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Wild Bootstrap Inference for Wildly Different Cluster Sizes

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  • James G. MacKinnon

    ()
    (Queen)

  • Matthew D. Webb

    ()
    (University of Calgary)

Abstract

The cluster robust variance estimator (CRVE) relies on the number of clusters being large. The precise meaning of 'large' is ambiguous, but a shorthand 'rule of 42' has emerged in the literature. We show that this rule depends crucially on the assumption of equal-sized clusters. Monte Carlo evidence suggests that rejection frequencies can be much higher when a dataset has 50 clusters proportional to the populations of the US states than when it has 50 equal-sized clusters. In contrast, using a cluster wild bootstrap procedure generally works well in both cases. We also show that, when the test regressor is a dummy variable, as in a difference-in-differences framework, both conventional and bootstrap tests perform badly when the proportion of clusters treated is very small or very large. However, bootstrap tests perform very well when that is not the case. A third set of simulations studies placebo laws and finds that bootstrap tests usually perform very much better than conventional ones.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1314.pdf
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1314.

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Length: 22 pages
Date of creation: Nov 2013
Date of revision:
Handle: RePEc:qed:wpaper:1314

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Keywords: CRVE; grouped data; clustered data; panel data; cluster wild bootstrap; difference in differences; placebo laws;

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  1. 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.
  2. Russell Davidson & Emmanuel Flachaire, 2001. "The Wild Bootstrap, Tamed at Last," Working Papers 1000, Queen's University, Department of Economics.
  3. Matthew D. Webb, 2014. "Reworking Wild Bootstrap Based Inference for Clustered Errors," Working Papers 2013-20, Department of Economics, University of Calgary, revised 13 Jan 2014.
  4. Abadie, Alberto & Diamond, Alexis & Hainmueller, Jens, 2010. "Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 493-505.
  5. Kloek, T, 1981. "OLS Estimation in a Model Where a Microvariable Is Explained by Aggregates and Contemporaneous Disturbances Are Equicorrelated," Econometrica, Econometric Society, vol. 49(1), pages 205-07, January.
  6. 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.
  7. 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.
  8. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
  9. 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.
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Cited by:
  1. Matthew D. Webb, 2013. "Reworking Wild Bootstrap Based Inference for Clustered Errors," Working Papers 1315, Queen's University, Department of Economics.

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