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

  • Antoine Bommier


    (ETH Zurich, Switzerland)

  • François Le Grand


    (EMLyon Business School, France and ETH Zurich, Switzerland)

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.

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Paper provided by CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich in its series CER-ETH Economics working paper series with number 12/157.

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Length: 48 pages
Date of creation: Jul 2012
Date of revision:
Handle: RePEc:eth:wpswif:12-157
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  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. 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, 02.
  3. Antoine Bommier & Arnold Chassagnon & François Le Grand, 2010. "Comparative Risk Aversion: A Formal Approach with Applications to Saving Behaviors," CER-ETH Economics working paper series 10/134, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
  4. Inkmann, Joachim & Lopes, Paula & Michaelides, Alexander, 2010. "How Deep is the Annuity Market Participation Puzzle?," CEPR Discussion Papers 7940, C.E.P.R. Discussion Papers.
  5. Mariacristina deNardi, 2000. "Wealth Inequality and Intergenerational Links," Econometric Society World Congress 2000 Contributed Papers 0547, Econometric Society.
  6. Motohiro Yogo, 2009. "Portfolio Choice in Retirement: Health Risk and the Demand for Annuities, Housing, and Risky Assets," NBER Working Papers 15307, National Bureau of Economic Research, Inc.
  7. 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.
  8. 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.
  9. 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 304-09, May.
  10. 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.
  11. van der Ploeg, Frederick, 1993. "A Closed-Form Solution for a Model of Precautionary Saving," Review of Economic Studies, Wiley Blackwell, vol. 60(2), pages 385-95, April.
  12. 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.
  13. 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.
  14. Giacomo Ponzetto, 2003. "Risk aversion and the utility of annuities," CeRP Working Papers 31, Center for Research on Pensions and Welfare Policies, Turin (Italy).
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