Analytic inference with two-way clustering

TL;DR

This paper proposes a new analytic inference method for two-way clustering that addresses variance positivity and non-Gaussian regimes, providing valid and conservative tests with uniform validity and practical comparisons.

Contribution

It introduces a simple fix for inference issues in two-way clustering, ensuring validity across Gaussian and non-Gaussian regimes, and compares it with existing methods.

Findings

Tests are asymptotically exact in Gaussian regimes

Tests are asymptotically conservative in non-Gaussian regimes

Simulation results demonstrate the effectiveness of the proposed approach

Abstract

This paper studies analytic inference along two dimensions of clustering. In such setups, the commonly used approach has two drawbacks. First, the corresponding variance estimator is not necessarily positive. Second, inference is invalid in non-Gaussian regimes, namely when the estimator of the parameter of interest is not asymptotically Gaussian. We consider a simple fix that addresses both issues. In Gaussian regimes, the corresponding tests are asymptotically exact and equivalent to usual ones. Otherwise, the new tests are asymptotically conservative. We also establish their uniform validity over a certain class of data generating processes. Independently of our tests, we highlight potential issues with multiple testing and nonlinear estimators under two-way clustering. Finally, we compare our approach with existing ones through simulations.