A Global Regression Discontinuity Design: Theory and Application to Grade Retention Policies

We use a marginal treatment effect (MTE) representation of a fuzzy regression discontinuity setting to propose a novel estimator. The estimator can be thought of as extrapolating the traditional fuzzy regression discontinuity estimate or as an observational study that adjusts for endogenous selection into treatment using information at the discontinuity. We show in a frequentest framework that it is consistent under weaker assumptions than existing approaches and then discuss conditions in a Bayesian framework under which it can be considered the posterior mean given the observed conditional moments. We then use this approach to examine the effects of early grade retention. We show that the benefits of early grade retention policies are larger for students with lower baseline achievement and smaller for low-performing students who are exempt from retention. These findings imply that (1) the benefits of early grade retention policies are larger than have been estimated using traditional fuzzy regression discontinuity designs but that (2) retaining additional students would have a limited effect on student outcomes.