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Bootstrap With Cluster‐Dependence in Two or More Dimensions

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  • Konrad Menzel

Abstract

We propose a bootstrap procedure for data that may exhibit cluster‐dependence in two or more dimensions. The asymptotic distribution of the sample mean or other statistics may be non‐Gaussian if observations are dependent but uncorrelated within clusters. We show that there exists no procedure for estimating the limiting distribution of the sample mean under two‐way clustering that achieves uniform consistency. However, we propose bootstrap procedures that achieve adaptivity with respect to different uniformity criteria. Important cases and extensions discussed in the paper include regression inference, U‐ and V‐statistics, subgraph counts for network data, and non‐exhaustive samples of matched data.

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  • Konrad Menzel, 2021. "Bootstrap With Cluster‐Dependence in Two or More Dimensions," Econometrica, Econometric Society, vol. 89(5), pages 2143-2188, September.
    • Handle: RePEc:wly:emetrp:v:89:y:2021:i:5:p:2143-2188
    DOI: 10.3982/ECTA15383
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    References listed on IDEAS

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    1. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2021. "Wild Bootstrap and Asymptotic Inference With Multiway Clustering," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 505-519, March.
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    Citations

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    Cited by:

    1. Kojevnikov, Denis & Song, Kyungchul, 2023. "Some impossibility results for inference with cluster dependence with large clusters," Other publications TiSEM 80b8e4ed-54bc-4a34-883f-f, Tilburg University, School of Economics and Management.
    2. Wang, Wenjie & Zhang, Yichong, 2024. "Wild bootstrap inference for instrumental variables regressions with weak and few clusters," Journal of Econometrics, Elsevier, vol. 241(1).
    3. 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.
    4. Diegert, Paul & Jochmans, Koen, 2024. "Nonparametric Identification of Models for Dyadic Data”," TSE Working Papers 24-1574, Toulouse School of Economics (TSE).
    5. Kojevnikov, Denis & Song, Kyungchul, 2023. "Some impossibility results for inference with cluster dependence with large clusters," Journal of Econometrics, Elsevier, vol. 237(2).
    6. MacKinnon, James G. & Nielsen, Morten Ørregaard & Webb, Matthew D., 2023. "Testing for the appropriate level of clustering in linear regression models," Journal of Econometrics, Elsevier, vol. 235(2), pages 2027-2056.
    7. Lu, Xun & Su, Liangjun, 2023. "Uniform inference in linear panel data models with two-dimensional heterogeneity," Journal of Econometrics, Elsevier, vol. 235(2), pages 694-719.
    8. Kaicheng Chen & Timothy J. Vogelsang, 2023. "Fixed-b Asymptotics for Panel Models with Two-Way Clustering," Papers 2309.08707, arXiv.org, revised Aug 2024.
    9. Nan Liu & Yanbo Liu & Yuya Sasaki, 2024. "Estimation and Inference for Causal Functions with Multiway Clustered Data," Papers 2409.06654, arXiv.org.
    10. Harold D Chiang & Bruce E Hansen & Yuya Sasaki, 2022. "Standard errors for two-way clustering with serially correlated time effects," Papers 2201.11304, arXiv.org, revised Dec 2023.
    11. Freeman, Hugo & Weidner, Martin, 2023. "Linear panel regressions with two-way unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 237(1).
    12. James G. MacKinnon & Morten {O}rregaard Nielsen & Matthew D. Webb, 2024. "Jackknife inference with two-way clustering," Papers 2406.08880, arXiv.org.
    13. Matthew D. Webb, 2023. "Reworking wild bootstrap‐based inference for clustered errors," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 56(3), pages 839-858, August.
    14. Christis Katsouris, 2024. "Robust Estimation in Network Vector Autoregression with Nonstationary Regressors," Papers 2401.04050, arXiv.org.
    15. Hugo Freeman & Martin Weidner, 2021. "Linear panel regressions with two-way unobserved heterogeneity," CeMMAP working papers CWP39/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. MacKinnon, James G., 2023. "Using large samples in econometrics," Journal of Econometrics, Elsevier, vol. 235(2), pages 922-926.
    17. Batkeyev, Birzhan & DeRemer, David R., 2023. "Mountains of evidence: The effects of abnormal air pollution on crime," Journal of Economic Behavior & Organization, Elsevier, vol. 210(C), pages 288-319.
    18. Hugo Freeman, 2022. "Linear multidimensional regression with interactive fixed-effects," Papers 2209.11691, arXiv.org, revised Aug 2024.

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