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Permutation inference with a finite number of heterogeneous clusters

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  • Andreas Hagemann

Abstract

I introduce a simple permutation procedure to test conventional (non-sharp) hypotheses about the effect of a binary treatment in the presence of a finite number of large, heterogeneous clusters when the treatment effect is identified by comparisons across clusters. The procedure asymptotically controls size by applying a level-adjusted permutation test to a suitable statistic. The adjustments needed for most empirically relevant situations are tabulated in the paper. The adjusted permutation test is easy to implement in practice and performs well at conventional levels of significance with at least four treated clusters and a similar number of control clusters. It is particularly robust to situations where some clusters are much more variable than others. Examples and an empirical application are provided.

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  • Andreas Hagemann, 2019. "Permutation inference with a finite number of heterogeneous clusters," Papers 1907.01049, arXiv.org, revised Feb 2023.
    • Handle: RePEc:arx:papers:1907.01049
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    References listed on IDEAS

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    Cited by:

    1. James G. MacKinnon & Matthew D. Webb, 2020. "When and How to Deal with Clustered Errors in Regression Models," Working Paper 1421, Economics Department, Queen's University.
    2. MacKinnon, James G. & Nielsen, Morten Ørregaard & Webb, Matthew D., 2023. "Cluster-robust inference: A guide to empirical practice," Journal of Econometrics, Elsevier, vol. 232(2), pages 272-299.
    3. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    4. Johannes W. Ligtenberg, 2023. "Inference in IV models with clustered dependence, many instruments and weak identification," Papers 2306.08559, arXiv.org, revised Mar 2024.
    5. Andreas Hagemann, 2023. "Inference on quantile processes with a finite number of clusters," Papers 2301.04687, arXiv.org, revised Jun 2023.
    6. Andreas Hagemann, 2020. "Inference with a single treated cluster," Papers 2010.04076, arXiv.org.

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