Birth cohort size variation and the estimation of class size effects

We show that in school systems with grade retention or redshirting, birth cohort size is negatively related to the grade-level share of students who are too old for their grade. This compositional effect gives rise to an upward bias in estimates of class size effects based on commonly used research designs exploiting within-school variation in birth cohort size. Using data for all primary schools in one federal state of Germany, we find support for this compositional effect. Correcting for the resulting bias, we find that not only are smaller classes beneficial for test scores, but also for reducing grade repetitions