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Difference-in-Difference Estimators with Continuous Treatments and No Stayers

Author

Listed:
  • Clément de Chaisemartin
  • Xavier D'Haultfœuille
  • Gonzalo Vazquez-Bare

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," AEA Papers and Proceedings, American Economic Association, vol. 114, pages 610-613, May.
    • Handle: RePEc:aea:apandp:v:114:y:2024:p:610-13
    DOI: 10.1257/pandp.20241049
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    Cited by:

    1. 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.
    2. Collins, Matthew & Dempsey, Seraphim & Griffin, Míde & Finan, Olivia, 2026. "A Reproducibility Assessment of "Immigration Restrictions as Active Labor Market Policy: Evidence from the Mexican Bracero Exclusion"," I4R Discussion Paper Series 298, The Institute for Replication (I4R).
    3. Peter John Lambert & Yannick Schindler, 2026. "The broken ladder: AI, remote work, and early-career hiring," CEP Discussion Papers dp2193, Centre for Economic Performance, LSE.
    4. Hoyos, Mateo, 2026. "Tariffs and growth: Heterogeneity by economic structure," Journal of Comparative Economics, Elsevier, vol. 54(1), pages 99-115.
    5. repec:osf:socarx:v75aw_v1 is not listed on IDEAS
    6. Bargain, Olivier & Jara, H. Xavier & Rivera, David, 2024. "Tax disincentives to formal employment in Latin America," LSE Research Online Documents on Economics 125368, London School of Economics and Political Science, LSE Library.
    7. 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.
    8. Li, Yue & Zhao, Jing, 2026. "The effectiveness of carbon emission trading system: Evidence from China's regional markets," Journal of Development Economics, Elsevier, vol. 179(C).
    9. 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.
    10. Lambert, Peter John & Schindler, Yannick, 2026. "The Broken Ladder: AI, Remote Work, and Early-Career Hiring," CAGE Online Working Paper Series 808, Competitive Advantage in the Global Economy (CAGE).
    11. Neri-Lainé, Matteo, 2026. "Firms under fire! How insecurity affects formal firms’ existence," Journal of Development Economics, Elsevier, vol. 180(C).
    12. 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).
    13. Baragwanath, Kathryn & Shinde, Nilesh, 2025. "Beyond the canopy: How satellite data detection thresholds influence policy evaluation and deforestation behavior," Journal of Environmental Economics and Management, Elsevier, vol. 134(C).

    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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