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.

Additional Metadata
Keywords CRVE, grouped data, clustered data, wild bootstrap, wild cluster bootstrap, subclustering, treatment model, difference-in-differences, robust inference
JEL Simulation Methods; Monte Carlo Methods; Bootstrap Methods (jel C15), Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions (jel C21), Models with Panel Data (jel C23)
Publisher Department of Economics
Series Carleton Economic Papers (CEP)
James G. MacKinnon, & Webb, M. (2016). The Subcluster Wild Bootstrap for Few (Treated) Clusters (No. CEP 16-13). Carleton Economic Papers (CEP). Department of Economics.