Wild Bootstrap Inference for Wildly Different Cluster Sizes

The cluster robust variance estimator (CRVE) relies on the number of clusters being large. A shorthand "rule of 42'' has emerged, but we show that unbalanced clusters invalidate it. Monte Carlo evidence suggests that rejection frequencies are higher for datasets with 50 clusters proportional to US state populations rather than 50 balanced clusters. Using critical values based on the wild cluster bootstrap performs much better. However, this procedure fails when a small number of clusters is treated. We explain why this happens, study the ``effective number'' of clusters, and simulate placebo laws with dummy variable regressors to provide further evidence.