lynx   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/osf/socarx/dg5ps.html
   My bibliography  Save this paper

Group-specific linear trends and the triple-differences in time design

Author

Listed:
  • Strezhnev, Anton
Abstract
Differences-in-differences designs for estimating causal effects rely on an assumption of ``parallel trends" -- that in the absence of the intervention, treated units would have followed the same outcome trajectory as observed in control units. When parallel trends fails, researchers often turn to alternative strategies that relax this identifying assumption. One popular approach is the inclusion of a group-specific linear time trend in the commonly used two-way fixed effects (TWFE) estimator. In a setting with a single post-treatment and two pre-treatment periods it is well known that this is equivalent to a non-parametric ``triple-differences" estimator which is valid under a ``parallel trends-in-trends" assumption (Egami and Yamauchi, 2023). This paper analyzes the TWFE estimator with group-specific linear time trends in the more general setting with many pre- and post-treatment periods. It shows that this estimator can be interpreted as an average over triple-differences terms involving both pre-treatment and post-treatment observations. As a consequence, this estimator does not identify a convex average of post-treatment ATTs without additional effect homogeneity assumptions even when there is no staggering in treatment adoption. A straightforward solution is to make the TWFE specification fully dynamic with a separate parameter for each relative treatment time. However, identification requires that researchers omit at least two pre-treatment relative treatment time indicators to estimate a group-specific linear trend. The paper shows how to properly extend this estimator to the staggered adoption setting using the approach of Sun and Abraham (2021), correcting a perfect collinearity error in recent implementations of this method in Hassell and Holbein (2024). It concludes with a note of caution for researchers, showing through a replication of Kogan (2021) how inferences from group-specific time trend specifications can be extremely sensitive to arbitrary specification choices when parallel trends violations are present but do not follow an easily observed functional form.

Suggested Citation

  • Strezhnev, Anton, 2024. "Group-specific linear trends and the triple-differences in time design," SocArXiv dg5ps, Center for Open Science.
    • Handle: RePEc:osf:socarx:dg5ps
    DOI: 10.31219/osf.io/dg5ps
    as

    Download full text from publisher

    File URL: https://osf.io/download/66d72e9378f89f1123a3c815/
    Download Restriction: no
    File URL: https://libkey.io/10.31219/osf.io/dg5ps?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Abdelgadir, Aala & Fouka, Vasiliki, 2020. "Political Secularism and Muslim Integration in the West: Assessing the Effects of the French Headscarf Ban," American Political Science Review, Cambridge University Press, vol. 114(3), pages 707-723, August.
    2. Ricardo Mora & Iliana Reggio, 2019. "Alternative diff-in-diffs estimators with several pretreatment periods," Econometric Reviews, Taylor & Francis Journals, vol. 38(5), pages 465-486, May.
    3. Arindrajit Dube & Daniele Girardi & Òscar Jordà & Alan M. Taylor, 2023. "A Local Projections Approach to Difference-in-Differences," NBER Working Papers 31184, National Bureau of Economic Research, Inc.
    4. Ashesh Rambachan & Jonathan Roth, 2023. "A More Credible Approach to Parallel Trends," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(5), pages 2555-2591.
    5. Albert Chiu & Xingchen Lan & Ziyi Liu & Yiqing Xu, 2023. "Causal Panel Analysis under Parallel Trends: Lessons from a Large Reanalysis Study," Papers 2309.15983, arXiv.org, revised Jun 2025.
    6. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    7. Taylor, Alan M. & Dube, Arindrajit & Girardi, Daniele & Jordà , Òscar, 2023. "A Local Projections Approach to Difference-in-Differences Event Studies," CEPR Discussion Papers 18141, C.E.P.R. Discussion Papers.
    8. George Ward, 2020. "Happiness and Voting: Evidence from Four Decades of Elections in Europe," American Journal of Political Science, John Wiley & Sons, vol. 64(3), pages 504-518, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:osf:socarx:dg5ps_v1 is not listed on IDEAS
    2. Tang, Lianzhou & Xu, Wenli, 2025. "Patronage and pollution," Journal of Environmental Economics and Management, Elsevier, vol. 130(C).
    3. Yechan Park & Yuya Sasaki, 2024. "Matching $\leq$ Hybrid $\leq$ Difference in Differences," Papers 2411.07952, arXiv.org, revised Feb 2025.
    4. Mark Kattenberg & Bas Scheer & Jurre Thiel, 2023. "Causal forests with fixed effects for treatment effect heterogeneity in difference-in-differences," CPB Discussion Paper 452, CPB Netherlands Bureau for Economic Policy Analysis.
    5. Anna Laura Baraldi & Claudia Cantabene & Alessandro De Iudicibus & Giovanni Fosco & Erasmo Papagni, 2025. "Shocks and Selection: How Earthquakes Shape Local Political Representation," EERI Research Paper Series EERI RP 2025/06, Economics and Econometrics Research Institute (EERI), Brussels.
    6. Guerin, Adrian & Najjar, Nouri & Schaufele, Brandon, 2024. "The Surprising Static and Dynamic Effects of Oil and Gas Flaring on Agriculture," 2024 Annual Meeting, July 28-30, New Orleans, LA 343660, Agricultural and Applied Economics Association.
    7. repec:fip:fedrwp:98029 is not listed on IDEAS
    8. Deng, Liuchun & Müller, Steffen & Plümpe, Verena & Stegmaier, Jens, 2024. "Robots, occupations, and worker age: A production-unit analysis of employment," European Economic Review, Elsevier, vol. 170(C).
    9. Masahiro Tanaka, 2025. "Quasi-Bayesian Local Projections: Simultaneous Inference and Extension to the Instrumental Variable Method," Papers 2503.20249, arXiv.org, revised Sep 2025.
    10. Arin, K. Peren & Marti Arnau, Josep & Boduroglu, Elif & Celik, Esref Ugur, 2024. "Shaken, stirred and indebted: Firm-level effects of earthquakes," The Quarterly Review of Economics and Finance, Elsevier, vol. 97(C).
    11. Jordà, Òscar & Nechio, Fernanda, 2023. "Inflation and wage growth since the pandemic," European Economic Review, Elsevier, vol. 156(C).
    12. Arne Henningsen & Guy Low & David Wuepper & Tobias Dalhaus & Hugo Storm & Dagim Belay & Stefan Hirsch, 2024. "Estimating Causal Effects with Observational Data: Guidelines for Agricultural and Applied Economists," IFRO Working Paper 2024/03, University of Copenhagen, Department of Food and Resource Economics.
    13. M. V. Lee Badgett & Christopher S. Carpenter & Maxine J. Lee & Dario Sansone, 2025. "A review of the effects of legal access to same‐sex marriage," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 44(1), pages 266-294, January.
    14. Morris, Todd & Dostie, Benoit, 2023. "Graying and Staying on the Job: The Welfare Implications of Employment Protection for Older Workers," IZA Discussion Papers 16430, Institute of Labor Economics (IZA).
    15. Òscar Jordà & Alan M. Taylor, 2024. "Local Projections," NBER Working Papers 32822, National Bureau of Economic Research, Inc.
    16. Griller, Stefan & Huber, Florian & Pfarrhofer, Michael, 2024. "Financial markets and legal challenges to unconventional monetary policy," European Economic Review, Elsevier, vol. 163(C).
    17. Ayoubi, Charles & Pezzoni, Michele & Visentin, Fabiana, 2019. "The important thing is not to win, it is to take part: What if scientists benefit from participating in research grant competitions?," Research Policy, Elsevier, vol. 48(1), pages 84-97.
    18. Msefula, Griffin & Hou, Tony Chieh-Tse & Lemesi, Tina, 2024. "Dynamics of legal structure and geopolitical influence on carbon tax in response to green transportation," Applied Energy, Elsevier, vol. 371(C).
    19. Baraldi, Anna Laura & Cantabene, Claudia & de Iudicibus, Alessandro & Fosco, Giovanni & iacopo, Grassi, 2025. "When Green Turns Costly: The Fiscal Fallout of EU Waste Management Funds in Italian Municipalities," MPRA Paper 125150, University Library of Munich, Germany.
    20. Imam, Patrick A. & Temple, Jonathan R.W., 2024. "Political institutions and output collapses," European Journal of Political Economy, Elsevier, vol. 85(C).
    21. Gabriel, Ricardo Duque, 2024. "The Credit Channel of Public Procurement," Journal of Monetary Economics, Elsevier, vol. 147(S).
    22. Leek, Lauren Caroline & Bischl, Simeon, 2024. "How Central Bank Independence Shapes Monetary Policy Communication: A Large Language Model Application," SocArXiv yrhka, Center for Open Science.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:osf:socarx:dg5ps. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: OSF (email available below). General contact details of provider: https://arabixiv.org .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.
    Лучший частный хостинг