Bootstrap-Based Improvements for Inference with Clustered Errors
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 (5-30) 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 ten percent using standard methods can be reduced to the nominal size of five percent using our methods.
We thank an anonymous referee and participants at The Australian National University, UC Berkeley, UC Riverside, Dartmouth College, Florida State University, Indiana University, and MIT for useful comments. Miller acknowledges funding from the National Institute on Aging, through Grant Number T32-AG00186 to the NBER. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.