The Effect of Age at School Entry on Educational Attainment: An Application of Instrumental Variables with Moments from Two Samples

Abstract

We present a model in which 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 starting age created by children's dates of birth provides a natural experiment for estimating 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 estimate and 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 compulsory attendance laws constrain roughly 10% of students to stay in school.