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
    ---><---

    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 LP, 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. de Chaisemartin, Clement & D'Haultfoeuille, Xavier, 2014. "Fuzzy Changes-in Changes," CAGE Online Working Paper Series 184, Competitive Advantage in the Global Economy (CAGE).
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, January.
    15. 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.
    16. 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. 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.
    6. 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.
    7. Isabella Giorgetti & Matteo Picchio, 2021. "One billion euro programme for early childcare services in Italy," Metroeconomica, Wiley Blackwell, vol. 72(3), pages 460-492, July.
    8. Sonia Bhalotra & Martin Karlsson & Therese Nilsson & Nina Schwarz, 2022. "Infant Health, Cognitive Performance, and Earnings: Evidence from Inception of the Welfare State in Sweden," The Review of Economics and Statistics, MIT Press, vol. 104(6), pages 1138-1156, November.
    9. 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.
    10. Ting Ye & Ashkan Ertefaie & James Flory & Sean Hennessy & Dylan S. Small, 2023. "Instrumented difference‐in‐differences," Biometrics, The International Biometric Society, vol. 79(2), pages 569-581, June.
    11. Michael Greenstone & Guojun He & Ruixue Jia & Tong Liu, 2020. "Can Technology Solve the Principal-Agent Problem? Evidence from China’s War on Air Pollution," Working Papers 2020-87, Becker Friedman Institute for Research In Economics.
    12. 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.
    13. Yong Geng & Wei Liu & Hanshu Chen & Xinyu Zou, 2023. "The Spillover Effects of Environmental Regulations: A Perspective of Chinese Unregulated Firms' Tax Burden," China & World Economy, Institute of World Economics and Politics, Chinese Academy of Social Sciences, vol. 31(2), pages 84-111, March.
    14. Charles Angelucci & Julia Cagé & Michael Sinkinson, 2024. "Media Competition and News Diets," American Economic Journal: Microeconomics, American Economic Association, vol. 16(2), pages 62-102, May.
    15. Roth, Jonathan & Sant’Anna, Pedro H.C. & Bilinski, Alyssa & Poe, John, 2023. "What’s trending in difference-in-differences? A synthesis of the recent econometrics literature," Journal of Econometrics, Elsevier, vol. 235(2), pages 2218-2244.
    16. Aaron M. Gamino, 2024. "The impact of juvenile curfews on teenage birth rates," Health Economics, John Wiley & Sons, Ltd., vol. 33(7), pages 1528-1545, July.
    17. 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.
    18. Alberto Posso & Udeni De Silva Perera & Ankita Mishra, 2021. "Community‐level health programs and child labor: Evidence from Ethiopia," Health Economics, John Wiley & Sons, Ltd., vol. 30(12), pages 2995-3015, December.
    19. repec:spo:wpmain:info:hdl:2441/4ec86lkes59hv9tfv77ld1p5fr is not listed on IDEAS
    20. Kai Hu & Dandan Li & Daqian Shi & Wenli Xu, 2023. "Environmental regulation and energy efficiency: evidence from daily penalty policy in China," Journal of Regulatory Economics, Springer, vol. 63(1), pages 1-29, April.
    21. D’Haultfœuille, Xavier & Hoderlein, Stefan & Sasaki, Yuya, 2023. "Nonparametric difference-in-differences in repeated cross-sections with continuous treatments," Journal of Econometrics, Elsevier, vol. 234(2), pages 664-690.

    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.