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Regression discontinuity designs are extensively used for causal inference inobservational studies. However, they are usually confined to settings withsimple treatment rules, determined by a single running variable, with a singlecutoff. Motivated by the problem of estimating the impact of grade retention oneducational and juvenile crime outcomes in Chile, we propose a framework andmethods for complex discontinuity designs that encompasses multiple treatmentrules. In this framework, the observed covariates play a central role foridentification, estimation, and generalization of causal effects.Identification is non-parametric and relies on a local strong ignorabilityassumption. Estimation proceeds as in any observational study under strongignorability, yet in a neighborhood of the cutoffs of the running variables. Wediscuss estimation approaches based on matching and weighting, includingcomplementary regression modeling adjustments. We present assumptions forgeneralization; that is, for identification and estimation of average treatmenteffects for target populations. We also describe two approaches to select theneighborhood for analysis. We find that grade retention in Chile has a negativeimpact on future grade retention, but is not associated with dropping out ofschool or committing a juvenile crime.

Complex Discontinuity Designs Using Covariates: Impact of School Grade Retention on Later Life Outcomes in Chile