IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/58656.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/58656/1/Paulo%20Brito.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    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. Brito, Paulo, 2008. "Equilibrium asset prices and bubbles in a continuous time OLG model," MPRA Paper 10701, University Library of Munich, Germany.
    6. Author-Name: John Geanakoplos & Michael Magill & Martine Quinzii, 2004. "Demography and the Long-Run Predictability of the Stock Market," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 35(1), pages 241-326.
    7. 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.
    8. Eugene F. Fama, 2006. "The Behavior of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 19(2), pages 359-379.
    9. 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.
    10. 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.
    11. John Geanakoplos, 2008. "Overlapping Generations Models of General Equilibrium," Cowles Foundation Discussion Papers 1663, Cowles Foundation for Research in Economics, Yale University.
    12. 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.
    13. John Geanakoplos, 2008. "Overlapping Generations Models of General Equilibrium," Levine's Working Paper Archive 122247000000002225, David K. Levine.
    14. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    15. 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.
    16. Michael Magill, 2004. "Demography and the Stock Market," Theory workshop papers 658612000000000080, UCLA Department of Economics.
    17. 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.
    18. 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.
    19. Blanchard, Olivier J, 1985. "Debt, Deficits, and Finite Horizons," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 223-247, April.
    20. S. Demichelis & H. Polemarchakis, 2007. "The determinacy of equilibrium in economies of overlapping generations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 461-475, September.
    21. Tirole, Jean, 1985. "Asset Bubbles and Overlapping Generations," Econometrica, Econometric Society, vol. 53(6), pages 1499-1528, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2015. "Local determinacy of prices in an overlapping generations model with continuous trading," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 16-24.
    3. Augeraud-Véron, Emmanuelle & D'Albis, Hippolyte, 2009. "Continuous-Time Overlapping Generations Models," TSE Working Papers 09-047, Toulouse School of Economics (TSE).
    4. Jochen Mierau & Stephen Turnovsky, 2014. "Capital accumulation and the sources of demographic change," Journal of Population Economics, Springer;European Society for Population Economics, vol. 27(3), pages 857-894, July.
    5. David Oxborrow & Stephen J. Turnovsky, 2017. "Closing the Small Open Economy Model: A Demographic Approach," Review of International Economics, Wiley Blackwell, vol. 25(1), pages 44-75, February.
    6. Jochen Mierau & Stephen Turnovsky, 2014. "Demography, growth, and inequality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 29-68, January.
    7. Hippolyte d'Albis & Emmanuelle Augeraud-Véron, 2013. "Frequency of trade and the determinacy of equilibrium in economies of overlapping generations," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 85-100, March.
    8. Brito, Paulo, 2008. "Equilibrium asset prices and bubbles in a continuous time OLG model," MPRA Paper 10701, University Library of Munich, Germany.
    9. 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.
    10. Hippolyte D'Albis & Emmanuelle Augeraud-Veron, 2008. "Endogenous Retirement and Monetary Cycles," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(4), pages 214-229.
    11. Rajnish Mehra & Facundo Piguillem & Edward C. Prescott, 2011. "Costly financial intermediation in neoclassical growth theory," Quantitative Economics, Econometric Society, vol. 2(1), pages 1-36, March.
    12. 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.
    13. Andreas Irmen, 2017. "Capital‐ And Labor‐Saving Technical Change In An Aging Economy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58(1), pages 261-285, February.
    14. Mizushima, Atsue, 2009. "Intergenerational transfers of time and public long-term care with an aging population," Journal of Macroeconomics, Elsevier, vol. 31(4), pages 572-581, December.
    15. Bruce, Neil & Turnovsky, Stephen J., 2013. "Social security, growth, and welfare in overlapping generations economies with or without annuities," Journal of Public Economics, Elsevier, vol. 101(C), pages 12-24.
    16. Lee, R., 2016. "Macroeconomics, Aging, and Growth," Handbook of the Economics of Population Aging, in: Piggott, John & Woodland, Alan (ed.), Handbook of the Economics of Population Aging, edition 1, volume 1, chapter 0, pages 59-118, Elsevier.
    17. Lau, Sau-Him Paul, 2014. "Fertility and mortality changes in an overlapping-generations model with realistic demography," Economic Modelling, Elsevier, vol. 38(C), pages 512-521.
    18. Jean-François Mertens & Anna Rubinchik, 2013. "Equilibria in an overlapping generations model with transfer policies and exogenous growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 537-595, November.
    19. d'Albis, Hippolyte, 2007. "Demographic structure and capital accumulation," Journal of Economic Theory, Elsevier, vol. 132(1), pages 411-434, January.
    20. Anton Belyakov & Josef Haunschmied & Vladimir Veliov, 2014. "Heterogeneous consumption in OLG model with horizontal innovations," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 13(3), pages 167-193, December.

    More about this item

    Keywords

    OLG; endogenous fertility; Arrow-Debreu; integral equations;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:58656. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.