IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i10p1556-d1396103.html
   My bibliography  Save this article

Extreme Treatment Effect: Extrapolating Dose-Response Function into Extreme Treatment Domain

Author

Listed:
  • Juraj Bodik

    (Faculty of Business and Economics (HEC Lausanne), University of Lausanne, 1015 Lausanne, Switzerland
    Expertise Center for Climate Extremes (ECCE), University of Lausanne, 1015 Lausanne, Switzerland)

Abstract

The potential outcomes framework serves as a fundamental tool for quantifying causal effects. The average dose–response function μ ( t ) (also called the effect curve) is typically of interest when dealing with a continuous treatment variable (exposure). The focus of this work is to determine the impact of an extreme level of treatment, potentially beyond the range of observed values—that is, estimating μ ( t ) for very large t . Our approach is grounded in the field of statistics known as extreme value theory. We outline key assumptions for the identifiability of the extreme treatment effect. Additionally, we present a novel and consistent estimation procedure that can potentially reduce the dimension of the confounders to at most 3. This is a significant result since typically, the estimation of μ ( t ) is very challenging due to high-dimensional confounders. In practical applications, our framework proves valuable when assessing the effects of scenarios such as drug overdoses, extreme river discharges, or extremely high temperatures on a variable of interest.

Suggested Citation

  • Juraj Bodik, 2024. "Extreme Treatment Effect: Extrapolating Dose-Response Function into Extreme Treatment Domain," Mathematics, MDPI, vol. 12(10), pages 1-36, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1556-:d:1396103
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/10/1556/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/10/1556/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2009. "Dealing with limited overlap in estimation of average treatment effects," Biometrika, Biometrika Trust, vol. 96(1), pages 187-199.
    2. Noémi Kreif & Richard Grieve & Iván Díaz & David Harrison, 2015. "Evaluation of the Effect of a Continuous Treatment: A Machine Learning Approach with an Application to Treatment for Traumatic Brain Injury," Health Economics, John Wiley & Sons, Ltd., vol. 24(9), pages 1213-1228, September.
    3. James J. Heckman & John Eric Humphries & Gregory Veramendi, 2018. "Returns to Education: The Causal Effects of Education on Earnings, Health, and Smoking," Journal of Political Economy, University of Chicago Press, vol. 126(S1), pages 197-246.
    4. Michela Bia & Carlos A. Flores & Alfonso Flores-Lagunes & Alessandra Mattei, 2014. "A Stata package for the application of semiparametric estimators of dose–response functions," Stata Journal, StataCorp LP, vol. 14(3), pages 580-604, September.
    5. Hamish Low & Costas Meghir, 2017. "The Use of Structural Models in Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 33-58, Spring.
    6. Victor Chernozhukov, 2005. "Extremal quantile regression," Papers math/0505639, arXiv.org.
    7. Edward H. Kennedy, 2019. "Nonparametric Causal Effects Based on Incremental Propensity Score Interventions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 645-656, April.
    8. Sebastian Engelke & Adrien S. Hitz, 2020. "Graphical models for extremes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(4), pages 871-932, September.
    9. Donald B. Rubin, 2005. "Causal Inference Using Potential Outcomes: Design, Modeling, Decisions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 322-331, March.
    10. Richard A. Davis, 1982. "The rate of convergence in distribution of the maxima," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 36(1), pages 31-35, March.
    11. van der Wal, Willem M. & Geskus, Ronald B., 2011. "ipw: An R Package for Inverse Probability Weighting," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i13).
    12. Kosuke Imai & David A. van Dyk, 2004. "Causal Inference With General Treatment Regimes: Generalizing the Propensity Score," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 854-866, January.
    13. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(1), pages 105-121, February.
    14. Kosuke Imai & Gary King & Elizabeth A. Stuart, 2008. "Misunderstandings between experimentalists and observationalists about causal inference," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(2), pages 481-502, April.
    15. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, November.
    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. Newham, Melissa & Valente, Marica, 2024. "The cost of influence: How gifts to physicians shape prescriptions and drug costs," Journal of Health Economics, Elsevier, vol. 95(C).
    2. Tingting Zhou & Michael R. Elliott & Roderick J. A. Little, 2022. "Addressing Disparities in the Propensity Score Distributions for Treatment Comparisons from Observational Studies," Stats, MDPI, vol. 5(4), pages 1-17, December.
    3. Valente, Marica, 2023. "Policy evaluation of waste pricing programs using heterogeneous causal effect estimation," Journal of Environmental Economics and Management, Elsevier, vol. 117(C).
    4. Markku Maula & Wouter Stam, 2020. "Enhancing Rigor in Quantitative Entrepreneurship Research," Entrepreneurship Theory and Practice, , vol. 44(6), pages 1059-1090, November.
    5. Tübbicke Stefan, 2022. "Entropy Balancing for Continuous Treatments," Journal of Econometric Methods, De Gruyter, vol. 11(1), pages 71-89, January.
    6. Tenglong Li & Kenneth A. Frank & Mingming Chen, 2024. "A Conceptual Framework for Quantifying the Robustness of a Regression-Based Causal Inference in Observational Study," Mathematics, MDPI, vol. 12(3), pages 1-14, January.
    7. Ruth T. Chepchirchir & Ibrahim Macharia & Alice W. Murage & Charles A. O. Midega & Zeyaur R. Khan, 2017. "Impact assessment of push-pull pest management on incomes, productivity and poverty among smallholder households in Eastern Uganda," Food Security: The Science, Sociology and Economics of Food Production and Access to Food, Springer;The International Society for Plant Pathology, vol. 9(6), pages 1359-1372, December.
    8. Swen Kuh & Grace S. Chiu & Anton H. Westveld, 2020. "Latent Causal Socioeconomic Health Index," Papers 2009.12217, arXiv.org, revised Oct 2023.
    9. Tenglong Li & Kenneth A. Frank, 2020. "The probability of a robust inference for internal validity and its applications in regression models," Papers 2005.12784, arXiv.org.
    10. Pablo Geraldo Bast'ias, 2024. "Credible causal inference beyond toy models," Papers 2402.11659, arXiv.org.
    11. Tenglong Li & Kenneth A. Frank, 2019. "On the probability of a causal inference is robust for internal validity," Papers 1906.08726, arXiv.org.
    12. Zachary K. Collier & Walter L. Leite & Allison Karpyn, 2021. "Neural Networks to Estimate Generalized Propensity Scores for Continuous Treatment Doses," Evaluation Review, , vol. 45(1-2), pages 3-33, February.
    13. Noémi Kreif & Richard Grieve & Iván Díaz & David Harrison, 2015. "Evaluation of the Effect of a Continuous Treatment: A Machine Learning Approach with an Application to Treatment for Traumatic Brain Injury," Health Economics, John Wiley & Sons, Ltd., vol. 24(9), pages 1213-1228, September.
    14. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.
    15. Marco Caliendo & Stefan Tübbicke, 2020. "New evidence on long-term effects of start-up subsidies: matching estimates and their robustness," Empirical Economics, Springer, vol. 59(4), pages 1605-1631, October.
    16. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    17. Caloffi, Annalisa & Freo, Marzia & Ghinoi, Stefano & Mariani, Marco & Rossi, Federica, 2022. "Assessing the effects of a deliberate policy mix: The case of technology and innovation advisory services and innovation vouchers," Research Policy, Elsevier, vol. 51(6).
    18. Ida D'Attoma & Silvia Pacei, 2018. "Evaluating the Effects of Product Innovation on the Performance of European Firms by Using the Generalised Propensity Score," German Economic Review, Verein für Socialpolitik, vol. 19(1), pages 94-112, February.
    19. Carina Steckenleiter & Michael Lechner & Tim Pawlowski & Ute Schüttoff, 2023. "Do local expenditures on sports facilities affect sports participation?," Economic Inquiry, Western Economic Association International, vol. 61(4), pages 1103-1128, October.
    20. Daniel Burkhard & Christian P. R. Schmid & Kaspar Wüthrich, 2019. "Financial incentives and physician prescription behavior: Evidence from dispensing regulations," Health Economics, John Wiley & Sons, Ltd., vol. 28(9), pages 1114-1129, September.

    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:gam:jmathe:v:12:y:2024:i:10:p:1556-:d:1396103. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.