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The wild bootstrap for few (treated) clusters

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  • James G. MacKinnon
  • Matthew D. Webb

Abstract

SummaryInference 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.

Suggested Citation

  • James G. MacKinnon & Matthew D. Webb, 2018. "The wild bootstrap for few (treated) clusters," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 114-135.
  • Handle: RePEc:oup:emjrnl:v:21:y:2018:i:2:p:114-135.
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    File URL: http://hdl.handle.net/10.1111/ectj.12107
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    Keywords

    Clustered data; Cluster‐robust variance estimator; Difference‐in‐differences; Grouped data; Robust inference; Subclustering; Treatment model; Wild bootstrap; Wild cluster bootstrap;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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