Estimation of Class-Size Effects, Using "Maimonides' Rule" and Other Instruments: the Case of French Junior High Schools

Using a rich sample of students from French junior high schools with a panel structure, we obtain small but significant and negative effects of class size on probabilities of being promoted to the next grade, in grades 6 and 7. In grade 6 a 10-student reduction in class size would put the child of a blue collar worker on an equal footing with the child of an educated professional. These effects vanish in grades 8 and 9. Angrist and Lavy's (1999) "Maimonides' rule", inducing a regression discontinuity based on class-opening thresholds, doesn't work well with our data, in spite of being strong in the first-stage regression. We show that an approach based on the random variations of total grade enrollment, conditional on total school enrollment gives substantially better results. This is possible since actual class size, total grade and total school enrollment are available in our exceptional data set. Using a Probit framework to model transitions from one grade to another (and thus grade repetitions), we then simultaneously estimate the student's probabilities of success over 4 years in junior high school. The simultaneous equation model allows for the estimation of a general covariance structure of the error terms affecting latent student performance and class-size equations, which sheds light on the endogeneity of class-size.