An Estimation Approach of Causal Effectiveness in Matching with Unobserved Preferences

This paper studies many-to-one matching markets, such as school choice. We propose an estimation approach that requires matching outcomes only but no submitted preferences information, to decompose students’ performance into peer quality, school effectiveness, and match effect, respectively. The approach is based on the framework introduced in Abdulkadiroglu et al. (2020) where they use data of applicants’ rank-ordered choice lists to measure preferences. To deal with unobserved preferences, we utilize the techniques in Agarwal (2015) which studies hospital-intern programs to control for mutual selection in matching. We impose vertical preferences assumption and stability assumption for identification purposes. We also construct a simulated matching market to test the performance of our approach