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Wild Bootstrap Inference for Wildly Different Cluster Sizes

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  • James G. MacKinnon
  • 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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Bibliographic Info

Paper provided by Department of Economics, University of Calgary in its series Working Papers with number 2013-17.

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Date of creation: 13 Jan 2014
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Handle: RePEc:clg:wpaper:2013-17

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  1. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
  2. 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.
  3. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2007. "Bootstrap-Based Improvements for Inference with Clustered Errors," NBER Technical Working Papers 0344, National Bureau of Economic Research, Inc.
  4. Davidson, R. & Flachaire, E., 1999. "The Wild Bootstrap, Tamed at Last," G.R.E.Q.A.M. 99a32, Universite Aix-Marseille III.
  5. Matthew D. Webb, 2013. "Reworking Wild Bootstrap Based Inference for Clustered Errors," Working Papers 1315, Queen's University, Department of Economics.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
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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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