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Inference in Regression Discontinuity Designs with Clustered Data

Claudia Noack, Tomasz Olma, Christoph Rothe

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.

Inference in Regression Discontinuity Designs with Clustered Data

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.
Paper Structure (48 sections, 10 theorems, 126 equations, 1 figure, 1 table, 1 algorithm)

This paper contains 48 sections, 10 theorems, 126 equations, 1 figure, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Setting and preview of the results
  3. Clustered Sampling
  4. Local Linear RD Estimator
  5. Preview of Asymptotic Results
  6. Standard Errors
  7. Asymptotic Normality under high-level conditions
  8. High-Level Conditions
  9. Asymptotic Normality
  10. Asymptotic Frameworks
  11. General Assumptions
  12. Small Effective Cluster Sizes
  13. Assumptions
  14. Theoretical results
  15. Large Effective Cluster Sizes
  16. ...and 33 more sections

Key Result

Theorem 3.1

Figures (1)

  • Figure 6.1: Visualization of cluster structures in the empirical applications.

Theorems & Definitions (20)

  • Remark 2.1
  • Remark 3.1
  • Theorem 3.1
  • Example 1
  • Example 2
  • Proposition 4.1
  • Example 1: Equal Cluster Sizes, cont'd
  • Example 2: Heterogeneous Cluster Sizes, cont'd
  • Proposition 4.2
  • Lemma 4.1
  • ...and 10 more