IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2511.06243.html

A sensitivity analysis for the average derivative effect

Author

Listed:
  • Jeffrey Zhang

Abstract

In observational studies, exposures are often continuous rather than binary or discrete. At the same time, sensitivity analysis is an important tool that can help determine the robustness of a causal conclusion to a certain level of unmeasured confounding, which can never be ruled out in an observational study. Sensitivity analysis approaches for continuous exposures have now been proposed for several causal estimands. In this article, we focus on the average derivative effect (ADE). We obtain closed-form bounds for the ADE under a sensitivity model that constrains the odds ratio (at any two dose levels) between the latent and observed generalized propensity score. We propose flexible, efficient estimators for the bounds, as well as point-wise and simultaneous (over the sensitivity parameter) confidence intervals. We examine the finite sample performance of the methods through simulations and illustrate the methods on a study assessing the effect of parental income on educational attainment and a study assessing the price elasticity of petrol.

Suggested Citation

  • Jeffrey Zhang, 2025. "A sensitivity analysis for the average derivative effect," Papers 2511.06243, arXiv.org, revised Dec 2025.
    • Handle: RePEc:arx:papers:2511.06243
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2511.06243
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jesse Y. Hsu & Dylan S. Small, 2013. "Calibrating Sensitivity Analyses to Observed Covariates in Observational Studies," Biometrics, The International Biometric Society, vol. 69(4), pages 803-811, December.
    2. Guildo W. Imbens, 2003. "Sensitivity to Exogeneity Assumptions in Program Evaluation," American Economic Review, American Economic Association, vol. 93(2), pages 126-132, May.
    3. Tan, Zhiqiang, 2006. "A Distributional Approach for Causal Inference Using Propensity Scores," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1619-1637, December.
    4. Jacob Dorn & Kevin Guo, 2021. "Sharp Sensitivity Analysis for Inverse Propensity Weighting via Quantile Balancing," Papers 2102.04543, arXiv.org, revised Aug 2023.
    5. Jeffrey Zhang & Dylan S Small & Siyu Heng, 2024. "Sensitivity analysis for matched observational studies with continuous exposures and binary outcomes," Biometrika, Biometrika Trust, vol. 111(4), pages 1349-1368.
    6. Jacob Dorn & Kevin Guo, 2023. "Sharp Sensitivity Analysis for Inverse Propensity Weighting via Quantile Balancing," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(544), pages 2645-2657, October.
    7. Matteo Bonvini & Edward H. Kennedy, 2022. "Sensitivity Analysis via the Proportion of Unmeasured Confounding," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1540-1550, September.
    8. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
    9. 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.
    10. Abhinandan Dalal & Eric J. Tchetgen Tchetgen, 2025. "Partial Identification of Causal Effects for Endogenous Continuous Treatments," Papers 2508.13946, arXiv.org.
    11. Zhiqiang Tan, 2025. "Sensitivity models and bounds under sequential unmeasured confounding in longitudinal studies," Biometrika, Biometrika Trust, vol. 112(1), pages 2645-2657.
    12. Melody Huang & Samuel D Pimentel, 2025. "Variance-based sensitivity analysis for weighting estimators results in more informative bounds," Biometrika, Biometrika Trust, vol. 112(1), pages 235-240.
    13. Newey, Whitney K & Stoker, Thomas M, 1993. "Efficiency of Weighted Average Derivative Estimators and Index Models," Econometrica, Econometric Society, vol. 61(5), pages 1199-1223, September.
    14. Emily Oster, 2019. "Unobservable Selection and Coefficient Stability: Theory and Evidence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 187-204, April.
    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. Abhinandan Dalal & Eric J. Tchetgen Tchetgen, 2025. "Partial Identification of Causal Effects for Endogenous Continuous Treatments," Papers 2508.13946, arXiv.org.
    2. Aditya Ghosh & Dominik Rothenhausler, 2025. "Assumption-robust Causal Inference," Papers 2505.08729, arXiv.org, revised Jun 2025.
    3. Melody Huang & Cory McCartan, 2025. "Relative Bias Under Imperfect Identification in Observational Causal Inference," Papers 2507.23743, arXiv.org.
    4. Zequn Jin & Gaoqian Xu & Xi Zheng & Yahong Zhou, 2025. "Policy Learning under Unobserved Confounding: A Robust and Efficient Approach," Papers 2507.20550, arXiv.org.
    5. Stéphane Bonhomme & Martin Weidner, 2022. "Minimizing sensitivity to model misspecification," Quantitative Economics, Econometric Society, vol. 13(3), pages 907-954, July.
    6. Matthew A. Masten & Alexandre Poirier & Muyang Ren, 2025. "A General Approach to Relaxing Unconfoundedness," Papers 2501.15400, arXiv.org.
    7. Kaido, Hiroaki, 2017. "Asymptotically Efficient Estimation Of Weighted Average Derivatives With An Interval Censored Variable," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1218-1241, October.
    8. 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.
    9. Oyenubi, Adeola & Kollamparambil, Umakrishnan, 2023. "Does noncompliance with COVID-19 regulations impact the depressive symptoms of others?," Economic Modelling, Elsevier, vol. 120(C).
    10. Stéphane Bonhomme & Martin Weidner, 2020. "Minimizing Sensitivity to Model Misspecification," CeMMAP working papers CWP37/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Yukitoshi Matsushita & Taisuke Otsu, 2017. "Likelihood inference on semiparametric models: Average derivative and treatment effect," STICERD - Econometrics Paper Series 592, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    12. Julius Schaper, 2025. "Residualised Treatment Intensity and the Estimation of Average Partial Effects," Papers 2502.10301, arXiv.org.
    13. Coppejans, Mark, 2001. "Estimation of the binary response model using a mixture of distributions estimator (MOD)," Journal of Econometrics, Elsevier, vol. 102(2), pages 231-269, June.
    14. Semenova, Vira, 2023. "Debiased machine learning of set-identified linear models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1725-1746.
    15. Escanciano, Juan Carlos & Song, Kyungchul, 2010. "Testing single-index restrictions with a focus on average derivatives," Journal of Econometrics, Elsevier, vol. 156(2), pages 377-391, June.
    16. Arbour, William & Lacroix, Guy & Marchand, Steeve, 2021. "Prison Rehabilitation Programs: Efficiency and Targeting," IZA Discussion Papers 14022, Institute of Labor Economics (IZA).
    17. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    18. Yang Ning & Sida Peng & Jing Tao, 2020. "Doubly Robust Semiparametric Difference-in-Differences Estimators with High-Dimensional Data," Papers 2009.03151, arXiv.org.
    19. Deepankar Basu, 2023. "Formal Covariate Benchmarking to Bound Omitted Variable Bias," Papers 2306.10562, arXiv.org.
    20. Nathan Kallus, 2023. "Treatment Effect Risk: Bounds and Inference," Management Science, INFORMS, vol. 69(8), pages 4579-4590, August.

    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:2511.06243. 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.