Efficient Covariate Balancing for the Local Average Treatment Effect

Abstract

This article develops an empirical balancing approach for the estimation of treatment effects under two-sided noncompliance using a binary instrumental variable. The method weighs both treatment and outcome information with inverse probabilities to impose exact finite sample balance across instrument level groups. It is free of functional form assumptions on the outcome or the treatment selection step. By tailoring the loss function for the instrument propensity scores, the resulting treatment effect estimates are automatically weight normalized and exhibit both low bias and reduced variance in finite samples compared to conventional inverse probability weighting methods. We provide conditions for asymptotic normality and semiparametric efficiency and demonstrate how to use additional information about the treatment selection step for bias reduction in finite samples. A doubly robust extension is proposed as well. Monte Carlo simulations suggest that the theoretical advantages translate well to finite samples. The method is illustrated in an empirical example.

Keywords:

• Instrumental variable
• Inverse probability weighting
• Treatment effect

Supplementary Materials

The supplementary material contains all proofs and derivations as well as code and replication files.

Acknowledgments

I thank to the Editor, three anonymous referees, Michael Knaus, Winfried Pohlmeier, Julian Schssler, Qingyuan Zhao, Toru Kitagawa, and the participants of the Rotterdam Winter Meeting of the Econometric Society 2019 and the St. Gallen Causal Machine Learning Workshop 2020 for fruitful discussions and comments that helped to greatly improve the article. All remaining errors are mine.

Additional information

Funding

The author gratefully acknowledges the financial support from the German Research Foundation through Project 219805061 and by the Graduate School of Decision Sciences (University of Konstanz).