Causal Inference in Matching Markets : Cutoff Mechanisms

We formalize an econometric model for two-sided matching mechanisms in a school choice context, where identification exploits similarity between students who just qualify for a school and those who just fail to qualify for a school. We discuss estimation and inference of the locally linear regression estimator for such a setting, using theoretical results developed in Chen (2019b). Our approach allows us to clarify and relax the simplifying large-market assumption made in earlier work (Abdulkadiroğlu et al., 2017, 2019), and we show that classical regression discontinuity procedures extend to settings where the discontinuity cutoff is endogenously chosen. Our results provide a rigorous statistical basis for causal inference and program evaluation in a number of settings where treatment assignment is complex