Bootstrap-Based Improvements for Inference with Clustered Errors

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. Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.

Patent thickets, defensive patenting, and induced R&D: an empirical analysis of the costs and potential benefits of fragmentation in patent ownership

“…Their estimated statistically significant 33 The number of replications in both nonparametric bootstrapping and wild bootstrapping is 1000. For a detailed explanation of nonparametric and wild bootstrapping procedures, refer to Cameron et al (2007). direct impact similar to my study implies that higher fragmentation translates to lower market value for software and manufacturing firms.…”

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