This paper tests the hypothesis that compulsory school attendance
laws, which typically require school attendance until a specified birthday,
induce a relationship between years of schooling and age at school entry.
Variation in school start age created by children's date of birth provides
a natural experiment for estimation of the effect of age at school entry.
Because no large data set contains information on both age at school entry
and educational attainment, we use an Instrumental Variables (IV) estimator
with data derived from the 1960 and 1980 Censuses to test the age-at-entry/compulsory schooling model. In most IV applications, the two
covariance matrices that form the estimator are constructed from the same
sample. We use a method of moments framework to discuss IV estimators that
combine moments from different data sets. In our application, quarter of
birth dummies are the instrumental variables used to link the 1960 Census,
from which age at school entry can be derived for one cohort of students,
to the 1980 Census, which contains educational attainment for the same
cohort of students. The results suggest that roughly l0 percent of
students were constrained to stay in school by compulsory schooling laws.

During the Vietnam draft priority for military service was randomly
assigned to draft-age men in a series of lotteries. However, many men
managed to avoid military service by enrolling in school and obtaining an
educational deferment. This paper uses the draft lottery as a natural
experiment to estimate the return to education and the veteran premium.
Estimates are based on special extracts of the Current Population Survey
that the Census Bureau assembled for 1979 and 1981-85. The results suggest
that an extra year of schooling acquired in response to the lottery is
associated with 6.6 percent higher weekly earnings. This figure is about
10 percent higher the OLS estimate of the return to education for this
sample, which suggests there is little ability bias in conventional
estimates of the return to education. Our findings are robust to a variety
of "alternative assumptions about the effect of veteran status on earnings.

Estimates of the effect of veteran status on civilian earnings may be biased
by the fact that certain types of men are more likely to serve in the armed
forces. In this paper, an estimation strategy is employed that enables
measurement of the effects of veteran status while controlling for differences in
other personal characteristics related to earnings. The randomly assigned risk
of induction generated by the Vietnam era draft lottery is used to construct
instrumental variables that are correlated with earnings solely by virtue of
their correlation with veteran status. Instrumental variables estimates
tabulated from Social Security Administration records indicate that in the early
1980's the earnings of white veterans were approximately 15 percent less than
nonveteran earnings. In contrast, there is no evidence that nonwhite veterans
suffered any lasting reduction in earnings. In an attempt to explain the loss of
earnings to white veterans, experience-earnings profiles are estimated jointly
with time-varying veteran status coefficients. The estimates suggest that the
effect of Vietnam era military service on white veterans is equivalent to a loss
of two years of civilian labor market experience.

Two approaches to estimation and testing of fixed effects models are
commonly found in the econometrics literature. The first involves variations on
instrumental variables. The second, a Minimum Chi-Square (MCS) procedure
introduced by Chamberlain, minimizes a quadratic form in the difference between
unrestricted regression coefficients and the restrictions implied by the fixed
effects model. This paper is concerned with the relationship between Three-Stage
Least Squares (3SLS) and MCS. A 3SLS equivalent of the MCS estimator is
presented and, in the usual case wherein the time varying error component has a
scalar covariance matrix, 3SLS is shown to simplify to the conventional
deviations from means estimator. Furthermore, the corresponding over-
identification test statistic is the degrees of freedom times the R2 from a
regression of residuals on all leads and lags of right hand side variables. The
relationship between MCS and some recently introduced efficient instrumental
variables procedures is also considered.
An empirical example from the literature on life-cycle labor supply is used
to illustrate properties of 3SLS procedures for panel data under alternative
assumptions regarding residual covariance. Estimated labor supply elasticities
and standard errors appear to be insensitive to these assumptions. In contrast,
the over-identification test statistics are found to be substantially smaller
when residuals are allowed to be intertemporally correlated and heteroscedastic.
At conventional levels of significance, however, even the smallest of the test
statistics leads to rejection of the over-identifying restrictions implicit in
the labor supply models.

Veterans of World War II are widely believed to earn more than
nonveterans of the same age. Theoretical justifications for the World War
II veteran premium include the subsidization of education and training, and
preference for veterans in hiring. In this paper, we propose and test an
alternative view: that the observed World War II veteran premium reflects
the fact that men with higher earnings potential were more likely to have
been selected into the Armed Forces. An empirical strategy is developed
that allows estimation of the effects of veteran status while controlling
for correlation with unobserved earnings potential. The estimation is
based on the fact that from 1942 to 1947 priority for conscription was
determined in chronological order of birth. Information on individuals’
dates of birth may therefore be used to construct instruments for veteran
status. Empirical results from the 1960, 1970, and 1980 Censuses, along
with two other micro data sets, support a conclusion that World War II
veterans earn no more than comparable nonveterans, and may well earn less.
These results suggest that OLS estimates of the World War II veteran
premium are severely biased by nonrandom selection into military service,
and that the civilian labor market experiences of veterans of World War II
were not very different from the experiences of Vietnam-era veterans.

This paper presents evidence showing that individuals’ season of birth is
related to their educational attainment because of the combined effects of
school start age policy and compulsory school attendance laws. In most school
districts, individuals born in the beginning of the year start school at a
slightly older age, and therefore are eligible to drop out of school after
completing fewer years of schooling than individuals born near the end of the
year. Our estimates suggest that as many as 25 percent of potential dropouts
remain in school because of compulsory schooling laws. We estimate the impact
of compulsory schooling on earnings by using quarter of birth as an
instrumental variable for education in an earnings equation. This provides a
valid identification strategy because date of birth is unlikely to be
correlated with omitted earnings determinants. The instrumental variables
estimate of the rate of return to education is remarkably close to the
ordinary least squares estimate, suggesting that there is little ability bias
in conventional estimates of the return to education. The results also imply
that individuals who are compelled to attend school longer than they desire by
compulsory schooling laws reap a substantial return for their extra schooling.

In discussions of the incidence of Vietnam era military service, it is often
observed that blacks were over-represented among draftees in the early 1970's.
The racial composition of the armed forces, however, was determined jointly by
armed forces eligibility criteria and voluntary enlistment as well as by the
failure of draftees to avoid conscription. The interaction of these selection
criteria makes it impossible to use the armed forces racial mix as prima facie
evidence regarding the burden of conscription. In this paper, a modeling
strategy is developed that may be used to identify some of the parameters
affecting the process of selection for military service. The approach taken here
exploits the fact that in the early 1970's, the risk of conscription was randomly
allocated in a series of lotteries.
Data on enlistments during the 1971 draft lottery are fit to a behavioral
model using the technique of Modified Minimum Chi-Square. The empirical work
shows that although nonwhites were more likely than whites to be drafted and less
likely to meet armed forces eligibility criteria, they were also more likely to
consider military service an attractive alternative to civilian life. An
additional and related finding is that the draft induced proportionately more
whites than nonwhites to enlist. The elasticity of white enlistments with
respect to the probability of conscription is shown to be twice as large as the
elasticity of nonwhite enlistment. Thus, other things equal, conscription of
equal numbers of whites and nonwhites may actually reduce nonwhite representation
in the armed forces.

Instrumental Variables (IV) estimates tend to be biased in the same direction as
Ordinary Least Squares (OLS) in finite samples if the instruments are weak. To address
this problem we propose a new IV estimator which we call Split Sample Instrumental
Variables (SSIV). SSIV works as follows: we randomly split the sample in half, and use
one half of the sample to estimate parameters of the first-stage equation. We then use these
estimated first-stage parameters to construct fitted values and second-stage parameter
estimates using data from the other half sample. SSIV is biased toward zero, rather than
toward the plim of the OLS estimate. However, an unbiased estimate of the attenuation
bias of SSIV can be calculated. We use this estimate of the attenuation bias to derive an
estimator that is asymptotically unbiased as the number of instruments tends to infinity,
holding the number of observations per instrument fixed. We label this new estimator
Unbiased Split Sample Instrumental Variables (USSIV). We apply SSIV and USSIV to the
data used by Angrist and Krueger (1991) to estimate the payoff to education.