Direct Bayesian Additive Regression Trees for Conditional Average Treatment Effects in Regression Discontinuity Designs

TL;DR

This paper introduces a Bayesian nonparametric method using BART to estimate and model complex heterogeneous treatment effects in regression discontinuity designs, enhancing causal inference accuracy.

Contribution

It develops a novel Bayesian framework with a pseudo-model and bandwidth selection for flexible, local modeling of treatment effect heterogeneity in RDD.

Findings

Effectively captures complex heterogeneity structures

Demonstrates improved estimation accuracy in experiments

Provides a flexible, nonparametric approach for RDD analysis

Abstract

Regression discontinuity designs (RDD) are widely used for causal inference. In many empirical applications, treatment effects vary substantially with covariates, and ignoring such heterogeneity can lead to misleading conclusions, which motivates flexible modeling of heterogeneous treatment effects in RDD. To this end, we propose a Bayesian nonparametric approach to estimating heterogeneous treatment effects based on Bayesian Additive Regression Trees (BART). The key feature of our method lies in adopting a general Bayesian framework using a pseudo-model defined through a loss function for fitting local linear models around the cutoff, which gives direct modeling of heterogeneous treatment effects by BART. Optimal selection of the bandwidth parameter for the local model is implemented using the Hyv\"arinen score. Through numerical experiments, we demonstrate that the proposed approach flexibly captures complicated structures of heterogeneous treatment effects as a function of covariates.