IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2025-01.html
   My bibliography  Save this paper

Two-way Fixed Effects and Differences-in-Differences in Heterogeneous Adoption Designs without Stayers

Author

Listed:
  • Clément de Chaisemartin

    (Sciences Po Paris)

  • Diego Ciccia

    (Northwestern University, Kellogg School of Management)

  • Xavier D’Haultfoeuille

    (CREST-ENSAE)

  • Felix Knau

    (University of Munich)

Abstract

We consider treatment-effect estimation under a parallel trends assumption, in designs where no unit is treated at period one, all units receive a strictly positive dose at period two, and the dose varies across units. There are therefore no true control groups in such cases. First, we develop a test of the assumption that the treatment effect is mean independent of the treatment, under which the commonly-used two-way-fixed-effects estimator is consistent. When this test is rejected or lacks power, we propose alternative estimators, robust to heterogeneous effects. If there are units with a period-two treatment arbitrarily close to zero, the robust estimator is a difference-in-difference using units with a period-two treatment below a bandwidth as controls. Without such units, we propose non-parametric bounds, and an estimator relying on a parametric specification of treatment-effect heterogeneity. We use our results to revisit Pierce and Schott (2016) and Enikolopov et al. (2011).

Suggested Citation

  • Clément de Chaisemartin & Diego Ciccia & Xavier D’Haultfoeuille & Felix Knau, 2024. "Two-way Fixed Effects and Differences-in-Differences in Heterogeneous Adoption Designs without Stayers," Working Papers 2025-01, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2025-01
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2025-01.pdf
    File Function: CREST working paper version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ruben Enikolopov & Maria Petrova & Ekaterina Zhuravskaya, 2011. "Media and Political Persuasion: Evidence from Russia," American Economic Review, American Economic Association, vol. 101(7), pages 3253-3285, December.
    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. Mark Duggan & Fiona Scott Morton, 2010. "The Effect of Medicare Part D on Pharmaceutical Prices and Utilization," American Economic Review, American Economic Association, vol. 100(1), pages 590-607, March.
    4. Clément de Chaisemartin & Xavier D'Haultfœuille, 2020. "Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects," American Economic Review, American Economic Association, vol. 110(9), pages 2964-2996, September.
    5. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    6. Thiemo Fetzer, 2019. "Did Austerity Cause Brexit?," American Economic Review, American Economic Association, vol. 109(11), pages 3849-3886, November.
    7. Victor Chernozhukov & Wooyoung Kim & Sokbae Lee & Adam M. Rosen, 2015. "Implementing intersection bounds in Stata," Stata Journal, StataCorp LLC, vol. 15(1), pages 21-44, March.
    8. Sebastian Calonico & Matias D. Cattaneo & Rocio Titiunik, 2014. "Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs," Econometrica, Econometric Society, vol. 82, pages 2295-2326, November.
    9. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
    10. Justin R. Pierce & Peter K. Schott, 2016. "The Surprisingly Swift Decline of US Manufacturing Employment," American Economic Review, American Economic Association, vol. 106(7), pages 1632-1662, July.
    11. Guido W. Imbens & Donald B. Rubin & Bruce I. Sacerdote, 2001. "Estimating the Effect of Unearned Income on Labor Earnings, Savings, and Consumption: Evidence from a Survey of Lottery Players," American Economic Review, American Economic Association, vol. 91(4), pages 778-794, September.
    12. C de Chaisemartin & X D’HaultfŒuille, 2018. "Fuzzy Differences-in-Differences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(2), pages 999-1028.
    13. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, January.
    14. Bryan S. Graham & James L. Powell, 2012. "Identification and Estimation of Average Partial Effects in “Irregular” Correlated Random Coefficient Panel Data Models," Econometrica, Econometric Society, vol. 80(5), pages 2105-2152, September.
    15. Clément de Chaisemartin & Xavier d'Haultfoeuille & Antoine Deeb, 2019. "TWOWAYFEWEIGHTS: Stata module to estimate the weights and measure of robustness to treatment effect heterogeneity attached to two-way fixed effects regressions," SciencePo Working papers Main hal-03946777, HAL.
    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. Cl'ement de Chaisemartin & Diego Ciccia Xavier D'Haultf{oe}uille & Felix Knau, 2024. "Two-way Fixed Effects and Differences-in-Differences Estimators in Heterogeneous Adoption Designs," Papers 2405.04465, arXiv.org, revised Nov 2024.
    2. Cl'ement de Chaisemartin & Xavier D'Haultf{oe}uille, 2021. "Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey," Papers 2112.04565, arXiv.org, revised Jun 2022.
    3. Clément de Chaisemartin & Xavier D’Haultfœuille, 2023. "Two-way fixed effects and differences-in-differences with heterogeneous treatment effects: a survey," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 1-30.
    4. de Chaisemartin, Clement & D'Haultfoeuille, Xavier, "undated". "Supplement to Fuzzy Differences-in-Differences," Economic Research Papers 270217, University of Warwick - Department of Economics.
    5. Cl'ement de Chaisemartin & Xavier D'Haultf{oe}uille, 2020. "Difference-in-Differences Estimators of Intertemporal Treatment Effects," Papers 2007.04267, arXiv.org, revised Dec 2024.
    6. Clément de Chaisemartin & Xavier D'Haultfœuille, 2020. "Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects," American Economic Review, American Economic Association, vol. 110(9), pages 2964-2996, September.
    7. C de Chaisemartin & X D’HaultfŒuille, 2018. "Fuzzy Differences-in-Differences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(2), pages 999-1028.
    8. Andrew E Clark & Rong Zhu, 2024. "Taking Back Control? Quasi-Experimental Evidence on the Impact of Retirement on Locus of Control," The Economic Journal, Royal Economic Society, vol. 134(660), pages 1465-1493.
    9. Yoichi Arai & Yu‐Chin Hsu & Toru Kitagawa & Ismael Mourifié & Yuanyuan Wan, 2022. "Testing identifying assumptions in fuzzy regression discontinuity designs," Quantitative Economics, Econometric Society, vol. 13(1), pages 1-28, January.
    10. Alperovych, Yan & Divakaruni, Anantha & Le Grand, François, 2022. "FinTech Lending under Austerity," SocArXiv atsk9, Center for Open Science.
    11. Divakaruni, Anantha & Alperovych, Yan & Le Grand, François, 2022. "FinTech Lending under Austerity," OSF Preprints m4tps_v1, Center for Open Science.
    12. Alperovych, Yan & Divakaruni, Anantha & Le Grand, François, 2022. "FinTech Lending under Austerity," SocArXiv atsk9_v1, Center for Open Science.
    13. Divakaruni, Anantha & Alperovych, Yan & Le Grand, François, 2022. "FinTech Lending under Austerity," OSF Preprints m4tps, Center for Open Science.
    14. Kaido, Hiroaki, 2017. "Asymptotically Efficient Estimation Of Weighted Average Derivatives With An Interval Censored Variable," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1218-1241, October.
    15. Eibich, Peter & Siedler, Thomas, 2020. "Retirement, intergenerational time transfers, and fertility," European Economic Review, Elsevier, vol. 124(C).
    16. Chernozhukov, Victor & Fernández-Val, Iván & Hoderlein, Stefan & Holzmann, Hajo & Newey, Whitney, 2015. "Nonparametric identification in panels using quantiles," Journal of Econometrics, Elsevier, vol. 188(2), pages 378-392.
    17. Marco Manacorda & Guido Tabellini & Andrea Tesei, 2022. "Mobile internet and the rise of political tribalism in Europe," CEP Discussion Papers dp1877, Centre for Economic Performance, LSE.
    18. Balila Acurio & Alessandro Tomarchio, 2024. "The Effects of Business Credit Support Programs: Evidence from a Regression Discontinuity Design," IHEID Working Papers 20-2024, Economics Section, The Graduate Institute of International Studies.
    19. Britto, Diogo G.C. & Fiorin, Stefano, 2020. "Corruption and legislature size: Evidence from Brazil," European Journal of Political Economy, Elsevier, vol. 65(C).
    20. Mellace, Giovanni & Ventura, Marco, 2019. "Intended and unintended effects of public incentives for innovation. Quasi-experimental evidence from Italy," Discussion Papers on Economics 9/2019, University of Southern Denmark, Department of Economics.

    More about this item

    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:crs:wpaper:2025-01. 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: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

    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.