Causal Inference in Matching Markets: Simulable Mechanisms

We formalize an econometric model for two-sided matching mechanisms in a school choice context, where exogenous variation is generated by using lotteries as a tie-breaking mechanism. Our model accommodates a wide range of matching algorithms studied in the theoretical market design literature. We propose a Horvitz–Thompson estimator for the average treatment effect that is exactly unbiased, compatible with multiple treatments, and compatible with heterogeneous treatment effects. We present theoretical properties of the estimator and inference procedures. Our work clarifies the econometric model used in Abdulkadiroglu et al. (2017) and provides a robustness check on their results.