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How Powerful is Demography? The Serendipity Theorem Revisited

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Author Info

  • David de la CROIX

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques etSsociales (IRES) and Center for Operations Research and Econometrics (CORE))

  • Pierre PESTIEAU

    (University of Liege, CORE, Paris School of Economics and CEPR)

  • Gregory PONTHIERE

    (Paris School of Economics and Ecole Normale Superieure, Paris)

Abstract

Introduced by Samuelson (1975), the Serendipity Theorem states that the competitive economy will converge towards the optimum steady-state provided the optimum population growth rate is imposed. This paper aims at exploring whether the Serendipity Theorem still holds in an economy with risky lifetime. We show that, under general conditions, including a perfect annuity market with actuarially fair return, imposing the optimum fertility rate and the optimum survival rate leads the competitive economy to the optimum steady-state. That Extended Serendipity Theorem is also shown to hold in economies where old adults work some fraction of the old-age, whatever the retirement age is fixed or chosen by the agents.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) in its series Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) with number 2009040.

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Length: 20
Date of creation: 11 Dec 2009
Date of revision:
Handle: RePEc:ctl:louvir:2009040

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Keywords: Serendipity Theorem; fertility; mortality; overlapping generations; retirement;

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References

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  1. David, DE LA CROIX, 2008. "On the Golden Rule of capital accumulation under endogenous longevity," Discussion Papers (ECON - Département des Sciences Economiques) 2008032, Université catholique de Louvain, Département des Sciences Economiques.
  2. Oded Galor & Omer Moav, 2004. "Natural Selection and the Evolution of Life Expectancy," GE, Growth, Math methods 0409004, EconWPA.
  3. Samuelson, Paul A, 1975. "The Optimum Growth Rate for Population," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(3), pages 531-38, October.
  4. MICHEL, Philippe & PESTIEAU, Pierre, . "Population growth and optimality. When does serendipity hold?," CORE Discussion Papers RP -1072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Blackburn, Keith & Cipriani, Giam Pietro, 2002. "A model of longevity, fertility and growth," Journal of Economic Dynamics and Control, Elsevier, vol. 26(2), pages 187-204, February.
  6. Matthias Doepke, 2004. "Accounting for Fertility Decline During the Transition to Growth," Journal of Economic Growth, Springer, vol. 9(3), pages 347-383, 09.
  7. Hu, Sheng Cheng, 1979. "Social Security, the Supply of Labor, and Capital Accumulation," American Economic Review, American Economic Association, vol. 69(3), pages 274-83, June.
  8. Alexandra Rillaers & David de la Croix & Geraldine Mahieu, 2003. "How Should The Allocation Of Resources Adjust To The Baby Bust?," Working Papers. Serie AD 2003-27, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  9. David de la Croix & Omar Licandro, 2013. "The Child is Father Of the Man: Implications for the Demographic Transition," Economic Journal, Royal Economic Society, vol. 123(567), pages 236-261, 03.
  10. Chakraborty, Shankha, 2004. "Endogenous lifetime and economic growth," Journal of Economic Theory, Elsevier, vol. 116(1), pages 119-137, May.
  11. Gemma Abio, 2003. "Interiority of the optimal population growth rate with endogenous fertility," Economics Bulletin, AccessEcon, vol. 10(4), pages 1-7.
  12. Deardorff, Alan V, 1976. "The Optimum Growth Rate for Population: Comment," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 510-15, June.
  13. de la Croix,David & Michel,Philippe, 2002. "A Theory of Economic Growth," Cambridge Books, Cambridge University Press, number 9780521806428, April.
  14. Pierre-André Jouvet & Pierre Pestieau & Grégory Ponthière, 2007. "Longevity and environmental quality in an OLG model," EconomiX Working Papers 2007-19, University of Paris West - Nanterre la Défense, EconomiX.
  15. repec:ebl:ecbull:v:10:y:2003:i:4:p:1-7 is not listed on IDEAS
  16. Gregory Ponthiere, 2009. "Rectangularization And The Rise In Limit-Longevity In A Simple Overlapping Generations Model," Manchester School, University of Manchester, vol. 77(1), pages 17-46, 01.
  17. Tomas J. Philipson & Gary S. Becker, 1998. "Old-Age Longevity and Mortality-Contingent Claims," Journal of Political Economy, University of Chicago Press, vol. 106(3), pages 551-573, June.
  18. 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.
  19. Klaus Jaeger & Wolfgang Kuhle, 2009. "The optimum growth rate for population reconsidered," Journal of Population Economics, Springer, vol. 22(1), pages 23-41, January.
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Citations

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Cited by:
  1. Pierre Pestieau & Gregory Ponthiere, 2014. "Optimal fertility along the life cycle," Economic Theory, Springer, vol. 55(1), pages 185-224, January.
  2. repec:hal:psewpa:halshs-00746913 is not listed on IDEAS
  3. PESTIEAU, Pierre & PONTHIERE, Grégory, 2012. "The public economics of increasing longevity," CORE Discussion Papers 2012005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. repec:hal:wpaper:halshs-00746913 is not listed on IDEAS
  5. Thomas Renstrom & Luca Spataro, 2014. "Population growth and human capital: a welfarist approach," Public Finance Research Papers 3, Istituto di Economia e Finanza, DIGEF, Sapienza University of Rome.
  6. repec:hal:wpaper:halshs-00676492 is not listed on IDEAS
  7. Grégory Ponthière, 2012. "Fair Accumulation under Risky Lifetime," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-00746913, HAL.
  8. Luciano Fanti & Luca Gori, 2014. "Endogenous fertility, endogenous lifetime and economic growth: the role of child policies," Journal of Population Economics, Springer, vol. 27(2), pages 529-564, April.
  9. Luciano Fanti & Luca Gori, 2012. "Public Expenditure on Health and Private Old-Age Insurance in an OLG Growth Model with Endogenous Fertility: Chaotic Dynamics Under Perfect Foresight," Computational Economics, Society for Computational Economics, vol. 40(4), pages 333-353, December.
  10. repec:hal:wpaper:hal-00612609 is not listed on IDEAS

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