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.