IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2408.10509.html
   My bibliography  Save this paper

Continuous difference-in-differences with double/debiased machine learning

Author

Listed:
  • Lucas Zhang

Abstract

This paper extends difference-in-differences to settings involving continuous treatments. Specifically, the average treatment effect on the treated (ATT) at any level of continuous treatment intensity is identified using a conditional parallel trends assumption. In this framework, estimating the ATTs requires first estimating infinite-dimensional nuisance parameters, especially the conditional density of the continuous treatment, which can introduce significant biases. To address this challenge, estimators for the causal parameters are proposed under the double/debiased machine learning framework. We show that these estimators are asymptotically normal and provide consistent variance estimators. To illustrate the effectiveness of our methods, we re-examine the study by Acemoglu and Finkelstein (2008), which assessed the effects of the 1983 Medicare Prospective Payment System (PPS) reform. By reinterpreting their research design using a difference-in-differences approach with continuous treatment, we nonparametrically estimate the treatment effects of the 1983 PPS reform, thereby providing a more detailed understanding of its impact.

Suggested Citation

  • Lucas Zhang, 2024. "Continuous difference-in-differences with double/debiased machine learning," Papers 2408.10509, arXiv.org.
    • Handle: RePEc:arx:papers:2408.10509
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2408.10509
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Clément de Chaisemartin & Xavier d'Haultfoeuille & Félix Pasquier & Gonzalo Vazquez-Bare, 2022. "Difference-in-Differences Estimators for Treatments Continuously Distributed at Every Period," SciencePo Working papers Main hal-03873926, HAL.
    2. Daron Acemoglu & Amy Finkelstein, 2008. "Input and Technology Choices in Regulated Industries: Evidence from the Health Care Sector," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 837-880, October.
    3. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    4. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 1-19.
    5. Neng-Chieh Chang, 2020. "Double/debiased machine learning for difference-in-differences models," The Econometrics Journal, Royal Economic Society, vol. 23(2), pages 177-191.
    6. Qingliang Fan & Yu-Chin Hsu & Robert P. Lieli & Yichong Zhang, 2022. "Estimation of Conditional Average Treatment Effects With High-Dimensional Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 313-327, January.
    7. Fan, Jianqing & Yao, Qiwei & Tong, Howell, 1996. "Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems," LSE Research Online Documents on Economics 6704, London School of Economics and Political Science, LSE Library.
    8. 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.
    9. Lisa D Cook & Maggie E C Jones & Trevon D Logan & David Rosé, 2023. "The Evolution of Access to Public Accommodations in the United States," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 138(1), pages 37-102.
    10. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    11. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    12. Su, Liangjun & Ura, Takuya & Zhang, Yichong, 2019. "Non-separable models with high-dimensional data," Journal of Econometrics, Elsevier, vol. 212(2), pages 646-677.
    13. 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.
    14. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    15. Elizabeth Ananat & Benjamin Glasner & Christal Hamilton & Zachary Parolin, 2022. "Effects of the Expanded Child Tax Credit on Employment Outcomes: Evidence from Real-World Data from April to December 2021," NBER Working Papers 29823, National Bureau of Economic Research, Inc.
    16. Brantly Callaway & Andrew Goodman-Bacon & Pedro H. C. Sant'Anna, 2021. "Difference-in-Differences with a Continuous Treatment," Papers 2107.02637, arXiv.org, revised Jan 2024.
    17. Lu Li & Niwen Zhou & Lixing Zhu, 2022. "Outcome regression-based estimation of conditional average treatment effect," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 987-1041, October.
    18. Vira Semenova & Victor Chernozhukov, 2021. "Debiased machine learning of conditional average treatment effects and other causal functions," The Econometrics Journal, Royal Economic Society, vol. 24(2), pages 264-289.
    19. Edward H. Kennedy & Zongming Ma & Matthew D. McHugh & Dylan S. Small, 2017. "Non-parametric methods for doubly robust estimation of continuous treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1229-1245, September.
    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. Nan Liu & Yanbo Liu & Yuya Sasaki, 2024. "Estimation and Inference for Causal Functions with Multiway Clustered Data," Papers 2409.06654, arXiv.org.
    2. Yang Ning & Sida Peng & Jing Tao, 2020. "Doubly Robust Semiparametric Difference-in-Differences Estimators with High-Dimensional Data," Papers 2009.03151, arXiv.org.
    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. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    5. Mark Kattenberg & Bas Scheer & Jurre Thiel, 2023. "Causal forests with fixed effects for treatment effect heterogeneity in difference-in-differences," CPB Discussion Paper 452, CPB Netherlands Bureau for Economic Policy Analysis.
    6. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    7. Gregory Faletto, 2023. "Fused Extended Two-Way Fixed Effects for Difference-in-Differences With Staggered Adoptions," Papers 2312.05985, arXiv.org, revised Oct 2024.
    8. Nora Bearth, 2024. "Beyond Baby Blues: The Child Penalty in Mental Health in Switzerland," Papers 2410.20861, arXiv.org.
    9. Christoph Breunig & Ruixuan Liu & Zhengfei Yu, 2024. "Semiparametric Bayesian Difference-in-Differences," Papers 2412.04605, arXiv.org, revised Dec 2024.
    10. 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.
    11. Michael Lechner & Jana Mareckova, 2024. "Comprehensive Causal Machine Learning," Papers 2405.10198, arXiv.org.
    12. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    13. Arne Henningsen & Guy Low & David Wuepper & Tobias Dalhaus & Hugo Storm & Dagim Belay & Stefan Hirsch, 2024. "Estimating Causal Effects with Observational Data: Guidelines for Agricultural and Applied Economists," IFRO Working Paper 2024/03, University of Copenhagen, Department of Food and Resource Economics.
    14. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP54/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. Adam Baybutt & Manu Navjeevan, 2023. "Doubly-Robust Inference for Conditional Average Treatment Effects with High-Dimensional Controls," Papers 2301.06283, arXiv.org.
    16. Kyle Colangelo & Ying-Ying Lee, 2020. "Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments," Papers 2004.03036, arXiv.org, revised Sep 2023.
    17. Melnik, Walter & Smyth, Andrew, 2024. "R&D tax credits and innovation," Journal of Public Economics, Elsevier, vol. 236(C).
    18. Jeffrey M Wooldridge, 2023. "Simple approaches to nonlinear difference-in-differences with panel data," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 31-66.
    19. 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.
    20. Deschenes, Olivier & Malloy, Christopher & McDonald, Gavin, 2023. "Causal effects of Renewable Portfolio Standards on renewable investments and generation: The role of heterogeneity and dynamics," Resource and Energy Economics, Elsevier, vol. 75(C).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2408.10509. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.