Robust Inference with Multi-Way Clustering

34 Pages Posted: 6 Oct 2006 Last revised: 13 Jun 2007

See all articles by A. Colin Cameron

A. Colin Cameron

University of California, Davis - Department of Economics

Jonah B. Gelbach

University of Pennsylvania Law School

Douglas L. Miller

University of California, Davis - Department of Economics

Date Written: September 2006

Abstract

In this paper we propose a new variance estimator for OLS as well as for nonlinear estimators such as logit, probit and GMM, that provcides cluster-robust inference when there is two-way or multi-way clustering that is non-nested. The variance estimator extends the standard cluster-robust variance estimator or sandwich estimator for one-way clustering (e.g. Liang and Zeger (1986), Arellano (1987)) and relies on similar relatively weak distributional assumptions. Our method is easily implemented in statistical packages, such as Stata and SAS, that already offer cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random effects model; a Monte Carlo analysis of a placebo law that extends the state-year effects example of Bertrand et al. (2004) to two dimensions; and by application to two studies in the empirical public/labor literature where two-way clustering is present.

Suggested Citation

Cameron, A. Colin and Gelbach, Jonah B. and Miller, Douglas L., Robust Inference with Multi-Way Clustering (September 2006). NBER Working Paper No. t0327. Available at SSRN: https://ssrn.com/abstract=927374

A. Colin Cameron

University of California, Davis - Department of Economics ( email )

One Shields Drive
Davis, CA 95616-8578
United States

Jonah B. Gelbach (Contact Author)

University of Pennsylvania Law School ( email )

3501 Sansom Street
Philadelphia, PA 19104
United States

Douglas L. Miller

University of California, Davis - Department of Economics ( email )

One Shields Drive
Davis, CA 95616-8578
United States
530-752-8490 (Phone)

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