Bayesian analysis of regression discontinuity designs with heterogeneous treatment effects

2025-04-14

AI Summary

This paper addresses the estimation and inference of heterogeneous treatment effects across multiple subpopulations in regression discontinuity designs (RDD). We propose a Bayesian hierarchical model based on Gaussian processes, operating within a nonparametric framework that enables information sharing across subpopulations. To our knowledge, this is the first application of Gaussian processes to heterogeneity analysis in RDD, yielding a posterior-consistent Bayesian inference framework that overcomes limitations of conventional parametric modeling and isolated subgroup analyses. Posterior computation is efficiently implemented via Metropolis–Hastings-within-Gibbs sampling. Simulation studies demonstrate that the proposed method achieves significantly higher estimation accuracy and statistical power compared to existing approaches. An empirical application to U.S. Senate election data reveals temporally evolving heterogeneous patterns in incumbent-party advantage.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Regression Discontinuity Design (RDD) is a popular framework for estimating a causal effect in settings where treatment is assigned if an observed covariate exceeds a fixed threshold. We consider estimation and inference in the common setting where the sample consists of multiple known sub-populations with potentially heterogeneous treatment effects. In the applied literature, it is common to account for heterogeneity by either fitting a parametric model or considering each sub-population separately. In contrast, we develop a Bayesian hierarchical model using Gaussian process regression which allows for non-parametric regression while borrowing information across sub-populations. We derive the posterior distribution, prove posterior consistency, and develop a Metropolis-Hastings within Gibbs sampling algorithm. In extensive simulations, we show that the proposed procedure outperforms existing methods in both estimation and inferential tasks. Finally, we apply our procedure to U.S. Senate election data and discover an incumbent party advantage which is heterogeneous over different time periods.

Problem

• Estimating causal effects in RDD with heterogeneous treatment effects
• Developing Bayesian hierarchical model for non-parametric regression
• Improving estimation accuracy across diverse sub-populations

Innovation

• Bayesian hierarchical model for heterogeneous effects
• Gaussian process regression for non-parametric analysis
• Metropolis-Hastings within Gibbs sampling algorithm