The wild bootstrap for few (treated) clusters

Inference based on cluster-robust standard errors in linear regression models, using either the Student's t-distribution 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,...

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Bibliographic Details
Published in:The econometrics journal 2018-06, Vol.21 (2), p.114-135
Main Authors: Mackinnon, James G., Webb, Matthew D.
Format: Article
Language:English
Subjects:
Clustered data
Cluster‐robust variance estimator
Difference‐in‐differences
Economic models
Grouped data
Regression analysis
Robust inference
Subclustering
Treatment methods
Treatment model
Wild bootstrap
Wild cluster bootstrap
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Summary:Inference based on cluster-robust standard errors in linear regression models, using either the Student's t-distribution 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, which includes the ordinary wild bootstrap as a limiting case. In the case of pure treatment models, where all observations within clusters are either treated or not, the latter procedure can work remarkably well. The key requirement is that all cluster sizes, regardless of treatment, should be similar. Unfortunately, the analogue 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.
ISSN:1368-4221
1368-423X
DOI:10.1111/ectj.12107