Bootstrap-Based Improvements for Inference with Clustered Errors

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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 Mullai-nathan (2004). Rejection rates of 10% using standard methods can be reduced to the nominal size of 5% using our methods.