Generalised regression estimators for average treatment effect with multicollinearity in high-dimensional covariates

Abstract

In this paper, a two-stage estimation procedure is proposed to obtain an efficient propensity score (PS) based estimator for the average treatment effect (ATE) with multicollinearity in high-dimensional covariates. In the first stage, we adjust the usual Horvitz–Thompson estimator of the ATE by incorporating instrumental variables in parametric PS models to avoid model misspecification and then propose the generalised regression estimator by utilising the auxiliary information from covariates related to the potential outcomes. In the second stage, we adapt the Elastic-net method to solve the multicollinearity issue and further improve the estimation efficiency based on the selected important covariates. The finite-sample performance of the proposed estimator is studied through simulation, and two applications to HER2 breast cancer and employees' weekly wages are also presented.

Keywords:

• Average treatment effect
• causal inference
• Elastic-net
• propensity score
• regression adjustment

AMS Subject Classifications:

• 62G05
• 62G20

Acknowledgments

The authors are grateful to the Editor, an associate editor and two anonymous referees for their insightful comments and suggestions, which have led to significant improvements. The first two authors contributed equally to this work.

Disclosure statement

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

Additional information

Funding

This paper was supported by the National Natural Science Foundation of China [grant numbers 11871287, 11771144, 11801359], the Fundamental Research Funds for the Central Universities, the Key Laboratory for Medical Data Analysis and Statistical Research of Tianjin, the Laboratory for Economic Behaviors and Policy Simulation, Nankai University.