possibly on a set of state-specific constants:
where Q,, is a vector of measures of the quality of the education
system in statej during the time that cohort c attended school. In this
specification any permanent differences in the returns to education
arising, for example, from differences in the distributions of ability
across states are absorbed by the state of birth effects (a,) in (2).
Under these assumptions, the effects of a particular measure of
education quality can be obtained in one step by estimating a loglinear
earnings function that includes state of birth effects, state of
residence effects, interactions of region of residence with education,
We normalize the coefficients y,, and p,, by setting C,f,,p,, = 0, where f,, is the
fraction of cohort c living in one of the nine census regions.
5RETURNS TO EDUCATION
and interactions of education with state of birth effects and the quality
measures for statej and cohort c. However, we prefer to proceed in
two steps: first, estimating the average rate of return to education for
individuals born in cohort c in state j, controlling for state of birth,
state of residence, and any regional differences in the return to education;
and then using a second-step regression to relate the estimated
rates of return (by cohort and state of birth) to the quality variables.
The two-step procedure has several important advantages. In the
first place, it provides a convenient reduction of the data and allows
us to illustrate the diversity in the returns to education and their
relation to measures of school quality. A two-step procedure also
facilitates extremely general models of the earnings function (I),including
models with cohort-specific state of birth and state of residence
effects, and models with permanent state of birth effects in
the return to education. In addition, we can incorporate a simple
correction for the interstate mobility of children. A disadvantage of
the two-step procedure is that cohorts must be defined fairly broadly
to obtain reliable estimates of the state- and cohort-specific returns
to education. In the analysis below we use 10-year intervals of births.
This aggregation eliminates any within-cohort variation in school
quality or the returns to education and leads to some efficiency loss.
Since individuals are assigned the mean levels of school quality for
their state of birth and cohort, however, aggregation does not introduce
classical measurement error into the quality measures (see Griliches
1986, p. 1478).
A. Functional Form
The assumption of a linear relation between schooling and (log)earnings
is widely used in applied studies of earnings and is often found
to perform as well as or better than simple alternatives (e.g.,Heckman
and Polachek 1974).However, most studies pool samples of individuals
from different states and birth cohorts with no allowance for regional
or cohort differences in returns. It is conceivable that the log
earnings-schooling relation is approximately linear in pooled samples
but is nonlinear for particular subsamples. It is also conceivable that
changes in the quality of public schooling shift the returns to elementary
or secondary education more (or less)than the returns to college.
If so, then the specification of the return to education function should
allow for kinks at 12 years of education.
In an effort to obtain some simple evidence on these issues, we
estimated a series of unrestricted earnings-schooling models using
narrowly defined subsamples of individuals in the 1980census. These
models include a complete set of dummy variables for 0-20 years of
6 JOURNAL OF POLITICAL ECONOMY
a
0 2 4 6 8 10 12 14 16 18
Yeors of Comoleted Educotion
0 2 4 6 8 10 12 14 16 18 2o
Years of Completed Education
FIG. 1.-Wages vs. schooling, by cohort and state of birth: a, white men born in
Alabama or Georgia; b, white men born in California.
education, as well as controls for potential labor market experience,
marital status, state of residence, and residence in an SMSA.4Figure
1 graphs the estimated return to education relationships for six of the
subsamples: three cohorts of white men born in Alabama or Georgia
(1920-29, 1930-39, and 1940-49) and three cohorts of white men
born in California. Figure 2 graphs the estimated return to education
Specifically, the models include linear and quadratic terms in potential experience,
a dummy variable for being married with spouse present, a dummy variable for residence
in an SMSA, and unrestricted dummy variables for residence in each of the 50
states. Additionally, dummy variables indicating state of birth were included if the
sample combined observations from more than one state. The models are estimated
on subgroups of the sample described in App. B.
20
a
0 - 1 Std. Enor
A + 1 Std. Enor
0 2 1 8 10 32
r a a c0W.l.a -by
FIG. 2.-Return to single years of education: a, white men born 1920-29, nationwide;
b, white men born 1930-39, nationwide; c, white men born 1940-49, nationwide.
20
8 JOURNAL OF POLITICAL ECONOMY
relationships (together with their standard error bounds) for national
samples of white men in the same three cohorts.
The figures illustrate three general findings. First, for a particular
cohort and state of birth group, the earnings-education relation is
approximately log-linear for levels of education above a minimum
threshold. Although there is some evidence of a college graduation
effect, departures from log-linearity above the threshold level are
small. Second, the threshold varies widely across states and over time
within states. It is relatively low for older cohorts and for individuals
from states with lower average educational attainment. This phenomenon
is also evident in the national samples in figure 2: the threshold
is at approximately 2 years of education for men born between 1920
and 1929, at 3 years of education for those born during 1930-39,
and at 5 years for those born in 1940-49. Third, the rate of return
to education (for years of education above the threshold level) is
higher for later cohorts.
The positive correlation between the average educational attainment
of a state of birth and cohort group and the kink or threshold
point in their return to education function led us to investigate the
determinants of this threshold more carefully. For each of 13 larger
states (or pairs of contiguous states) and each of three 10-year birth
cohorts, we first estimated a nonparametric version of the return to
education function (using 20 unrestricted dummy variables) and
found the approximate threshold point in the return to education
relation. We then compared this point to various percentiles of the
education distribution in each state-cohort group. This comparison
led us to a simple empirical relation: across different cohorts and
states of birth and different race groups, the threshold point corresponds
approximately to the grade level attained by the second percentile
of the education distribution of workers. For example, a simple
linear regression of the estimated threshold point on the grade
attained by the second percentile of the education distribution has an
estimated coefficient of 0.88 with an estimated standard error of 0.13
and an R' of .57.'
Given the pattern of the nonparametric estimates of the return to
education function for the larger states, in the remainder of the paper
we concentrate on measuring the return to education for years of
schooling above the second percentile of the education distribution
of an individual's state of birth and cohort. Specifically, we replace
Further details of our investigation, including tabulations of the estimated threshold
points and education percentiles, are available on request. The 13 state groups
include 11 individual states (California, New York, Ohio, Texas, Pennsylvania, Illinois,
Michigan, New Jersey, Massachusetts, North Carolina, and Virginia) and two pairs of
states (AlabamaiGeorgia and KentuckyiTennessee).
9RETURNS TO EDUCATION
an individual's completed education by the following linear spline:
min{E+ - T,,, 0), where T,, is the second percentile of the education
distribution for men born in state j in cohort c. We present some
evidence on the effects of ignoring the threshold in Section IIIE.
Since only 2 percent of those in the sample have levels of education
below the threshold point, the estimated rates of return to years of
education above the threshold turn out to be quite similar to the
estimated returns from a conventional log-linear earnings-schooling
model.
11. Measures of the Quality of Public Schooling
Since the late nineteenth century the U.S. Office of Education has
published a regular summary of the characteristics of the public
school systems in each state. These data are available on a semiannual
basis from 1918 to 1958 in the Biennial Survey of Education and annually
since 1960 in the Digest of Education Statistics. The Office of Education
tabulates the results of questionnaires sent to the state offices of
education inquiring about statewide enrollment, revenues, number
of teaching positions, length of school term, average teacher salaries,
and other variables.
The Biennial Survey of Education is a rich source of information
on the average characteristics of public schools in different states at
different points in time. From the available data we have assembled
information on three main characteristics: the ratio of enrolled students
to instructional staff in the state (pupillteacher ratio), the average
length of the school term (term length), and average annual
teacher salaries (see App. A for more information). We hypothesize
that increases in term length increase the amount of material covered
in a school year and thereby increase the economic value of additional
years of schooling. We similarly hypothesize that reductions in the
pupillteacher ratio improve the quality of classroom instruction and
lead to higher returns for each year of completed education. Finally,
we hypothesize that higher teacher salaries enable schools to attract
and retain more qualified and highly motivated teachers, leading to
improved classroom instruction and higher returns to education.
Several previous authors, including Morgan and Sirageldin (1968),
Johnson and Stafford (1973),Wachte1(1976),and Rizzuto and Wachtel
(1980), have used total expenditures per pupil as an index of
school quality. We suspect that the quality of education is more directly
linked to indexes of pupillteacher ratios and teacher salaries
than to total expenditures per pupil, and indeed this is suggested by
the results in Welch (1966).Nevertheless, roughly 60 percent of total
education expenditures go for instructional salaries. Since the per
10 JOURNAL OF POLITICAL ECONOMY
capita expenditure on instructional salaries is simply the ratio of the
average teacher wage to the pupillteacher ratio, differences in
teacher salaries and pupillteacher ratios account for a majority of the
variation in total expenditures per pupil.
Given geographic differences in the cost of living and in the level
of alternative wages available to potential teachers, it seems unlikely
that the level of teacher wages is an adequate index of teacher quality
in different states. We have therefore normalized teacher wages in
each state by the level of average wages in the state. We use average
weekly earnings of employees covered by the social security system
to adjust wage rates from 1940 onward. Prior to 1940, we use a
regional wage rate for workers on federal construction projects to
normalize average teacher salaries. The comparison wage series are
index-linked between 1940 and 1944 as described in Appendix A. In
view of the changing coverage of the social security wage index and
given the necessity of index-linking disparate wage series, we have
chosen to remove the trend in average relative teacher salaries during
our sample period. Specifically, we divide the relative teacher wage
in each state by the national average of this ratio in the same year.
This procedure eliminates any time-series variability in the average
value of relative teacher salaries, while preserving the interstate variation
in relative teacher wages at a point in time.
A summary of these three measures of school quality is presented
in table 1. We report statewide averages of the quality measures for
three cohorts of students: those born between 1920 and 1929, those
born between 1930 and 1939, and those born between 1940 and
1949. The averages for a cohort assume that each person attends
public school for 12 years and that the number of individuals born
per year in any cohort is constant. By assuming 12years of education,
we measure the potential quality of the schooling available to individuals
in a particular cohort and abstract from the possible endogeneity
of school quality and average schooling. Nevertheless, when the averages
are computed using individual-specific years of education for
the men in each cohort, the quality measures are virtually identical.
The data in table 1show substantial variation in education "quality"
across states. For the 1920-29 birth cohort, pupillteacher ratios range
from 20 (in the Dakotas, Montana, and Wyoming) to over 35 (in
Arkansas, Mississippi, and North Carolina). Average term lengths for
this cohort range from 139 days (in Mississippi) to over 180 days (in
the middle-Atlantic states). Similarly, relative teacher wages range
from 0.75 or lower (in many southern states) to over 1.25 (in many
northeastern states). As one might expect, the interstate variation in
our measures of education quality is much lower for the later cohorts.
1 1RETURNS TO EDUCATION
This is particularly true of the term length variable, which falls in a
narrow range for individuals born in the latest cohort.
The trends in school quality during our sample period vary widely
across states. Most of the southern states show uniform improvements
in quality. Other states, such as Michigan and Missouri, show almost
no change in the quality variables, and some states show declines in
certain dimensions of quality. The differences are most pronounced
in relative teacher wages. For example, teachers in Alabama and
Georgia show strong relative wage gains, and teachers in Massachusetts,
New Jersey, and New York show relative wage losses during
our sample period.
111.	 Returns to Education by Cohort and State of
Birth for White Men
In this section we present estimates of the average rates of return to
education for white men born in the 48 mainland states and the
District of Columbia between 1920 and 1949. We divide the samples
of men born in these states into three 10-yearbirth cohorts and obtain
estimated rates of return for 147 separate state and cohort groups.
We then perform a second-step analysis of the relation between rates
of return to schooling and the school quality measures in table 1. We
explore the effects of some other characteristics of the school systems
in each state and contrast these to the effects of some measures of
family background. We also discuss the results of a simple correction
for the measurement error induced by the interstate mobility of children.
Finally, we present a brief analysis of the rates of return to
education obtained from models that ignore the minimum thresholds
highlighted in figures 1 and 2.
A. Rates of Return to Education by State and Cohort
Our estimated rates of return to education are obtained from three
cohort-specific regressions fitted to individual data on log weekly
earnings for 1979. The data samples are taken from the 5 percent
Public-Use A Sample of the 1980 census (see App. B for details).
Following the specification of equation (I), the explanatory variables
in each regression include a set of 50 indicator variables for an individual's
current state of residence, a set of 48 indicator variables for
an individual's state of birth, and controls for potential experience
and its square, marital status, and residence within an SMSA. To
control for differences in the rate of return to education across
different labor markets in the country, the models also include interactions
between nine current region of residence dummies and com-
----
AVERAGES QUALITY FOR BORN 1920-29, 1930-39, 1940-49 (Black and White Students Combined)OF SCHOOL VARIABLES COHORTS IN AND
Alabama
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
New Hampshire
--.- --- .PUPILITEACHERRATIO
TERMLENGTH(Days) RELATIVETEACHERWAGE
1920-29 1930-39 1940-49 1920-29 1930-39 1940-49 1920-29 1930-39 1940-49
New Jersey 

New Mexico 

New York 

North Carolina 

North Dakota 

Ohio 

Oklahoma 

Oregon 

Pennsylvania 

Rhode Island 

South Carolina 

South Dakota 

Tennessee 

Texas 

Utah 

Vermont 

Virginia

,-	 Washington
West Virginia
Wisconsin
Wyoming
District of Columbia
NOTE.-Cohort averages are formed under the assumption of 12 years of elementary and secondary education. See App. A for sources
'4 JOURNAL OF POLITICAL ECONOMY
pleted ed~cation.~Finally, the models include state of birth-specific
interactions with individual education, where, as described in Section
I, individual education is modeled as the maximum of zero and years
of education over and above the second percentile of the education
distribution in an individual's state of birth and cohort. These interactions
are interpreted as estimates of the rate of return to education
for individuals from a particular cohort and state.
The estimated rates of return, together with their estimated sampling
errors, are presented in table 2. The lower panel of the table
reports the weighted means and standard deviations of the estimated
returns across the 49 states, together with their correlations with the
three cohort-specific quality measures. Despite the fact that the estimates
are obtained from highly parameterized models (there are 158
explanatory variables in the regression equation for each cohort), the
estimates are relatively precise, with standard errors in the range of
0.1-0.3 percent for most states. As the patterns in figures 1 and 2
suggest, average rates of return to education are much lower for
older workers: 5.1 percent per year for the oldest cohort (age 50-59
in 1979) versus 7.4 percent for the youngest cohort (age 30-39 in
1979). The interstate dispersion in returns (corrected for sampling
error) shows the opposite trend, being largest for the oldest cohort
and smallest for the youngest.
The correlations in the lower panel of table 2 suggest that returns
to education are significantly related to all three measures of school
quality. The connection is illustrated in figure 3, which plots the rate
of return for each state of birth (for the 1920-29 cohort) against the
relative teacher wage in the state. We have divided the states into
three groups, on the basis of the pupillteacher ratio, and denoted
states in each group by a different symbol. The pattern of the plot
suggests that returns are higher among states with lower pupil1
teacher ratios when teacher wages are controlled for, and higher
among states with higher relative teacher pay when the pupillteacher
ratio is controlled for.
A second illustration of the relation between school quality and
returns to education is provided by figure 4, which plots the intrastate
change in the return to education between the 1920-29 and the
1940-49 cohorts against the corresponding change in the cohort average
pupillteacher ratio. As implied by the sampling errors in table 2,
the intercohort changes in the returns to education are imprecisely
The estimated coefficients suggest that rates of return to education vary across
regions of residence by as much as 2 percent per year of education. Returns are
lowest in the Mountain and Pacific regions and highest in the East-South Central and
West-South Central regions. These patterns are consistent with those reported by
Chiswick (1974) in an earlier analysis of the regional variation in returns to education.
Alabama
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
TABLE 2 (Continued)
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
District of Columbia
Mean over all states
Standard deviation
Correlation with:
Pupillteacher ratio
Term length
Relative teacher wage
NOTE.--Column entries are estimated rates of return to education, based on samples in the 1980 census. The
estimated standard deviation of returns is adjusted for the expected contribution of sampling variability.Standard
errors are in parentheses.
16
0.02 1 I I I I I I I I I I I 

I 

0.6 	 0.8 1 1.2 1.4 1.6 1.8
Relative Teacher Wage
FIG. 3.-Relative teacher wage vs. return to school, with high, low, and medium
pupillteacher ratio indicated.
I 

I I I I I 

Change I n Pupll/Teacher Ratlo 

-8 -6 -4 -2 0 2 

FIG.4.-Change in returns vs. change in pupillteacher ratio, 1940s cohort minus
1920s cohort.
18 JOURNAL OF POLITICAL ECONOMY
estimated for some of the smaller states. We have therefore plotted
each state observation with a circle that is proportional to the inverse
sampling variance of the estimated change in returns. We have also
plotted the weighted-least-squares regression line (weighted by the
inverse sampling variance of the change in the estimated return) relating
the intrastate changes in returns to the corresponding changes
in the pupillteacher ratio. The figure indicates that rates of return
to education rose more quickly between the 1920-29 cohort and the
1940-49 cohort in states that experienced a larger reduction in pupil1
teacher ratios.
B. Rates of Return and the Quality of Schools
Table 3 presents estimation results for a series of regression models
fitted to the estimated rates of return presented in table 2. The models
are estimated by weighted least squares, using as weights the inverse
sampling variances of the estimated return^.^ The first set of
models, in columns 1-5, excludes any state-specificinformation other
than the measured quality variables; the second set, in columns 6- 11,
includes a set of 49 unrestricted state effects. These models therefore
rely on the within-state covariation between rates of return to education
and measured school quality to estimate the effect of the quality
variables.
The model in column 1 includes only dummy variables for the
second and third cohorts. These two variables alone explain 71 percent
of the (weighted) variance in the returns to education.' The
estimated coefficients show significantly higher returns for the later
cohorts: approximately 1.2 percent per decade. The three quality
variables are introduced individually into the regression model in
columns 2-4 andjointly in column 5. Individually, all three variables
are strongly correlated with returns to education, with t-statistics of
-3.3, 7.0, and 7.2 for the pupillteacher ratio, term length, and the
relative teacher wage, respectively. When the three quality variables
are enteredjointly, however, the effects of term length and the pupil1
An optimal second-step estimation scheme should take account of the covariances
between the estimated returns for different states. We have experimented with such
a procedure and found few differences from the simpler weighting scheme described
in the text. The reason for this is that the estimated returns by state of birth are
"almost" independent. The only source of covariation between them arises from the
fact that the same regression parameters are used to adjust for other control variables
in the first-stage regressions.
The R' coefficients in row 6 can be used to form x2test statistics for the hypothesis
that the included explanatory variables explain all the nonsampling variation in the
state and cohort returns. The X2 test statistic for the model in col. 1 is 1,164, with 144
degrees of freedom. On the other hand, the test statistic for the model in col. 10 is
165.5, with 93 degrees of freedom.
20 JOURNAL OF POLITICAL ECONOMY
teacher ratio are smaller and less precisely determined, presumably
as a result of the multicollinearity among the quality variables.
The models with state effects lead to conclusions broadly similar to
those of the models in columns 1-5, although the estimated coefficient
of the pupillteacher ratio is larger in absolute value when state
effects are included, and the estimated coefficients of the other two
quality measures are smaller. When the three quality variables are
included jointly (in col. lo), the estimated coefficient of the term
length variable falls to zero. Evidently, only two dimensions of school
quality can be identified in the data once state-specific effects are
i n c l ~ d e d . ~
The magnitudes of the estimated school quality coefficients suggest
a quantitatively important effect of school quality on the return to
education. For example, the estimates in column 10 show that a decrease
in the pupillteacher ratio by 10 students is associated with a
0.9 percent increase in the return to years of schooling above the
threshold level. If the threshold is 8 years of schooling (and is unaffected
by the change in school quality), this reduction in the pupil1
teacher ratio will raise the earnings of high school graduates by 3.6
percent. A 30 percent increase in relative teacher salaries is similarly
predicted to raise the rate of return to education by roughly 0.3
percent, and the earnings of high school graduates by 1.2 percent
(again, if the threshold level of education is constant at 8 years).
Despite the joint significance of the quality variables, they explain
relatively little of the intercohort trend in returns to education. When
the models in columns 5 and 1are compared, for example, the quality
measures explain only 12 percent of the increased return to education
between the earliest and the middle cohorts, and 6 percent of
the increase between the middle and latest cohorts. In the models
with state effects, the quality variables explain more of the intercohort
trend in returns to education: about 20 percent of the increase between
the 1920-29 cohort and the 1930-39 cohort, and 10 percent
of the increase between the 1930-39 and 1940-49 cohort. Nevertheless,
the cohort dummies are highly significant, and their omission
leads to a substantial overstatement of the quality effects. For example,
when the cohort effects are excluded in column 11, the coefficient
of the pupillteacher variable rises to - 50.1.
One possible difficulty with the term length variable is that teachers would prefer
a shorter term. This suggests that teacher quality may decline with term length, with
teacher wages held constant. We have reestimated the models in table 3 using the
teacher wage expressed in terms of days worked per year (using term length as days
worked). This change has the effect of raising the coefficient on the term length
variable by about 0.5, with little or no effect on the other coefficients in the model.
Even with this adjustment, the term length effects in col. 10are insignificantly different
from zero.
RETURNS TO EDUCATION 2 1
The higher average rates of return for younger workers do not
necessarily reflect true cohort effects. If there is any relation between
age and the return to education, the estimated cohort dummies in
table 3 confound cohort and age effects. To provide some crude
evidence on the relative importance of age and cohort effects, we
used the 1970 census to estimate rates of return to education for our
two older cohorts 10 years earlier. The following table shows the
estimated rates of return for the two cohorts in 1970 and 1980:
If we assume that the 1930-39 cohort had the same (or only slightly
better) quality schooling as the earlier cohort, these data indicate an
overall decline in the average return to education between 1970 and
1980 of at least 0.50 percent (when the 6.73 percent return for the
1920-29 cohort in 1970 is compared to the 6.25 percent return far
the 1930-39 cohort in 1980).With this estimate of the relative period
effect, the implied age effects indicate a 1.2-percentage-point decline
in the return to education between the ages of 40-49 and 50-59
and a 0.7-percentage-point decline between ages 30-39 and 40-49.
Together with our finding that school quality variables explain relatively
little of the cohort effects, these results suggest that most of the
higher return to education observed for younger workers in the 1980
cross section is attributable to age effects.
Finally, we note that the estimated state effects in table 3 are highly
significant. For example, a comparison of the models in columns 5
and 10 leads to a X 2 statistic of 642 for the joint significance of the
state effects (with 48 degrees of freedom). This suggests that some
important state-specific determinants of the return to education are
missing from our analysis. Examination of the estimated state effects
indicates that returns to education are relatively low (when measured
quality is controlled for) for men born in the South and in the North
CentralINorthwest regions and relatively high in the Midwest and
Northeast.
A finding of relatively low returns for white men from the southern
states may be somewhat surprising, given that the quality measures
in our analysis refer to the entire school system in each state. States
that operated segregated school systems before 1954 typically had
lower pupillteacher ratios, longer term lengths, and higher teacher
salaries in white schools than in black schools (see Card and Krueger
2 2 JOURNAL OF POLITICAL ECONOMY
1992). As a result, average quality measures based on total student
enrollments understate the quality of the white schools in these states.
Nevertheless, when a dummy variable for the segregated states is
added to the model in column 5 of table 3, it has an estimated coefficient
of -0.41 (with a standard error of 0.13). Furthermore, when
the segregated states are stratified into those with 20 percent or
higher black enrollment and those with less than 20 percent black
enrollment, the returns to education are even lower in the states with
higher black enrollments (0.42 percent vs. 0.31 percent lower in states
with less than 20 percent black enrollment). These findings are inconsistent
with a simple mismeasurement hypothesis for the quality of
white schools in the South. Rather, they suggest that other dimensions
of quality were significantly lower in the South or that other characteristics
of the southern states affect the returns to education.
C. Other Characteristics of Schools and States
We have analyzed the effects of several other school and state-level
characteristics on the returns to education. Table 4 summarizes our
main findings. In each case we have included the three basic measures
of school quality as well as state-specific fixed effects. To preview the
results, we find that the estimated coefficients of the school quality
variables are largely unaffected by the addition of controls for other
characteristics, including characteristics of teachers, average income
in the state, educational attainment, and characteristics of private
schools.
Columns 1-3 of table 4 address the effect of family background
characteristics on the return to education. A number of previous
studies (includingColeman et al. [1966])have found a strong association
between family background factors, such as parental education
and income, and student performance on standardized tests. If these
family background characteristics are correlated with school quality
and if these characteristics change substantially over time within states
(SO they are not absorbed by the state fixed effects), our estimates of
the effect of school quality may be confounded by the effect of family
background variables.
Although the census lacks direct information on the education of
individuals' parents, we can at least partially control for differences
in parental education by including the median level of education
among adults who lived in the state when the men in our sample
attended school (row 4). Likewise, we include the log of real per
capita income in the state at the time the cohorts in our sample entered
school (row 5).1°Regardless of whether they are included sepa'O
These and subsequent covariates are described in App. A.
ADDITIONAL OF THE RETURN WHITEMENDETERMINANTS TO EDUCATION:
(Dependent Variable: Percentage Return to Education, Fixed-Effects Estimates)
-
1. Pupillteacher ratio ( t 100)
2. Term length (hundreds of 

days) 

3. Relative teacher wage
4. 	Median education of parents' 

generation 

5. 	Log real per capita income of 

parents' generation 

6. Fraction male teachers
7. 	Mean years of education of 

teachers 

8. 	Mean years of experience of 

teachers 

9. 	Fraction high school grads in 

cohort 

10. Fraction college grads in cohort
11. Fraction of enrollment in private
schools
12. Weighted gap between pupil1
teacher ratio in Catholic and
public schools
13. Dummy for born 1930-39
14. Dummy for born 1940-49
NOTE-See note to table 3 All equations ~nclude48 slate effects Standard errors are m parentheses
JOURNAL OF POLITICAL ECONOMY*4
rately or jointly, each of these variables has a relatively small and
statistically insignificant effect on the return to education. Moreover,
the estimated effects of the three main school quality variables (pupil1
teacher ratio, term length, and relative teacher wage) are unaffected
by the inclusion of these family background variables.
Teacher Characteristics
Columns 4-6 explore the role of teacher characteristics on the returns
to schooling. The fraction of male teachers is included because,
holding constant the level of teacher salaries, one might expect the
quality of the teaching staff to vary with the fraction of male teachers.
For example, assuming that female teachers were paid less than otherwise
identical males during the period 1926-66, one can view the
percentage of male teachers as a proxy for lower-quality teachers.
Alternatively, one can view the fraction of male teachers as an indicator
of higher nonwage compensation or better working conditions
within the schools, which would be likely to attract relatively more
men into the teaching profession, with relative wages held constant.
The results indicate that an increase in the fraction of male teachers
in the state has a substantial negative impact on students' return to
education. An increase in the fraction of male teachers from 19 to
42 percent, which is the range observed across states in 1966,is associated
with an 0.8-percentage-point reduction in the return to years of
education above the threshold. Whether the fraction of male teachers
influences the return to education because males are less effective
teachers, or through some other channel, is difficult to ascertain.
Columns 5 and 6 add the mean years of education of teachers
in the state to the regression equation. The estimated coefficient
of mean teacher education is positive and statistically significant,
whereas the estimated effect of teachers' experience is negligible. Notice
that the pupillteacher ratio and relative teacher wage continue
to be significant determinants of the return to education when these
teacher quality variables are included; in fact, their estimated coefficients
are hardly affected by the addition of the teacher quality variables.
Furthermore, the addition of controls for the average education
and experience of teachers hardly changes the estimated
coefficient of the fraction of male teachers.
Educational Distribution
Estimates of the high school completion rate and the college completion
rate for each state of birth and cohort group are included in the
models in columns 8 and 9. These variables are added to control for
25RETURNS TO EDUCATION
biases that may arise as more schooling is acquired by a higher fraction
of a given cohort. For example, suppose that more schools are
built in a state, leading to a decrease in the travel time for students
and a reduction in the pupillteacher ratio. Suppose further that individuals
differ in their expected returns to education and that as more
schools are built some students with lower expected returns to education
stay in school longer. In this case, one might expect increases in
school quality to be correlated with lower returns to education, reflecting
a negative correlation between the average rate of return to
education and the fraction of individuals with higher education. In
our data there is a strong positive correlation (both in a cross section
and within particular states over time) between average educational
attainment and measures of education quality.11Therefore, if rates
of return vary systematically across the population and if individuals
with higher expected returns choose more schooling, there is a possible
downward bias in our estimates of the effect of schooling quality
on returns to education. This can be controlled in part by including
measures of the fraction of individuals at higher education levels in
each cohort.
Neither the high school graduation rate nor the college graduation
rate has a statistically significant effect on the return to education.
Moreover, the high school graduation rate has a negative coefficient,
and the college graduation rate has a small, positive coefficient. These
results provide no evidence that students sort themselves into different
education levels on the basis of different expected returns to
schooling.
We have also explored the effect of the dispersion in educational
attainment in a state on the return to education. As discussed further
below, improvements in school quality are associated with lower dispersion
in the distribution of education. Some models of ability bias
in the estimated return to schooling predict that a reduction in the
dispersion in the educational distribution is associated with higher
returns to education. We find little support for this hypothesis in our
data. For example, the standard deviation of years of education has
a small and statistically insignificant (t = -0.59) negative effect if it
is added to the model in column 10 of table 3. The inclusion of this
variable hardly changes the impact of the school quality variables.
Private Schools
Our measures of school quality are based on the characteristics of the
public school system in each state. Not all students attend public
" For example, across our three cohorts and 49 states of birth, the correlation between
the fraction who completed high school and the pupillteacher ratio is - .71.
26 JOURNAL OF POLITICAL ECONOMY
schools, however. During the period 1920-60, the fraction of students
enrolled in private schools grew from 7.5 percent to 13.6 percent.
The fraction of private school enrollment also varies across
states: in 1938, for example, the share of private enrollments ranged
from less than 2 percent in many southern states to over 20 percent in
New Hampshire and Rhode Island. The presence of private schools
introduces two potential sources of unobserved variation in school
quality. First, private schools may be more or less effective than public
schools.12Second, private schools may have different staffing levels,
teacher salaries, and term lengths than the public schools. In an effort
to examine these issues, we collected information on private school
enrollments and pupillteacher ratios by state and cohort. Our information
on the pupillteacher ratio in private schoolsis limited to Catholic
schools, but 90 percent of private-school students attended Catholic
schools during our sample period.
Evidence on the effect of accounting for private school enrollment
is presented in columns 9 and 10 of table 4. In column 9 we include
the fraction of students enrolled in all private schools as an additional
explanatory variable for the rate of return to education. When pupil1
teacher ratios, term length, and relative teacher salaries in the public
schools are controlled for, the coefficient of the private school enrollment
variable is numerically small and statistically insignificant. These
results suggest that increases in private school enrollment do not by
themselves affect returns to education.
The specification in column 10 is an attempt to measure the biases
created by using data for the public schools to proxy pupillteacher
ratios for the state as a whole. The average pupillteacher ratio in a
state is a weighted average of ratios in the public and private systems.
Hence, the measurement error in using the public school ratio as a
proxy for the overall state average is the product of the fraction of
enrollment in private schools and the gap between the private and
public school ratios.13An estimate of this error component is included
in the model in column 10. As predicted by a naive model of attenuation
bias, the addition of this control variable raises the estimated
coefficient of the pupillteacher ratio. Furthermore, the estimated coefficient
of the error component is (roughly) equal to the estimated
Coleman, Hoffer, and Kilgore (1982) present data on standardized test scores that
indicate higher achievement levels among students in private (mainlyCatholic) schools.
The interpretation of these data is an issue of some dispute: see Goldberger and Cain
(1982), Murnane (1984), and San Segundo (1988).
l3 Let p represent the pupillteacher ratio for all students, pl the ratio in the public
school system,p2 the ratio in the private school system,andf the fraction of enrollment
in private schools. Then p = (1 - f ) .pl + f .p2. Hence p - pi = f . (p2 - PI).
RETURNS TO EDUCATION 2 7
coefficient of the pupillteacher ratio in the public schools. Nevertheless,
the relatively modest changes in the coefficients of the public
school quality variables suggest that the biases introduced by measuring
only the quality of public schools are small.
Up to this point we have proceeded by considering individually
extensions to the basic quality variables (family background, teacher
quality, educational attainment, and private schools). In column 1 1
we include several of the additional variablesjointly. With the exception
of the term length variable, the school quality variables have
their expected signs and are statistically significant. In contrast, the
variables measuring family background characteristics, student educational
achievement, and private school attendance generally have
insignificant and small effects. The data seem to accord a greater role
to school quality than to other variables in determining the return to
education.
Evidence for Black and White Men Born
in the South
Despite the limited evidence of family background effects in the return
to education, the wide variation in school quality for men from
different states and cohorts presumably reflects differences in incomes
and tastes for education over time and across states. To the
extent that unmeasured differences in family incomes and tastes affect
individuals' returns to education, the estimated school quality effects
in tables 3 and 4 may be overstated. A potentially better test of the
effects of school quality is based on the earnings experiences of
blacks. The rapid improvements in school quality that occurred in
the black schools of the segregated southern states between 1920 and
1960 provide an arguably exogenous experiment for studying the
effects of school quality.
In a related paper (Card and Krueger 1992), we have examined
the effects of school quality on the returns to education for southernborn
black and white men who worked in northern cities in 1960,
1970, or 1980. Our results are qualitatively and quantitatively similar
to those in tables 3 and 4. For example, the estimated coefficient of
the pupillteacher ratio in a model similar to the one in column 7 of
table 3 is - 5.9, with a standard error of 2.39. The estimated coefficients
of term length and teacher wages are also similar to those in
table 3. We believe that our findings for southern-born black and
white men provide additional support for a causal interpretation of
the school quality effects in tables 3 and 4.
28 JOURNAL OF POLITICAL ECONOMY
D. Adjustments for Mobility of Preschool and
School-Age Children
In our analysis so far, we have implicitly assumed that an individual
attends public school in his state of birth. Interstate mobility of preschool
and school-age children introduces a problem similar to measurement
error in the interpretation of the returns to education for
individuals born in a particular state. To proceed, it is useful to concentrate
on a single cohort and to assume that individuals are educated
in only one state. Let yj represent the estimated rate of return
to education for individuals born in state j (in a particular cohort),
and let y t represent the rate of return for individuals educated in state
i. Finally, let pij represent the probability that an individual attended
school in state i, given that he was born in statej. Then
Let P represent a matrix whose i,j element is p,,. Then the vector of
coefficients y is related to the vector of true returns y* by y = Py*.
Given estimates of y and P,one can obtain an estimate of y* by y*
= P-'y.Notice that if individuals are always educated in their state
of birth, then P is an identity matrix and y* = y.
We obtained an estimate of the matrix P by cross-tabulating state
of birth with current state of residence for white children aged 6-12
(both male and female) in the Public-Use Sample of the 1940 census.
For most states, the probability that a 6-12-year-old is living in his
or her state of birth is around 90 percent, although it is lower for
children born in the District of Columbia (62 percent). In principle,
this estimate of the matrix P is appropriate only for children born
between 1928 and 1934, and only for those with 1-6 years of schooling.
Nonetheless, we used this transition matrix to transform the estimated
rates of return for each of the three birth cohorts into estimates
of the rate of return for attending school in different states.
We then reestimated the regression models in table 3, using the corrected
rates of return as dependent variables.14
The mobility-adjusted results are qualitatively similar to those in
table 3. The correction has the effect of expanding the standard
deviation of the estimated returns by 19 percent for the 1920-29
birth cohort, 11 percent for the 1930-39 cohort, and 8 percent for
the 1940-49 cohort. As a consequence, the magnitudes of the estimated
coefficients for the school quality variables are typically 5-15
l4 We also used the estimated P matrix to obtain estimated sampling variances for
the corrected returns. These sampling variances were used to weight the regressions.
A table containing these results is available on request.
29RETURNS TO EDUCATION
percent larger than in the uncorrected model, although the associated
standard errors rise by roughly the same proportion. On balance, the
results suggest that adjustments for interstate mobility have a relatively
minor impact on the qualitative and quantitative conclusions in
table 3. This reflects the relatively low mobility rates of preschool and
school-age children and the absence of a strong connection between
interstate mobility and the geographic pattern of the measured quality
of education.
E. Log-Linear SpeciJicatzon
The preceding estimates examine the relationship between school
quality and the return to education for years of schooling beyond the
level attained by the second percentile of the education distribution.
This specification of the education variable was selected for its ability
to capture the nonlinear return structure illustrated in figures 1 and
2. Compared to a conventional log-linear specification, the linearspline
specification provides a slightly better fit to the micro data: the
difference in maximized log likelihoods between the spline model
and a conventional linear return to education model is 99.0 for the
1920-29 cohort, 150.0 for the 1930-39 cohort, and 315.1 for the
1940-49 cohort.
Nevertheless, a log-linear specification is widely used in the literature,
and it is useful to check the sensitivity of our estimates to the
functional form assumptions. Consequently, we have reestimated the
returns to education by state and cohort using a linear specification
for education. The two sets of returns have very similar weighted
means (6.42 for the spline estimates vs. 6.45 for the linear estimates)
and are highly correlated (thecorrelation coefficient across 147observations
is .997). The close correspondence between the two sets of
estimated returns is understandable, given that the spline specification
differs from the linear specification for only 2 percent of the
sample.
Table 5 presents estimates of the relation between our school quality
measures and the returns to education derived from a log-linear
specification. Except for the choice of the dependent variable, the
models are the same as in table 3. The coefficient estimates in table
5 are 10-20 percent smaller than those in table 3. Regardless of
specification, however, the school quality variables have statistically
significant and sizable effects on the return to education. These results
suggest that the relationship between school quality and the
return to education is not particularly sensitive to the specification
used to estimate the return to education.
Ist.ZX
SLC
5"
RETURNS TO EDUCATION 	 3l
IV. 	 The Effects of School Quality on Education
and Earnings
Our analysis of the relation between school quality and the return to
education has the advantage of controlling for unobserved differences
across cohort and state of birth groups. Any background factors
(such as family income) that raise the earnings of individuals from a
particular group are absorbed by the cohort-specific state of birth
effects included in our first-stage equation. A disadvantage of concentrating
on the return to education is that changes in school quality
may simply widen the distribution of earnings without raising average
incomes. It is even conceivable that changes in school quality alter
the distribution of schooling, and the slope of the earnings-schooling
relation, with no effect on the distribution of earnings.
To explore these issues, we proceed in two steps. First we analyze
the influence of changes in school quality on the location and shape
of the earnings-schooling relationship. This requires that we analyze
the effect of school quality on the educational distribution (in particular,
on the level of education attained by the second percentile of the
distribution) and on the intercepts of the schooling-earnings relation.
Second, we present some simple reduced-form evidence on the connection
between school quality and the levels of education and earnings.
In contrast to our analysis of the returns to education, the effects
of school quality on the education distribution and on the levels of
earnings cannot be identified in models that include unrestricted
cohort-specific state of birth effects. This limitation should be kept in
mind in interpreting the results.
A. 	 Location and Shape of the Earnings-Education
Relationship
Figure 5a illustrates the effect of a reduction in the pupillteacher
ratio by 10 students on the earnings-schooling relationship, under
the assumption that the educational distribution is unaffected by a
reduction in class size. The parameters for the figure are obtained
from column 10 of table 3. This figure is a simplification of the actual
impact of a reduction in class size on earnings for two reasons. First,
the level of education achieved by the second percentile of the education
distribution (the kink point) increases as class size declines. An
auxiliary regression of the threshold level of education (the second
percentile) on state effects, cohort effects, and the three quality measures
indicates that a 10-student decline in the pupillteacher ratio is
associated with an increase in the kink point of 1.13years (t = 2.08).
Second, a decrease in the pupillteacher ratio is associated with a small
JOURNAL OF POLITICAL ECONOMY
..-
base
1,P
0.8...
reduce ratio by 10
1
8
::::0.2-

0-

0 4 8 12 16 20 

Years of Education
b 

Years of Education
FIG.5.-Effect of reducing pupillteacher ratio by 10:a, ignoring effects on intercept
and education distribution;b, including effects on intercept and education distribution.
(albeit statistically insignificant) upward shift in the intercepts of the
earnings-schooling relation. A regression of the state of birth-specific
intercepts of the earnings-schooling relation on state of birth effects,
cohort effects, and the three school quality variables yields coefficients
of -0.25 (t = 0.68) for the pupillteacher ratio (divided by loo),
-0.17 (t = - 1.43) for the term length variable (divided by loo),and
0.11 (t = 1.88) for the relative teacher wage. The quality variables
are jointly insignificant (p-value = .31) in this model.
Figure 56 illustrates the effect of a 10-student reduction in the
pupillteacher ratio including these additional effects. It is clear from
the figure that a decrease in the pupillteacher ratio rotates and shifts
out the earnings-schooling relationship, with a crossover point
around the twelfth or thirteenth grade level. (In fact, when we narrow
the sample to individuals who have exactly 12 years of schooling,
we find that school quality has an insignificant effect on earnings,
suggesting that the crossover point is around the twelfth grade.) At
RETURNS TO EDUCATION 33
a fixed level of education, individuals with postsecondary education
appear to benefit from improved school quality, whereas those with
less than a high school education appear to earn less. However, an
increase in school quality raises schooling levels, particularly in the
lower tail of the education distribution. These gains in education
offset the apparent losses associated with the shift in the earningsschooling
function, leaving individuals in the lower tail of the earnings
distribution approximately as well off and individuals in the mid
and upper portions of the earnings distribution better off.
To further study the effects of changes in school quality on individuals
in the lower tail of the earnings distribution,we used a regression
of log earnings on state of residence effects, age, age squared, marital
status, and SMSA residence to compute earnings residuals within
state of birth and cohort cells. We then regressed the tenth and
twenty-fifth percentiles of the adjusted earnings distributions for each
cell on state of birth dummies, cohort dummies, and the school quality
measures. These regressions indicated small but generally positive
(and marginally significant) effects of higher school quality on earnings
of the tenth and twenty-fifth percentiles. There is certainly no
evidence of a negative effect of school quality on the lower tail of the
earnings distribution.
B. Reduced-Form Estimates
To summarize the effect of school quality on mean earnings, we conclude
with some simple reduced-form estimates of the effect of school
quality on log earnings and education. The results are presented
in table 6. These reduced-form models include the school quality
measures, state of residence and state of birth effects, and demographic
variables (age, age squared, and indicators for marital status
and residence in an SMSA). Notice that education is excluded from
the earnings models in columns 1-6: the estimated school quality
effects therefore incorporate any effects on the level of education, as
well as effects on the return to each year of schooling. We emphasize
that these models are estimated using a pooled sample of men from
the three 10-year birth cohorts we have analyzed throughout this
paper. Unlike our earlier models, these models therefore constrain
the state of birth and state of residence effects to be similar across
cohorts.
The results in table 6 suggest that increases in school quality are
associated with increases in both mean earnings and average years of
education. When the quality variables are included individually, each
is a significant determinant of earnings and average education. When
the three variables are includedjointly, the pattern of coefficient esti-
--
TABLE 6
~ - ------ - - - ------ --- - - - Log
Weekly Wage Education
- - - - - - - - - - ~-- ~ - - - - - - VARIABLEINDEPENDENT
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
--- - - - -- - - - --- - - - - - - -- - -- .- - - - - - ----- .Pupil/teacher
ratio ( l 1,000) -4.24 . . . . . . -4.15 -7.10 -4.29 -59.18 . . . . .. -59.71
(.59) (.fig) (.26) (59) (3.47) (4.00)
Term length ( + 1,000) . . . 1.20 . . . .I8 .15 .30 . . . 15.23 . . . 1.16
(.15) (.22) (.14) (.23) (1.32)
Relative teacher wage (+ 100) . . . . . . 4.77 4.48 10.93 3.49 . . . . . . 60.13 59.77
(.68) (.93) (.47) (.94) (3.96) (5.43)
50 state of residence dummies yes yes yes yes Yes no yes yes Yes Yes
48 state of birth dummies yes yes yes Yes no Yes Yes Yes Yes Yes
R~ .088 ,088 .088 .088 ,085 ,075 ,100 ,100 .lo0 .lo0
p-value for F-test of quality variables .. . . . . . . . .0001 .0001 .0001 . . . . .. ... .0001
-p 

-- - - - - -- - - - - - - -- - -~ -------p-----p--p-p----p---pp...N
o , r -Each quatlon also includra age and its square, a du~nnlyindicating current nrarital status, two cohort dunroriea, and a dummy indicating residence in an SMSA. Sample size ia 1,018,477.
Standard rrrors are in parentheses.
RETURNS TO EDUCATION 35
mates is similar to the pattern we found in tables 3-5: the pupil1
teacher ratio and the relative teacher wage remain significant, and
the term length variable falls to insignificance. For reference we also
report two restrictive specifications of the earnings models. The
model in column 5 excludes the state of birth dummies and therefore
uses both within-state and between-state variation in school characteristics
to estimate the school quality effects. This exclusion, which is
implicit in models reported by Rizzuto and Wachtel (1980), yields
much larger school quality effects. The model in column 6 includes
the state of birth effects but excludes current state of residence effects.
This exclusion lowers the goodness of fit of the earnings model
but has little impact on the magnitude of the school quality coeffi-
cients.
According to the estimates in columns 4 and 10, a decrease in the
pupillteacher ratio by 10 students is predicted to raise average earnings
by 4.2 percent and raise average education by 0.6 years. In this
sample the conventional return to education (i.e.,the coefficient of
education when it is added to the list of variables in the earnings
model and the school quality variables are excluded) is 5.38 percent.
Thus a 0.6-year increase in average education might be expected to
increase earnings by 3.2 percent. The overall gain in earnings from
a reduction in the pupillteacher ratio is therefore 30 percent bigger
than would be expected on the basis of the increase in average education
alone. A similar calculation for the relative teacher wage shows
that a 30 percent increase in teacher wages increases average education
by 0.18 years and average log wages by 1.34 percent. The gain
in earnings is roughly 40 percent bigger than would be expected on
the basis of the increase in education alone.
We have also used the 1970 census to estimate reduced-form equations
similar to the ones in table 6 for a sample of white men born in
1913-39. The results are comparable, although the effects of the
relative teacher wage variable on mean earnings for the 1970 sample
are smaller and statistically insignificant (except when the state of
birth effects are excluded from the model). The coefficient of the
pupillteacher variable on mean earnings is larger in 1970 than in
1980,whereas the coefficients of the quality variables on mean education
are uniformly smaller. However, the 1970 sample is substantially
smaller (378,000 vs. 1,018,000in 1980) and the sampling errors are
large enough that few of these differences are highly significant.
We draw two conclusions from the reduced-form relations between
earnings, education, and school quality. First, increases in school quality
during the past century are associated with increases in years of
schooling and average wages. Second, the increases in earnings appear
to reflect both a gain for the added years of education and
36 JOURNAL OF POLITICAL ECONOMY
an increase in the return for each existing year of education. Both
conclusions should be tempered by our inability to control for unobserved
cohort-specific factors that may raise the earnings of individuals
from states with better schools in the reduced-form models. When
these conclusions are taken together with the evidence we have assembled
on the returns to education, however, we believe that there is
strong support for the conclusion that increases in school quality lead
to higher earnings.
V. Conclusion and Discussion
The estimates presented in this paper provide new evidence that the
quality of schooling affects earnings. Men who are educated in states
with higher-quality school systems earn higher economic returns for
their years of schooling. Although the evidence is necessarily nonexperimental,
we believe that our findings are consistent with a causal
interpretation of the role of school quality. In the first place, our
findings are based on statistical models that control for any differences
across state of birth and cohort groups in the overall level of
earnings. Second, we have controlled for differences in the rates of
return to education earned by current residents in different regions
of the country. Third, we have controlled for any permanent differences
across states in the return to education earned by different
cohorts of men and for differences in family background measures
(education and earnings of the parents' generation) that may affect
subsequent labor market performance. Finally, our reduced-form
analysis confirms that increases in school quality increase the average
earnings of students. Thus the effects of school quality are not simply
redistributive, nor are they an artifact of changes in the distribution
of schooling attainments.
Our findings underscore the paradox we noted in the Introduction:
school quality appears to have an important effect on labor
market performance but is widely believed to have no impact on
standardized achievement tests. We note, however, that two recent
experimental studies of school characteristics and test scores are consistent
with positive school quality effects. A large-scale randomized
study of class sizes in Tennessee suggests that reductions in the pupil/
teacher ratio for elementary school students significantlyincrease test
scores on reading and math exams (see Finn and Achilles 1990).
Another recent randomized study finds that lengthening the school
term by providing extra instruction during the summer has a positive
effect on disadvantaged students' test scores (see Sipe, Grossman, and
Milliner 1988).Although more work is needed to resolve the available
37RETURNS T O EDUCATION
evidence, we believe that success in the labor market is at least as
important a yardstick for measuring the performance of the education
system as success on standardized tests. At a minimum, our finding
of a positive link between school quality and the economic returns
to education should give pause to those who argue that investments
in the public school system have no benefits for students.
Appendix A
Data Sources
A. Basic Data on School Quality
The following series were extracted from various issues of the Biennial Suruey
of Education and the Digest of Education Statistics: (a) the number of pupils
enrolled in full-time public elementary and secondary schools; (b) the average
number of days in the school term (full-timepublic elementary and secondary
schools); (c) the average number of days attended by each enrolled student
(full-time public elementary and secondary schools) (1920-58 only); (d) the
number of instructional staff, including supervisors and principals (full-time
public elementary and secondary schools); (e)the percentage of teachers who
are male (full-time public elementary and secondary schools); and (f) the
average annual salary per member of the instructional staff (full-timepublic
elementary and secondary schools).
These data were collected by state for alternating years, beginning with
1919-20. In some cases, the figures in the most recently published Biennial
Survey were revised in subsequent editions. We have attempted to incorporate
as many of these revisions as possible. For 1960 and later we collected a
variable representing the percentage of school days attended by enrolled
students. This percentage was then used to construct an estimate of average
days attended from the series on the length of the school term. The data
from the biennial editions of the survey are allocated to the previous two
years: for example, data from the 1937-38 edition are used for both 1937
and 1938.
B. Construction of the Relative Teacher Wage
Two wage series were combined to create a relative wage index for teachers
in each state. For 1920-38, we used the wage paid to laborers on federal
road construction projects. This wage is availableon a regional basis (for nine
census regions) in the StatisticalAbstract of the United States. Data for 1920-29
are taken from the 1930 edition, table 358. Data for 1930-56 are taken from
the 1957 edition, table 271. For 1940-66, we use the average state-level wage
of workers covered by the social security system, from U.S. Department of
Labor Employment and Training Administration Handbook Number 394.
To convert the regional construction wage rates into state-level averages, we
formed the average ratio of the state social security wage to the regional
construction wage in the period 1940-44. This average ratio was then applied
to the construction wage in the period 1920-38 to obtain a state-specific
average.
3t3 JOURNAL OF POLITICAL ECONOMY
C. Data on Education and Experience of Teachers
We used the Public-Use Sample of the 1940 census to form extracts of teachers
in each of the 48 (mainland) states and District of Columbia. Teachers
were identified by industry (educational services) and occupation (teachers
not elsewhere classified). We sampled only those teachers who reported either
white or black race and who reported positive earnings and weeks worked
and nonallocated age, sex, race, industry, occupation, and years of education.
The extract contains 9,161 teachers.
We used the Public-Use Sample of the 1950 census to form extracts of teachers
in each of the 48 (mainland) states and District of Columbia. (Owing
to technical difficulties, our Public-Use Sample excludes one-eighth of the
available sample.) Teachers were identified by industry (educational services)
and occupation (teachers not elsewhere classified). We sampled only those
teachers who reported either white or black race and who reported nonallocated
age, sex, race, industry, occupation, and years of education. The extract
contains 3,206 teachers.
We used the Public-Use Sample of the 1960census to form extracts of teachers
in each of the 48 (mainland) states and District of Columbia. Teachers
were identified by industry (educational services) and occupation (elementary
school teachers and secondary school teachers). We sampled only those teachers
who reported either white or black race and who reported nonallocated
age. The extract contains 16,052 teachers.
D. Data on Family Background
1. Average Per Capita Income
We collected average personal income per capita by state for the years 1930,
1940, and 1950 from State Personal Income: Estimates for 1929-1 982, Revised
Estimates (Bureau of Economic Analysis, 1984).The income data were originally
derived from the National Income and Product Accounts. The consumer
price index was used to convert the data into real dollars. The statelevel
per capita income in 1930 was assigned to the cohort of men born in
the 1920s, the state-level per capita income in 1940was assigned to the cohort
of men born in the 1930s, and the state-level per capita income in 1950
was assigned to the cohort of men born in the 1940s. These years roughly
correspond to the years in which educational expenditures for each cohort
would have been determined.
2. Median Education of Parents' Generation
As a measure of the education of each cohort's parents, we collected information
on the median education of white persons aged 25 or older by state in
1940, 1950, and 1960. These data are reported in Statistical Abstract of the
United States (nos. 66, 75, 85) and were originally derived from the 1940,
RETURNS T O EDUCATION 39
1950, and 1960 censuses. In 1940, the education data are reported only for
native-born individuals, and in 1950 and 1960 the data pertain to native
and foreign-born individuals. The median education of adults in 1940 was
assigned to the 1920s cohort, the median education of adults in 1950 was
assigned to the 1930s cohort, and the median education of adults in 1960
was assigned to the 1940s cohort.
E. Private Schools
State-level data on the number of students enrolled in private schools, the
number of students enrolled in Catholic schools, and the number of teachers
in Catholic schools were collected from the Biennial Suroey. Unfortunately,
these variables are available only on an irregular basis. Data for 1937-38 were
assigned to the cohort born in the 1920s,data for 1949-50 were assigned to
the cohort born in the 1930s, and data for 1955-56 were assigned to the
cohort born in the 1940s.
Appendix B
1980 Micro Data Samples
Our samples are taken from the Public-Use A Sample of the 1980 census (a
5 percent sample of the population). The samples consist of men born in the
48 mainland states or the District of Columbia between 1920 and 1949 and
currently living in any of the 50 states or District of Columbia. Year of birth
is estimated from information on age and quarter of birth. We include only
those individuals whose race is identified as "white." Individuals with imputed
information on age, race, sex, education, weeks worked, or total annual earnings
are excluded, as are individuals who report no weeks of work in 1979.
In addition, individuals with wage or salary income in 1979 less than $101
and those with average weekly wage and salary income of less than $36 or
greater than $2,500 are excluded. The final sample sizes are 279,008 for
those born in 1920-29,299,063 for those born in 1930-39, and 441,675 for
those born in 1940-49. These samples are used to form the first-stage estimates
of the returns to education in our two-step procedure and the
reduced-form estimates presented in table 6.
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