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Optimal Cycles and Chaos: A Survey

Author

Listed:
  • Nishimura Kazuo

    (Institute of Economic Research Kyoto University Japan)

  • Sorger Gerhard

    (Department of Economics University of Vienna Austria)

Abstract
This paper surveys the literature on cyclical and chaotic equilibrium paths in deterministic optimal growth models with infinitely lived agents. We focus on discrete time models but also briefly mention results for continuous time models. We start by reviewing those results that have been proved for optimal growth models in reduced form. Then we discuss results for two-sector optimal growth models in primitive form. Finally, we summarize a few results that have been obtained for other variants of the model, including models with recursive preferences and models with heterogeneous agents.

Suggested Citation

  • Nishimura Kazuo & Sorger Gerhard, 1996. "Optimal Cycles and Chaos: A Survey," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(1), pages 1-20, April.
    • Handle: RePEc:bpj:sndecm:v:1:y:1996:i:1:n:3
    DOI: 10.2202/1558-3708.1009
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    Citations

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    Cited by:

    1. Orlando Gomes, 2010. "Deterministic randomness in a model of finance and growth," Journal of Evolutionary Economics, Springer, vol. 20(1), pages 95-114, January.
    2. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2015. "Self-similar measures in multi-sector endogenous growth models," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 40-56.
    3. Barnett, William A. & Serletis, Apostolos & Serletis, Demitre, 2015. "Nonlinear And Complex Dynamics In Economics," Macroeconomic Dynamics, Cambridge University Press, vol. 19(8), pages 1749-1779, December.
    4. La Torre, Davide & Marsiglio, Simone & Privileggi, Fabio, 2011. "Fractals and Self-Similarity in Economics: the Case of a Stochastic Two-Sector Growth Model," POLIS Working Papers 157, Institute of Public Policy and Public Choice - POLIS.
    5. Brock, W.A. & Hommes, C.H., 1997. "Models of Compelxity in Economics and Finance," Working papers 9706, Wisconsin Madison - Social Systems.
    6. Gomes, Orlando, 2008. "Too much of a good thing: Endogenous business cycles generated by bounded technological progress," Economic Modelling, Elsevier, vol. 25(5), pages 933-945, September.
    7. Tancrède Voituriez, 1998. "Dynamique non linéaire du marché mondial des huiles et des graisses," Économie rurale, Programme National Persée, vol. 243(1), pages 22-29.
    8. Vivaldo M. Mendes & Diana A. Mendes, 2006. "Active Interest Rate Rules and the Role of Stabilization Policy R&D Tax Credits," Working Papers Series 1 ercwp0208, ISCTE-IUL, Business Research Unit (BRU-IUL).
    9. Guo, Jang-Ting & Lansing, Kevin J., 2002. "Fiscal Policy, Increasing Returns, And Endogenous Fluctuations," Macroeconomic Dynamics, Cambridge University Press, vol. 6(5), pages 633-664, November.
    10. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
    11. Kamihigashi, Takashi, 1999. "Chaotic dynamics in quasi-static systems: theory and applications1," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 183-214, March.
    12. Vivaldo M. Mendes & Diana A. Mendes & José Sousa Ramos, 2008. "Symbolic Dynamics and Control in a Matching Labor Market Model," Working Papers Series 1 ercwp1308, ISCTE-IUL, Business Research Unit (BRU-IUL).
    13. Anjan Mukherji, 2003. "Competitive Equilibria: Convergence, Cycles or Chaos," ISER Discussion Paper 0591, Institute of Social and Economic Research, Osaka University.
    14. Bosi, Stefano & Ha-Huy, Thai, 2023. "A multidimensional, nonconvex model of optimal growth," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    15. Richard H. Day & Oleg V. Pavlov, 2022. "Computing Economic Chaos," Papers 2211.02441, arXiv.org.
    16. Orlando Gomes, 2010. "Consumer confidence, endogenous growth and endogenous cycles," Journal of Economic Studies, Emerald Group Publishing Limited, vol. 37(4), pages 377-404, September.

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