Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects

Abstract

This paper develops a semi-parametric Bayesian regression model for estimating heterogeneous treatment effects from observational data. Standard nonlinear regression models, which may work quite well for prediction, can yield badly biased estimates of treatment effects when fit to data with strong confounding. Our Bayesian causal forests model avoids this problem by directly incorporating an estimate of the propensity function in the specification of the response model, implicitly inducing a covariate-dependent prior on the regression function. This new parametrization also allows treatment heterogeneity to be regularized separately from the prognostic effect of control variables, making it possible to informatively “shrink to homogeneity”, in contrast to existing Bayesian non- and semi-parametric approaches.

Keywords: causal inference, treatment effects, heterogeneous effects, subgroup effects, tree methods, Bayesian, nonparametric regression, nonlinear regression

JEL Classification: C11, C14, C30, C45