Complex Discontinuity Designs Using Covariates for Policy Impact Evaluation

Regression discontinuity designs are extensively used for causal inference in observational studies. However, they are usually confined to settings with simple treatment rules, determined by a single running variable, with a single cutoff. Motivated by the problem of estimating the impact of grade retention on educational and juvenile crime outcomes, in this paper we propose a framework and methods for complex discontinuity designs that encompasses multiple treatment rules. In this framework, the observed covariates play a central role for identification, estimation, and generalization of causal effects. Identification is non-parametric and relies on a local strong ignorability assumption. Estimation proceeds as in any observational study under strong ignorability, yet in a neighborhood of the cutoffs of the running variables. We discuss estimation approaches based on matching and weighting, including complementary regression modeling adjustments. We present assumptions for generalization; that is, for identification and estimation of average treatment effects for target populations. We also describe two approaches to select the neighborhood for analysis. We find that grade retention has a negative impact on future grade retention, but is not associated with dropping out of school or committing a juvenile crime.