Genuinely Robust Inference for Clustered Data

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.