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Partial identification using random set theory

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  • Beresteanu, Arie
  • Molchanov, Ilya
  • Molinari, Francesca

Abstract

This paper illustrates how the use of random set theory can benefit partial identification analysis. We revisit the origins of Manski’s work in partial identification (e.g., Manski (1989, 1990)) focusing our discussion on identification of probability distributions and conditional expectations in the presence of selectively observed data, statistical independence and mean independence assumptions, and shape restrictions. We show that the use of the Choquet capacity functional and the Aumann expectation of a properly defined random set can simplify and extend previous results in the literature. We pay special attention to explaining how the relevant random set needs to be constructed, depending on the econometric framework at hand. We also discuss limitations in the applicability of specific tools of random set theory to partial identification analysis.

Suggested Citation

  • Beresteanu, Arie & Molchanov, Ilya & Molinari, Francesca, 2012. "Partial identification using random set theory," Journal of Econometrics, Elsevier, vol. 166(1), pages 17-32.
  • Handle: RePEc:eee:econom:v:166:y:2012:i:1:p:17-32
    DOI: 10.1016/j.jeconom.2011.06.003
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    1. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    2. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
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    10. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2011. "Sharp Identification Regions in Models With Convex Moment Predictions," Econometrica, Econometric Society, vol. 79(6), pages 1785-1821, November.
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    Cited by:

    1. Liao, Yuan & Simoni, Anna, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," MPRA Paper 43262, University Library of Munich, Germany.
    2. Vishal Kamat, 2018. "On the Identifying Content of Instrument Monotonicity," Papers 1807.01661, arXiv.org, revised Oct 2019.
    3. Jiaying Gu & Thomas M. Russell, 2021. "Partial Identification in Nonseparable Binary Response Models with Endogenous Regressors," Papers 2101.01254, arXiv.org, revised Jul 2021.
    4. Lukáš Lafférs, 2019. "Identification in Models with Discrete Variables," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 657-696, February.
    5. Magnac, Thierry, 2013. "Identification partielle : méthodes et conséquences pour les applications empiriques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 89(4), pages 233-258, Décembre.
    6. Toulis, Panos, 2021. "Estimation of Covid-19 prevalence from serology tests: A partial identification approach," Journal of Econometrics, Elsevier, vol. 220(1), pages 193-213.
    7. Christian Bontemps & Thierry Magnac, 2017. "Set Identification, Moment Restrictions, and Inference," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 103-129, September.
    8. Raffaella Giacomini & Toru Kitagawa, 2021. "Robust Bayesian Inference for Set‐Identified Models," Econometrica, Econometric Society, vol. 89(4), pages 1519-1556, July.
    9. Sara Bleninger, 2013. "Welfare Effects of the Euro Cash Changeover: Do Assumptions Really Matter?," SOEPpapers on Multidisciplinary Panel Data Research 577, DIW Berlin, The German Socio-Economic Panel (SOEP).
    10. Panos Toulis, 2020. "Estimation of Covid-19 Prevalence from Serology Tests: A Partial Identification Approach," Papers 2006.16214, arXiv.org.
    11. Hoshino, Tadao, 2013. "Partial identification in binary response models with nonignorable nonresponses," Economics Letters, Elsevier, vol. 121(1), pages 74-78.
    12. Juan Carlos Escanciano & Lin Zhu, 2013. "Set inferences and sensitivity analysis in semiparametric conditionally identified models," CeMMAP working papers CWP55/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.
    14. Tatiana Komarova & Denis Nekipelov, 2020. "Identification and Formal Privacy Guarantees," Papers 2006.14732, arXiv.org, revised May 2021.
    15. Yuan Liao & Anna Simoni, 2016. "Bayesian Inference for Partially Identified Convex Models: Is it Valid for Frequentist Inference?," Departmental Working Papers 201607, Rutgers University, Department of Economics.
    16. Panos Toulis, 2020. "Estimation of COVID-19 Prevalence from Serology Tests: A Partial Identification Approach," Working Papers 2020-54_Revised, Becker Friedman Institute for Research In Economics.

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