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Economic Growth and Longevity Risk with Adverse Selection

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  • Ben J. Heijdra
  • Laurie S. M. Reijnders

Abstract

We study a closed economy featuring heterogeneous agents and exhibiting endogenous economic growth due to interfirm external effects. Individual agents differ in terms of their mortality profile. At birth, nature assigns a health status to each agent. Health type is private information and annuity firms can only observe an agent’s age. In the presence of longevity risk, agents want to annuitize their wealth conform the classic result by Yaari (1965). In the first-best case with perfect annuities, the market would feature a separating equilibrium (SE) in which each health type obtains an actuarially fair perfect insurance. In the SE all agents are savers throughout their lives. The informational asymmetry precludes the attainment of the first-best equilibrium, however, as healthy individuals have a strong incentive to misrepresent their type by claiming to be unhealthy. Using the equilibrium concept of Pauly (1974) and Abel (1986), we prove the existence of a second-best pooling equilibrium (PE) in which individuals of all types annuitize at a common pooling rate. As the unhealthy get close to their maximum attainable age, the pooling rate prompts such individuals to become net borrowers. But borrowing would reveal their health status, so the best the unhealthy can do is to impose a borrowing constraint on themselves during their autumn years. Using a plausibly calibrated version of the model we find that the growth- and welfare effects of PE versus SE are rather small, whilst those of PE versus no annuities at all (NAE) are rather large. An imperfect insurance is better than no insurance at all, both at the microeconomic and at the macroeconomic level.

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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2898.

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Date of creation: 2009
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Handle: RePEc:ces:ceswps:_2898

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Keywords: annuity markets; adverse selection; endogenous growth; overlapping generations; demography;

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References

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  1. de la Grandville,Olivier, 2009. "Economic Growth," Cambridge Books, Cambridge University Press, number 9780521898010, April.
  2. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2002. "Vintage Human Capital, Demographic Trends, and Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 104(2), pages 340-375, June.
  3. Leung, Siu Fai, 1994. "Uncertain Lifetime, the Theory of the Consumer, and the Life Cycle Hypothesis," Econometrica, Econometric Society, vol. 62(5), pages 1233-39, September.
  4. Benjamin M. Friedman & Mark Warshawsky, 1988. "Annuity Prices and Saving Behavior in the United States," NBER Chapters, in: Pensions in the U.S. Economy, pages 53-84 National Bureau of Economic Research, Inc.
  5. Wilson, Charles, 1977. "A model of insurance markets with incomplete information," Journal of Economic Theory, Elsevier, vol. 16(2), pages 167-207, December.
  6. Andrew B. Abel, 1985. "Capital Accumulation and Uncertain Lifetimes with Adverse Selection," NBER Working Papers 1664, National Bureau of Economic Research, Inc.
  7. Zvi Bodie & John B. Shoven & David A. Wise, 1988. "Pensions in the U.S. Economy," NBER Books, National Bureau of Economic Research, Inc, number bodi88-1, June.
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  9. Pauly, Mark V, 1974. "Overinsurance and Public Provision of Insurance: The Roles of Moral Hazard and Adverse Selection," The Quarterly Journal of Economics, MIT Press, vol. 88(1), pages 44-62, February.
  10. Heijdra, Ben J. & Mierau, Jochen O., 2012. "The individual life-cycle, annuity market imperfections and economic growth," Journal of Economic Dynamics and Control, Elsevier, vol. 36(6), pages 876-890.
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  13. Amy Finkelstein & James Poterba, 2002. "Selection Effects in the United Kingdom Individual Annuities Market," Economic Journal, Royal Economic Society, vol. 112(476), pages 28-50, January.
  14. de la Grandville,Olivier, 2009. "Economic Growth," Cambridge Books, Cambridge University Press, number 9780521725200, April.
  15. Finkelstein, Amy & Poterba, James & Rothschild, Casey, 2009. "Redistribution by insurance market regulation: Analyzing a ban on gender-based retirement annuities," Journal of Financial Economics, Elsevier, vol. 91(1), pages 38-58, January.
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  19. Walliser, Jan, 2000. " Adverse Selection in the Annuities Market and the Impact of Privatizing Social Security," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(3), pages 373-93, June.
  20. Amy Finkelstein & James Poterba, 2000. "Adverse Selection in Insurance Markets: Policyholder Evidence from the U.K. Annuity Market," NBER Working Papers 8045, National Bureau of Economic Research, Inc.
  21. Ben J. Heijdra & Ward E. Romp, 2008. "A life-cycle overlapping-generations model of the small open economy," Oxford Economic Papers, Oxford University Press, vol. 60(1), pages 88-121, January.
  22. Leung, Siu Fai, 2007. "The existence, uniqueness, and optimality of the terminal wealth depletion time in life-cycle models of saving under uncertain lifetime and borrowing constraint," Journal of Economic Theory, Elsevier, vol. 134(1), pages 470-493, May.
  23. Rothschild, Michael & Stiglitz, Joseph E, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, MIT Press, vol. 90(4), pages 630-49, November.
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  28. Ben Heijdra & Laurie Reijnders, 2012. "Adverse Selection in Private Annuity Markets and the Role of Mandatory Social Annuitization," De Economist, Springer, vol. 160(3), pages 311-337, September.
  29. Attanasio, Orazio P & Weber, Guglielmo, 1995. "Is Consumption Growth Consistent with Intertemporal Optimization? Evidence from the Consumer Expenditure Survey," Journal of Political Economy, University of Chicago Press, vol. 103(6), pages 1121-57, December.
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Cited by:
  1. Shuyun May Li & Solmaz Moslehi & Siew Ling Yew, 2012. "Public-Private Mix of Health Expenditure: A Political Economy Approach and A Quantitative Exercise," Development Research Unit Working Paper Series 11-12, Monash University, Department of Economics.
  2. Ben Heijdra & Jochen Mierau, 2011. "The Individual Life Cycle and Economic Growth: An Essay on Demographic Macroeconomics," De Economist, Springer, vol. 159(1), pages 63-87, March.
  3. Ben Heijdra & Laurie Reijnders, 2012. "Adverse Selection in Private Annuity Markets and the Role of Mandatory Social Annuitization," De Economist, Springer, vol. 160(3), pages 311-337, September.

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