COMPLEX DISCONTINUITY DESIGNS USING COVARIATES: IMPACT OF SCHOOL GRADE RETENTION ON LATER LIFE OUTCOMES IN CHILE

Regression discontinuity designs are extensively used for causal inference in observational studies. However, they are usually confined to settings with simple treatment rules and 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 Chile, we propose a framework and methods for complex discontinuity designs that encompass multiple treatment rules. In this framework the observed covariates play a central role for identification, estimation, and generalization of causal effects. Identification is nonparametric 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 in Chile has a negative impact on future grade retention but is not associated with dropping out of school or committing a juvenile crime.

Automated summary

Regression discontinuity designs are commonly used for causal inference, but are limited to simple settings. We propose a framework for complex discontinuity designs that encompass multiple treatment rules. Covariates play a central role in identification, estimation, and generalization of causal effects. We discuss estimation approaches based on matching and weighting, and find that grade retention in Chile has a negative impact on future grade retention but is not associated with dropping out of school or committing a juvenile crime.