Robust Inference with Multi-way Clustering

by Douglas Miller of the University of California, Davis,
A. Colin Cameron of the University of California, Davis, and
Jonah Gelbach of the University of Arizona

May 1, 2009

Abstract: In this paper we propose a variance estimator for the OLS estimator as well as for nonlinear estimators such as logit, probit and GMM. This variance estimator enables 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 studies in the empirical literature where two-way clustering is present.

JEL Classification: C12, C21, C23.

Keywords: cluster-robust standard errors, two-way clustering, multi-way clustering

Published in: Journal of Business and Economic Statistics, Vol. 29, No. 2, (April 2011), pp. 238-249.

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