Regularization and confounding in linear regression for treatment effect estimation

TL;DR

This paper explores how regularization can bias treatment effect estimates in observational studies and proposes a new model to mitigate this issue, improving causal inference accuracy.

Contribution

It introduces the concept of regularization-induced confounding and presents a novel regression model that avoids re-confounding when using regularization priors.

Findings

Regularization can bias treatment effect estimates due to over-shrinking.

A new regression model reduces re-confounding in treatment effect estimation.

The model performs well on synthetic and real data.

Abstract

This paper investigates the use of regularization priors in the context of treatment effect estimation using observational data where the number of control variables is large relative to the number of observations. First, the phenomenon of regularization-induced confounding is introduced, which refers to the tendency of regularization priors to adversely bias treatment effect estimates by over-shrinking control variable regression coefficients. Then, a simultaneous regression model is presented which permits regularization priors to be specified in a way that avoids this unintentional re-confounding. The new model is illustrated on synthetic and empirical data.