"General Conditions for Valid Inference in Multi-Way Clustering" - Luther Yap

Abstract

This paper proves a new central limit theorem for a sample that exhibits multi-way dependence and heterogeneity across clusters. Statistical inference for situations where there is both multi-way dependence and cluster heterogeneity has thus far been an open issue. Existing theory for multi-way clustering inference requires identical distributions across clusters (implied by the so-called separate exchangeability assumption). Yet no such homogeneity requirement is needed in the existing theory for one-way clustering. The new result therefore theoretically justifies the view that multi-way clustering is a more robust version of one-way clustering, consistent with applied practice. The result is applied to linear regression, where it is shown that a standard plug-in variance estimator is valid for inference.