Abstract
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.
Acknowledgments
The authors thank Zach Branson, Kosuke Imai, Luke Keele, Yige Li, Luke Miratrix, Bijan Niknam, Paul Rosenbaum, Zirui Song, Stefan Wager, the Editor, and two anonymous reviewers for helpful comments and inputs. The authors were supported in part by award ME-2019C1-16172 from the Patient-Centered Outcomes Research Institute (PCORI) and grants G-2018-10118 and G-2020-13946 from the Alfred P. Sloan Foundation.
Citation
Juan D. Díaz. José R. Zubizarreta. "Complex discontinuity designs using covariates: Impact of school grade retention on later life outcomes in Chile." Ann. Appl. Stat. 17 (1) 67 - 88, March 2023. https://doi.org/10.1214/22-AOAS1616
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