Entropy balancing is doubly robust

TL;DR

Entropy Balancing (EB) is a covariate balancing method that is doubly robust and achieves optimal variance when models are correctly specified, offering a promising alternative to traditional propensity score weighting.

Contribution

This paper proves that EB is doubly robust and attains the semiparametric variance bound without explicitly modeling outcomes or treatment assignment.

Findings

EB is doubly robust with respect to outcome and propensity score models.

EB reaches the semiparametric variance bound when both models are correct.

Simulations show EB outperforms conventional weighting estimators.

Abstract

Covariate balance is a conventional key diagnostic for methods used estimating causal effects from observational studies. Recently, there is an emerging interest in directly incorporating covariate balance in the estimation. We study a recently proposed entropy maximization method called Entropy Balancing (EB), which exactly matches the covariate moments for the different experimental groups in its optimization problem. We show EB is doubly robust with respect to linear outcome regression and logistic propensity score regression, and it reaches the asymptotic semiparametric variance bound when both regressions are correctly specified. This is surprising to us because there is no attempt to model the outcome or the treatment assignment in the original proposal of EB. Our theoretical results and simulations suggest that EB is a very appealing alternative to the conventional weighting estimators that estimate the propensity score by maximum likelihood.