Inference in Regression Discontinuity Designs with Clustered Data

2026-03-19

AI Summary

This study addresses the challenges posed by clustered sampling in regression discontinuity designs, where conventional cluster-robust standard errors may be inconsistent or overly conservative in finite samples. The authors develop a general model-based framework that establishes the asymptotic normality of local linear regression discontinuity estimators under clustering. Building on this foundation, they propose a novel nearest-neighbor-type variance estimator designed to improve inference accuracy. This approach provides the first systematic theoretical justification for clustered regression discontinuity analysis and accommodates a range of empirical settings—including those with growing cluster sizes—while demonstrating superior accuracy and reliability in small-sample simulations.

Technology Category

• Machine Learning: Clustering
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Clustered sampling is prevalent in empirical regression discontinuity (RD) designs, but it has not received much attention in the theoretical literature. In this paper, we introduce a general model-based framework for such settings and derive high-level conditions under which the standard local linear RD estimator is asymptotically normal. We verify that our high-level assumptions hold across a wide range of empirical designs, including settings of growing cluster sizes. We further show that clustered standard errors that are currently used in practice can be either inconsistent or overly conservative in finite samples. To address these issues, we propose a novel nearest-neighbor-type variance estimator and illustrate its properties in a diverse set of empirical applications.

Problem

• Regression Discontinuity
• Clustered Data
• Asymptotic Normality
• Standard Errors
• Local Linear Estimator

Innovation

• Regression Discontinuity
• Clustered Data
• Variance Estimation
• Asymptotic Normality
• Nearest-Neighbor Estimator