Refined Cluster Robust Inference

TL;DR

This paper introduces a refined inference method for clustered data that improves accuracy with small numbers of clusters by using a critical value based on the conditional Cramér-Edgeworth expansion, avoiding resampling.

Contribution

It proposes a third-order refined critical value for cluster-robust inference that performs well with few clusters, without resampling, and applies to both discrete and continuous regressors.

Findings

Improves size control with as few as 10 clusters.

Achieves third-order refinement in inference accuracy.

Avoids resampling methods like bootstrap.

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 $t$-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 $t$-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.