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. 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.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Albert Chiu & Xingchen Lan & Ziyi Liu & Yiqing Xu, 2023. "What To Do (and Not to Do) with Causal Panel Analysis under Parallel Trends: Lessons from A Large Reanalysis Study," Papers 2309.15983, arXiv.org, revised Jun 2024.
    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. 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.
    2. 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.
    3. repec:fip:fedrwp:98029 is not listed on IDEAS
    4. Jordà, Òscar & Nechio, Fernanda, 2023. "Inflation and wage growth since the pandemic," European Economic Review, Elsevier, vol. 156(C).
    5. Arindrajit Dube & Attila Lindner, 2024. "Minimum Wages in the 21st Century," RF Berlin - CReAM Discussion Paper Series 2524, Rockwool Foundation Berlin (RF Berlin) - Centre for Research and Analysis of Migration (CReAM).
    6. Todd Morris & Benoit Dostie, 2023. "Graying and staying on the job: The welfare implications of employment protection for older workers," Cahiers de recherche / Working Papers 15, Institut sur la retraite et l'épargne / Retirement and Savings Institute.
    7. Òscar Jordà & Alan M. Taylor, 2024. "Local Projections," NBER Working Papers 32822, National Bureau of Economic Research, Inc.
    8. Griller, Stefan & Huber, Florian & Pfarrhofer, Michael, 2024. "Financial markets and legal challenges to unconventional monetary policy," European Economic Review, Elsevier, vol. 163(C).
    9. 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.
    10. Dominguez, Kathryn M.E. & Foschi, Andrea, 2024. "Whatever-it-takes policymaking during the pandemic," Journal of International Economics, Elsevier, vol. 149(C).
    11. Fu, Hongqiao & Cheng, Terence C. & Zhan, Jiajia & Xu, Duo & Yip, Winnie, 2024. "Dynamic effects of the COVID-19 pandemic on the demand for telemedicine services: Evidence from China," Journal of Economic Behavior & Organization, Elsevier, vol. 220(C), pages 531-557.
    12. Martin, Diego A. & Romero, Dario A., 2024. "Social distancing and COVID-19 under violence: Evidence from Colombia," Journal of Development Economics, Elsevier, vol. 170(C).
    13. Jean-Baptiste Bonnier, 2024. "A Split-Treatment Design," Working Papers 2024-11, CRESE.
    14. Dubé, Jean & Le Gallo, Julie & Des Rosiers, François & Legros, Diègo & Champagne, Marie-Pier, 2024. "An integrated causal framework to evaluate uplift value with an example on change in public transport supply," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 185(C).
    15. Guilherme Amorim & Diogo Britto & Alexandre Fonseca & Breno Sampaio, 2022. "Job Loss, Unemployment Insurance and Health: Evidence from Brazil," BAFFI CAREFIN Working Papers 22192, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    16. Yiqing Xu & Anqi Zhao & Peng Ding, 2024. "Factorial Difference-in-Differences," Papers 2407.11937, arXiv.org, revised Aug 2024.
    17. Oliveira, Gustavo Magalhães de & Miranda, Bruno Varella & Saes, Maria Sylvia Macchione & Martino, Gaetano, 2023. "Opening the “black box” of food safety policy implementation: The efficiency-enhancing role of a private meso-institution," Food Policy, Elsevier, vol. 121(C).
    18. Fang, Francis Haoyu & Vlaicu, Razvan, 2024. "Local Banking Supply and Private Firm Activity: Evidence from Branch Closures," IDB Publications (Working Papers) 13645, Inter-American Development Bank.
    19. Jingyi Tian & Jun Nagayasu, 2023. "Financial Systemic Risk behind Artificial Intelligence:Evidence from China," TUPD Discussion Papers 44, Graduate School of Economics and Management, Tohoku University.
    20. Mutarindwa, Samuel & Schäfer, Dorothea & Stephan, Andreas, 2020. "Central banks' supervisory guidance on corporate governance and bank stability: Evidence from African countries," Emerging Markets Review, Elsevier, vol. 43(C).
    21. Diogo G. C. Britto & Roberto Hsu Rocha & Paolo Pinotti & Breno Sampaio, 2024. "Small Children, Big Problems: Childbirth and Crime," CESifo Working Paper Series 11083, CESifo.

    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.