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Can there be short-period deterministic cycles when people are long lived?

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  • S. Rao Aiyagari

Abstract

This paper considers whether short-period deterministic cycles can exist in a class of stationary overlapping generations models with long- (but finite-) lived agents. It shows that if agents discount the future positively, then as life spans get large, nonmonetary cycles will disappear. Further, neither constant monetary steady states nor stationary monetary cycles can exist. It also shows that if agents discount the future negatively, then there are robust examples in which constant monetary steady states as well as stationary monetary cycles (with undiminished amplitude) can occur no matter how long agents live.

Suggested Citation

  • S. Rao Aiyagari, 1988. "Can there be short-period deterministic cycles when people are long lived?," Staff Report 114, Federal Reserve Bank of Minneapolis.
    • Handle: RePEc:fip:fedmsr:114
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    References listed on IDEAS

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    1. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    2. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
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    4. 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.
    5. Woodford, Michael, 1986. "Stationary sunspot equilibria in a finance constrained economy," Journal of Economic Theory, Elsevier, vol. 40(1), pages 128-137, October.
    6. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
    7. Spear, Stephen E., 1984. "Sufficient conditions for the existence of sunspot equilibria," Journal of Economic Theory, Elsevier, vol. 34(2), pages 360-370, December.
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    Cited by:

    1. Jones, Larry E. & Manuelli, Rodolfo E., 1992. "Finite lifetimes and growth," Journal of Economic Theory, Elsevier, vol. 58(2), pages 171-197, December.
    2. Ponthiere, Gregory, 2011. "Existence and stability of overconsumption equilibria," Economic Modelling, Elsevier, vol. 28(1), pages 74-90.
    3. Barnett, William A. & Duzhak, Evgeniya Aleksandrovna, 2008. "Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3817-3825.
    4. Hippolyte D'Albis & Emmanuelle Augeraud-Veron, 2008. "Endogenous Retirement and Monetary Cycles," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(4), pages 214-229.
    5. D'ALBIS Hippolyte & AUGERAUD-VÉRON Emmanuelle, 2009. "Continuous-Time Overlapping Generations Models," LERNA Working Papers 09.15.291, LERNA, University of Toulouse.
    6. Lovo, Stefano & Polemarchakis, Herakles, 2010. "Myopia and monetary equilibria," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 925-936, September.
    7. 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.
    8. William Barnett & Evgeniya Duzhak, 2010. "Empirical assessment of bifurcation regions within New Keynesian models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 99-128, October.
    9. Stefano Lovo, 2000. "Infinitely Lived Representative Agent Exchange Economy with Myopia," Working Papers hal-00598167, HAL.
    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. Simonovits, Andras, 1999. "Are there cycles in realistic overlapping cohorts models?," Structural Change and Economic Dynamics, Elsevier, vol. 10(2), pages 261-275, June.
    12. 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.
    13. 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.
    14. Citanna, Alessandro & Siconolfi, Paolo, 2007. "Short-memory equilibrium in stochastic overlapping generations economies," Journal of Economic Theory, Elsevier, vol. 134(1), pages 448-469, May.
    15. 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.

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    Keywords

    Business cycles; Monetary theory;

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