Multiply robust estimation for average treatment effect among treated

Abstract

We propose a multiply robust estimator for the Average Treatment Effect Among the Treated (ATT). The proposed estimation procedure can simultaneously accommodate multiple working models for both the propensity score and the conditional mean of the counterfactual outcome given covariates. In addition, it can explicitly balance a set of user-specified moments of the covariate distributions between the treatment groups. The resulting estimator is consistent if any working model is correctly specified. With the data generating process typically unknown for observational studies, the proposed method provides substantial robustness against possible model misspecifications compared to existing estimators of the ATT. Simulation results show the excellent finite sample performance of the proposed estimator.

Keywords:

• Causal inference
• covariate balancing
• empirical likelihood
• multiple robustness
• propensity score

Acknowledgments

We thank the Editor, Associate Editor and a referee for their valuable comments that have helped improve the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).