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Wild Bootstrap Randomization Inference For Few Treated Clusters

Author

Listed:
  • James G. MacKinnon

    (Queen's University)

  • Matthew D. Webb

    (Carleton University)

Abstract

When there are few treated clusters in a pure treatment or difference-in-differences setting, t tests based on a cluster-robust variance estimator (CRVE) can severely over-reject. Although procedures based on the wild cluster bootstrap often work well when the number of treated clusters is not too small, they can either over-reject or under-reject seriously when it is. In a previous paper, we showed that procedures based on randomization inference (RI) can work well in such cases. However, RI can be impractical when the number of possible randomizations is small. We propose a bootstrap-based alternative to randomization inference, whichmitigates the discrete nature of RI P values in the few-clusters case. We also compare it to two other procedures. None of them works perfectly when the number of clusters is very small, but they can worksurprisingly well.

Suggested Citation

  • James G. MacKinnon & Matthew D. Webb, 2018. "Wild Bootstrap Randomization Inference For Few Treated Clusters," Working Paper 1404, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1404
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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1404.pdf
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    Keywords

    randomization inference; CRVE; grouped data; clustered data; panel data; wild cluster bootstrap; difference-in-differences; DiD; kernel-smoothed P value;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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