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How powerful is demography ? The Serendipity Theorem revisited

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  • DE LA CROIX, David

    (Université catholique de Louvain, CORE and IRES, B-1348 Louvain-la-Neuve, Belgium)

  • PESTIEAU, Pierre

    (Université catholique de Louvain, CORE and IRES, B-1348 Louvain-la-Neuve, Belgium)

  • PONTHIERE, Gregory

    (Paris School of Economics and Ecole Normale Supérieure, Paris, France)

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

Suggested Citation

  • DE LA CROIX, David & PESTIEAU, Pierre & PONTHIERE, Gregory, 2009. "How powerful is demography ? The Serendipity Theorem revisited," LIDAM Discussion Papers CORE 2009076, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2009076
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    References listed on IDEAS

    as
    1. Blackorby,Charles & Bossert,Walter & Donaldson,David J., 2005. "Population Issues in Social Choice Theory, Welfare Economics, and Ethics," Cambridge Books, Cambridge University Press, number 9780521825511.
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    7. 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, January.
    8. de la Croix, David & Ponthiere, Gregory, 2010. "On the Golden Rule of capital accumulation under endogenous longevity," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 227-238, March.
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    14. de la Croix,David & Michel,Philippe, 2002. "A Theory of Economic Growth," Cambridge Books, Cambridge University Press, number 9780521806428.
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    18. Blackorby,Charles & Bossert,Walter & Donaldson,David J., 2005. "Population Issues in Social Choice Theory, Welfare Economics, and Ethics," Cambridge Books, Cambridge University Press, number 9780521532587.
    19. Hu, Sheng Cheng, 1979. "Social Security, the Supply of Labor, and Capital Accumulation," American Economic Review, American Economic Association, vol. 69(3), pages 274-283, June.
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    22. repec:ebl:ecbull:v:10:y:2003:i:4:p:1-7 is not listed on IDEAS
    23. 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.
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    Citations

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    Cited by:

    1. Pierre Pestieau & Gregory Ponthiere, 2017. "Optimal fertility under age-dependent labour productivity," Journal of Population Economics, Springer;European Society for Population Economics, vol. 30(2), pages 621-646, April.
    2. Gori, Luca & Manfredi, Piero & Sodini, Mauro, 2021. "A Parsimonious Model Of Longevity, Fertility, Hiv Transmission And Development," Macroeconomic Dynamics, Cambridge University Press, vol. 25(5), pages 1155-1174, July.
    3. Pierre Pestieau & Gregory Ponthiere, 2014. "Optimal fertility along the life cycle," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 185-224, January.
    4. Paolo Melindi-Ghidi & Willem Sas, 2015. "Invest as You Go: How Public Health Investment Keeps Pension Systems Healthy," AMSE Working Papers 1525, Aix-Marseille School of Economics, France.
    5. Luciano Fanti & Luca Gori, 2014. "Endogenous fertility, endogenous lifetime and economic growth: the role of child policies," Journal of Population Economics, Springer;European Society for Population Economics, vol. 27(2), pages 529-564, April.
    6. Gregory Ponthiere, 2013. "Fair Accumulation under Risky Lifetime," Scottish Journal of Political Economy, Scottish Economic Society, vol. 60(2), pages 210-230, May.
    7. Stelter, Robert, 2014. "Over-aging: Are present human populations too old?," Thuenen-Series of Applied Economic Theory 137, University of Rostock, Institute of Economics.
    8. Pierre Pestieau & Gregory Ponthiere, 2012. "The Public Economics of Increasing Longevity," Hacienda Pública Española / Review of Public Economics, IEF, vol. 200(1), pages 41-74, March.
    9. Cipriani, Giam Pietro & Fioroni, Tamara, 2022. "Social security and endogenous demographic change: child support and retirement policies," Journal of Pension Economics and Finance, Cambridge University Press, vol. 21(3), pages 307-325, July.
    10. Ziesemer, Thomas, 2018. "The serendipity theorem for an endogenous open economy growth model," MERIT Working Papers 2018-001, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    11. Momota, Akira & Sakagami, Tomoya & Shibata, Akihisa, 2019. "Reexamination of the Serendipity Theorem from the stability viewpoint," Journal of Demographic Economics, Cambridge University Press, vol. 85(1), pages 43-70, March.
    12. Momota, Akira, 2016. "Intensive and extensive margins of fertility, capital accumulation, and economic welfare," Journal of Public Economics, Elsevier, vol. 133(C), pages 90-110.
    13. Stefan Felder, 2016. "“How powerful is demography? The serendipity theorem revisited” comment on De la Croix et al. (2012)," Journal of Population Economics, Springer;European Society for Population Economics, vol. 29(3), pages 957-967, July.
    14. Thomas I. Renström & Luca Spataro, 2015. "Population Growth and Human Capital: A Welfarist Approach," Manchester School, University of Manchester, vol. 83, pages 110-141, December.
    15. Robert TAMURA & David CUBERES, 2020. "Equilibrium and A-efficient Fertility with Increasing Returns to Population and Endogenous Mortality," JODE - Journal of Demographic Economics, Cambridge University Press, vol. 86(2), pages 157-182, June.
    16. 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, Springer;Society for Computational Economics, vol. 40(4), pages 333-353, December.
    17. repec:hal:pseose:halshs-00746913 is not listed on IDEAS
    18. Stelter, Robert, 2016. "Over-aging — Are present-day human populations too old?," Mathematical Social Sciences, Elsevier, vol. 82(C), pages 116-143.

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    More about this item

    Keywords

    Serendipity Theorem; fertility; mortality; overlapping generations; retirement;
    All these keywords.

    JEL classification:

    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health
    • J10 - Labor and Demographic Economics - - Demographic Economics - - - General

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