Focused Information Criterion for Propensity Score Matching Estimators

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This paper studies the model selection problem for propensity score matching estimators of the average treatment effect (ATE) and the average treatment effect on the treated (ATET). I derive the large-sample distributions of these estimators in a local asymptotic framework and characterize their asymptotic bias and variance with respect to the first-stage propensity score model choice. The result shows that the largest propensity score model achieves the smallest asymptotic mean squared error for the ATE estimator. For the ATET estimator, I show that the propensity score model choice induces a nontrivial asymptotic bias-variance trade-off. Based on these findings, I 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 demonstrates that the proposed method generally achieves a smaller mean squared error than other methods with a modest sample size.