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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, S. & Larcom, S. & She, P-W., 2024. "Do Religious People Cope Better in a Crisis? Evidence from the UK Pandemic Lockdowns," Cambridge Working Papers in Economics 2403, Faculty of Economics, University of Cambridge.
    2. MacKinnon, James G., 2023. "Fast cluster bootstrap methods for linear regression models," Econometrics and Statistics, Elsevier, vol. 26(C), pages 52-71.
    3. 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.
    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. James J. Heckman & Rodrigo Pinto & Azeem Shaikh, 2023. "Dealing with Imperfect Randomization: Inference for the HighScope Perry Preschool Program," NBER Working Papers 31982, National Bureau of Economic Research, Inc.
    6. Felipe Gonzalez & Luis R. Martinez & Pablo Munoz & Mounu Prem, 2023. "Higher education and mortality: legacies of an authoritarian college contraction," Working Papers 965, Queen Mary University of London, School of Economics and Finance.

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