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Pitfalls When Estimating Treatment Effects Using Clustered Data

Author

Listed:
  • James G. MacKinnon

    () (Queen's University)

  • Matthew D. Webb

    () (Carleton University)

Abstract

Inference for estimates of treatment effects with clustered data requires great care when treatment is assigned at the group level. This is true for both pure treatment models anddifference-in-differences regressions. Even when the number of clusters is quite large, cluster-robust standard errors can be much too small if the number of treated (or control) clusters is small. Standard errors also tend to be too small when cluster sizes vary a lot, resulting in too many false positives. Bootstrap methods generally perform better than t-tests, but they can also yield very misleading inferences in some cases.

Suggested Citation

  • James G. MacKinnon & Matthew D. Webb, 2017. "Pitfalls When Estimating Treatment Effects Using Clustered Data," Working Paper 1387, Economics Department, Queen's University.
  • Handle: RePEc:qed:wpaper:1387
    as

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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1387.pdf
    File Function: First version 2017
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    References listed on IDEAS

    as
    1. James G. MacKinnon & Matthew D. Webb, 2016. "Randomization Inference for Difference-in-Differences with Few Treated Clusters," Carleton Economic Papers 16-11, Carleton University, Department of Economics.
    2. 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.
    3. repec:clg:wpaper:2013-20 is not listed on IDEAS
    4. repec:tpr:restat:v:99:y:2017:i:4:p:698-709 is not listed on IDEAS
    5. 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.
    6. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(3), pages 361-376, June.
    7. 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.
    8. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    9. repec:wly:emjrnl:v:21:y:2018:i:2:p:114-135 is not listed on IDEAS
    10. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    11. 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.
    12. 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.
    13. James G. MacKinnon & Matthew D. Webb, 2018. "The wild bootstrap for few (treated) clusters," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 114-135, June.
    14. Bruno Ferman & Cristine Pinto, 2019. "Inference in Differences-in-Differences with Few Treated Groups and Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 452-467, July.
    15. 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.
    16. repec:wly:emetrp:v:85:y:2017:i::p:1013-1030 is not listed on IDEAS
    17. 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.
    18. Matthew D. Webb, 2014. "Reworking Wild Bootstrap Based Inference For Clustered Errors," Working Paper 1315, Economics Department, Queen's University.
    19. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    20. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. David Roodman & James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2019. "Fast and wild: Bootstrap inference in Stata using boottest," Stata Journal, StataCorp LP, vol. 19(1), pages 4-60, March.
    2. Biewen, Martin & Schwerter, Jakob, 2019. "Does More Math in High School Increase the Share of Female STEM Workers? Evidence from a Curriculum Reform," IZA Discussion Papers 12236, Institute of Labor Economics (IZA).
    3. 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.

    More about this item

    Keywords

    CRVE; grouped data; clustered data; panel data; wild cluster bootstrap; difference-in-differences; DiD regression;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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