Joshua Angrist

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In this paper, the random assignment of the risk of induction generated by the
draft lottery is used to estimate the effect of military service on civilian
wages, earnings and weeks worked- Data from the National Longitudinal Survey of
Young Men in 1981 offer no conclusive evidence of an effect on earnings or weeks
worked- However, marginally significant negative wage effects are found for
white veterans, while positive wage effects are found for black veterans-
Conventional ordinary least squares estimates which do not exploit the
randomization of the draft lottery fail to identify these effects, suggesting the
presence of selection bias in conventional estimates, Finally, an attempt is
made to gauge whether instrumental variables estimates which do not exploit the
lottery generate similar inferences regarding the effects of military service-
Two sets of conventionally available instruments result in estimates which differ
greatly from those constructed using lottery based instruments- However, both
the least variance ratio and the generalized method of moments tests of over-
identifying restrictions provide some help in isolating the most misleading
conventional specifications.

Year of Publication
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Citation Key
Angrist, J. (1987). The Effect of Military Service of Civilian Labor Market Experience. Retrieved from (Original work published July 1987)
Working Papers

Labor supply research has not yet produced a clear statement of the size of
the labor supply elasticity nor how it should be measured. Measurement error in
hourly wage data and the use of inappropriate identifying assumptions can account
for the poor performance of some empirical labor supply models. I propose here a
generalization of Wald's method of fitting straight lines that is robust to
measurement error, imposes mild testable identifying assumptions, and is useful
for the estimation of life-cycle labor supply models with panel data. A
convenient Two-Stage Least Squares (TSLS) equivalent of the generalized Wald
estimator is presented and a TSLS over-identification test statistic is shown to
be the test statistic for equality of alternative Wald estimates of the same
parameter. These results are applied to labor supply models using a sample of
continuously employed prime-age males. Labor supply elasticities from the two
best-fitting models that pass tests of over-identifying restrictions range from
0.6 to 0.8 . A test for measurement error based on the difference between
generalized Wald and Analysis of Covariance estimators is also proposed.
Application of the test indicates that measurement error can account for low or
negative Analysis of Covariance estimates of labor supply elasticities.

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Journal of Econometrics, Vol. 47, February/March 1991
Angrist, J. (1988). Grouped Data Estimation and Testing in Simple Labor Supply Models. Retrieved from (Original work published July 1988)
Working Papers

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.

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Journal of the American Statistical Association, Vol. 87, No. 418, June 1992
Angrist, J., & Krueger, A. (1990). The Effect of Age at School Entry on Educational Attainment: An Application of Instrumental Variables with Moments from Two Samples. Retrieved from (Original work published October 1990)
Working Papers

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.

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NBER Working Paper No. 4067, May, 1992
Angrist, J., & Krueger, A. (1991). Estimating the Payoff to Schooling Using the Vietnam-era Draft Lottery. Retrieved from (Original work published August 1991)
Working Papers

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.

Year of Publication
Date Published
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Citation Key
American Economic Review, June 1990
Angrist, J. (1989). Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records. Retrieved from (Original work published April 1989)
Working Papers

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.

Year of Publication
Date Published
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Citation Key
Journal of Business & Economic Statistics, Vol. 9, No. 3, Jul.y, 1991
Angrist, J., & Newey, W. (1989). Minimum Chi-Square and Three-Stage Least Squares in Fixed Effects Models. Retrieved from (Original work published January 1989)
Working Papers

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.

Year of Publication
Date Published
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Citation Key
Journal of Labor Economics, Vol. 12, No. 1, January, 1994
Angrist, J., & Krueger, A. (1989). Why Do World War II Veterans Earn More Than Nonveterans?. Retrieved from (Original work published June 1989)
Working Papers
Year of Publication
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Journal of Economic Perspectives, Vol. 15, No 4, Fall 2001
Angrist, J., & Krueger, A. (2001). Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments. Retrieved from (Original work published August 2001)
Working Papers

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.

Year of Publication
Date Published
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Citation Key
Quarterly Journal of Economics, Vol. 106, No. 4, November 1991
Angrist, J., & Krueger, A. (1990). Does Compulsory School Attendance Affect Schooling and Earnings?. Retrieved from (Original work published June 1990)
Working Papers