How The Timing of Grade Retention Affects Outcomes: Identification and Estimation of Time-Varying Treatment Effects.

In many countries, grade retention is viewed as a useful tool for helping students who fall behind in their achievement. We show how the effect of grade retention varies by abilities, by timing of retention and as time since retention elapses. While existing studies of grade retention also recognize the importance of studying variation by abilities and timing, the existing methods are not well-equipped to deal with the possibility that students retained at different grades differ in unobservable abilities (dynamic selection) and the effects of retention also vary by the student's abilities and the time at which the student is retained. We extend existing factor analytic methods for identifying treatment effects to control for dynamic selection in our time-varying treatment effect setting. This approach can be understood as a hybrid between a control function and a generalization of the fixed effects approach. Applying our method to nationally-representative, longitudinal data, we find evidence of dynamic selection into retention and that the treatment effect of retention varies considerably across grades and unobservable abilities of students. Our strategy can be applied more broadly to many time-varying or multiple treatment settings.