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Ambiguous Life Expectancy and the Demand for Annuities

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  • Hippolyte d'Albis

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Emmanuel Thibault

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique, CDED - Centre de Droit Economique et du Développement - UPVD - Université de Perpignan Via Domitia, IDEI - Institut d'Economie Industrielle - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse)

Abstract

In this paper, ambiguity aversion to uncertain survival probabilities is introduced in a life-cycle model with a bequest motive to study the optimal demand for annuities. Provided that annuities return is sufficiently large, and notably when it is fair, positive annuitization is known to be optimal strategy of ambiguity neutral individuals. Conversely, we show that the demand for annuities decreases with ambiguity aversion and that there exists a finite degree of aversion above which the demand is non positive : the optimal strategy is then to either sell annuities short or to hold zero annuities if the former option is not available. To conclude, ambiguity aversion appears as a relevant candidate for explaining the annuity puzzle.

Suggested Citation

  • Hippolyte d'Albis & Emmanuel Thibault, 2012. "Ambiguous Life Expectancy and the Demand for Annuities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00721281, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00721281
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00721281
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    References listed on IDEAS

    as
    1. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    2. Alexander Zimper & Alexander Ludwig & Max Groneck, 2012. "A Life-Cycle Consumption Model with Ambiguous Survival Beliefs," 2012 Meeting Papers 693, Society for Economic Dynamics.
    3. Thomas Davidoff & Jeffrey R. Brown & Peter A. Diamond, 2005. "Annuities and Individual Welfare," American Economic Review, American Economic Association, vol. 95(5), pages 1573-1590, December.
    4. Treich, Nicolas, 2010. "The value of a statistical life under ambiguity aversion," Journal of Environmental Economics and Management, Elsevier, vol. 59(1), pages 15-26, January.
    5. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
    6. Drouhin, Nicolas, 2015. "A rank-dependent utility model of uncertain lifetime," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 208-224.
    7. repec:dau:papers:123456789/9807 is not listed on IDEAS
    8. Antoine Bommier, 2006. "Uncertain Lifetime And Intertemporal Choice: Risk Aversion As A Rationale For Time Discounting," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(4), pages 1223-1246, November.
    9. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    10. Post, Thomas & Hanewald, Katja, 2010. "Stochastic mortality, subjective survival expectations, and individual saving behavior," SFB 649 Discussion Papers 2010-040, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    11. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    12. Drouhin, Nicolas, 2015. "A rank-dependent utility model of uncertain lifetime," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 208-224.
    13. 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.
    14. Eytan Sheshinski, 2007. "The Economic Theory of Annuities," Economics Books, Princeton University Press, edition 1, volume 1, number 8536.
    15. d’Albis, Hippolyte & Thibault, Emmanuel, 2012. "Optimal annuitization, uncertain survival probabilities, and maxmin preferences," Economics Letters, Elsevier, vol. 115(2), pages 296-299.
    16. Christian Gollier, 2011. "Portfolio Choices and Asset Prices: The Comparative Statics of Ambiguity Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1329-1344.
    17. Lex Borghans & Bart H. H. Golsteyn & James J. Heckman & Huub Meijers, 2009. "Gender Differences in Risk Aversion and Ambiguity Aversion," Journal of the European Economic Association, MIT Press, vol. 7(2-3), pages 649-658, 04-05.
    18. Shlomo Benartzi & Alessandro Previtero & Richard H. Thaler, 2011. "Annuitization Puzzles," Journal of Economic Perspectives, American Economic Association, vol. 25(4), pages 143-164, Fall.
    19. Giacomo Ponzetto, 2003. "Risk aversion and the utility of annuities," CeRP Working Papers 31, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    20. A. Ludwig & A. Zimper, 2013. "A parsimonious model of subjective life expectancy," Theory and Decision, Springer, vol. 75(4), pages 519-541, October.
    21. Jeffrey R. Brown, 2007. "Rational and Behavioral Perspectives on the Role of Annuities in Retirement Planning," NBER Working Papers 13537, National Bureau of Economic Research, Inc.
    22. Joachim Inkmann & Paula Lopes & Alexander Michaelides, 2011. "How Deep Is the Annuity Market Participation Puzzle?," The Review of Financial Studies, Society for Financial Studies, vol. 24(1), pages 279-319.
    23. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    24. Ryan D. Edwards & Shripad Tuljapurkar, 2005. "Inequality in Life Spans and a New Perspective on Mortality Convergence Across Industrialized Countries," Population and Development Review, The Population Council, Inc., vol. 31(4), pages 645-674, December.
    25. Huang, Huaxiong & Milevsky, Moshe A. & Salisbury, Thomas S., 2012. "Optimal retirement consumption with a stochastic force of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 282-291.
    26. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    27. Viscusi, W Kip & Aldy, Joseph E, 2003. "The Value of a Statistical Life: A Critical Review of Market Estimates throughout the World," Journal of Risk and Uncertainty, Springer, vol. 27(1), pages 5-76, August.
    28. Jeffrey R. Brown & Jeffrey R. Kling & Sendhil Mullainathan & Marian V. Wrobel, 2008. "Why Don’t People Insure Late-Life Consumption? A Framing Explanation of the Under-Annuitization Puzzle," American Economic Review, American Economic Association, vol. 98(2), pages 304-309, May.
    29. repec:reg:rpubli:282 is not listed on IDEAS
    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. 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.
    32. Antoine Bommier, Francois Le Grand, "undated". "Too Risk Averse to Purchase Insurance? A Theoretical Glance at the Annuity Puzzle," Working Papers ETH-RC-12-002, ETH Zurich, Chair of Systems Design.
    33. Bernheim, B Douglas, 1991. "How Strong Are Bequest Motives? Evidence Based on Estimates of the Demand for Life Insurance and Annuities," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 899-927, October.
    34. Eeckhoudt, Louis & Gollier, Christian, 1995. "Demand for Risky Assets and the Monotone Probability Ratio Order," Journal of Risk and Uncertainty, Springer, vol. 11(2), pages 113-122, September.
    35. Peijnenburg, Kim & Nijman, Theo & Werker, Bas J.M., 2016. "The annuity puzzle remains a puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 18-35.
    36. repec:hal:pseose:hal-00670320 is not listed on IDEAS
    37. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
    38. Previtero, Alessandro, 2014. "Stock market returns and annuitization," Journal of Financial Economics, Elsevier, vol. 113(2), pages 202-214.
    39. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    40. Peijnenburg, Kim, 2018. "Life-Cycle Asset Allocation with Ambiguity Aversion and Learning," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 53(5), pages 1963-1994, October.
    41. Post Thomas, 2012. "Individual Welfare Gains from Deferred Life-Annuities under Stochastic Mortality," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 6(2), pages 1-26, June.
    42. Louis Eeckhoudt & Meglena Jeleva, 2004. "Décision médicale et probabilités imprécises," Revue économique, Presses de Sciences-Po, vol. 55(5), pages 869-881.
    43. Horneff, Wolfram J. & Maurer, Raimond H. & Stamos, Michael Z., 2008. "Life-cycle asset allocation with annuity markets," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3590-3612, November.
    44. 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.
    45. None, 2008. "None," NBER Working Papers 13800, National Bureau of Economic Research, Inc.
    46. Felix Reichling & Kent Smetters, 2015. "Optimal Annuitization with Stochastic Mortality and Correlated Medical Costs," American Economic Review, American Economic Association, vol. 105(11), pages 3273-3320, November.
    47. Lex Borghans & Bart H.H. Golsteyn & James J. Heckman & Huub Meijers, 2009. "Gender Differences in Risk Aversion and Ambiguity," Working Papers 200903, Geary Institute, University College Dublin.
    48. Mary Riddel & W. Shaw, 2006. "A theoretically-consistent empirical model of non-expected utility: An application to nuclear-waste transport," Journal of Risk and Uncertainty, Springer, vol. 32(2), pages 131-150, March.
    49. Post, Thomas & Hanewald, Katja, 2013. "Longevity risk, subjective survival expectations, and individual saving behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 86(C), pages 200-220.
    50. Lee Lockwood, 2012. "Bequest Motives and the Annuity Puzzle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 226-243, April.
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    Cited by:

    1. d’Albis, Hippolyte & Kalk, Andrei, 2021. "Why do we postpone annuity purchases?," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    2. Han, Nan-Wei & Hung, Mao-Wei, 2021. "The annuity puzzle and consumption hump under ambiguous life expectancy," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 76-88.
    3. Drouhin, Nicolas, 2015. "A rank-dependent utility model of uncertain lifetime," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 208-224.
    4. d’Albis, Hippolyte & Attanasi, Giuseppe & Thibault, Emmanuel, 2020. "An experimental test of the under-annuitization puzzle with smooth ambiguity and charitable giving," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 694-717.
    5. Caliendo, Frank N. & Gorry, Aspen & Slavov, Sita, 2020. "Survival ambiguity and welfare," Journal of Economic Behavior & Organization, Elsevier, vol. 170(C), pages 20-42.
    6. Eric André & Antoine Bommier & François Le Grand, 2022. "The impact of risk aversion and ambiguity aversion on annuity and saving choices," Journal of Risk and Uncertainty, Springer, vol. 65(1), pages 33-56, August.
    7. Johanna Etner & Meglena Jeleva & Olivier Renault, 2024. "Dynamic decision-making when ambiguity attitudes depend on exogenous events," Theory and Decision, Springer, vol. 96(2), pages 269-295, March.

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    More about this item

    Keywords

    Demand for annuities; uncertain survival probabilities; ambiguity aversion; Rente viagère; probabilité de survie incertaine; aversion à l'ambigüité;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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