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Ergodic Chaos in Optimal Growth Models with Low Discount Rates

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  • Nishimura, Kazuo
  • Sorger, Gerhard
  • Yano, Makoto

Abstract

We show that for every discount factor rho epsilon(O,1) one can find infinitely many strictly concave discrete-time optimal growth models in reduced form which have optimal policy functions exhibiting ergodic chaos. These reduced form models are interpreted in a two-sector optimal growth setting with utility functions depending on consumption as well as on capital.

Suggested Citation

  • Nishimura, Kazuo & Sorger, Gerhard & Yano, Makoto, 1994. "Ergodic Chaos in Optimal Growth Models with Low Discount Rates," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(5), pages 705-717, August.
  • Handle: RePEc:spr:joecth:v:4:y:1994:i:5:p:705-17
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    Cited by:

    1. Joshi, Sumit, 2003. "The stochastic turnpike property without uniformity in convex aggregate growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1289-1315, May.
    2. Katrin Erdlenbruch & Alain Jean-Marie & Michel Moreaux & Mabel Tidball, 2013. "Optimality of impulse harvesting policies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(2), pages 429-459, March.
    3. Gomes, Orlando, 2007. "Time preference and cyclical endogenous growth," MPRA Paper 3282, University Library of Munich, Germany.
    4. Gomes, Orlando, 2007. "Nonlinear dynamics in a model of financial development with a risk premium," MPRA Paper 2887, University Library of Munich, Germany.
    5. KONDO Atsumasa, "undated". "The Role of Productivity Growth Rates for Rising Inequality in an Economy with Heterogeneous Agents," ESRI Discussion paper series 326, Economic and Social Research Institute (ESRI).
    6. Montrucchio, Luigi & Sorger, Gerhard, 1996. "Topological entropy of policy functions in concave dynamic optimization models," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 181-194.
    7. Aditya Goenka & Lin Liu, 2012. "Infectious diseases and endogenous fluctuations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 125-149, May.
    8. Cesar Guerrero-Luchtenberg, 1998. "- A Turnpike Theoreme For A Family Of Functions," Working Papers. Serie AD 1998-07, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    9. Baierla, Gary & Nishimura, Kazuo & Yano, Makoto, 1998. "The role of capital depreciation in multi-sectoral models," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 467-479, January.
    10. Orlando Gomes, 2007. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing, vol. 33(6), pages 437-468, January.
    11. Orlando Gomes, 2008. "Time Preference and Cyclical Endogenous Growth in an AK Growth Model," Notas Económicas, Faculty of Economics, University of Coimbra, issue 28, pages 32-55, December.
    12. Takashi Kamihigashi, 2013. "Ergodic chaos and aggregate stability: A deterministic discrete-choice model of wealth distribution dynamics," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 45-56, March.
    13. Orlando Gomes, 2006. "Local Bifurcations and Global Dynamics in a Solow-type Endogenous Business Cycles Model," Annals of Economics and Finance, Society for AEF, vol. 7(1), pages 91-127, May.
    14. Gomes, Orlando, 2009. "A two-dimensional non-equilibrium dynamic model," Structural Change and Economic Dynamics, Elsevier, vol. 20(3), pages 221-238, September.
    15. Orlando Gomes, 2010. "Consumer confidence, endogenous growth and endogenous cycles," Journal of Economic Studies, Emerald Group Publishing, vol. 37(4), pages 377-404, September.
    16. Mitra, Tapan & Nishimura, Kazuo, 2001. "Discounting and Long-Run Behavior: Global Bifurcation Analysis of a Family of Dynamical Systems," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 256-293, January.
    17. Orlando Gomes, 2006. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing, vol. 33(6), pages 437-468, November.
    18. Mitra, Tapan, 1998. "On the relationship between discounting and complicated behavior in dynamic optimization models," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 421-434, January.
    19. Goenka, Aditya & Poulsen, Odile, 2004. "Factor Intensity Reversal and Ergodic Chaos," Working Papers 04-13, University of Aarhus, Aarhus School of Business, Department of Economics.
    20. César L. Guerrero-Luchtenberg, 2004. "Chaos vs. patience in a macroeconomic model of capital accumulation: New applications of a uniform neighborhood turnpike theorem," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 19(1), pages 45-60.
    21. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, January.
    22. Kopel, M. & Dawid, H. & Feichtinger, G., 1998. "Periodic and chaotic programs of intertemporal optimization models with non-concave net benefit function," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 435-447, January.
    23. Jean-Pierre Drugeon, 2013. "On the emergence of competitive equilibrium growth cycles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 397-427, January.
    24. repec:eee:jetheo:v:172:y:2017:i:c:p:451-477 is not listed on IDEAS
    25. Akhmet, Marat & Akhmetova, Zhanar & Fen, Mehmet Onur, 2014. "Chaos in economic models with exogenous shocks," Journal of Economic Behavior & Organization, Elsevier, vol. 106(C), pages 95-108.

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