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Delayed probabilistic risk attitude: a parametric approach

Author

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  • Jinrui Pan

    (Durham University)

  • Craig S. Webb

    (University of Manchester)

  • Horst Zank

    (University of Manchester)

Abstract

Experimental studies suggest that individuals exhibit more risk aversion in choices among prospects when the payment and resolution of uncertainty are immediate relative to when it is delayed. This leads to preference reversals that cannot be attributed to discounting. When data suggest that utility is time-independent, probability weighting functions, such as those used to model prospect theory preferences, can accommodate such reversals. We propose a simple descriptive model with a two-parameter probability weighting function where one of these parameters depends on the time at which a prospect is resolved. The time-dependent parameter is responsible for the curvature of the probability weighting function and is regarded as an index of (in)sensitivity towards changes in probabilities. We provide conditions that characterize increased sensitivity towards more distant probabilities; this can account for the observed relatively less risk aversion towards delayed prospects. In our framework, the discount function is unrestricted, such that the model is compatible with empirical findings of non-constant discounting. In a simple application to bargaining we illustrate when it is advantageous for an individual to advance or delay the bargaining resolution time if an opponent displays increased sensitivity towards probability changes with delay.

Suggested Citation

  • 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.
  • Handle: RePEc:kap:theord:v:87:y:2019:i:2:d:10.1007_s11238-019-09712-9
    DOI: 10.1007/s11238-019-09712-9
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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Craig S. Webb, 2017. "Piecewise linear rank-dependent utility," Theory and Decision, Springer, vol. 82(3), pages 403-414, March.
    3. Ulrich Schmidt & Horst Zank, 2008. "Risk Aversion in Cumulative Prospect Theory," Management Science, INFORMS, vol. 54(1), pages 208-216, January.
    4. Drazen Prelec & George Loewenstein, 1991. "Decision Making Over Time and Under Uncertainty: A Common Approach," Management Science, INFORMS, vol. 37(7), pages 770-786, July.
    5. Keren, Gideon & Roelofsma, Peter, 1995. "Immediacy and Certainty in Intertemporal Choice," Organizational Behavior and Human Decision Processes, Elsevier, vol. 63(3), pages 287-297, September.
    6. Conley, John P. & Wilkie, Simon, 1991. "The bargaining problem without convexity : Extending the egalitarian and Kalai-Smorodinsky solutions," Economics Letters, Elsevier, vol. 36(4), pages 365-369, August.
    7. Mohammed Abdellaoui & Aurelien Baillon & Laetitia Placido & Peter P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," American Economic Review, American Economic Association, vol. 101(2), pages 695-723, April.
    8. Anke Gerber & Kirsten I. M. Rohde, 2018. "Weighted temporal utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(1), pages 187-212, July.
    9. 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.
    10. Weber, Bethany J. & Chapman, Gretchen B., 2005. "The combined effects of risk and time on choice: Does uncertainty eliminate the immediacy effect? Does delay eliminate the certainty effect?," Organizational Behavior and Human Decision Processes, Elsevier, vol. 96(2), pages 104-118, March.
    11. Manel Baucells & Franz Heukamp, 2010. "Common ratio using delay," Theory and Decision, Springer, vol. 68(1), pages 149-158, February.
    12. Han Bleichrodt & Jose Luis Pinto, 2000. "A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis," Management Science, INFORMS, vol. 46(11), pages 1485-1496, November.
    13. 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.
    14. Quiggin, John & Horowitz, John, 1995. "Time and Risk," Journal of Risk and Uncertainty, Springer, vol. 10(1), pages 37-55, January.
    15. 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.
    16. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    17. Mohammed Abdellaoui & Han Bleichrodt & Olivier l'Haridon & Corina Paraschiv, 2013. "Is There One Unifying Concept of Utility?An Experimental Comparison of Utility Under Risk and Utility Over Time," Management Science, INFORMS, vol. 59(9), pages 2153-2169, September.
    18. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    19. Stevenson, Mary Kay, 1992. "The impact of temporal context and risk on the judged value of future outcomes," Organizational Behavior and Human Decision Processes, Elsevier, vol. 52(3), pages 455-491, August.
    20. Busch, Lutz-Alexander & Wen, Quan, 1995. "Perfect Equilibria in Negotiation Model," Econometrica, Econometric Society, vol. 63(3), pages 545-565, May.
    21. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 185-199.
    22. 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.
    23. Thomas Epper & Helga Fehr-Duda, 2015. "Risk Preferences Are Not Time Preferences: Balancing on a Budget Line: Comment," American Economic Review, American Economic Association, vol. 105(7), pages 2261-2271, July.
    24. 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.
    25. 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.
    26. Mohammed Abdellaoui & Enrico Diecidue & Ayse Öncüler, 2011. "Risk Preferences at Different Time Periods: An Experimental Investigation," Management Science, INFORMS, vol. 57(5), pages 975-987, May.
    27. Dilip Abreu & Faruk Gul, 2000. "Bargaining and Reputation," Econometrica, Econometric Society, vol. 68(1), pages 85-118, January.
    28. Booij, Adam S. & van Praag, Bernard M.S., 2009. "A simultaneous approach to the estimation of risk aversion and the subjective time discount rate," Journal of Economic Behavior & Organization, Elsevier, vol. 70(1-2), pages 374-388, May.
    29. Rubinstein, Ariel, 1985. "A Bargaining Model with Incomplete Information about Time Preferences," Econometrica, Econometric Society, vol. 53(5), pages 1151-1172, September.
    30. Chew, Soo Hong & Ho, Joanna L, 1994. "Hope: An Empirical Study of Attitude toward the Timing of Uncertainty Resolution," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 267-288, May.
    31. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    32. Mohammed Abdellaoui & Frank Vossmann & Martin Weber, 2005. "Choice-Based Elicitation and Decomposition of Decision Weights for Gains and Losses Under Uncertainty," Management Science, INFORMS, vol. 51(9), pages 1384-1399, September.
    33. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    34. James Andreoni & Charles Sprenger, 2012. "Risk Preferences Are Not Time Preferences," American Economic Review, American Economic Association, vol. 102(7), pages 3357-3376, December.
    35. Stephen L. Cheung, 2015. "Risk Preferences Are Not Time Preferences: On the Elicitation of Time Preference under Conditions of Risk: Comment," American Economic Review, American Economic Association, vol. 105(7), pages 2242-2260, July.
    36. Craig Webb, 2015. "Piecewise additivity for non-expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 371-392, October.
    37. Lisa Anderson & Sarah Stafford, 2009. "Individual decision-making experiments with risk and intertemporal choice," Journal of Risk and Uncertainty, Springer, vol. 38(1), pages 51-72, February.
    38. Manel Baucells & Franz H. Heukamp, 2006. "Stochastic Dominance and Cumulative Prospect Theory," Management Science, INFORMS, vol. 52(9), pages 1409-1423, September.
    39. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 573-597.
    40. Selden, Larry, 1978. "A New Representation of Preferences over "Certain A Uncertain" Consumption Pairs: The "Ordinal Certainty Equivalent" Hypothesis," Econometrica, Econometric Society, vol. 46(5), pages 1045-1060, September.
    41. 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.
    42. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    43. Vital Anderhub & Werner Güth & Uri Gneezy & Doron Sonsino, 2001. "On the Interaction of Risk and Time Preferences: An Experimental Study," German Economic Review, Verein für Socialpolitik, vol. 2(3), pages 239-253, August.
    44. Keith Coble & Jayson Lusk, 2010. "At the nexus of risk and time preferences: An experimental investigation," Journal of Risk and Uncertainty, Springer, vol. 41(1), pages 67-79, August.
    45. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
    46. Kobberling, Veronika & Peters, Hans, 2003. "The effect of decision weights in bargaining problems," Journal of Economic Theory, Elsevier, vol. 110(1), pages 154-175, May.
    47. Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1102-1118, May.
    48. Chateauneuf, Alain & Cohen, Michele, 1994. "Risk Seeking with Diminishing Marginal Utility in a Non-expected Utility Model," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 77-91, July.
    49. Yoram Halevy, 2008. "Strotz Meets Allais: Diminishing Impatience and the Certainty Effect," American Economic Review, American Economic Association, vol. 98(3), pages 1145-1162, June.
    50. Partha Dasgupta & Eric Maskin, 2005. "Uncertainty and Hyperbolic Discounting," American Economic Review, American Economic Association, vol. 95(4), pages 1290-1299, September.
    51. Charles Noussair & Ping Wu, 2006. "Risk tolerance in the present and the future: an experimental study," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 27(6), pages 401-412.
    52. Craig R. Fox & Amos Tversky, 1995. "Ambiguity Aversion and Comparative Ignorance," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 585-603.
    53. Bin Miao & Songfa Zhong, 2015. "Risk Preferences Are Not Time Preferences: Separating Risk and Time Preference: Comment," American Economic Review, American Economic Association, vol. 105(7), pages 2272-2286, July.
    54. Gul, Faruk & Sonnenschein, Hugo, 1988. "On Delay in Bargaining with One-Sided Uncertainty," Econometrica, Econometric Society, vol. 56(3), pages 601-611, May.
    55. Larry G. Epstein, 2008. "Living with Risk," Review of Economic Studies, Oxford University Press, vol. 75(4), pages 1121-1141.
    56. Henry Stott, 2006. "Cumulative prospect theory's functional menagerie," Journal of Risk and Uncertainty, Springer, vol. 32(2), pages 101-130, March.
    57. Ryan, Matthew J., 2006. "Risk aversion in RDEU," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 675-697, September.
    58. 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.
    59. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    60. George Wu, 1999. "Anxiety and Decision Making with Delayed Resolution of Uncertainty," Theory and Decision, Springer, vol. 46(2), pages 159-199, April.
    61. Nathalie Etchart-Vincent, 2004. "Is Probability Weighting Sensitive to the Magnitude of Consequences? An Experimental Investigation on Losses," Journal of Risk and Uncertainty, Springer, vol. 28(3), pages 217-235, May.
    62. Manel Baucells & Franz H. Heukamp, 2012. "Probability and Time Trade-Off," Management Science, INFORMS, vol. 58(4), pages 831-842, April.
    63. Chew, Soo Hong & Epstein, Larry G., 1990. "Nonexpected utility preferences in a temporal framework with an application to consumption-savings behaviour," Journal of Economic Theory, Elsevier, vol. 50(1), pages 54-81, February.
    64. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    65. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    66. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    67. Veronika Köbberling & Peter P. Wakker, 2003. "Preference Foundations for Nonexpected Utility: A Generalized and Simplified Technique," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 395-423, August.
    68. Martin Ahlbrecht & Martin Weber, 1997. "Preference for gradual resolution of uncertainty," Theory and Decision, Springer, vol. 43(2), pages 167-185, September.
    69. Abdellaoui, Mohammed & Barrios, Carolina & Wakker, Peter P., 2007. "Reconciling introspective utility with revealed preference: Experimental arguments based on prospect theory," Journal of Econometrics, Elsevier, vol. 138(1), pages 356-378, May.
    70. 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.
    71. Steffen Andersen & Glenn W. Harrison & Morten I. Lau & E. Elisabet Rutström, 2008. "Lost In State Space: Are Preferences Stable?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(3), pages 1091-1112, August.
    72. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," Review of Economic Studies, Oxford University Press, vol. 4(2), pages 155-161.
    73. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    74. Mohammed Abdellaoui & Olivier l’Haridon & Horst Zank, 2009. "Separating Curvature and Elevation: A Parametric Weighting Function," Economics Discussion Paper Series 0901, Economics, The University of Manchester.
    75. Nicholas C. Barberis, 2013. "Thirty Years of Prospect Theory in Economics: A Review and Assessment," Journal of Economic Perspectives, American Economic Association, vol. 27(1), pages 173-196, Winter.
    76. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
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