Multi-Way Clustering

Multi-Way Clustering - TECHNICAL WORKING PAPER SERIES...

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TECHNICAL WORKING PAPER SERIES ROBUST INFERENCE WITH MULTI-WAY CLUSTERING A. Colin Cameron Jonah B. Gelbach Douglas L. Miller Technical Working Paper 327 http://www.nber.org/papers/T0327 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 September 2006 This paper has benefitted from presentations at the University of California - Berkely, the University of California - Riverside, and Dartmouth College. Miller gratefully acknowledges funding from the National Institute on Aging, through Grant Number T32-AG00186 to the NBER. ©2006 by A. Colin Cameron, Jonah B. Gelbach, and Douglas L. Miller. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
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Robust Inference with Multi-way Clustering A. Colin Cameron, Jonah B. Gelbach, and Douglas L. Miller NBER Technical Working Paper No. 327 September 2006 JEL No. C14, C21, C52 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. A. Colin Cameron Department of Economics UC Davis Davis, CA 95616 accameron@ucdavis.edu Jonah Gelbach Department of Economics University of Maryland College Park, MD 20742 and College of Law Florida State University 425 West Jefferson Street Tallahassee, FL 32303 and NBER gelbach@glue.umd.edu Douglas Miller Department of Economics UC Davis Davis, CA 95616 and NBER dlmiller@ucdavis.edu
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1. Introduction A key component of empirical research is conducting accurate statistical inference. One challenge to this is the possibility of clustered (or non-independent) errors. In this paper we propose a new variance estimator for commonly used estimators, such as OLS, probit, and logit, that provides cluster-robust inference when there is multi-way non- nested clustering. The variance estimator extends the standard cluster-robust variance estimator for one-way clustering, and relies on similar relatively weak distributional assumptions. Our method is easily implemented in any statistical package that provides cluster-robust standard errors with one-way clustering.
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Multi-Way Clustering - TECHNICAL WORKING PAPER SERIES...

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