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Interest rates and endogenous population growth: joint age-dependent dynamics

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  • Brito, Paulo

Abstract

This paper presents a uncertain-lifetime overlapping-generations continuous time model for an Arrow-Debreu economy with endogenous fertility, in which age-dependent variables are explicitly introduced. The general equilibrium paths for the discount factor and newborns are derived from a system of two coupled forward-backward integral equations. The forward mechanism is related to aggregation between cohorts and the backward mechanism to life-cycle decisions. We study changes in the age-dependent profiles of age-dependent distributions for productivity and time use. We show that high maximum ages of productivity and child-rearing fitness increase the long run interest and growth rates, and low maximum ages can lead to asset pricing bubbles and negative population growth rates.

Suggested Citation

  • Brito, Paulo, 2014. "Interest rates and endogenous population growth: joint age-dependent dynamics," MPRA Paper 58656, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:58656
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    File URL: https://mpra.ub.uni-muenchen.de/58656/1/Paulo%20Brito.pdf
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    References listed on IDEAS

    as
    1. Hippolyte d'Albis & Emmanuelle Augeraud-véron, 2009. "Competitive Growth In A Life-Cycle Model: Existence And Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(2), pages 459-484, May.
    2. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    3. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66, pages 467-467.
    4. Edmond, Chris, 2008. "An integral equation representation for overlapping generations in continuous time," Journal of Economic Theory, Elsevier, vol. 143(1), pages 596-609, November.
    5. Barro, Robert J & Becker, Gary S, 1989. "Fertility Choice in a Model of Economic Growth," Econometrica, Econometric Society, vol. 57(2), pages 481-501, March.
    6. 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.
    7. Brito, Paulo, 2008. "Equilibrium asset prices and bubbles in a continuous time OLG model," MPRA Paper 10701, University Library of Munich, Germany.
    8. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Schubert, Katheline, 2010. "Demographic-economic equilibria when the age at motherhood is endogenous," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1211-1221, November.
    9. Santos, Manuel S. & Bona, Jerry L., 1989. "On the structure of the equilibrium price set of overlapping-generations economies," Journal of Mathematical Economics, Elsevier, vol. 18(3), pages 209-230, June.
    10. Brito, Paulo & Dilão, Rui, 2010. "Equilibrium price dynamics in an overlapping-generations exchange economy," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 343-355, May.
    11. Antoine Bommier & Ronald D. Lee, 2003. "Overlapping generations models with realistic demography," Journal of Population Economics, Springer;European Society for Population Economics, vol. 16(1), pages 135-160, February.
    12. Eugene F. Fama, 2006. "The Behavior of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 19(2), pages 359-379.
    13. Blanchard, Olivier J, 1985. "Debt, Deficits, and Finite Horizons," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 223-247, April.
    14. Gary S. Becker & Robert J. Barro, 1988. "A Reformulation of the Economic Theory of Fertility," The Quarterly Journal of Economics, Oxford University Press, vol. 103(1), pages 1-25.
    15. Tirole, Jean, 1985. "Asset Bubbles and Overlapping Generations," Econometrica, Econometric Society, vol. 53(6), pages 1499-1528, November.
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    More about this item

    Keywords

    OLG; endogenous fertility; Arrow-Debreu; integral equations;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment
    • J1 - Labor and Demographic Economics - - Demographic Economics

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