  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.
