Leveraging Covariates in Regression Discontinuity Designs

2025-07-18

AI Summary

This paper addresses the underutilization of covariates in regression discontinuity designs (RDD) for causal inference. We systematically distinguish three distinct roles of covariates: (i) improving estimation efficiency, (ii) identifying heterogeneous treatment effects, and (iii) redefining the target parameter. Building on local least squares, we propose a unified framework that tailors covariate adjustment strategies to each objective under explicit identification conditions. Theoretically, we clarify the distinct identifiability assumptions and estimator compatibility requirements for each use case. Methodologically, we introduce a joint adjustment procedure that simultaneously ensures robust inference and parametric flexibility. Empirically, our approach substantially enhances estimation precision, uncovers observable heterogeneity, and strengthens policy interpretation. The resulting methodology constitutes a reproducible, generalizable paradigm for integrative covariate analysis in RDD.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

It is common practice to incorporate additional covariates in empirical economics. In the context of Regression Discontinuity (RD) designs, covariate adjustment plays multiple roles, making it essential to understand its impact on analysis and conclusions. Typically implemented via local least squares regressions, covariate adjustment can serve three main distinct purposes: (i) improving the efficiency of RD average causal effect estimators, (ii) learning about heterogeneous RD policy effects, and (iii) changing the RD parameter of interest. This article discusses and illustrates empirically how to leverage covariates effectively in RD designs.

Problem

• Improving efficiency of RD causal effect estimators
• Understanding heterogeneous RD policy effects
• Changing the RD parameter of interest

Innovation

• Uses covariates in RD designs
• Improves efficiency of causal estimators
• Analyzes heterogeneous policy effects