Refined Cluster Robust Inference
Econometrics
2026-03-27 v1 Statistics Theory
Statistics Theory
Abstract
It has become standard for empirical studies to conduct inference robust to cluster dependence and heterogeneity. With a small number of clusters, the normal approximation for the -statistics of regression coefficients may be poor. This paper tackles this problem using a critical value based on the conditional Cram\'er-Edgeworth expansion for the -statistics. Our approach guarantees third-order refinement, regardless of whether a regressor is discrete or not, and, unlike the cluster pairs bootstrap, avoids resampling data. Simulations show that our proposal can make a difference in size control with as few as 10 clusters.
Keywords
Cite
@article{arxiv.2603.24786,
title = {Refined Cluster Robust Inference},
author = {Bulat Gafarov and Takuya Ura},
journal= {arXiv preprint arXiv:2603.24786},
year = {2026}
}