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Simple Difference-in-Differences Estimation in Fixed-T Panels

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  • Nicholas Brown
  • Kyle Butts
  • Joakim Westerlund

Abstract

The present paper proposes a new treatment effects estimator that is valid when the number of time periods is small, and the parallel trends condition holds conditional on covariates and unobserved heterogeneity in the form of interactive fixed effects. The estimator also allow the control variables to be affected by treatment and it enables estimation of the resulting indirect effect on the outcome variable. The asymptotic properties of the estimator are established and their accuracy in small samples is investigated using Monte Carlo simulations. The empirical usefulness of the estimator is illustrated using as an example the effect of increased trade competition on firm markups in China.

Suggested Citation

  • Nicholas Brown & Kyle Butts & Joakim Westerlund, 2023. "Simple Difference-in-Differences Estimation in Fixed-T Panels," Papers 2301.11358, arXiv.org, revised Jun 2023.
    • Handle: RePEc:arx:papers:2301.11358
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    References listed on IDEAS

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    1. Marc K. Chan & Simon S. Kwok, 2022. "The PCDID Approach: Difference-in-Differences When Trends Are Potentially Unparallel and Stochastic," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1216-1233, June.
    2. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    3. Xu, Yiqing, 2017. "Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models," Political Analysis, Cambridge University Press, vol. 25(1), pages 57-76, January.
    4. Laurent Gobillon & Thierry Magnac, 2016. "Regional Policy Evaluation: Interactive Fixed Effects and Synthetic Controls," The Review of Economics and Statistics, MIT Press, vol. 98(3), pages 535-551, July.
    5. Jeffrey M. Wooldridge, 2005. "Fixed-Effects and Related Estimators for Correlated Random-Coefficient and Treatment-Effect Panel Data Models," The Review of Economics and Statistics, MIT Press, vol. 87(2), pages 385-390, May.
    6. Jörg Breitung & Philipp Hansen, 2021. "Alternative estimation approaches for the factor augmented panel data model with small T," Empirical Economics, Springer, vol. 60(1), pages 327-351, January.
    7. Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2011. "Weak and strong cross‐section dependence and estimation of large panels," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 45-90, February.
    8. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    9. Callaway, Brantly & Sant’Anna, Pedro H.C., 2021. "Difference-in-Differences with multiple time periods," Journal of Econometrics, Elsevier, vol. 225(2), pages 200-230.
    10. Hyungsik Roger Moon & Martin Weidner, 2015. "Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects," Econometrica, Econometric Society, vol. 83(4), pages 1543-1579, July.
    11. Joakim Westerlund & Yana Petrova & Milda Norkute, 2019. "CCE in fixed‐T panels," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(5), pages 746-761, August.
    12. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    13. Carolina Caetano & Brantly Callaway, 2022. "Difference-in-Differences with Time-Varying Covariates in the Parallel Trends Assumption," Papers 2202.02903, arXiv.org, revised May 2023.
    14. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    15. Jörg Breitung & Philipp Hansen, 2021. "Correction to: Alternative estimation approaches for the factor augmented panel data model with small T," Empirical Economics, Springer, vol. 61(6), pages 3557-3558, December.
    16. Nicholas Brown & Kyle Butts, 2022. "A Unified Framework for Dynamic Treatment Effect Estimation in Interactive Fixed Effect Models," Working Paper 1495, Economics Department, Queen's University.
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    Cited by:

    1. Brown, Nicholas & Westerlund, Joakim, 2023. "Testing factors in CCE," Economics Letters, Elsevier, vol. 230(C).

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