Wild Bootstrap Inference for Wildly Different Cluster Sizes - James G. MacKinnon; Matthew D. Webb (Queen's University, Department of Economics, 2014)
The cluster robust variance estimator (CRVE) relies on the number of clusters being large. The precise meaning of 'large' is ambiguous, but a shorthand 'rule of 42' has emerged in the literature. We show that this rule depends crucially on the assumption of equal-sized clusters. Monte Carlo evidence suggests that rejection frequencies at the five percent level can be more than twice the desired size when a dataset has 50 clusters proportional to the populations of the US states. In contrast, using a cluster wild bootstrap procedure for the same dataset usually results in very accurate rejection frequencies. We also show that, when the test regressor is a dummy variable, both conventional and bootstrap tests perform badly when the proportion of clusters treated is very small or very large. A third set of simulations uses placebo laws to see whether similar results hold in a difference-in-differences framework.
Keywords: C15; C21; C23; 330; CRVE; grouped data; clustered data; panel data; cluster wild bootstrap; difference in differences; effective number of clusters; placebo laws