Nonparametric Treatment Effect Identification in School Choice

We study identification and estimation of treatment effects in common school choice settings, under unrestricted heterogeneity in individual potential outcomes. We propose two notions of identification, corresponding to design- and sampling-based uncertainty, respectively. We characterize the set of causal estimands that are identified for a large variety of school choice mechanisms, including ones that feature both random and non-random tie-breaking; we discuss their policy implications. We also study the asymptotic behavior of nonparametric estimators for these causal estimands. Lastly, we connect our approach to the propensity score approach proposed in Abdulkadiroglu, Angrist, Narita, and Pathak (2017a, forthcoming), and derive the implicit estimands of the latter approach, under fully heterogeneous treatment effects.