IDEAS home Printed from https://ideas.repec.org/a/taf/mpopst/v15y2008i4p214-229.html
   My bibliography  Save this article

Endogenous Retirement and Monetary Cycles

Author

Listed:
  • HIPPOLYTE D'ALBIS
  • EMMANUELLE AUGERAUD-VERON

Abstract

In a model of overlapping generations with a continuum of finitely lived individuals, the aggregate price dynamics is characterized by a functional differential equation of mixed type. Delays and advances are exogenous when age at retirement is mandatory; they become state-dependent when individuals are allowed to choose their age at retirement. Using the Hopf bifurcation theorem, periodic solutions in the neighborhood of the monetary steady state appearing with a mandatory retirement age vanish with a chosen age.

Suggested Citation

  • Hippolyte D'Albis & Emmanuelle Augeraud-Veron, 2008. "Endogenous Retirement and Monetary Cycles," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(4), pages 214-229.
    • Handle: RePEc:taf:mpopst:v:15:y:2008:i:4:p:214-229
    DOI: 10.1080/08898480802440786
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/08898480802440786
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/08898480802440786?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    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. 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. de la Croix, David & Licandro, Omar, 1999. "Life expectancy and endogenous growth," Economics Letters, Elsevier, vol. 65(2), pages 255-263, November.
    4. Kehoe, Timothy J. & Levine, David K., 1984. "Regularity in overlapping generations exchange economies," Journal of Mathematical Economics, Elsevier, vol. 13(1), pages 69-93, April.
    5. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    6. 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.
    7. 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.
    8. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    9. Balasko, Yves & Cass, David & Shell, Karl, 1980. "Existence of competitive equilibrium in a general overlapping-generations model," Journal of Economic Theory, Elsevier, vol. 23(3), pages 307-322, December.
    10. Benhabib, Jess & Laroque, Guy, 1988. "On competitive cycles in productive economies," Journal of Economic Theory, Elsevier, vol. 45(1), pages 145-170, June.
    11. Chang, Fwu-Ranq, 1991. "Uncertain Lifetimes, Retirement and Economic Welfare," Economica, London School of Economics and Political Science, vol. 58(230), pages 215-232, May.
    12. C. Nourry & A. Venditti, 2006. "Overlapping Generations Model with Endogenous Labor Supply: General Formulation," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 355-377, February.
    13. David Cass & Menahem E. Yaari, 1965. "Individual Saving, Aggregate Capital Accumulation, and Efficient Growth," Cowles Foundation Discussion Papers 198, Cowles Foundation for Research in Economics, Yale University.
    14. Bhattacharya, Joydeep & Russell, Steven, 2003. "Two-period cycles in a three-period overlapping generations model," Journal of Economic Theory, Elsevier, vol. 109(2), pages 378-401, April.
    15. 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.
    16. Ghiglino, Christian & Tvede, Mich, 1995. "Endowments, stability, and fluctuations in OG models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(3), pages 621-653, April.
    17. Simonovits, Andras, 1999. "Are there cycles in realistic overlapping cohorts models?," Structural Change and Economic Dynamics, Elsevier, vol. 10(2), pages 261-275, June.
    18. Sebnem Kalemli-Ozcan & David Weil, 2010. "Mortality change, the uncertainty effect, and retirement," Journal of Economic Growth, Springer, vol. 15(1), pages 65-91, March.
    19. Reichlin, Pietro, 1992. "Endogenous cycles with long-lived agents," Journal of Economic Dynamics and Control, Elsevier, vol. 16(2), pages 243-266, April.
    20. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
    21. Swanson, Charles E., 1998. "A volatility bound for endogenous business cycles: the case of even period lives with additive utility in a monetary economy," Economics Letters, Elsevier, vol. 61(3), pages 339-344, December.
    22. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    23. 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.
    24. Sebnem Kalemli-Ozcan & David Weil, 2010. "Mortality change, the uncertainty effect, and retirement," Journal of Economic Growth, Springer, vol. 15(1), pages 65-91, March.
    25. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October.
    26. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
    27. Guido Cazzavillan & Patrick A. Pintus, 2004. "Robustness of Multiple Equilibria in OLG Economies," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 7(2), pages 456-475, April.
    28. 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.
    29. Jullien, Bruno, 1988. "Competitive business cycles in an overlapping generations economy with productive investment," Journal of Economic Theory, Elsevier, vol. 46(1), pages 45-65, October.
    30. 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.
    31. Whitesell, William, 1986. "Endogenous cycles with uncertain lifespans in continuous time," Economics Letters, Elsevier, vol. 22(2-3), pages 153-158.
    Full references (including those not matched with items on IDEAS)

    Citations

    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Visite guidée au coeur des travaux du Meilleur jeune économiste 2012 (1/2)
      by Matthieu Solignac in Regards croisés sur l'économie on 2012-05-29 00:26:09

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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. Augeraud-Véron, Emmanuelle & D'Albis, Hippolyte, 2009. "Continuous-Time Overlapping Generations Models," TSE Working Papers 09-047, Toulouse School of Economics (TSE).
    3. Sánchez-Romero, Miguel & Sambt, Jože & Prskawetz, Alexia, 2013. "Quantifying the role of alternative pension reforms on the Austrian economy," Labour Economics, Elsevier, vol. 22(C), pages 94-114.
    4. dʼAlbis, Hippolyte & Lau, Sau-Him Paul & Sánchez-Romero, Miguel, 2012. "Mortality transition and differential incentives for early retirement," Journal of Economic Theory, Elsevier, vol. 147(1), pages 261-283.
    5. Heijdra, Ben J. & Romp, Ward E., 2009. "Retirement, pensions, and ageing," Journal of Public Economics, Elsevier, vol. 93(3-4), pages 586-604, April.
    6. Sánchez-Romero, Miguel & d׳Albis, Hippolyte & Prskawetz, Alexia, 2016. "Education, lifetime labor supply, and longevity improvements," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 118-141.
    7. 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.
    8. Nicolas Drouhin, 2018. "Theoretical considerations on the retirement consumption puzzle and the optimal age of retirement," Working Papers halshs-01767096, HAL.
    9. Klaus Prettner & David Canning, 2014. "Increasing life expectancy and optimal retirement in general equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 191-217, May.
    10. repec:dau:papers:123456789/6825 is not listed 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. Augeraud-Véron, Emmanuelle & D'Albis, Hippolyte, 2009. "Continuous-Time Overlapping Generations Models," TSE Working Papers 09-047, Toulouse School of Economics (TSE).
    2. 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.
    3. Tvede Mich, 2009. "Fluctuations in Overlapping Generations Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-19, May.
    4. 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.
    5. Molnar, Gyorgy & Simonovits, Andras, 1998. "Expectations, (in)stability and (in)viability in realistic overlapping cohorts models," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 303-332, September.
    6. Simonovits, Andras, 1999. "Are there cycles in realistic overlapping cohorts models?," Structural Change and Economic Dynamics, Elsevier, vol. 10(2), pages 261-275, June.
    7. Philippe Michel & Bertrand Wigniolle, 1993. "Une présentation simple des dynamiques complexes," Revue Économique, Programme National Persée, vol. 44(5), pages 885-912.
    8. 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.
    9. 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.
    10. Bhattacharya, Joydeep & Russell, Steven, 2003. "Two-period cycles in a three-period overlapping generations model," Journal of Economic Theory, Elsevier, vol. 109(2), pages 378-401, April.
    11. Gorokhovsky, Alexander & Rubinchik, Anna, 2022. "Necessary and sufficient conditions for determinacy of asymptotically stationary equilibria in OLG models," Journal of Economic Theory, Elsevier, vol. 204(C).
    12. Takuma Kunieda & Akihisa Shibata, 2014. "Credit Market Imperfections and Macroeconomic Instability," Pacific Economic Review, Wiley Blackwell, vol. 19(5), pages 592-611, December.
    13. 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.
    14. H. Polemarchakis & S. Demichelis, 2002. "Frequency of Trade and the Determinancy of Equilibrium Paths: Logarithmic Economies of Overlapping Generations Under Certainty," Working Papers 2002-16, Brown University, Department of Economics.
    15. Kehoe, Timothy J. & Levine, David K., 1990. "The economics of indeterminacy in overlapping generations models," Journal of Public Economics, Elsevier, vol. 42(2), pages 219-243, July.
    16. Cazzavillan, Guido & Pintus, Patrick A., 2005. "On competitive cycles and sunspots in productive economies with a positive money stock," Research in Economics, Elsevier, vol. 59(2), pages 137-147, June.
    17. Timothy J. Kehoe & David K. Levine & Andreu Mas-Colell & Michael Woodford, 1991. "Gross Substitutes in Large Square Economics," Levine's Working Paper Archive 2057, David K. Levine.
    18. Michael Assous & Pedro Garcia Duarte, 2017. "Challenging Lucas: from overlapping generations to infinite-lived agent models," Working Papers, Department of Economics 2017_03, University of São Paulo (FEA-USP).
    19. Ghiglino, Christian & Tvede, Mich, 1995. "Endowments, stability, and fluctuations in OG models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(3), pages 621-653, April.
    20. Philippe Michel & Alain Venditti & Claude Jessua, 1996. "Croissance optimale et cycles dans le modèle à générations imbriquées : un exemple," Revue Économique, Programme National Persée, vol. 47(3), pages 487-497.

    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:taf:mpopst:v:15:y:2008:i:4:p:214-229. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GMPS20 .

    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.