Regularization and confounding in linear regression for treatment effect estimation

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.