A Covariate Selection Criterion for Estimation of Treatment Effects

Abstract

We study how to select or combine estimators of the average treatment effect (ATE) and the average treatment effect on the treated (ATT) in the presence of multiple sets of covariates. We consider two cases: (1) all sets of covariates satisfy the unconfoundedness assumption and (2) some sets of covariates violate the unconfoundedness assumption locally. For both cases, we propose a data-driven covariate selection criterion (CSC) to minimize the asymptotic mean squared errors (AMSEs). Based on our CSC, we propose new average estimators of ATE and ATT, which include the selected estimators based on a single set of covariates as a special case. We derive the asymptotic distributions of our new estimators and propose how to construct valid confidence intervals. Our Monte Carlo simulations show that in finite samples, our new average estimators achieve substantial efficiency gains over the estimators based on a single set of covariates. We apply our new estimators to study the impact of inherited control on firm performance.

KEY WORDS:

• Focused information criterion
• Model averaging
• Treatment effect
• Unconfoundedness

ACKNOWLEDGMENTS

The author gratefully thanks the joint editor Rong Chen, the associate editor, and two anonymous referees for their many helpful comments. The author also thanks Manuel Arellano, Xiaohong Chen, Bruce Hansen, Hidehiko Ichimura, David Jacho- Chávez, Toru Kitagawa, Tong Li, Liangjun Su, and Alan T. K. Wan for their valuable comments and suggestions. The author acknowledges support from the Hong Kong Research Grants Council (RGC) under grant number 643711.