Nonparametric Treatment Effect Identification in School Choice

This paper studies nonparametric identification and estimation of causal effects in centralized school assignment. In many centralized assignment algorithms, students face both lottery-driven variation and regression discontinuity- (RD) driven variation. We characterize the full set of identified atomic treatment effects (aTEs), defined as the conditional average treatment effect between a pair of schools given student characteristics. Atomic treatment effects are the building blocks of more aggregated treatment contrasts, and common approaches to estimating aTE aggregations can mask important heterogeneity. In particular, many aggregations of aTEs put zero weight on aTEs driven by RD variation, and estimators of such aggregations put asymptotically vanishing weight on the RD-driven aTEs. We provide a diagnostic and recommend new aggregation schemes. Lastly, we provide estimators and asymptotic results for inference on these aggregations.