Jackknife inference with two-way clustering

TL;DR

This paper introduces new methods for improving inference in two-way clustered data models, including a novel jackknife-based variance estimator that provides more reliable confidence intervals and hypothesis tests.

Contribution

It proposes a new two-way cluster jackknife variance estimator and demonstrates its effectiveness through simulations, enhancing finite-sample inference accuracy.

Findings

The new jackknife-based estimator improves inference accuracy.

Simulations show better coverage probabilities with the proposed methods.

The software package 'twowayjack' implements these methods in Stata.

Abstract

For linear regression models with cross-section or panel data, it is natural to assume that the disturbances are clustered in two dimensions. However, the finite-sample properties of two-way cluster-robust tests and confidence intervals are often poor. We discuss several ways to improve inference with two-way clustering. Two of these are existing methods for avoiding, or at least ameliorating, the problem of undefined standard errors when a cluster-robust variance matrix estimator (CRVE) is not positive definite. One is a new method that always avoids the problem. More importantly, we propose a family of new two-way CRVEs based on the cluster jackknife and prove that they yield valid inferences asymptotically. Simulations for models with two-way fixed effects suggest that, in many cases, the cluster-jackknife CRVE combined with our new method yields surprisingly accurate inferences. We provide a software package, twowayjack for Stata, that implements our recommended variance estimator.