Fan, Jianqing, Kosuke Imai, Inbeom Lee, Han Liu, Yang Ning, and Xiaolin Yang. (2023). ``Optimal Covariate Balancing Conditions in Propensity Score Estimation.'' Journal of Business & Economic Statistics, Vol. 41, No. 1, pp. 97-110.

 

  Abstract

Inverse probability of treatment weighting (IPTW) is a popular method for estimating the average treatment effect (ATE). However, empirical studies show that the IPTW estimators can be sensitive to the misspecification of the propensity score model. To address this problem, researchers have proposed to estimate propensity score by directly optimizing the balance of pre-treatment covariates. While these methods appear to empirically perform well, little is known about how the choice of balancing conditions affects their theoretical properties. To fill this gap, we first characterize the asymptotic bias and efficiency of the IPTW estimator based on the Covariate Balancing Propensity Score (CBPS) methodology under local model misspecification. Based on this analysis, we show how to optimally choose the covariate balancing functions and propose an optimal CBPS-based IPTW estimator. This estimator is doubly robust; it is consistent for the ATE if either the propensity score model or the outcome model is correct. In addition, the proposed estimator is locally semiparametric efficient when both models are correctly specified. To further relax the parametric assumptions, we extend our method by using a sieve estimation approach. We show that the resulting estimator is globally efficient under a set of much weaker assumptions and has a smaller asymptotic bias than the existing estimators. Finally, we evaluate the finite sample performance of the proposed estimators via simulation and empirical studies. An open-source software package is available for implementing the proposed methods.
An earlier version of the paper was entitled, ``Improving Covariate Balancing Propensity Score: A Doubly Robust and Efficient Approach.''
See ``Covariate Balancing Propensity Score,'' for the original CBPS paper, ``Covariate Balancing Propensity Score for General Treatment Regimes,'' which generalizes the CBPS to the multi-valued and continuous treatments, and ``Robust Estimation of Inverse Probability Weights for Marginal Structural Models,'' which generalizes the CBPS to the longitudinal data settings.

  Software

Fong, Christian, Marc Ratkovic, and Kosuke Imai. ``CBPS: R Package for Covariate Balancing Propensity Score.'' available through The Comprehensive R Archive Network. 2014.

© Kosuke Imai
 Last modified: Fri Dec 16 14:29:26 EST 2022