Inference in Regression Discontinuity Designs with Clustered Data

TL;DR

This paper develops a theoretical framework for regression discontinuity designs with clustered data, revealing limitations of current standard errors and proposing a new variance estimator to improve inference accuracy.

Contribution

It introduces a general model-based approach for clustered RD data and proposes a novel variance estimator to address inconsistency and conservativeness of existing methods.

Findings

Standard local linear RD estimator is asymptotically normal under broad conditions.

Existing clustered standard errors can be inconsistent or overly conservative.

Proposed nearest-neighbor variance estimator improves inference in empirical applications.

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.