Genuinely Robust Inference for Clustered Data

Conventional cluster-robust inference methods are inconsistent when clusters are unignorably large. We derive a necessary and sufficient condition for consistency, which is violated in 77% of empirical studies published in American Economic Review and Econometrica (2020-2021). To address this, we propose two methods: (i) score subsampling, which retains the original estimator, and (ii) size-adjusted reweighting, which is easy to implement in software like Stata and remains valid if the cluster size follows Zipf's law. Simulations confirm the reliability and uniform size control of these approaches, offering robust alternatives where conventional methods fail.