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Difference-in-Difference Estimators with Continuous Treatments and No 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'Haultfœuille

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

  • Gonzalo Vazquez-Bare

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

Abstract

Many treatments, such as prices, taxes, or temperatures, are continuous in nature. Empirical researchers usually rely on two-way fixed effect regressions to estimate treatment effects in such cases. However, such estimators are not robust to heterogeneous treatment effects in general and rely on the linearity of treatment effects. We develop a difference-in-difference strategy for continuous treatments without imposing such restrictions when there are no stayers: treatment of all units changes between consecutive periods. We extend the nonparametric results of de Chaisemartin et al. (2023) to this setup and present a parametric approach that overcomes some limitations of the nonparametric approach.

Suggested Citation

  • Clément de Chaisemartin & Xavier d'Haultfœuille & Gonzalo Vazquez-Bare, 2024. "Difference-in-Difference Estimators with Continuous Treatments and No Stayers," Sciences Po Economics Publications (main) hal-04888940, HAL.
    • Handle: RePEc:hal:spmain:hal-04888940
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-04888940v1
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    1. is not listed on IDEAS
    2. Hoagland, Alex & Wang, Guan, 2025. "Prescribing power and equitable access to care: Evidence from pharmacists in Ontario, Canada," Journal of Health Economics, Elsevier, vol. 103(C).
    3. Lu, Hanjun & Rejesus, Roderick M. & Hively, Dean & Thieme, Alison & Jennewein, Jyoti, 2025. "Evaluating the Effectiveness of Maryland’s Cover Crop Program," 2025 AAEA & WAEA Joint Annual Meeting, July 27-29, 2025, Denver, CO 361072, Agricultural and Applied Economics Association.
    4. Carranza, Rafael & Prieto, Joaquín & Sehnbruch, Kirsten, 2025. "Job loss and earnings inequality: Distributional effects of formal re-employment in Chile," Economic Analysis and Policy, Elsevier, vol. 86(C), pages 1020-1036.
    5. Mevlude Akbulut-Yuksel & Dhaval M. Dave & Bilge Erten & Pinar Keskin & Catarina R. Meneses, 2026. "From Treatment to Safety: The Role of Substance Use Treatment in Preventing Intimate Partner Violence," NBER Working Papers 34642, National Bureau of Economic Research, Inc.
    6. repec:osf:socarx:v75aw_v1 is not listed on IDEAS
    7. Mateo Hoyos, 2024. "Tariffs and Growth: Heterogeneity by Economic Structure," Working Papers DTE 638, CIDE, División de Economía.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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