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The PCDID Approach: Difference-in-Differences When Trends Are Potentially Unparallel and Stochastic

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  • Marc K. Chan
  • Simon S. Kwok

Abstract

We develop a class of regression-based estimators, called Principal Components Difference-in-Differences (PCDID) estimators, for treatment effect estimation. Analogous to a control function approach, PCDID uses factor proxies constructed from control units to control for unobserved trends, assuming that the unobservables follow an interactive effects structure. We clarify the conditions under which the estimands in this regression-based approach represent useful causal parameters of interest. We establish consistency and asymptotic normality results of PCDID estimators under minimal assumptions on the specification of time trends. The PCDID approach is illustrated in an empirical exercise that examines the effects of welfare waiver programs on welfare caseloads in the United States.

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  • 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.
    • Handle: RePEc:taf:jnlbes:v:40:y:2022:i:3:p:1216-1233
    DOI: 10.1080/07350015.2021.1914636
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    3. Irene Botosaru & Raffaella Giacomini & Martin Weidner, 2023. "Forecasted Treatment Effects," Papers 2309.05639, arXiv.org, revised Jan 2024.
    4. Vanessa Boese-Schlosser & Markus Eberhardt, 2023. "How does democracy cause growth?," Discussion Papers 2023-13, Nottingham Interdisciplinary Centre for Economic and Political Research (NICEP).
    5. Eberhardt, Markus, 2022. "Democracy, growth, heterogeneity, and robustness," European Economic Review, Elsevier, vol. 147(C).
    6. Iv'an Fern'andez-Val & Hugo Freeman & Martin Weidner, 2020. "Low-Rank Approximations of Nonseparable Panel Models," Papers 2010.12439, arXiv.org, revised Mar 2021.
    7. Anish Agarwal & Vasilis Syrgkanis, 2022. "Synthetic Blip Effects: Generalizing Synthetic Controls for the Dynamic Treatment Regime," Papers 2210.11003, arXiv.org.
    8. Zunian Luo, 2022. "Powering Up a Slow Charging Market: How Do Government Subsidies Affect Charging Station Supply?," Papers 2210.14908, arXiv.org, revised Jan 2023.
    9. Keegan Harris & Anish Agarwal & Chara Podimata & Zhiwei Steven Wu, 2022. "Strategyproof Decision-Making in Panel Data Settings and Beyond," Papers 2211.14236, arXiv.org, revised Dec 2023.
    10. Rachel Cho & Rodolphe Desbordes & Markus Eberhardt, 2022. "The causal effects of the darker side of financial development," Discussion Papers 2022-04, University of Nottingham, GEP.
    11. Roberto Esposti, 2022. "The Coevolution of Policy Support and Farmers' Behaviour. An investigation on Italian agriculture over the 2008-2019 period," Working Papers 464, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    12. Xin Su & Shengwen Wang, 2024. "Impact of China’s free trade zones on the innovation performance of firms: evidence from a quasi-natural experiment," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-17, December.

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