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Title: Complex discontinuity designs using covariates Authors:  Juan Diaz - Universidad de Chile (Chile)
Jose Zubizarreta - Harvard University (United States) [presenting]
Abstract: A new framework is proposed for general discontinuity designs that encompasses complex treatment rules. These rules may be determined by multiple running variables, each with many cutoffs, and that possibly lead to the same treatment. Moreover, the running variables may be discrete and the treatments do not need to be binary. In this framework, the observed covariates play a central role, and identification relies on a local unconfoundedness 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 additional regression adjustments in doubly robust estimators. We present assumptions for generalization; that is, for identification and estimation of average treatment effects for target populations beyond the study sample that resides in a neighborhood of the cutoffs. We also examine a new approach to select the neighborhood for the analyses and assess the plausibility of the assumptions. We argue that, in a sense, traditional continuity-based and local-randomization frameworks for regression discontinuity designs are particular cases of our proposed framework. We motivate and illustrate this framework on a study of the impact of grade retention on juvenile crime.