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The Wild Bootstrap with a “Small†Number of “Large†Clusters

Author

Listed:
  • Ivan A. Canay

    (Northwestern University)

  • Andres Santos

    (UCLA)

  • Azeem M. Shaikh

    (University of Chicago)

Abstract

This paper studies the wild bootstrap–based test proposed in Cameron, Gelbach, and Miller (2008). Existing analyses of its properties require that number of clusters is “large.†In an asymptotic framework in which the number of clusters is “small,†we provide conditions under which an unstudentized version of the test is valid. These conditions include homogeneity-like restrictions on the distribution of covariates. We further establish that a studentized version of the test may only overreject the null hypothesis by a “small†amount that decreases exponentially with the number of clusters. We obtain a qualitatively similar result for “score†bootstrap-based tests, which permit testing in nonlinear models.

Suggested Citation

  • Ivan A. Canay & Andres Santos & Azeem M. Shaikh, 2021. "The Wild Bootstrap with a “Small†Number of “Large†Clusters," The Review of Economics and Statistics, MIT Press, vol. 103(2), pages 346-363, May.
    • Handle: RePEc:tpr:restat:v:103:y:2021:i:2:p:346-363
    DOI: 10.1162/rest_a_00887
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    Cited by:

    1. Iyer, Sriya & Larcom, Shaun & She, Po-Wen, 2024. "Do Religious People Cope Better in a Crisis? Evidence from the UK Pandemic Lockdowns," CEPR Discussion Papers 18830, C.E.P.R. Discussion Papers.
    2. Heckman, James & Pinto, Rodrigo & Shaikh, Azeem M., 2024. "Dealing with imperfect randomization: Inference for the highscope perry preschool program," Journal of Econometrics, Elsevier, vol. 243(1).
    3. MacKinnon, James G., 2023. "Fast cluster bootstrap methods for linear regression models," Econometrics and Statistics, Elsevier, vol. 26(C), pages 52-71.
    4. 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.
    5. Atsushi Inoue & `Oscar Jord`a & Guido M. Kuersteiner, 2023. "Inference for Local Projections," Papers 2306.03073, arXiv.org, revised Aug 2024.
    6. François Bareille & Raja Chakir, 2024. "Structural identification of weather impacts on crop yields: Disentangling agronomic from adaptation effects," American Journal of Agricultural Economics, John Wiley & Sons, vol. 106(3), pages 989-1019, May.
    7. Felipe González & Luis R Martínez & Pablo Muñoz & Mounu Prem, 2024. "Higher Education and Mortality: Legacies of an Authoritarian College Contraction," Journal of the European Economic Association, European Economic Association, vol. 22(4), pages 1762-1797.
    8. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2023. "Fast and reliable jackknife and bootstrap methods for cluster‐robust inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(5), pages 671-694, August.
    9. Chiara Berneri & Shaun Larcom & Congmin Peng & Po-Wen She, 2024. "The impact of law on moral and social norms: evidence from facemask fines in the UK," European Journal of Law and Economics, Springer, vol. 57(3), pages 311-346, June.
    10. David M. Ritzwoller & Joseph P. Romano & Azeem M. Shaikh, 2024. "Randomization Inference: Theory and Applications," Papers 2406.09521, arXiv.org.
    11. Weiss, Amanda, 2024. "How Much Should We Trust Modern Difference-in-Differences Estimates?," OSF Preprints bqmws, Center for Open Science.
    12. Òscar Jordà & Alan M. Taylor, 2024. "Local Projections," Working Paper Series 2024-24, Federal Reserve Bank of San Francisco.
    13. Cai, Yong & Rafi, Ahnaf, 2024. "On the performance of the Neyman Allocation with small pilots," Journal of Econometrics, Elsevier, vol. 242(1).
    14. Balmford, Ben & Collins, Joseph & Day, Brett & Lindsay, Luke & Peacock, James, 2023. "Pricing rules for PES auctions: Evidence from a natural experiment," Journal of Environmental Economics and Management, Elsevier, vol. 122(C).
    15. Kojevnikov, Denis & Song, Kyungchul, 2023. "Some impossibility results for inference with cluster dependence with large clusters," Journal of Econometrics, Elsevier, vol. 237(2).

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