Jackknife inference with two-way clustering

2024-06-13

AI Summary

This paper addresses the challenge of finite-sample inference for linear regression under two-way clustering (e.g., individual × time), where conventional cluster-robust variance estimators (CRVEs) often yield non-positive-definite estimates, suffer from undercoverage of confidence intervals, and exhibit low test power. We propose the first family of two-way clustered robust variance estimators that is guaranteed to be positive definite. Built upon a two-way clustered jackknife, our estimator is rigorously shown to be asymptotically valid and fully compatible with two-way fixed-effects models. Relative to leading alternatives, it substantially improves standard-error stability, confidence-interval coverage, and hypothesis-test power in small samples. We provide an accompanying Stata command, `twowayjack`, enabling one-click implementation. Monte Carlo simulations demonstrate its robust error control across diverse designs—including sparse clustering and heterogeneous interference—while maintaining nominal size and high power.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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 simple software package, twowayjack for Stata, that implements our recommended variance estimator.

Problem

• Improving inference for linear regression with two-way clustering
• Addressing poor finite-sample properties of cluster-robust tests
• Developing new cluster jackknife variance estimators for valid inference

Innovation

• Two-way cluster-robust variance estimators using jackknife
• New method avoiding undefined standard errors problem
• Software implementation for improved statistical inference