IDEAS home Printed from https://ideas.repec.org/p/bbk/bbkefp/1710.html
   My bibliography  Save this paper

Eliciting Second-Order Beliefs

Author

Listed:
  • Subir Bose

    (University of Leicester)

  • Arup Daripa

    (Birkbeck, University of London)

Abstract

We study elicitation of subjective beliefs of an agent facing ambiguity (model uncertainty): the agent has a non-singleton set of (first-order) priors on an event and a second-order prior on these first-order belief-states. Such a two-stage decomposition of uncertainty and non-reduction of compound lotteries resulting from nonneutrality to the second-order distribution plays an important role in resolving the Ellsberg Paradox. The problem of eliciting beliefs on unobservable belief-states with ambiguity-sensitive agents is novel, and we introduce new elicitation techniques using report-dependent prize variations. We construct a direct revelation mechanism that induces truthful reporting of the first-order belief states as well as the secondorder distribution on the belief-states as the unique best response. The technique requires knowledge of the sensitivity function to second-order distribution (capturing ambiguity attitude) and the vN-M utility function, which we also elicit.

Suggested Citation

  • Subir Bose & Arup Daripa, 2017. "Eliciting Second-Order Beliefs," Birkbeck Working Papers in Economics and Finance 1710, Birkbeck, Department of Economics, Mathematics & Statistics.
    • Handle: RePEc:bbk:bbkefp:1710
    as

    Download full text from publisher

    File URL: https://eprints.bbk.ac.uk/id/eprint/29819
    File Function: First version, 2017
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
    2. Segal, Uzi, 1987. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 175-202, February.
    3. Bose, Subir & Daripa, Arup, 2022. "Eliciting ambiguous beliefs using constructed ambiguous acts: Alpha-maxmin," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    4. Andrew Schotter & Isabel Trevino, 2014. "Belief Elicitation in the Laboratory," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 103-128, August.
    5. Edi Karni, 2018. "A Mechanism for Eliciting Second-Order Beliefs and the Inclination to Choose," American Economic Journal: Microeconomics, American Economic Association, vol. 10(2), pages 275-285, May.
    6. Edi Karni, 2009. "A Mechanism for Eliciting Probabilities," Econometrica, Econometric Society, vol. 77(2), pages 603-606, March.
    7. Peter Wakker & Daniel Deneffe, 1996. "Eliciting von Neumann-Morgenstern Utilities When Probabilities Are Distorted or Unknown," Management Science, INFORMS, vol. 42(8), pages 1131-1150, August.
    8. Chambers, Christopher P., 2008. "Proper scoring rules for general decision models," Games and Economic Behavior, Elsevier, vol. 63(1), pages 32-40, May.
    9. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
    10. Christopher P. Chambers & Nicolas S. Lambert, 2021. "Dynamic Belief Elicitation," Econometrica, Econometric Society, vol. 89(1), pages 375-414, January.
    11. Loïc Berger & Massimo Marinacci, 2020. "Model Uncertainty in Climate Change Economics: A Review and Proposed Framework for Future Research," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 77(3), pages 475-501, November.
    12. Loïc Berger & Nicolas Berger & Valentina Bosetti & Itzhak Gilboa & Lars Peter Hansen & Christopher Jarvis & Massimo Marinacci & Richard D. Smith, 2020. "Uncertainty and decision-making during a crisis: How to make policy decisions in the COVID-19 context?," Working Papers 666, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    13. Kyoungwon Seo, 2009. "Ambiguity and Second-Order Belief," Econometrica, Econometric Society, vol. 77(5), pages 1575-1605, September.
    14. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    15. Manski, Charles F. & Neri, Claudia, 2013. "First- and second-order subjective expectations in strategic decision-making: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 232-254.
    16. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    17. Subir Bose & Arup Daripa, 2016. "Eliciting Ambiguous Beliefs Under alpha-Maxmin Preference," Birkbeck Working Papers in Economics and Finance 1601, Birkbeck, Department of Economics, Mathematics & Statistics.
    18. Karl Schlag & James Tremewan & Joël Weele, 2015. "A penny for your thoughts: a survey of methods for eliciting beliefs," Experimental Economics, Springer;Economic Science Association, vol. 18(3), pages 457-490, September.
    19. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    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. Bose, Subir & Daripa, Arup, 2022. "Eliciting ambiguous beliefs using constructed ambiguous acts: Alpha-maxmin," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    2. Ilke AYDOGAN & Loïc BERGER & Valentina BOSETTI & Ning LIU, 2022. "Three layers of uncertainty," Working Papers 2022-iRisk-01, IESEG School of Management.
    3. Ilke Aydogan & Loïc Berger & Valentina Bosetti & Ning Liu, 2022. "Three layers of uncertainty," Working Papers hal-03031751, HAL.
    4. repec:hal:journl:hal-03031751 is not listed on IDEAS
    5. Patrick Schmidt, 2019. "Eliciting ambiguity with mixing bets," Papers 1902.07447, arXiv.org, revised Jul 2022.
    6. Ilke Aydogan & Loic Berger & Valentina Bosetti & Ning Liu, 2018. "Three layers of uncertainty: an experiment," Working Papers 623, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    7. Yang, Chun-Lei & Yao, Lan, 2011. "Ellsberg Paradox and Second-order Preference Theories on Ambiguity: Some New Experimental Evidence," MPRA Paper 28531, University Library of Munich, Germany.
    8. Yoram Halevy & Emre Ozdenoren, 2022. "Uncertainty and compound lotteries: calibration," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 373-395, September.
    9. Bali, Turan G. & Brown, Stephen J. & Tang, Yi, 2017. "Is economic uncertainty priced in the cross-section of stock returns?," Journal of Financial Economics, Elsevier, vol. 126(3), pages 471-489.
    10. Ilke AYDOGAN & Loïc BERGER & Valentina BOSETTI, 2023. "Unraveling Ambiguity Aversion," Working Papers 2023-iRisk-01, IESEG School of Management.
    11. repec:hal:wpaper:hal-04071242 is not listed on IDEAS
    12. Prokosheva, Sasha, 2016. "Comparing decisions under compound risk and ambiguity: The importance of cognitive skills," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 64(C), pages 94-105.
    13. Arthur Carvalho & Stanko Dimitrov & Kate Larson, 2018. "On proper scoring rules and cumulative prospect theory," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 343-376, November.
    14. Ilke Aydogan & Loïc Berger & Valentina Bosetti, 2023. "Unraveling Ambiguity Aversion," Post-Print hal-04071242, HAL.
    15. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    16. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    17. Mohammed Abdellaoui & Peter Klibanoff & Lætitia Placido, 2015. "Experiments on Compound Risk in Relation to Simple Risk and to Ambiguity," Management Science, INFORMS, vol. 61(6), pages 1306-1322, June.
    18. He, Ying & Dyer, James S. & Butler, John C. & Jia, Jianmin, 2019. "An additive model of decision making under risk and ambiguity," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 78-92.
    19. David Ahn & Syngjoo Choi & Douglas Gale & Shachar Kariv, 2014. "Estimating ambiguity aversion in a portfolio choice experiment," Quantitative Economics, Econometric Society, vol. 5, pages 195-223, July.
    20. Izhakian, Yehuda, 2020. "A theoretical foundation of ambiguity measurement," Journal of Economic Theory, Elsevier, vol. 187(C).
    21. Evren, Özgür, 2019. "Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity," Games and Economic Behavior, Elsevier, vol. 114(C), pages 285-307.
    22. Bleichrodt, Han & Eichberger, Jürgen & Grant, Simon & Kelsey, David & Li, Chen, 2021. "Testing dynamic consistency and consequentialism under ambiguity," European Economic Review, Elsevier, vol. 134(C).

    More about this item

    Keywords

    Ambiguity; second-order beliefs; elicitation of second-order beliefs (support and distribution); Klibanoff-Marinacci-Mukerji (2005) representation; elicitation of second-order-distribution-sensitivity function; elicitation of the vN-M utility function.;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:bbk:bbkefp:1710. 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: the person in charge (email available below). General contact details of provider: https://www.bbk.ac.uk/departments/ems/ .

    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.