Bootstrap-Based Improvements for Inference with Clustered Errors

52 Pages Posted: 12 Jan 2007

See all articles by A. Colin Cameron

A. Colin Cameron

University of California, Davis - Department of Economics

Jonah B. Gelbach

University of California, Berkeley - School of Law

Douglas L. Miller

University of California, Davis - Department of Economics

Date Written: January 2007

Abstract

Microeconometrics researchers have increasingly realized the essential need to account for any within-group dependence in estimating standard errors of regression parameter estimates. The typical preferred solution is to calculate cluster-robust or sandwich standard errors that permit quite general heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. In applications with few (5-30) clusters, standard asymptotic tests can over-reject considerably. We investigate more accurate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the much-cited diĀ¤erences-in-diĀ¤erences example of Bertrand, Mullainathan and Duflo (2004). In situations where standard methods lead to rejection rates in excess of ten percent (or more) for tests of nominal size 0:05, our methods can reduce this to five percent. In principle a pairs cluster bootstrap should work well, but in practice a Wild cluster bootstrap performs better.

Keywords: clustered errors, random effects, cluster robust

JEL Classification: C15, C12, C21

Suggested Citation

Cameron, A. Colin and Gelbach, Jonah B. and Miller, Douglas L., Bootstrap-Based Improvements for Inference with Clustered Errors (January 2007). FSU College of Law, Law and Economics Paper No. 07/002, Available at SSRN: https://ssrn.com/abstract=956890 or http://dx.doi.org/10.2139/ssrn.956890

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 California, Berkeley - School of Law ( email )

215 Boalt Hall
Berkeley, CA 94720-7200
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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