TY - JOUR
T1 - Optimal Covariate Balancing Conditions in Propensity Score Estimation
AU - Fan, Jianqing
AU - Imai, Kosuke
AU - Lee, Inbeom
AU - Liu, Han
AU - Ning, Yang
AU - Yang, Xiaolin
N1 - Funding Information:
Supported by NSF grants DMS-1854637, DMS-1712591, DMS-2053832, CAREER Award DMS-1941945, NIH grant R01-GM072611, and Sloan Grant 2020-13946. An earlier version of this article was entitled, “Improving Covariate Balancing Propensity Score: A Doubly Robust and Efficient Approach.”
Publisher Copyright:
© 2021 American Statistical Association.
PY - 2022
Y1 - 2022
N2 - 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 pretreatment 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.
AB - 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 pretreatment 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.
KW - Average treatment effect
KW - Causal inference
KW - Double robustness
KW - Model misspecification
KW - Semiparametric efficiency
KW - Sieve estimation
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U2 - 10.1080/07350015.2021.2002159
DO - 10.1080/07350015.2021.2002159
M3 - Article
AN - SCOPUS:85121687269
SN - 0735-0015
VL - 41
SP - 97
EP - 110
JO - Journal of Business and Economic Statistics
JF - Journal of Business and Economic Statistics
IS - 1
ER -