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Too Risk Averse to Purchase Insurance? A Theoretical Glance at the Annuity Puzzle

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  • Antoine Bommier, Francois Le Grand

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Abstract

This paper suggests a new explanation for the low level of annuitization, which is valid even if one assumes perfect markets. We show that, as soon there exists a positive bequest motive, sufficiently risk averse individuals should not purchase annuities. A model calibration accounting for temporal risk aversion generates a willingness-to-pay for annuities, which is significantly smaller than the one generated by a standard Yaari (1965) model. Moreover, the calibration predicts that riskless savings finances one third of consumption, in line with empirical findings. Keywords: annuity puzzle, insurance demand, bequest, intergenerational transfers, temporal risk aversion, multiplicative preferences.

Suggested Citation

  • 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.
  • Handle: RePEc:stz:wpaper:eth-rc-12-002
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    References listed on IDEAS

    as
    1. Skander J. van den Heuvel, 2008. "Temporal risk aversion and asset prices," Finance and Economics Discussion Series 2008-37, Board of Governors of the Federal Reserve System (U.S.).
    2. Bommier, Antoine & Chassagnon, Arnold & Le Grand, François, 2012. "Comparative risk aversion: A formal approach with applications to saving behavior," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1614-1641.
    3. 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.
    4. Yogo, Motohiro, 2016. "Portfolio choice in retirement: Health risk and the demand for annuities, housing, and risky assets," Journal of Monetary Economics, Elsevier, vol. 80(C), pages 17-34.
    5. Giacomo Ponzetto, 2003. "Risk aversion and the utility of annuities," CeRP Working Papers 31, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    6. Frederick van der Ploeg, 1993. "A Closed-form Solution for a Model of Precautionary Saving," Review of Economic Studies, Oxford University Press, vol. 60(2), pages 385-395.
    7. 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.
    8. Joachim Inkmann & Paula Lopes & Alexander Michaelides, 2011. "How Deep Is the Annuity Market Participation Puzzle?," Review of Financial Studies, Society for Financial Studies, vol. 24(1), pages 279-319.
    9. Mariacristina De Nardi & Eric French & John B. Jones, 2010. "Why Do the Elderly Save? The Role of Medical Expenses," Journal of Political Economy, University of Chicago Press, vol. 118(1), pages 39-75, February.
    10. John Ameriks & Andrew Caplin & Steven Laufer & Stijn Van Nieuwerburgh, 2007. "The Joy of Giving or Assisted Living? Using Strategic Surveys to Separate Bequest and Precautionary Motives," NBER Working Papers 13105, National Bureau of Economic Research, Inc.
    11. 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.
    12. Mariacristina De Nardi, 2004. "Wealth Inequality and Intergenerational Links," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 743-768.
    13. Pang, Gaobo & Warshawsky, Mark, 2010. "Optimizing the equity-bond-annuity portfolio in retirement: The impact of uncertain health expenses," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 198-209, February.
    14. 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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    More about this item

    Keywords

    annuity puzzle; insurance demand; bequest; intergenerational transfers; temporal risk aversion; multiplicative preferences;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • 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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