IDEAS home Printed from https://ideas.repec.org/p/hal/spmain/hal-03873926.html
   My bibliography  Save this paper

Difference-in-Differences for Continuous Treatments and Instruments with Stayers

Author

Listed:
  • Clément de Chaisemartin

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • Xavier d'Haultfoeuille

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

  • Félix Pasquier

    (CREST-INSEE - Centre de Recherche en Economie et en Statistique - INSEE - Institut national de la statistique et des études économiques (INSEE))

  • Doulo Sow

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • Gonzalo Vazquez-Bare

    (UC Santa Barbara - University of California [Santa Barbara] - UC - University of California)

Abstract

We propose difference-in-differences estimators in designs where the treatment is continuously distributed at every period, as is often the case when one studies the effects of taxes, tariffs, or prices. We assume that between consecutive periods, the treatment of some units, the switchers, changes, while the treatment of other units remains constant. We show that under a placebo-testable parallel-trends assumption, averages of the slopes of switchers' potential outcomes can be nonparametrically estimated. We generalize our estimators to the instrumental-variable case. We use our estimators to estimate the price-elasticity of gasoline consumption.

Suggested Citation

  • Clément de Chaisemartin & Xavier d'Haultfoeuille & Félix Pasquier & Doulo Sow & Gonzalo Vazquez-Bare, 2025. "Difference-in-Differences for Continuous Treatments and Instruments with Stayers," SciencePo Working papers Main hal-03873926, HAL.
  • Handle: RePEc:hal:spmain:hal-03873926
    DOI: 10.2139/ssrn.4011782
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03873926v2
    as

    Download full text from publisher

    File URL: https://sciencespo.hal.science/hal-03873926v2/document
    Download Restriction: no

    File URL: https://libkey.io/10.2139/ssrn.4011782?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Hoderlein, Stefan & White, Halbert, 2012. "Nonparametric identification in nonseparable panel data models with generalized fixed effects," Journal of Econometrics, Elsevier, vol. 168(2), pages 300-314.
    3. Sun, Liyang & Abraham, Sarah, 2021. "Estimating dynamic treatment effects in event studies with heterogeneous treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 175-199.
    4. Malani, Anup & Reif, Julian, 2015. "Interpreting pre-trends as anticipation: Impact on estimated treatment effects from tort reform," Journal of Public Economics, Elsevier, vol. 124(C), pages 1-17.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jacob E. Bastian, 2024. "The EITC in rural and economically distressed areas: More bang per buck?," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 31(1), pages 136-159, February.
    2. Fabra, Natalia & Gutiérrez, Eduardo & Lacuesta, Aitor & Ramos, Roberto, 2024. "Do renewable energy investments create local jobs?," Journal of Public Economics, Elsevier, vol. 239(C).
    3. Bhukta, Rikhia & Pakrashi, Debayan & Saha, Sarani & Sedai, Ashish, 2024. "Community electrification and women’s autonomy," Energy Economics, Elsevier, vol. 137(C).
    4. Rogne, Adrian F. & Knutsen, Tora Kjærnes & Modalsli, Jørgen, 2023. "A college on every cape: Gender equality, gender segregation and higher educational expansion," SocArXiv xej64, Center for Open Science.
    5. Rogne, Adrian F. & Knutsen, Tora Kjærnes & Modalsli, Jørgen, 2023. "A college on every cape: Gender equality, gender segregation and higher educational expansion," SocArXiv xej64_v1, Center for Open Science.
    6. 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.
    7. Bassier, Ihsaan & Manning, Alan & Petrongolo, Barbara, 2023. "Vacancy duration and wages," LSE Research Online Documents on Economics 121287, London School of Economics and Political Science, LSE Library.
    8. Gerard J. van den Berg & Stephanie von Hinke & Nicolai Vitt, 2023. "Early life exposure to measles and later-life outcomes: Evidence from the introduction of a vaccine," Papers 2301.10558, arXiv.org.
    9. Heeyun Kim, 2024. "A Fad or the New Norm for Student Access Today? Evaluating Enrollment Outcomes of Holistic Admissions in South Korea," Research in Higher Education, Springer;Association for Institutional Research, vol. 65(5), pages 1040-1064, August.
    10. Ali Enami & Sucharita Ghosh, 2024. "Subsidized wages, small businesses, and exports: Evidence from the paycheck protection program," Review of International Economics, Wiley Blackwell, vol. 32(4), pages 1671-1697, September.
    11. Bassier, Ihsaan & Manning, Alan & Petrongolo, Barbara, 2023. "Vacancy Duration and Wages," IZA Discussion Papers 16371, Institute of Labor Economics (IZA).
    12. Mo, Jiawei, 2023. "Heterogeneous effects of urban transport infrastructure on population distribution: The role of educational access," Regional Science and Urban Economics, Elsevier, vol. 101(C).
    13. Lebow, Jeremy & Moreno-Medina, Jonathan & Mousa, Salma & Coral, Horacio, 2024. "Migrant exposure and anti-migrant sentiment: The case of the Venezuelan exodus," Journal of Public Economics, Elsevier, vol. 236(C).
    14. Ihsaan Bassier & Alan Manning & Barbara Petrongolo, 2023. "Vacancy duration and wages," CEP Discussion Papers dp1943, Centre for Economic Performance, LSE.
    15. Lucas Zhang, 2024. "Continuous difference-in-differences with double/debiased machine learning," Papers 2408.10509, arXiv.org, revised Mar 2025.

    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. Luo, Lianfa & Cheng, Zhiming & Ye, Qingqing & Cheng, Yanjun & Smyth, Russell & Yang, Zhiqing & Zhang, Le, 2024. "Nonmonetary awards and innovation: Evidence from winning China's Top Brand Contest," China Economic Review, Elsevier, vol. 86(C).
    2. Aibo Gong, 2021. "Bounds for Treatment Effects in the Presence of Anticipatory Behavior," Papers 2111.06573, arXiv.org, revised Dec 2022.
    3. 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.
    4. Kurt Schmidheiny & Sebastian Siegloch, 2023. "On event studies and distributed‐lags in two‐way fixed effects models: Identification, equivalence, and generalization," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(5), pages 695-713, August.
    5. Cl'ement de Chaisemartin & Xavier D'Haultfoeuille & F'elix Pasquier & Doulo Sow & Gonzalo Vazquez-Bare, 2022. "Difference-in-Differences Estimators for Treatments Continuously Distributed at Every Period," Papers 2201.06898, arXiv.org, revised Jul 2024.
    6. Cesare Righi & Timothy Simcoe, 2022. "Patenting inventions or inventing patents? Continuation practice at the USPTO," Economics Working Papers 1820, Department of Economics and Business, Universitat Pompeu Fabra.
    7. Timothy Simcoe & Cesare Righi, 2022. "Patenting Inventions or Inventing Patents? Continuation Practice at the USPTO," Working Papers 1320, Barcelona School of Economics.
    8. Dalia Ghanem & Pedro H. C. Sant'Anna & Kaspar Wuthrich, 2022. "Selection and parallel trends," Papers 2203.09001, arXiv.org, revised Mar 2024.
    9. Philip Marx & Elie Tamer & Xun Tang, 2022. "Parallel Trends and Dynamic Choices," Papers 2207.06564, arXiv.org, revised Aug 2023.
    10. Jonathan Roth & Pedro H. C. Sant’Anna, 2023. "Efficient Estimation for Staggered Rollout Designs," Journal of Political Economy Microeconomics, University of Chicago Press, vol. 1(4), pages 669-709.
    11. Callaway, Brantly & Sant’Anna, Pedro H.C., 2021. "Difference-in-Differences with multiple time periods," Journal of Econometrics, Elsevier, vol. 225(2), pages 200-230.
    12. Bas Scheer & Wiljan van den Berge & Maarten Goos & Alan Manning & Anna Salomons, 2022. "Alternative Work Arrangements and Worker Outcomes: Evidence from Payrolling," CPB Discussion Paper 435, CPB Netherlands Bureau for Economic Policy Analysis.
    13. Katrin Huber & Geske Rolvering, 2023. "Public child care and mothers’ career trajectories," Working Papers 228, Bavarian Graduate Program in Economics (BGPE).
    14. Alex Hollingsworth & Krzysztof Karbownik & Melissa A. Thomasson & Anthony Wray, 2024. "The Gift of a Lifetime: The Hospital, Modern Medicine, and Mortality," American Economic Review, American Economic Association, vol. 114(7), pages 2201-2238, July.
    15. Bhalotra, Sonia & Clarke, Damian & Mühlrad, Hanna & Palme, Mårten, 2021. "Health and Labor Market Impacts of Twin Birth : Evidence from a Swedish IVF Policy Mandate," The Warwick Economics Research Paper Series (TWERPS) 1391, University of Warwick, Department of Economics.
    16. Jack (Peiyao) Ma & Andrea Mantovani & Carlo Reggiani & Annette Broocks & Néstor Duch-Brown, 2024. "The Price Effects of Prohibiting Price Parity Clauses: Evidence from International Hotel Groups," Economics Series Working Papers 1043, University of Oxford, Department of Economics.
    17. Baker, Michael & Halberstam, Yosh & Kroft, Kory & Mas, Alexandre & Messacar, Derek, 2024. "The impact of unions on wages in the public sector: Evidence from higher education," CLEF Working Paper Series 67, Canadian Labour Economics Forum (CLEF), University of Waterloo.
    18. Hashida, Yukiko & Dundas, Steven J., 2023. "The effects of a voluntary property buyout and acquisition program on coastal housing markets: Evidence from New York," Journal of Environmental Economics and Management, Elsevier, vol. 121(C).
    19. Jaraitė, Jūratė & Kurtyka, Oliwia & Ollivier, Hélène, 2022. "Take a ride on the (not so) green side: How do CDM projects affect Indian manufacturing firms’ environmental performance?," Journal of Environmental Economics and Management, Elsevier, vol. 114(C).
    20. Xin Nie & Jianxian Wu & Han Wang & Weijuan Li & Chengdao Huang & Lihua Li, 2022. "Contributing to carbon peak: Estimating the causal impact of eco‐industrial parks on low‐carbon development in China," Journal of Industrial Ecology, Yale University, vol. 26(4), pages 1578-1593, August.

    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:hal:spmain:hal-03873926. 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: Contact - Sciences Po Departement of Economics (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.