Optimal Covariate Balancing Conditions in Propensity Score Estimation

Inverse probability of treatment weighting (IPTW) is a popular method for estimating the average effect (ATE). However, empirical studies show that IPTW estimators can be sensitive to misspecification propensity score model. To address this problem, researchers have proposed estimate by directly optimizing balance pretreatment covariates. While these methods appear empirically perform well, little known about how choice balancing conditions affects their theoretical properties. fill gap, we first characterize asymptotic bias and efficiency estimator based on covariate (CBPS) methodology under local model misspecification. Based analysis, optimally choose functions propose an optimal CBPS-based estimator. This doubly robust; it consistent ATE if either or outcome correct. In addition, locally semiparametric efficient when both models are correctly specified. further relax parametric assumptions, extend our using sieve estimation approach. We resulting globally set much weaker assumptions has smaller than existing estimators. Finally, evaluate finite sample performance via simulation studies. An open-source software package available implementing methods.