IDEAS home Printed from https://ideas.repec.org/p/chu/wpaper/16-14.html
   My bibliography  Save this paper

Random Expected Utility and Certainty Equivalents: Mimicry of Probability Weighting Functions

Author

Listed:
  • Nathaniel T. Wilcox

    (Economic Science Institute, Chapman University)

Abstract

For simple prospects routinely used for certainty equivalent elicitation, random expected utility preferences imply a conditional expectation function that can mimic deterministic rank dependent preferences. That is, a subject with random expected utility preferences can have expected certainty equivalents exactly like those predicted by rank dependent probability weighting functions of the inverse-s shape discussed by Quiggin (1982) and advocated by Tversky and Kahneman (1992), Prelec (1998) and other scholars. Certainty equivalents may not nonparametrically identify preferences: Their conditional expectation (and critically, their interpretation) depends on assumptions concerning the source of their variability.

Suggested Citation

  • Nathaniel T. Wilcox, 2017. "Random Expected Utility and Certainty Equivalents: Mimicry of Probability Weighting Functions," Working Papers 16-14, Chapman University, Economic Science Institute.
    • Handle: RePEc:chu:wpaper:16-14
    as

    Download full text from publisher

    File URL: https://www.chapman.edu/research/institutes-and-centers/economic-science-institute/_files/WorkingPapers/Random-EU-and-CE-NWilcox-2017.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Loomes, Graham & Moffatt, Peter G & Sugden, Robert, 2002. "A Microeconometric Test of Alternative Stochastic Theories of Risky Choice," Journal of Risk and Uncertainty, Springer, vol. 24(2), pages 103-130, March.
    2. Loomes, Graham & Sugden, Robert, 1998. "Testing Different Stochastic Specifications of Risky Choice," Economica, London School of Economics and Political Science, vol. 65(260), pages 581-598, November.
    3. Grant, Simon & Polak, Ben, 2013. "Mean-dispersion preferences and constant absolute uncertainty aversion," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1361-1398.
    4. Camerer, Colin F & Hogarth, Robin M, 1999. "The Effects of Financial Incentives in Experiments: A Review and Capital-Labor-Production Framework," Journal of Risk and Uncertainty, Springer, vol. 19(1-3), pages 7-42, December.
    5. Mohammed Abdellaoui & Han Bleichrodt & Olivier L’Haridon, 2008. "A tractable method to measure utility and loss aversion under prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 245-266, June.
    6. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    7. Jehoshua Eliashberg & John R. Hauser, 1985. "A Measurement Error Approach for Modeling Consumer Risk Preference," Management Science, INFORMS, vol. 31(1), pages 1-25, January.
    8. Alex Voorhoeve & Ken Binmore & Arnaldur Stefansson & Lisa Stewart, 2016. "Ambiguity attitudes, framing, and consistency," Theory and Decision, Springer, vol. 81(3), pages 313-337, September.
    9. Pedro Bordalo & Nicola Gennaioli & Andrei Shleifer, 2012. "Salience Theory of Choice Under Risk," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1243-1285.
    10. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    11. Pedro Bordalo & Nicola Gennaioli & Andrei Shleifer, 2013. "Salience and Consumer Choice," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 803-843.
    12. Michael H. Birnbaum & Ulrich Schmidt, 2015. "The Impact of Learning by Thought on Violations of Independence and Coalescing," Decision Analysis, INFORMS, vol. 12(3), pages 144-152.
    13. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    14. Nathaniel T. Wilcox, 2023. "Unusual Estimates of Probability Weighting Functions," Research in Experimental Economics, in: Models of Risk Preferences: Descriptive and Normative Challenges, volume 22, pages 69-106, Emerald Group Publishing Limited.
    15. David S. Ahn & Todd Sarver, 2013. "Preference for Flexibility and Random Choice," Econometrica, Econometric Society, vol. 81(1), pages 341-361, January.
    16. Yoram Halevy, 2007. "Ellsberg Revisited: An Experimental Study," Econometrica, Econometric Society, vol. 75(2), pages 503-536, March.
    17. Karni, Edi & Safra, Zvi, 1987. ""Preference Reversal' and the Observability of Preferences by Experimental Methods," Econometrica, Econometric Society, vol. 55(3), pages 675-685, May.
    18. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    19. Nathaniel T Wilcox, 2006. "Theories of Learning in Games and Heterogeneity Bias," Econometrica, Econometric Society, vol. 74(5), pages 1271-1292, September.
    20. Wilcox, Nathaniel T., 2011. "'Stochastically more risk averse:' A contextual theory of stochastic discrete choice under risk," Journal of Econometrics, Elsevier, vol. 162(1), pages 89-104, May.
    21. Harrison, Glenn W. & Rutström, E. Elisabet, 2008. "Experimental Evidence on the Existence of Hypothetical Bias in Value Elicitation Methods," Handbook of Experimental Economics Results, in: Charles R. Plott & Vernon L. Smith (ed.), Handbook of Experimental Economics Results, edition 1, volume 1, chapter 81, pages 752-767, Elsevier.
    22. Graham Loomes & Ganna Pogrebna, 2014. "Measuring Individual Risk Attitudes when Preferences are Imprecise," Economic Journal, Royal Economic Society, vol. 0(576), pages 569-593, May.
    23. David J. Butler & Graham C. Loomes, 2007. "Imprecision as an Account of the Preference Reversal Phenomenon," American Economic Review, American Economic Association, vol. 97(1), pages 277-297, March.
    24. Daniel Navarro-Martinez & Graham Loomes & Andrea Isoni & David Butler & Larbi Alaoui, 2018. "Boundedly rational expected utility theory," Journal of Risk and Uncertainty, Springer, vol. 57(3), pages 199-223, December.
    25. Jonathan W. Leland & Mark Schneider, 2016. "Salience, Framing, and Decisions under Risk, Uncertainty, and Time," Working Papers 16-08, Chapman University, Economic Science Institute.
    26. Mohammed Abdellaoui & Han Bleichrodt & Corina Paraschiv, 2007. "Loss Aversion Under Prospect Theory: A Parameter-Free Measurement," Management Science, INFORMS, vol. 53(10), pages 1659-1674, October.
    27. George Wu & Richard Gonzalez, 1999. "Nonlinear Decision Weights in Choice Under Uncertainty," Management Science, INFORMS, vol. 45(1), pages 74-85, January.
    28. Pavlo R. Blavatskyy & Ganna Pogrebna, 2010. "Models of stochastic choice and decision theories: why both are important for analyzing decisions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(6), pages 963-986.
    29. Faruk Gul & Wolfgang Pesendorfer, 2006. "Random Expected Utility," Econometrica, Econometric Society, vol. 74(1), pages 121-146, January.
    30. Karni, Edi & Safra, Zvi, 2016. "A theory of stochastic choice under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 164-173.
    31. Voorhoeve, Alex & Binmore, Ken G & Stefansson, Arnaldur & Stewart, Lisa, 2016. "Ambiguity attitudes, framing, and consistency," LSE Research Online Documents on Economics 65577, London School of Economics and Political Science, LSE Library.
    32. 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.
    33. Krahnen, Jan Pieter & Rieck, Christian & Theissen, Erik, 1997. "Inferring risk attitudes from certainty equivalents: Some lessons from an experimental study," Journal of Economic Psychology, Elsevier, vol. 18(5), pages 469-486, September.
    34. Leland, Jonathan, 2010. "The hunt for a descriptive theory of choice under risk--A view from the road not taken," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 39(5), pages 568-577, October.
    35. Adrian Bruhin & Helga Fehr-Duda & Thomas Epper, 2010. "Risk and Rationality: Uncovering Heterogeneity in Probability Distortion," Econometrica, Econometric Society, vol. 78(4), pages 1375-1412, July.
    36. Joost M.E. Pennings & Ale Smidts, 2000. "Assessing the Construct Validity of Risk Attitude," Management Science, INFORMS, vol. 46(10), pages 1337-1348, October.
    37. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    38. Loewenstein, George, 1999. "Experimental Economics from the Vantage-Point of Behavioural Economics," Economic Journal, Royal Economic Society, vol. 109(453), pages 23-34, February.
    39. Ferdinand M. Vieider & Mathieu Lefebvre & Ranoua Bouchouicha & Thorsten Chmura & Rustamdjan Hakimov & Michal Krawczyk & Peter Martinsson, 2015. "Common Components Of Risk And Uncertainty Attitudes Across Contexts And Domains: Evidence From 30 Countries," Journal of the European Economic Association, European Economic Association, vol. 13(3), pages 421-452, June.
    40. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Daniel Navarro-Martinez & Graham Loomes & Andrea Isoni & David Butler & Larbi Alaoui, 2018. "Boundedly rational expected utility theory," Journal of Risk and Uncertainty, Springer, vol. 57(3), pages 199-223, December.
    2. Charles-Cadogan, G., 2018. "Probability interference in expected utility theory," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 163-175.

    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. Mark Schneider & Jonathan W. Leland & Nathaniel T. Wilcox, 2018. "Ambiguity framed," Journal of Risk and Uncertainty, Springer, vol. 57(2), pages 133-151, October.
      • Mark Schneider & Jonathan Leland & Nathaniel T. Wilcox, 2016. "Ambiguity Framed," Working Papers 16-11, Chapman University, Economic Science Institute.
    2. Laurent Denant-Boemont & Olivier L’Haridon, 2013. "La rationalité à l'épreuve de l'économie comportementale," Revue française d'économie, Presses de Sciences-Po, vol. 0(2), pages 35-89.
    3. Aurélien Baillon & Yoram Halevy & Chen Li, 2022. "Experimental elicitation of ambiguity attitude using the random incentive system," Experimental Economics, Springer;Economic Science Association, vol. 25(3), pages 1002-1023, June.
    4. Aurélien Baillon & Laure Cabantous & Peter Wakker, 2012. "Aggregating imprecise or conflicting beliefs: An experimental investigation using modern ambiguity theories," Journal of Risk and Uncertainty, Springer, vol. 44(2), pages 115-147, April.
    5. Glenn W. Harrison & J. Todd Swarthout, 2016. "Cumulative Prospect Theory in the Laboratory: A Reconsideration," Experimental Economics Center Working Paper Series 2016-04, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University.
    6. Jakusch, Sven Thorsten & Meyer, Steffen & Hackethal, Andreas, 2019. "Taming models of prospect theory in the wild? Estimation of Vlcek and Hens (2011)," SAFE Working Paper Series 146, Leibniz Institute for Financial Research SAFE, revised 2019.
    7. Nathaniel T. Wilcox, 2015. "Error and Generalization in Discrete Choice Under Risk," Working Papers 15-11, Chapman University, Economic Science Institute.
    8. Gijs van de Kuilen & Peter P. Wakker, 2011. "The Midweight Method to Measure Attitudes Toward Risk and Ambiguity," Management Science, INFORMS, vol. 57(3), pages 582-598, March.
    9. José Lara Resende & George Wu, 2010. "Competence effects for choices involving gains and losses," Journal of Risk and Uncertainty, Springer, vol. 40(2), pages 109-132, April.
    10. Luís Santos-Pinto & Adrian Bruhin & José Mata & Thomas Åstebro, 2015. "Detecting heterogeneous risk attitudes with mixed gambles," Theory and Decision, Springer, vol. 79(4), pages 573-600, December.
    11. Víctor González-Jiménez, 2021. "Incentive contracts when agents distort probabilities," Vienna Economics Papers vie2101, University of Vienna, Department of Economics.
    12. Peter Brooks & Simon Peters & Horst Zank, 2014. "Risk behavior for gain, loss, and mixed prospects," Theory and Decision, Springer, vol. 77(2), pages 153-182, August.
    13. Roxane Bricet, 2018. "Preferences for information precision under ambiguity," THEMA Working Papers 2018-09, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    14. Adrian Bruhin & Maha Manai & Luís Santos-Pinto, 2022. "Risk and rationality: The relative importance of probability weighting and choice set dependence," Journal of Risk and Uncertainty, Springer, vol. 65(2), pages 139-184, October.
    15. Matthew Ryan, 2018. "Uncertainty and binary stochastic choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(3), pages 629-662, May.
    16. Georgalos, Konstantinos & Paya, Ivan & Peel, David A., 2021. "On the contribution of the Markowitz model of utility to explain risky choice in experimental research," Journal of Economic Behavior & Organization, Elsevier, vol. 182(C), pages 527-543.
    17. Kpegli, Yao Thibaut & Corgnet, Brice & Zylbersztejn, Adam, 2023. "All at once! A comprehensive and tractable semi-parametric method to elicit prospect theory components," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    18. Königsheim, C. & Lukas, M. & Nöth, M., 2019. "Salience theory: Calibration and heterogeneity in probability distortion," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 477-495.
    19. Adam Booij & Bernard Praag & Gijs Kuilen, 2010. "A parametric analysis of prospect theory’s functionals for the general population," Theory and Decision, Springer, vol. 68(1), pages 115-148, February.
    20. Baillon, Aurélien & Placido, Lætitia, 2019. "Testing constant absolute and relative ambiguity aversion," Journal of Economic Theory, Elsevier, vol. 181(C), pages 309-332.

    More about this item

    Keywords

    Certainty Equivalence; Identification; Preference Estimation; Preference Measurement; Random Preference; Choice Under Risk and Uncertainty;
    All these keywords.

    JEL classification:

    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:chu:wpaper:16-14. 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: Megan Luetje (email available below). General contact details of provider: https://edirc.repec.org/data/esichus.html .

    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.