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Bootstrap-Based Improvements for Inference with Clustered Errors

A. Colin Cameron, Jonah B. Gelbach and Douglas L. Miller

Posted Online July 22, 2008
https://doi.org/10.1162/rest.90.3.414

Review of Economics and Statistics

Volume 90 | Issue 3 | August 2008
p.414-427
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Bootstrap-Based Improvements for Inference with Clustered Errors

A. Colin Cameron, Jonah B. Gelbach and Douglas L. Miller
https://doi.org/10.1162/rest.90.3.414
Received: June 15, 2006
Accepted: May 04, 2007
Published Online: July 22, 2008
Abstract

Abstract

Researchers have increasingly realized the need to account for within-group dependence in estimating standard errors of regression parameter estimates. The usual solution is to calculate cluster-robust standard errors that permit heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. Standard asymptotic tests can over-reject, however, with few (five to thirty) clusters. We investigate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the example of Bertrand, Duflo, and Mullainathan (2004). Rejection rates of 10% using standard methods can be reduced to the nominal size of 5% using our methods.

A. Colin Cameron
Department of Economics, University of California–Davis
Jonah B. Gelbach
Department of Economics, University of Arizona
Douglas L. Miller
Department of Economics, University of California–Davis
https://doi.org/10.1162/rest.90.3.414
Abstract

Abstract

Researchers have increasingly realized the need to account for within-group dependence in estimating standard errors of regression parameter estimates. The usual solution is to calculate cluster-robust standard errors that permit heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. Standard asymptotic tests can over-reject, however, with few (five to thirty) clusters. We investigate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the example of Bertrand, Duflo, and Mullainathan (2004). Rejection rates of 10% using standard methods can be reduced to the nominal size of 5% using our methods.

A. Colin Cameron
Department of Economics, University of California–Davis
Jonah B. Gelbach
Department of Economics, University of Arizona
Douglas L. Miller
Department of Economics, University of California–Davis
Download Options

Bootstrap-Based Improvements for Inference with Clustered Errors

A. Colin Cameron, Jonah B. Gelbach and Douglas L. Miller
https://doi.org/10.1162/rest.90.3.414
Received: June 15, 2006
Accepted: May 04, 2007
Published Online: July 22, 2008
Abstract

Abstract

Researchers have increasingly realized the need to account for within-group dependence in estimating standard errors of regression parameter estimates. The usual solution is to calculate cluster-robust standard errors that permit heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. Standard asymptotic tests can over-reject, however, with few (five to thirty) clusters. We investigate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the example of Bertrand, Duflo, and Mullainathan (2004). Rejection rates of 10% using standard methods can be reduced to the nominal size of 5% using our methods.

A. Colin Cameron
Department of Economics, University of California–Davis
Jonah B. Gelbach
Department of Economics, University of Arizona
Douglas L. Miller
Department of Economics, University of California–Davis
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