Regularization and Confounding in Linear Regression for Treatment Effect Estimation

Bayesian Analysis Volume 13, Number 1 (2018), 163-182. https://projecteuclid.org/euclid.ba/1484103680

20 Pages Posted: 8 Feb 2016 Last revised: 15 Oct 2018

See all articles by P. Richard Hahn

P. Richard Hahn

Arizona State University (ASU) - School of Mathematical and Statistical Sciences

Carlos M. Carvalho

University of Texas at Austin - Red McCombs School of Business

Jingyu He

City University of Hong Kong

David Puelz

University of Chicago - Booth School of Business

Date Written: 2018

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.

Keywords: linear regression, regularization, treatment effect estimation, shrinkage

JEL Classification: C11, C30, C50

Suggested Citation

Hahn, P. Richard and Carvalho, Carlos M. and He, Jingyu and Puelz, David, Regularization and Confounding in Linear Regression for Treatment Effect Estimation (2018). Bayesian Analysis Volume 13, Number 1 (2018), 163-182. https://projecteuclid.org/euclid.ba/1484103680, Available at SSRN: https://ssrn.com/abstract=2728512 or http://dx.doi.org/10.2139/ssrn.2728512

P. Richard Hahn

Arizona State University (ASU) - School of Mathematical and Statistical Sciences ( email )

Tempe, AZ 85287-1804
United States

Carlos M. Carvalho

University of Texas at Austin - Red McCombs School of Business ( email )

Austin, TX 78712
United States

Jingyu He

City University of Hong Kong ( email )

83 Tat Chee Avenue
Kowloon
Hong Kong

HOME PAGE: http://jingyuhe.com

David Puelz (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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