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

Daisuke Kondo, Shonosuke Sugasawa

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 Hyvärinen score. Through numerical experiments, we demonstrate that the proposed approach flexibly captures complicated structures of heterogeneous treatment effects as a function of covariates.

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

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 Hyvärinen score. Through numerical experiments, we demonstrate that the proposed approach flexibly captures complicated structures of heterogeneous treatment effects as a function of covariates.
Paper Structure (13 sections, 19 equations, 4 figures, 2 tables)

This paper contains 13 sections, 19 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. BART for Direct Inference on CATE in RDD
  3. Pseudo-model for direct inference on CATE
  4. BART prior for CATE
  5. Posterior Computation
  6. Bandwidth Adaptation
  7. Simulation Study
  8. Data Generating Processes
  9. (Scenario 1)
  10. (Scenario 2)
  11. Comparative Methods and Evaluation Criterion
  12. Results
  13. Concluding Remarks

Figures (4)

  • Figure 1: Boxplots of RMSE for in-sample units based on 15 replications for four methods under Scenario 1. The upper row corresponds to the small baseline variability case, while the lower row corresponds to the large baseline variability case. The left, middle, and right columns report results for noise variances $\sigma^2 = 0.25$, $0.5$, and $1$, respectively.
  • Figure 2: Boxplots of RMSE for out-of-sample units based on 15 replications for four methods under Scenario 1. The upper row corresponds to the small baseline variability case, while the lower row corresponds to the large baseline variability case. The left, middle, and right columns report results for noise variances $\sigma^2 = 0.25$, $0.5$, and $1$, respectively.
  • Figure 3: Boxplots of RMSE for in-sample units based on 15 replications for four methods under Scenario 2. The top, middle, and bottom panels correspond to the settings $\rho = 0$, $\rho = 0.25$, and $\rho = 0.5$, respectively. For each row, results are reported separately for noise variances $\sigma^2 = 0.5$ and $\sigma^2 = 1$.
  • Figure 4: Boxplots of RMSE for out-of-sample units based on 15 replications for four methods under Scenario 2. The top, middle, and bottom panels correspond to the settings $\rho = 0$, $\rho = 0.25$, and $\rho = 0.5$, respectively. For each row, results are reported separately for noise variances $\sigma^2 = 0.5$ and $\sigma^2 = 1$.