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A rank-dependent utility model of uncertain lifetime

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  • Nicolas Drouhin

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne)

Abstract

In a continuous time life cycle model of consumption with an uncertain lifetime, we use a non-parametric specification of rank-dependent utility theory to characterize the preferences of the agent. We prove that time consistency holds for a subclass of probability-weighting function, providing the foundation for a constant rate of time preference that interacts multiplicatively with the hazard rate instead of additively as in \citet{Yaari1965} seminal model. We calibrate both models to explain the hump in the life-cycle consumption, and show that the multiplicative model is more robust.

Suggested Citation

  • Nicolas Drouhin, 2015. "A rank-dependent utility model of uncertain lifetime," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01238589, HAL.
  • Handle: RePEc:hal:cesptp:halshs-01238589
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01238589
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    References listed on IDEAS

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    1. A. Ludwig & A. Zimper, 2013. "A parsimonious model of subjective life expectancy," Theory and Decision, Springer, vol. 75(4), pages 519-541, October.
    2. Charles M. Harvey, 1986. "Value Functions for Infinite-Period Planning," Management Science, INFORMS, vol. 32(9), pages 1123-1139, September.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Moresi, Serge, 1999. "Uncertain lifetime, risk aversion and intertemporal substitution," Economics Letters, Elsevier, vol. 62(2), pages 207-212, February.
    5. Nathalie Etchart, 2002. "Adequate Moods for non-eu Decision Making in a Sequential Framework," Theory and Decision, Springer, vol. 52(1), pages 1-28, February.
    6. Pierre-Olivier Gourinchas & Jonathan A. Parker, 2002. "Consumption Over the Life Cycle," Econometrica, Econometric Society, vol. 70(1), pages 47-89, January.
    7. Leung, Siu Fai, 1994. "Uncertain Lifetime, the Theory of the Consumer, and the Life Cycle Hypothesis," Econometrica, Econometric Society, vol. 62(5), pages 1233-1239, September.
    8. Partha Dasgupta & Eric Maskin, 2005. "Uncertainty and Hyperbolic Discounting," American Economic Review, American Economic Association, vol. 95(4), pages 1290-1299, September.
    9. Nicolas Drouhin, 2009. "Hyperbolic discounting may be time consistent," Economics Bulletin, AccessEcon, vol. 29(4), pages 2549-2555.
    10. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    11. Leung, Siu Fai, 2007. "The existence, uniqueness, and optimality of the terminal wealth depletion time in life-cycle models of saving under uncertain lifetime and borrowing constraint," Journal of Economic Theory, Elsevier, vol. 134(1), pages 470-493, May.
    12. Yoram Halevy, 2004. "Diminishing Impatience and Non-Expected Utility: A Unified Framework," Levine's Bibliography 122247000000000190, UCLA Department of Economics.
    13. Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1102-1118, May.
    14. Christopher D. Carroll, 1997. "Buffer-Stock Saving and the Life Cycle/Permanent Income Hypothesis," The Quarterly Journal of Economics, Oxford University Press, vol. 112(1), pages 1-55.
    15. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    16. Thurow, Lester C, 1969. "The Optimum Lifetime Distribution of Consumption Expenditures," American Economic Review, American Economic Association, vol. 59(3), pages 324-330, June.
    17. D'Albis, Hippolyte & Thibault, Emmanuel, 2012. "Ambiguous Life Expectancy and the Demand for Annuities," TSE Working Papers 12-323, Toulouse School of Economics (TSE).
    18. A. Nebout, 2014. "Sequential decision making without independence: a new conceptual approach," Theory and Decision, Springer, vol. 77(1), pages 85-110, June.
    19. repec:hal:journl:halshs-00721281 is not listed on IDEAS
    20. Barro, Robert J & Friedman, James W, 1977. "On Uncertain Lifetimes," Journal of Political Economy, University of Chicago Press, vol. 85(4), pages 843-849, August.
    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. Feigenbaum, James, 2008. "Can mortality risk explain the consumption hump?," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 844-872, September.
    23. Antoine Bommier, 2013. "Life-Cycle Preferences Revisited," Journal of the European Economic Association, European Economic Association, vol. 11(6), pages 1290-1319, December.
    24. Gary Hansen & Selahattin Imrohoroglu, 2008. "Consumption over the Life Cycle: The Role of Annuities," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(3), pages 566-583, July.
    25. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015, April.
    26. Antoine Bommier, 2007. "Risk Aversion, Intertemporal Elasticity of Substitution and Correlation Aversion," Economics Bulletin, AccessEcon, vol. 4(29), pages 1-8.
    27. Michael D. Hurd & Daniel L. McFadden & Li Gan, 1998. "Subjective Survival Curves and Life Cycle Behavior," NBER Chapters,in: Inquiries in the Economics of Aging, pages 259-309 National Bureau of Economic Research, Inc.
    28. Yoram Halevy, 2004. "Diminishing Impatience: Disentangling Time Preference from Uncertain Lifetime," Levine's Bibliography 122247000000000185, UCLA Department of Economics.
    29. 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.
    30. Antoine Bommier & François Grand, 2014. "Too risk averse to purchase insurance?," Journal of Risk and Uncertainty, Springer, vol. 48(2), pages 135-166, April.
    31. Nicolas Drouhin, 2001. "Lifetime Uncertainty and Time Preference," Theory and Decision, Springer, vol. 51(2), pages 145-172, December.
    32. Bleichrodt, Han & Eeckhoudt, Louis, 2006. "Survival risks, intertemporal consumption, and insurance: The case of distorted probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 335-346, April.
    33. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
    34. Mohammed Abdellaoui & Olivier l’Haridon & Horst Zank, 2009. "Separating Curvature and Elevation: A Parametric Weighting Function," The School of Economics Discussion Paper Series 0901, Economics, The University of Manchester.
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    Citations

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    Cited by:

    1. Nicolas Drouhin, 2017. "Non stationary additive utility and time consistency," Working Papers halshs-01238584, HAL.
    2. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2017. "The impact of biases in survival beliefs on savings behavior," SAFE Working Paper Series 169, Research Center SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt.
    3. Nicolas Drouhin, 2018. "Theoretical considerations on the retirement consumption puzzle and the optimal age of retirement," Working Papers halshs-01767096, HAL.
    4. Nicolas Drouhin, 2016. "Non stationary additive utility and time consistency," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01238584, HAL.

    More about this item

    Keywords

    intertemporal choice; life cycle theory of consumption and savings; uncertain lifetime; time consistency; rank-dependent utility; cumulative prospect theory; consumption hump; borrowing constraint; risk aversion; intertemporal substitution;

    JEL classification:

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

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