The Subcluster Wild Bootstrap for Few (Treated) Clusters
Inference based on cluster-robust standard errors or the wild cluster bootstrap is known to fail when the number of treated clusters is very small. We propose a family of new procedures called the subcluster wild bootstrap. In the case of pure treatment models, where all observations within clusters are either treated or not, the new procedures can work remarkably well. The key requirement is that all cluster sizes, regardless of treatment, should be similar. Unfortunately, the analog of this requirement is not likely to hold for difference-in-differences regressions. Our theoretical results are supported by extensive simulations and an empirical example.
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