A Bayesian Nonparametric Hypothesis Testing Approach for Regression Discontinuity Designs

TL;DR

This paper introduces a Bayesian nonparametric regression method for regression discontinuity designs, leveraging local randomization to improve causal inference in observational studies.

Contribution

It presents a novel Bayesian nonparametric approach that models local randomization around the cutoff, enabling flexible and robust causal effect estimation.

Findings

Applied to educational data, demonstrating causal link between skills and teaching ability.

Shows improved inference accuracy over traditional methods.

Validates the approach through real-world data analysis.

Abstract

The regression discontinuity (RD) design is a popular approach to causal inference in non-randomized studies. This is because it can be used to identify and estimate causal effects under mild conditions. Specifically, for each subject, the RD design assigns a treatment or non-treatment, depending on whether or not an observed value of an assignment variable exceeds a fixed and known cutoff value. In this paper, we propose a Bayesian nonparametric regression modeling approach to RD designs, which exploits a local randomization feature. In this approach, the assignment variable is treated as a covariate, and a scalar-valued confounding variable is treated as a dependent variable (which may be a multivariate confounder score). Then, over the model's posterior distribution of locally-randomized subjects that cluster around the cutoff of the assignment variable, inference for causal effects are made within this random cluster, via two-group statistical comparisons of treatment outcomes and non-treatment outcomes. We illustrate the Bayesian nonparametric approach through the analysis of a real educational data set, to investigate the causal link between basic skills and teaching ability.