Asymptotic Theory for Two-Way Clustering

TL;DR

This paper establishes a new central limit theorem for data with two-way dependence and heterogeneity, providing a theoretical foundation for valid statistical inference in complex clustered data scenarios.

Contribution

It introduces a novel CLT for two-way clustered data without requiring identical distributions across clusters, extending the robustness of one-way clustering theory.

Findings

Validates a standard variance estimator for two-way clustered data

Theoretically justifies two-way clustering as a robust extension of one-way clustering

Provides a foundation for reliable inference in complex clustered data

Abstract

This paper proves a new central limit theorem for a sample that exhibits two-way dependence and heterogeneity across clusters. Statistical inference for situations with both two-way dependence and cluster heterogeneity has thus far been an open issue. The existing theory for two-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 two-way clustering is a more robust version of one-way clustering, consistent with applied practice. In an application to linear regression, I show that a standard plug-in variance estimator is valid for inference.