IDEAS home Printed from https://ideas.repec.org/p/ifs/cemmap/27-18.html
   My bibliography  Save this paper

The wild bootstrap with a "small" number of "large" clusters

Author

Listed:
  • Ivan A. Canay

    (Institute for Fiscal Studies and Northwestern University)

  • Andres Santos

    () (Institute for Fiscal Studies and UC San Diego)

  • Azeem M. Shaikh

    (Institute for Fiscal Studies and University of Chicago)

Abstract

This paper studies the properties of the wild bootstrap-based test proposed in Cameron et al. (2008) in settings with clustered data. Cameron et al. (2008) provide simulations that suggest this test works well even in settings with as few as fi ve clusters, but existing theoretical analyses of its properties all rely on an asymptotic framework in which the number of clusters is "large." In contrast to these analyses, we employ an asymptotic framework in which the number of clusters is "small," but the number of observations per cluster is "large." In this framework, we provide conditions under which the limiting rejection probability of an un-Studentized version of the test does not exceed the nominal level. Importantly, these conditions require, among other things, certain homogeneity restrictions on the distribution of covariates. We further establish that the limiting rejection probability of a Studentized version of the test does not exceed the nominal level by more than an amount that decreases exponentially with the number of clusters. We study the relevance of our theoretical results for finite samples via a simulation study.

Suggested Citation

  • Ivan A. Canay & Andres Santos & Azeem M. Shaikh, 2018. "The wild bootstrap with a "small" number of "large" clusters," CeMMAP working papers CWP27/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:27/18
    as

    Download full text from publisher

    File URL: https://www.ifs.org.uk/uploads/CWP271818.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Daron Acemoglu & Davide Cantoni & Simon Johnson & James A. Robinson, 2011. "The Consequences of Radical Reform: The French Revolution," American Economic Review, American Economic Association, vol. 101(7), pages 3286-3307, December.
    2. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    3. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    4. Rustam Ibragimov & Ulrich K. Müller, 2016. "Inference with Few Heterogeneous Clusters," The Review of Economics and Statistics, MIT Press, vol. 98(1), pages 83-96, March.
    5. Matthew D. Webb, 2014. "Reworking Wild Bootstrap Based Inference For Clustered Errors," Working Paper 1315, Economics Department, Queen's University.
    6. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June.
    7. repec:clg:wpaper:2013-17 is not listed on IDEAS
    8. Jeffrey M. Wooldridge, 2003. "Cluster-Sample Methods in Applied Econometrics," American Economic Review, American Economic Association, vol. 93(2), pages 133-138, May.
    9. repec:tpr:restat:v:99:y:2017:i:4:p:698-709 is not listed on IDEAS
    10. Bester, C. Alan & Conley, Timothy G. & Hansen, Christian B., 2011. "Inference with dependent data using cluster covariance estimators," Journal of Econometrics, Elsevier, vol. 165(2), pages 137-151.
    11. repec:wly:emetrp:v:85:y:2017:i::p:1013-1030 is not listed on IDEAS
    12. Stephen G. Donald & Kevin Lang, 2007. "Inference with Difference-in-Differences and Other Panel Data," The Review of Economics and Statistics, MIT Press, vol. 89(2), pages 221-233, May.
    13. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, Oxford University Press, vol. 119(1), pages 249-275.
    14. James G. MacKinnon & Matthew D. Webb, 2017. "Wild Bootstrap Inference for Wildly Different Cluster Sizes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(2), pages 233-254, March.
    15. Ibragimov, Rustam & Müller, Ulrich K., 2010. "t-Statistic Based Correlation and Heterogeneity Robust Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 453-468.
    16. repec:oup:restud:v:82:y:2015:i:4:p:1568-1611. is not listed on IDEAS
    17. Antoine A. Djogbenou & James G. MacKinnon & Morten Ø. Nielsen, 2017. "Validity Of Wild Bootstrap Inference With Clustered Errors," Working Paper 1383, Economics Department, Queen's University.
    18. James G. MacKinnon & Matthew D. Webb & Morten Ø. Nielsen, 2017. "Bootstrap And Asymptotic Inference With Multiway Clustering," Working Paper 1386, Economics Department, Queen's University.
    19. Michael Kosfeld & Devesh Rustagi, 2015. "Leader Punishment and Cooperation in Groups: Experimental Field Evidence from Commons Management in Ethiopia," American Economic Review, American Economic Association, vol. 105(2), pages 747-783, February.
    20. Paola Giuliano & Antonio Spilimbergo, 2014. "Growing up in a Recession," Review of Economic Studies, Oxford University Press, vol. 81(2), pages 787-817.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. James G. MacKinnon & Matthew D. Webb, 2019. "When and How to Deal with Clustered Errors in Regression Models," Working Paper 1421, Economics Department, Queen's University.
    2. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2018. "Asymptotic results under multiway clustering," Papers 1807.07925, arXiv.org, revised Aug 2018.

    More about this item

    Keywords

    Wild bootstrap; Clustered Data; Randomization Tests;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ifs:cemmap:27/18. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Emma Hyman). General contact details of provider: http://edirc.repec.org/data/cmifsuk.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.