Genuinely Robust Inference for Clustered Data

Abstract

Conventional cluster-robust inference can be invalid when data contain clusters of unignorably large size. We formalize this issue by deriving a necessary and sufficient condition for its validity, and show that this condition is frequently violated in practice: specifications from 77% of empirical research articles in American Economic Review and Econometrica during 2020-2021 appear not to meet it. To address this limitation, we propose a genuinely robust inference procedure based on a new cluster score bootstrap. We establish its validity and size control across broad classes of data-generating processes where conventional methods break down. Simulation studies corroborate our theoretical findings, and empirical applications illustrate that employing the proposed method can substantially alter conventional statistical conclusions.

This paper supersedes the manuscripts previously circulated under the titles "On the Inconsistency of Cluster-Robust Inference and How Subsampling Can Fix It" and "Non-Robustness of the Cluster-Robust Inference: with a Proposal of a New Robust Method" (arXiv:2210.16991)