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Inference in Differences-in-Differences with Few Treated Groups and Heteroskedasticity

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  • Bruno Ferman

    (São Paulo School of Economics–FGV)

  • Cristine Pinto

    (São Paulo School of Economics–FGV)

Abstract

We derive an inference method that works in differences-in-differences settings with few treated and many control groups in the presence of heteroskedasticity. As a leading example, we provide theoretical justification and empirical evidence that heteroskedasticity generated by variation in group sizes can invalidate existing inference methods, even in data sets with a large number of observations per group. In contrast, our inference method remains valid in this case. Our test can also be combined with feasible generalized least squares, providing a safeguard against misspecification of the serial correlation.

Suggested Citation

  • 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.
    • Handle: RePEc:tpr:restat:v:101:y:2019:i:3:p:452-467
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    References listed on IDEAS

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    1. MacKinnon, James G. & Webb, Matthew D., 2020. "Randomization inference for difference-in-differences with few treated clusters," Journal of Econometrics, Elsevier, vol. 218(2), pages 435-450.
    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. Alberto Abadie & Javier Gardeazabal, 2003. "The Economic Costs of Conflict: A Case Study of the Basque Country," American Economic Review, American Economic Association, vol. 93(1), pages 113-132, March.
    4. 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.
    5. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    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. 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. Brewer Mike & Crossley Thomas F. & Joyce Robert, 2018. "Inference with Difference-in-Differences Revisited," Journal of Econometric Methods, De Gruyter, vol. 7(1), pages 1-16, January.
    9. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    10. Jeffrey M. Wooldridge, 2003. "Cluster-Sample Methods in Applied Econometrics," American Economic Review, American Economic Association, vol. 93(2), pages 133-138, May.
    11. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(1), pages 249-275.
    12. Kelly Bedard & Chau Do, 2005. "Are Middle Schools More Effective?: The Impact of School Structure on Student Outcomes," Journal of Human Resources, University of Wisconsin Press, vol. 40(3).
    13. 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.
    14. 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.
    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. Pettersson-Lidbom, Per, 2012. "Does the size of the legislature affect the size of government? Evidence from two natural experiments," Journal of Public Economics, Elsevier, vol. 96(3), pages 269-278.
    17. Choi, Moonkyung Kate, 2011. "The impact of Medicaid insurance coverage on dental service use," Journal of Health Economics, Elsevier, vol. 30(5), pages 1020-1031.
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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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