Treatment Effect Heterogeneity in Regression Discontinuity Designs

2025-03-17

AI Summary

Existing regression discontinuity (RD) designs often rely on ad hoc empirical exploration to investigate covariate-driven heterogeneity in treatment effects, lacking a unified and rigorous statistical inference framework. Method: We propose the first identifiable and estimable local functional linear interaction model, enabling unbiased causal interpretation for both discrete and continuous covariates. Our approach features bias-corrected robust inference, a data-driven optimal bandwidth selection criterion, and formal significance testing for inter-group heterogeneity differences. Contribution/Results: Under theoretical guarantees, the framework achieves high-precision estimation of heterogeneous treatment effects and valid hypothesis testing. An open-source software package ensures reproducibility, and extensive empirical applications—including educational interventions and policy evaluations—demonstrate its effectiveness and robustness in canonical RD settings.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Empirical studies using Regression Discontinuity (RD) designs often explore heterogeneous treatment effects based on pretreatment covariates. However, the lack of formal statistical methods has led to the widespread use of ad hoc approaches in applications. Motivated by common empirical practice, we develop a unified, theoretically grounded framework for RD heterogeneity analysis. We show that a fully interacted local linear (in functional parameters) model effectively captures heterogeneity while still being tractable and interpretable in applications. The model structure holds without loss of generality for discrete covariates, while for continuous covariates our proposed (local functional linear-in-parameters) model can be potentially restrictive, but it nonetheless naturally matches standard empirical practice and offers a causal interpretation for RD applications. We establish principled bandwidth selection and robust bias-corrected inference methods to analyze heterogeneous treatment effects and test group differences. We provide companion software to facilitate implementation of our results. An empirical application illustrates the practical relevance of our methods.

Problem

• Lack formal methods for RD heterogeneous treatment effect analysis
• Ad hoc approaches dominate current RD heterogeneity studies
• Need unified framework for RD heterogeneity with causal interpretation

Innovation

• Fully interacted local linear model
• Principled bandwidth selection method
• Robust bias-corrected inference