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Optimal life insurance and annuity demand under hyperbolic discounting when bequests are luxury goods

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  • Zhang, Jinhui
  • Purcal, Sachi
  • Wei, Jiaqin

Abstract

We operationalise the theoretical modelling of Marín-Solano and Jorge Navas (2010), seeking to understand the consequences for optimal consumption, life insurance and annuity demand in a time inconsistent world, by incorporating the insurance insights from Richard (1975). Richar, in particular, has an elegant treatment of optimal annuity demand, rarely harnessed in the literature. Central to Richard’s creation of demand for personal insurance is a bequest motive and, in addition to implementing time inconsistency through hyperbolic discounting, our analysis is further expanded to include naïve and sophisticated agents with a luxury bequest motive (Lockwood, 2012). Compared to a more simplistic ‘necessity’ bequest framework, luxury bequests (broadly) weaken optimal life insurance demand and strengthen optimal life annuity demand for the less wealthy. In contrast, time inconsistency offers a wide spectrum of outcomes, and our modelling, calibrated to Swiss data, contributes to understanding the annuity puzzle—observed low levels of (voluntary) purchases of life annuities.

Suggested Citation

  • Zhang, Jinhui & Purcal, Sachi & Wei, Jiaqin, 2021. "Optimal life insurance and annuity demand under hyperbolic discounting when bequests are luxury goods," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 80-90.
    • Handle: RePEc:eee:insuma:v:101:y:2021:i:pa:p:80-90
    DOI: 10.1016/j.insmatheco.2020.07.003
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    1. R. A. Pollak, 1968. "Consistent Planning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 201-208.
    2. Jesus Fernández-Villaverde & Dirk Krueger, 2007. "Consumption over the Life Cycle: Facts from Consumer Expenditure Survey Data," The Review of Economics and Statistics, MIT Press, vol. 89(3), pages 552-565, August.
    3. 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.
    4. Fedor Iskhakov & Susan Thorp & Hazel Bateman, 2015. "Optimal Annuity Purchases for Australian Retirees," The Economic Record, The Economic Society of Australia, vol. 91(293), pages 139-154, June.
    5. Marín-Solano, Jesús & Navas, Jorge & Roch, Oriol, 2013. "Non-constant discounting and consumption, portfolio and life insurance rules," Economics Letters, Elsevier, vol. 119(2), pages 186-190.
    6. Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
    7. 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.
    8. Amy Beech & Rosetta Dollman & Richard Finlay & Gianni La Cava, 2014. "The Distribution of Household Spending in Australia," RBA Bulletin (Print copy discontinued), Reserve Bank of Australia, pages 13-22, March.
    9. Kraft, Holger & Steffensen, Mogens, 2008. "Optimal Consumption and Insurance: A Continuous-time Markov Chain Approach," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 231-257, May.
    10. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    11. de-Paz, Albert & Marín-Solano, Jesús & Navas, Jorge & Roch, Oriol, 2014. "Consumption, investment and life insurance strategies with heterogeneous discounting," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 66-75.
    12. Jensen, N.R. & Steffensen, M., 2015. "Personal finance and life insurance under separation of risk aversion and elasticity of substitution," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 28-41.
    13. Mariacristina De Nardi, 2004. "Wealth Inequality and Intergenerational Links," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 743-768.
    14. Smith, James D., 1980. "Modeling the Distribution and Intergenerational Transmission of Wealth," National Bureau of Economic Research Books, University of Chicago Press, number 9780226764542, September.
    15. Marín-Solano, Jesús & Navas, Jorge, 2010. "Consumption and portfolio rules for time-inconsistent investors," European Journal of Operational Research, Elsevier, vol. 201(3), pages 860-872, March.
    16. Naohito Abe & Noriko Inakura & Tomoaki Yamada, 2007. "Consumption, Working Hours, and Wealth Determination in a Life Cycle Model," Bank of Japan Working Paper Series 07-E-14, Bank of Japan.
    17. Michael Hurd & James P. Smith, 2002. "Expected Bequests and Their Distribution," NBER Working Papers 9142, National Bureau of Economic Research, Inc.
    18. Paul Menchik, 1980. "The Importance of Material Inheritance: The Financial Link between Generations," NBER Chapters, in: Modeling the Distribution and Intergenerational Transmission of Wealth, pages 159-186, National Bureau of Economic Research, Inc.
    19. Sachi Purcal & John Piggott, 2008. "Explaining Low Annuity Demand: An Optimal Portfolio Application to Japan," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 493-516, June.
    20. repec:dau:papers:123456789/11473 is not listed on IDEAS
    21. Bruhn, Kenneth & Steffensen, Mogens, 2011. "Household consumption, investment and life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 315-325, May.
    22. Siqi Tang & Sachi Purcal & Jinhui Zhang, 2018. "Life Insurance and Annuity Demand under Hyperbolic Discounting," Risks, MDPI, vol. 6(2), pages 1-10, April.
    23. Ding, Jie & Kingston, Geoffrey & Purcal, Sachi, 2014. "Dynamic asset allocation when bequests are luxury goods," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 65-71.
    24. Lee M. Lockwood, 2018. "Incidental Bequests and the Choice to Self-Insure Late-Life Risks," American Economic Review, American Economic Association, vol. 108(9), pages 2513-2550, September.
    25. Amy Finkelstein & James Poterba, 2004. "Adverse Selection in Insurance Markets: Policyholder Evidence from the U.K. Annuity Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 183-208, February.
    26. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    27. Auten, Gerald & Joulfaian, David, 1996. "Charitable contributions and intergenerational transfers," Journal of Public Economics, Elsevier, vol. 59(1), pages 55-68, January.
    28. Pierre-Olivier Gourinchas & Jonathan A. Parker, 2002. "Consumption Over the Life Cycle," Econometrica, Econometric Society, vol. 70(1), pages 47-89, January.
    29. 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.
    30. 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.
    31. Monika Bütler & Federica Teppa, 2007. "The Choice between an Annuity and a Lump Sum: Results from Swiss Pension Funds," NBER Chapters, in: Public Policy and Retirement, Trans-Atlantic Public Economics Seminar (TAPES), pages 1944-1966, National Bureau of Economic Research, Inc.
    32. A. B. Atkinson, 1971. "Capital Taxes, the Redistribution of Wealth and Individual Savings," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 209-227.
    33. James D. Smith, 1980. "Modeling the Distribution and Intergenerational Transmission of Wealth," NBER Books, National Bureau of Economic Research, Inc, number smit80-1.
    34. Benjamin M. Friedman & Mark J. Warshawsky, 1990. "The Cost of Annuities: Implications for Saving Behavior and Bequests," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(1), pages 135-154.
    35. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    36. John Ameriks & Andrew Caplin & Steven Laufer & Stijn Van Nieuwerburgh, 2011. "The Joy of Giving or Assisted Living? Using Strategic Surveys to Separate Public Care Aversion from Bequest Motives," Journal of Finance, American Finance Association, vol. 66(2), pages 519-561, April.
    37. Robert J. Barro, 1999. "Ramsey Meets Laibson in the Neoclassical Growth Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(4), pages 1125-1152.
    38. Pliska, Stanley R. & Ye, Jinchun, 2007. "Optimal life insurance purchase and consumption/investment under uncertain lifetime," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1307-1319, May.
    39. 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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    3. Luo, Shangzhen & Wang, Mingming & Zhu, Wei, 2022. "Time-inconsistent life-cycle consumption and retirement choice with mortality risk," Applied Mathematics and Computation, Elsevier, vol. 433(C).

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    More about this item

    Keywords

    Finance; Annuity puzzle; Hyperbolic discounting; Luxury bequests; Dynamic programming;
    All these keywords.

    JEL classification:

    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving

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