IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v110y2023i2p485-498..html
   My bibliography  Save this article

Sample-constrained partial identification with application to selection bias

Author

Listed:
  • Matthew J Tudball
  • Rachael A Hughes
  • Kate Tilling
  • Jack Bowden
  • Qingyuan Zhao

Abstract

SummaryMany partial identification problems can be characterized by the optimal value of a function over a set where both the function and set need to be estimated by empirical data. Despite some progress for convex problems, statistical inference in this general setting remains to be developed. To address this, we derive an asymptotically valid confidence interval for the optimal value through an appropriate relaxation of the estimated set. We then apply this general result to the problem of selection bias in population-based cohort studies. We show that existing sensitivity analyses, which are often conservative and difficult to implement, can be formulated in our framework and made significantly more informative via auxiliary information on the population. We conduct a simulation study to evaluate the finite sample performance of our inference procedure, and conclude with a substantive motivating example on the causal effect of education on income in the highly selected UK Biobank cohort. We demonstrate that our method can produce informative bounds using plausible population-level auxiliary constraints. We implement this method in the $\texttt{R}$ package $\texttt{selectioninterval}$.

Suggested Citation

  • Matthew J Tudball & Rachael A Hughes & Kate Tilling & Jack Bowden & Qingyuan Zhao, 2023. "Sample-constrained partial identification with application to selection bias," Biometrika, Biometrika Trust, vol. 110(2), pages 485-498.
  • Handle: RePEc:oup:biomet:v:110:y:2023:i:2:p:485-498.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asac042
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Neil M. Davies & Matt Dickson & George Davey Smith & Gerard J. van den Berg & Frank Windmeijer, 2018. "The causal effects of education on health outcomes in the UK Biobank," Nature Human Behaviour, Nature, vol. 2(2), pages 117-125, February.
    2. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    3. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    4. repec:cwl:cwldpp:1840rr is not listed on IDEAS
    5. Qingyuan Zhao & Dylan S. Small & Bhaswar B. Bhattacharya, 2019. "Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(4), pages 735-761, September.
    6. L W Miratrix & S Wager & J R Zubizarreta, 2018. "Shape-constrained partial identification of a population mean under unknown probabilities of sample selection," Biometrika, Biometrika Trust, vol. 105(1), pages 103-114.
    7. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    8. Elizabeth A. Stuart & Stephen R. Cole & Catherine P. Bradshaw & Philip J. Leaf, 2011. "The use of propensity scores to assess the generalizability of results from randomized trials," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 174(2), pages 369-386, April.
    9. Peter M. Aronow & Donald K. K. Lee, 2013. "Interval estimation of population means under unknown but bounded probabilities of sample selection," Biometrika, Biometrika Trust, vol. 100(1), pages 235-240.
    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. 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.
    2. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2013. "Testing Many Moment Inequalities," CeMMAP working papers 65/13, Institute for Fiscal Studies.
    3. Steven T Berry & Giovanni Compiani, 2023. "An Instrumental Variable Approach to Dynamic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(4), pages 1724-1758.
    4. Kyunghoon Ban & Désiré Kédagni, 2022. "Nonparametric bounds on treatment effects with imperfect instruments [Instrument-based estimation with binarized treatments: Issues and tests for the exclusion restriction]," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 477-493.
    5. Chen, Le-Yu & Lee, Sokbae, 2019. "Breaking the curse of dimensionality in conditional moment inequalities for discrete choice models," Journal of Econometrics, Elsevier, vol. 210(2), pages 482-497.
    6. Mourifié, Ismael, 2015. "Sharp bounds on treatment effects in a binary triangular system," Journal of Econometrics, Elsevier, vol. 187(1), pages 74-81.
    7. Hsu, Yu-Chin & Shen, Shu, 2019. "Testing treatment effect heterogeneity in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 208(2), pages 468-486.
    8. Horowitz, Joel L. & Lee, Sokbae, 2017. "Nonparametric estimation and inference under shape restrictions," Journal of Econometrics, Elsevier, vol. 201(1), pages 108-126.
    9. Santiago Acerenza & Otávio Bartalotti & Désiré Kédagni, 2023. "Testing identifying assumptions in bivariate probit models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 407-422, April.
    10. Aradillas-López, Andrés & Rosen, Adam M., 2022. "Inference in ordered response games with complete information," Journal of Econometrics, Elsevier, vol. 226(2), pages 451-476.
    11. Semenova, Vira, 2023. "Debiased machine learning of set-identified linear models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1725-1746.
    12. Andrews, Donald W.K. & Shi, Xiaoxia, 2017. "Inference based on many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 196(2), pages 275-287.
    13. Kédagni, Désiré, 2023. "Identifying treatment effects in the presence of confounded types," Journal of Econometrics, Elsevier, vol. 234(2), pages 479-511.
    14. Bei, Xinyue, 2024. "Local linearization based subvector inference in moment inequality models," Journal of Econometrics, Elsevier, vol. 238(1).
    15. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers 706, University of Oxford, Department of Economics.
    16. Bugni, Federico A. & Canay, Ivan A. & Shi, Xiaoxia, 2015. "Specification tests for partially identified models defined by moment inequalities," Journal of Econometrics, Elsevier, vol. 185(1), pages 259-282.
    17. Federico A. Bugni & Ivan A. Canay & Xiaoxia Shi, 2014. "Inference for functions of partially identified parameters in moment inequality models," CeMMAP working papers 22/14, Institute for Fiscal Studies.
    18. Lukáš Lafférs, 2019. "Identification in Models with Discrete Variables," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 657-696, February.
    19. Chesher, Andrew & Kim, Dongwoo & Rosen, Adam M., 2023. "IV methods for Tobit models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1700-1724.
    20. Victor Chernozhukov & Christian Hansen & Kaspar Wuthrich, 2020. "Instrumental Variable Quantile Regression," Papers 2009.00436, arXiv.org.

    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:oup:biomet:v:110:y:2023:i:2:p:485-498.. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.