IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_10491.html
   My bibliography  Save this paper

Loss Aversion, Risk Aversion, and the Shape of the Probability Weighting Function

Author

Listed:
  • Matthew D. Rablen

Abstract

Loss aversion, risk aversion, and the probability weighting function (PWF) are three central concepts in explaining decisionmaking under risk. I examine interlinkages between these concepts in a model of decisionmaking that allows for loss averse/tolerant stochastic reference dependence and optimism/pessimism over probability distributions. I give a preference interpretation to commonly observed shapes of PWF and to risk aversion. In particular, I establish a connection between loss aversion and both risk aversion and the inverse-S PWF: loss aversion is a necessary condition to observe each of these phenomena. The results extend to distinct PWFs in the gain and loss domains, as under prospect theory.

Suggested Citation

  • Matthew D. Rablen, 2023. "Loss Aversion, Risk Aversion, and the Shape of the Probability Weighting Function," CESifo Working Paper Series 10491, CESifo.
    • Handle: RePEc:ces:ceswps:_10491
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo1_wp10491.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Diecidue, Enrico & Wakker, Peter P, 2001. "On the Intuition of Rank-Dependent Utility," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 281-298, November.
    2. Craig S. Webb, 2017. "Piecewise linear rank-dependent utility," Theory and Decision, Springer, vol. 82(3), pages 403-414, March.
    3. Botond Kőszegi & Matthew Rabin, 2006. "A Model of Reference-Dependent Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(4), pages 1133-1165.
    4. Wang, Di, 2021. "Attention-driven probability weighting," Economics Letters, Elsevier, vol. 203(C).
    5. Goeree, Jacob K. & Holt, Charles A. & Palfrey, Thomas R., 2002. "Quantal Response Equilibrium and Overbidding in Private-Value Auctions," Journal of Economic Theory, Elsevier, vol. 104(1), pages 247-272, May.
    6. Chew, S H & Epstein, Larry G & Segal, U, 1991. "Mixture Symmetry and Quadratic Utility," Econometrica, Econometric Society, vol. 59(1), pages 139-163, January.
    7. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-1059, July.
    8. Eddie Dekel & Barton L. Lipman, 2010. "How (Not) to Do Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 257-282, September.
    9. Marc Oliver Rieger & Mei Wang & Thorsten Hens, 2017. "Estimating cumulative prospect theory parameters from an international survey," Theory and Decision, Springer, vol. 82(4), pages 567-596, April.
    10. Walther, Herbert, 2003. "Normal-randomness expected utility, time preference and emotional distortions," Journal of Economic Behavior & Organization, Elsevier, vol. 52(2), pages 253-266, October.
    11. John D. Hey, 1984. "The Economics of Optimism and Pessimism," Kyklos, Wiley Blackwell, vol. 37(2), pages 181-205, May.
    12. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    13. Kunreuther, Howard & Novemsky, Nathan & Kahneman, Daniel, 2001. "Making Low Probabilities Useful," Journal of Risk and Uncertainty, Springer, vol. 23(2), pages 103-120, September.
    14. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    15. 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.
    16. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    17. Polkovnichenko, Valery & Zhao, Feng, 2013. "Probability weighting functions implied in options prices," Journal of Financial Economics, Elsevier, vol. 107(3), pages 580-609.
    18. Despoina Alempaki & Emina Canic & Timothy L. Mullett & William J. Skylark & Chris Starmer & Neil Stewart & Fabio Tufano, 2019. "Reexamining How Utility and Weighting Functions Get Their Shapes: A Quasi-Adversarial Collaboration Providing a New Interpretation," Management Science, INFORMS, vol. 65(10), pages 4841-4862, October.
    19. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    20. Mohammed Abdellaoui, 2002. "A Genuine Rank-Dependent Generalization of the Von Neumann-Morgenstern Expected Utility Theorem," Econometrica, Econometric Society, vol. 70(2), pages 717-736, March.
    21. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    22. Bruno Jullien & Bernard Salanie, 2000. "Estimating Preferences under Risk: The Case of Racetrack Bettors," Journal of Political Economy, University of Chicago Press, vol. 108(3), pages 503-530, June.
    23. McClelland, Gary H & Schulze, William D & Coursey, Don L, 1993. "Insurance for Low-Probability Hazards: A Bimodal Response to Unlikely Events," Journal of Risk and Uncertainty, Springer, vol. 7(1), pages 95-116, August.
    24. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    25. 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.
    26. Botond Koszegi & Matthew Rabin, 2007. "Reference-Dependent Risk Attitudes," American Economic Review, American Economic Association, vol. 97(4), pages 1047-1073, September.
    27. John D. Hey & Chris Orme, 2018. "Investigating Generalizations Of Expected Utility Theory Using Experimental Data," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 3, pages 63-98, World Scientific Publishing Co. Pte. Ltd..
    28. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
    29. Philippe Delquié & Alessandra Cillo, 2006. "Disappointment without prior expectation: a unifying perspective on decision under risk," Journal of Risk and Uncertainty, Springer, vol. 33(3), pages 197-215, December.
    30. Jianying Qiu & Eva-Maria Steiger, 2011. "Understanding the Two Components of Risk Attitudes: An Experimental Analysis," Management Science, INFORMS, vol. 57(1), pages 193-199, January.
    31. Alan Piper, 2022. "Optimism, pessimism and life satisfaction: an empirical investigation," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 69(2), pages 177-208, June.
    32. Grevenbrock, Nils, 2020. "Dispositional optimism (and pessimism), wealth, and stock market participation," Journal of Economic Psychology, Elsevier, vol. 81(C).
    33. 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.
    34. David Dillenberger & Andrew Postlewaite & Kareen Rozen, 2017. "Optimism and Pessimism with Expected Utility," Journal of the European Economic Association, European Economic Association, vol. 15(5), pages 1158-1175.
    35. 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.
    36. Colin F. Camerer & Howard Kunreuther, 1989. "Decision processes for low probability events: Policy implications," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 8(4), pages 565-592.
    37. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    38. Yusufcan Masatlioglu & Collin Raymond, 2016. "A Behavioral Analysis of Stochastic Reference Dependence," American Economic Review, American Economic Association, vol. 106(9), pages 2760-2782, September.
    39. Segal, Uzi, 1987. "Some remarks on Quiggin's anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 8(1), pages 145-154, March.
    40. repec:lmu:muenar:20868 is not listed on IDEAS
    41. Michael Kilka & Martin Weber, 2001. "What Determines the Shape of the Probability Weighting Function Under Uncertainty?," Management Science, INFORMS, vol. 47(12), pages 1712-1726, December.
    42. GlennW. Harrison & StevenJ. Humphrey & Arjan Verschoor, 2010. "Choice under Uncertainty: Evidence from Ethiopia, India and Uganda," Economic Journal, Royal Economic Society, vol. 120(543), pages 80-104, March.
    43. David E. Bell, 1985. "Disappointment in Decision Making Under Uncertainty," Operations Research, INFORMS, vol. 33(1), pages 1-27, February.
    44. Humphrey, Steven J. & Verschoor, Arjan, 2004. "The probability weighting function: experimental evidence from Uganda, India and Ethiopia," Economics Letters, Elsevier, vol. 84(3), pages 419-425, September.
    45. Mohammed Abdellaoui & Olivier L’Haridon & Horst Zank, 2010. "Separating curvature and elevation: A parametric probability weighting function," Journal of Risk and Uncertainty, Springer, vol. 41(1), pages 39-65, August.
    46. Menon, Geeta & Kyung, Ellie J. & Agrawal, Nidhi, 2009. "Biases in social comparisons: Optimism or pessimism?," Organizational Behavior and Human Decision Processes, Elsevier, vol. 108(1), pages 39-52, January.
    47. Neil Stewart & Stian Reimers & Adam J. L. Harris, 2015. "On the Origin of Utility, Weighting, and Discounting Functions: How They Get Their Shapes and How to Change Their Shapes," Management Science, INFORMS, vol. 61(3), pages 687-705, March.
    48. Weber, Elke U & Kirsner, Britt, 1997. "Reasons for Rank-Dependent Utility Evaluation," Journal of Risk and Uncertainty, Springer, vol. 14(1), pages 41-61, January.
    49. 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)

    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. Rablen, Matthew D., 2019. "Foundations of the Rank-Dependent Probability Weighting Function," IZA Discussion Papers 12701, Institute of Labor Economics (IZA).
    2. Katarzyna M. Werner & Horst Zank, 2019. "A revealed reference point for prospect theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(4), pages 731-773, June.
    3. Thomas Epper & Helga Fehr-Duda, 2012. "The missing link: unifying risk taking and time discounting," ECON - Working Papers 096, Department of Economics - University of Zurich, revised Oct 2018.
    4. Epper, Thomas & Fehr-Duda, Helga, 2017. "A Tale of Two Tails: On the Coexistence of Overweighting and Underweighting of Rare Extreme Events," Economics Working Paper Series 1705, University of St. Gallen, School of Economics and Political Science.
    5. Arjan Verschoor & Ben D’Exelle, 2022. "Probability weighting for losses and for gains among smallholder farmers in Uganda," Theory and Decision, Springer, vol. 92(1), pages 223-258, February.
    6. Aurélien Baillon & Han Bleichrodt & Vitalie Spinu, 2020. "Searching for the Reference Point," Management Science, INFORMS, vol. 66(1), pages 93-112, January.
    7. Jinrui Pan & Craig S. Webb & Horst Zank, 2019. "Delayed probabilistic risk attitude: a parametric approach," Theory and Decision, Springer, vol. 87(2), pages 201-232, September.
    8. Mohammed Abdellaoui & Olivier L’Haridon & Horst Zank, 2010. "Separating curvature and elevation: A parametric probability weighting function," Journal of Risk and Uncertainty, Springer, vol. 41(1), pages 39-65, August.
    9. Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1102-1118, May.
    10. 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.
    11. Martina Nardon & Paolo Pianca, 2019. "Behavioral premium principles," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 229-257, June.
    12. Martina Nardon & Paolo Pianca, 2019. "European option pricing under cumulative prospect theory with constant relative sensitivity probability weighting functions," Computational Management Science, Springer, vol. 16(1), pages 249-274, February.
    13. Webb, Craig S. & Zank, Horst, 2011. "Accounting for optimism and pessimism in expected utility," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 706-717.
    14. Mohammed Abdellaoui & Horst Zank, 2023. "Source and rank-dependent utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 949-981, May.
    15. 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.
    16. 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.
    17. Aurélien Baillon & Han Bleichrodt & Vitalie Spinu, 2020. "Searching for the Reference Point," Management Science, INFORMS, vol. 66(1), pages 93-112, January.
    18. Pavlo Blavatskyy, 2018. "A second-generation disappointment aversion theory of decision making under risk," Theory and Decision, Springer, vol. 84(1), pages 29-60, January.
    19. 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).
    20. Yao Thibaut Kpegli, 2023. "Smoothing Spline Method for Measuring Prospect Theory Components," Working Papers 2303, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.

    More about this item

    Keywords

    probability weighting; rank dependent expected utility; loss aversion; risk aversion; reference dependence; optimism; pessimism; prospect theory;
    All these keywords.

    JEL classification:

    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

    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:ces:ceswps:_10491. 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: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.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.