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Permutation inference with a finite number of heterogeneous clusters

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  • Andreas Hagemann

Abstract

I introduce a simple permutation procedure to test conventional (non-sharp) hypotheses about the effect of a binary treatment in the presence of a finite number of large, heterogeneous clusters when the treatment effect is identified by comparisons across clusters. The procedure asymptotically controls size by applying a level-adjusted permutation test to a suitable statistic. The adjustments needed for most empirically relevant situations are tabulated in the paper. The adjusted permutation test is easy to implement in practice and performs well at conventional levels of significance with at least four treated clusters and a similar number of control clusters. It is particularly robust to situations where some clusters are much more variable than others. Examples and an empirical application are provided.

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  • Andreas Hagemann, 2019. "Permutation inference with a finite number of heterogeneous clusters," Papers 1907.01049, arXiv.org.
    • Handle: RePEc:arx:papers:1907.01049
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    References listed on IDEAS

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    1. James G. MacKinnon, 2019. "How cluster-robust inference is changing applied econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 52(3), pages 851-881, August.
    2. Ivan A. Canay & Joseph P. Romano & Azeem M. Shaikh, 2017. "Randomization Tests Under an Approximate Symmetry Assumption," Econometrica, Econometric Society, vol. 85, pages 1013-1030, May.
    3. 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.
    4. Guido W. Imbens & Michal Kolesár, 2016. "Robust Standard Errors in Small Samples: Some Practical Advice," The Review of Economics and Statistics, MIT Press, vol. 98(4), pages 701-712, October.
    5. Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, vol. 150(1), pages 86-98, May.
    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. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    8. 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.
    9. Hagemann, Andreas, 2019. "Placebo inference on treatment effects when the number of clusters is small," Journal of Econometrics, Elsevier, vol. 213(1), pages 190-209.
    10. Djogbenou, Antoine A. & MacKinnon, James G. & Nielsen, Morten Ørregaard, 2019. "Asymptotic theory and wild bootstrap inference with clustered errors," Journal of Econometrics, Elsevier, vol. 212(2), pages 393-412.
    11. Timothy G. Conley & Christopher R. Taber, 2011. "Inference with "Difference in Differences" with a Small Number of Policy Changes," The Review of Economics and Statistics, MIT Press, vol. 93(1), pages 113-125, February.
    12. 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.
    13. Joshua Angrist & Victor Lavy, 2009. "The Effects of High Stakes High School Achievement Awards: Evidence from a Randomized Trial," American Economic Review, American Economic Association, vol. 99(4), pages 1384-1414, September.
    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. A. Colin Cameron & Douglas L. Miller, 2015. "A Practitioner’s Guide to Cluster-Robust Inference," Journal of Human Resources, University of Wisconsin Press, vol. 50(2), pages 317-372.
    16. Janssen, Arnold, 1997. "Studentized permutation tests for non-i.i.d. hypotheses and the generalized Behrens-Fisher problem," Statistics & Probability Letters, Elsevier, vol. 36(1), pages 9-21, November.
    17. 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.
    18. Moulton, Brent R, 1990. "An Illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Unit," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 334-338, May.
    19. Andrew V. Carter & Kevin T. Schnepel & Douglas G. Steigerwald, 2017. "Asymptotic Behavior of a t -Test Robust to Cluster Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 99(4), pages 698-709, July.
    20. Tymon S{l}oczy'nski, 2018. "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights," Papers 1810.01576, arXiv.org, revised May 2020.
    21. 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 205-207, January.
    22. 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.
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    Cited by:

    1. James G. MacKinnon & Matthew D. Webb, 2020. "When and How to Deal with Clustered Errors in Regression Models," Working Paper 1421, Economics Department, Queen's University.
    2. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    3. Andreas Hagemann, 2020. "Inference with a single treated cluster," Papers 2010.04076, arXiv.org.

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