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Activity Number: 589
Type: Topic Contributed
Date/Time: Wednesday, August 12, 2015 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #317020
Title: Bayesian Regularized Regression for Treatment Effect Estimation: A Latent Error Modeling Approach
Author(s): Richard Hahn* and Carlos M. Carvalho
Companies: The University of Chicago Booth School of Business and The University of Texas at Austin
Keywords: treatment effect estimation ; regression ; regularization ; causal inference
Abstract:

Bayesian regression models are widely and successfully used in prediction/forecasting contexts. It turns out, however, that such methods are not suitable for causal effect inference without careful modification. Conditional on the observed co-linearities between the treatment and the control variables, the regularization prior actually biases the treatment effect variable away from zero! The impact of this bias can be substantial and difficult to anticipate, given that the vector of control variables may be many times larger than the treatment effect parameter (which is often a scalar). In this talk I will describe reparametrizations of standard regression models that provide direct control over the impact of regularization on the bias of the treatment effect. Our main technique will be to specify a structural equation model in terms of latent error variables and to induce regularization priors on reduce-form regression coefficients via priors on these latent noise terms. The resulting priors need not be well-known distributions because computation can be done directly in the latent variable representation.


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