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

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.