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Continuous-Time Overlapping Generations Models

Author

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  • Hippolyte d'Albis

    (LERNA - Economie des Ressources Naturelles - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - CEA - Commissariat à l'énergie atomique et aux énergies alternatives)

  • Emmanuelle Augeraud-Véron

    (MIA - Mathématiques, Image et Applications - EA 3165 - ULR - La Rochelle Université)

Abstract

Age structured populations are studied in economics through overlapping generations models. These models allow for a realistic characterization of life-cycle behaviors and display intertemporal equilibrium that are not necessarily efficient. This article uses the latest developments in continuous time overlapping generations models to show the influence of the vintage structure of the population on the volatility of intertemporal prices. Permanent cycles can be found on the neighborhood of steady-states while the transitional dynamics are generically governed by short run fluctuations.

Suggested Citation

  • Hippolyte d'Albis & Emmanuelle Augeraud-Véron, 2011. "Continuous-Time Overlapping Generations Models," Post-Print hal-00424799, HAL.
  • Handle: RePEc:hal:journl:hal-00424799
    Note: View the original document on HAL open archive server: https://hal.science/hal-00424799
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    References listed on IDEAS

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    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. Hippolyte d’Albis & Emmanuelle Augeraud-Véron, 2007. "Balanced cycles in an OLG model with a continuum of finitely-lived individuals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 181-186, January.
    3. d'Albis, Hippolyte, 2007. "Demographic structure and capital accumulation," Journal of Economic Theory, Elsevier, vol. 132(1), pages 411-434, January.
    4. de la Croix, David & Licandro, Omar, 1999. "Life expectancy and endogenous growth," Economics Letters, Elsevier, vol. 65(2), pages 255-263, November.
    5. Bernheim, B Douglas, 1991. "How Strong Are Bequest Motives? Evidence Based on Estimates of the Demand for Life Insurance and Annuities," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 899-927, October.
    6. d'Albis, Hippolyte & Decreuse, Bruno, 2009. "Parental altruism, life expectancy and dynamically inefficient equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1897-1911, November.
    7. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    8. Davies, James B, 1981. "Uncertain Lifetime, Consumption, and Dissaving in Retirement," Journal of Political Economy, University of Chicago Press, vol. 89(3), pages 561-577, June.
    9. 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(6), pages 467-467.
    10. Raouf Boucekkine & David Croix & Omar Licandro, 2004. "MODELLING VINTAGE STRUCTURES WITH DDEs: PRINCIPLES AND APPLICATIONS," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 151-179.
    11. Hippolyte D'Albis & Emmanuelle Augeraud-Veron, 2008. "Endogenous Retirement and Monetary Cycles," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(4), pages 214-229.
    12. Kim, Oliver, 1983. "Balanced equilibrium in a consumption loans model," Journal of Economic Theory, Elsevier, vol. 29(2), pages 339-346, April.
    13. 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.
    14. Théophile T. Azomahou & Raouf Boucekkine & Bity Diene, 2009. "A closer look at the relationship between life expectancy and economic growth," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(2), pages 201-244, June.
    15. 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.
    16. Bullard, James & Russell, Steven, 1999. "An empirically plausible model of low real interest rates and unbacked government debt," Journal of Monetary Economics, Elsevier, vol. 44(3), pages 477-508, December.
    17. Willem H. Buiter, 1986. "Death, Population Growth, Productivity Growth and Debt Neutrality," NBER Working Papers 2027, National Bureau of Economic Research, Inc.
    18. Antoine Bommier, 2006. "Uncertain Lifetime And Intertemporal Choice: Risk Aversion As A Rationale For Time Discounting," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(4), pages 1223-1246, November.
    19. Benhabib, Jess & Rustichini, Aldo, 1991. "Vintage capital, investment, and growth," Journal of Economic Theory, Elsevier, vol. 55(2), pages 323-339, December.
    20. 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.
    21. Simonovits, Andras, 1999. "Are there cycles in realistic overlapping cohorts models?," Structural Change and Economic Dynamics, Elsevier, vol. 10(2), pages 261-275, June.
    22. Bloom, David E. & Canning, David & Mansfield, Richard K. & Moore, Michael, 2007. "Demographic change, social security systems, and savings," Journal of Monetary Economics, Elsevier, vol. 54(1), pages 92-114, January.
    23. Rao Aiyagari, S., 1988. "Nonmonetary steady states in stationary overlapping generations models with long lived agents and discounting: Multiplicity, optimality, and consumption smoothing," Journal of Economic Theory, Elsevier, vol. 45(1), pages 102-127, June.
    24. Ghiglino, Christian & Tvede, Mich, 1995. "No-trade and uniqueness of steady states," Journal of Economic Dynamics and Control, Elsevier, vol. 19(3), pages 655-661, April.
    25. Heijdra, Ben J. & Romp, Ward E., 2009. "Retirement, pensions, and ageing," Journal of Public Economics, Elsevier, vol. 93(3-4), pages 586-604, April.
    26. 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.
    27. Hamid Faruqee, 2003. "Debt, Deficits, and Age-specific Mortality," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(2), pages 300-312, April.
    28. Natali Hritonenko & Yuri Yatsenko, 2008. "Can Technological Change Sustain Retirement in an Aging Population?," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(2), pages 96-113.
    29. Azariadis, Costas & Bullard, James & Ohanian, Lee, 2004. "Trend-reverting fluctuations in the life-cycle model," Journal of Economic Theory, Elsevier, vol. 119(2), pages 334-356, December.
    30. S. Rao Aiyagari, 1989. "Can There Be Short-Period Deterministic Cycles When People Are Long Lived?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(1), pages 163-185.
    31. 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.
    32. Blanchard, Olivier J, 1985. "Debt, Deficits, and Finite Horizons," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 223-247, April.
    33. Weil, Philippe, 1989. "Overlapping families of infinitely-lived agents," Journal of Public Economics, Elsevier, vol. 38(2), pages 183-198, March.
    34. Laitner, John, 2007. "Comment on: David Bloom, David Canning, Rick Mansfield, and Michael Moore's "Demographic change, social security systems, and savings"," Journal of Monetary Economics, Elsevier, vol. 54(1), pages 115-117, January.
    35. 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.
    36. Lau, Sau-Him Paul, 2009. "Demographic structure and capital accumulation: A quantitative assessment," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 554-567, March.
    37. Kehoe, Timothy J. & Levine, David K. & Mas-Colell, Andreu & Woodford, Michael, 1991. "Gross substitutability in large-square economies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 1-25, June.
    38. Arthur, W Brian & McNicoll, Geoffrey, 1978. "Samuelson, Population and Intergenerational Transfers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(1), pages 241-246, February.
    39. Burke, Jonathan L., 1996. "Equilibrium for Overlapping Generations in Continuous Time," Journal of Economic Theory, Elsevier, vol. 70(2), pages 364-390, August.
    40. Ronald Lee, 1980. "Age Structure, Intergenerational Transfers and Economic Growth : an Overview," Revue Économique, Programme National Persée, vol. 31(6), pages 1129-1156.
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    1. Visite guidée au coeur des travaux du Meilleur jeune économiste 2012 (2/2)
      by Matthieu Solignac in Regards croisés sur l'économie on 2012-06-11 03:05:40

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    Cited by:

    1. 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.
    2. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Stability and determinacy conditions for mixed-type functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 119-129.
    3. Can Askan Mavi, 2019. "What can catastrophic events tell us about sustainability?," Post-Print halshs-02142121, HAL.

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    Keywords

    overlapping generations; continuous time; life-cycle; intertemporal prices.; intertemporal prices;
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