Focused Information Criterion for Propensity Score Matching Estimators

Abstract
This paper studies the model selection problem for propensity score matching estimators of the average treatment effect (ATE) and the average treatment effect on treated (ATET). I derive the large sample distribution of propensity score matching estimators in a local asymptotic framework and characterize the asymptotic bias with respect to the first stage propensity score model choice. I show that the propensity score model choice induces a nontrivial asymptotic bias-variance trade-off for the ATET estimator. I also show that the largest propensity score model achieves the smallest asymptotic mean squared error for the ATE estimator. I then propose a focused information criterion for the propensity score matching estimator of the ATET that aims to minimize the estimated mean squared error. A simulation study indicates that the proposed method generally achieves a smaller mean squared error than other methods.