Variable Selection in Causal Inference using a Simultaneous Penalization Method

TL;DR

This paper introduces a simultaneous penalization method for variable selection in causal inference, improving confounder identification in high-dimensional data to reduce bias and variance in treatment effect estimation.

Contribution

It proposes a novel penalized objective function that considers outcome and treatment models simultaneously, achieving the oracle property in confounder selection.

Findings

Method attains the oracle property under regularity conditions.

Simulation studies demonstrate improved variable selection accuracy.

Application to economic data shows practical effectiveness.

Abstract

In the causal adjustment setting, variable selection techniques based on one of either the outcome or treatment allocation model can result in the omission of confounders, which leads to bias, or the inclusion of spurious variables, which leads to variance inflation, in the propensity score. We propose a variable selection method based on a penalized objective function which considers the outcome and treatment assignment models simultaneously. The proposed method facilitates confounder selection in high-dimensional settings. We show that under regularity conditions our method attains the oracle property. The selected variables are used to form a doubly robust regression estimator of the treatment effect. We show that under some conditions our method attains the oracle property. Simulation results are presented and economic growth data are analyzed. Specifically, we study the effect of life expectancy as a measure of population health on the average growth rate of gross domestic product per capita.