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

  • Antoine Bommier, Francois Le Grand

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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.

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Paper provided by ETH Zurich, Chair of Systems Design in its series Working Papers with number ETH-RC-12-002.

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Handle: RePEc:stz:wpaper:eth-rc-12-002
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  1. repec:www:resrep:4 is not listed on IDEAS
  2. Mariacristina Nardi, 2004. "Wealth Inequality and Intergenerational Links," Review of Economic Studies, Wiley Blackwell, vol. 71, pages 743-768, 07.
  3. Motohiro Yogo, 2009. "Portfolio Choice in Retirement: Health Risk and the Demand for Annuities, Housing and Risky Assets," Working Papers, Center for Retirement Research at Boston College wp2009-3, Center for Retirement Research, revised Jan 2009.
  4. Mariacristina De Nardi & Eric French & John Bailey Jones, 2009. "Why do the elderly save? the role of medical expenses," Working Paper Series WP-09-02, Federal Reserve Bank of Chicago.
  5. 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.
  6. Mullainathan, Sendhil & Brown, Jeffrey R. & Kling, Jeffrey R. & Wrobel, Marian Vaillant, 2008. "Why Don't People Insure Late Life Consumption? A Framing Explanation of the Under-Annuitization Puzzle," Scholarly Articles 2799056, Harvard University Department of Economics.
  7. Joachim Inkmann & Paula Lopes & Alexander Michaelides, 2007. "How deep is the annuity market participation puzzle?," LSE Research Online Documents on Economics 24488, London School of Economics and Political Science, LSE Library.
  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. Benjamin Eden, 2008. "Substitution, Risk Aversion and Asset Prices: An Expected Utility Approach," Vanderbilt University Department of Economics Working Papers 0803, Vanderbilt University Department of Economics.
  10. Skander J. Van den Heuvel, 2008. "Temporal Risk Aversion and Asset Prices," 2008 Meeting Papers 46, Society for Economic Dynamics.
  11. 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.
  12. Le Grand, François & Chassagnon, Arnold & Bommier, Antoine, 2012. "Comparative Risk Aversion: A Formal Approach with Applications to Saving Behaviors," Economics Papers from University Paris Dauphine 123456789/4434, Paris Dauphine University.
  13. 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.
  14. 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.
  15. Giacomo Ponzetto, 2003. "Risk aversion and the utility of annuities," CeRP Working Papers 31, Center for Research on Pensions and Welfare Policies, Turin (Italy).
  16. 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.
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