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Chaos vs. patience in a macroeconomic model of capital accumulation: New applications of a uniform neighborhood turnpike theorem

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  • César L. Guerrero-Luchtenberg

    (Centro de Investigación y Docencia Económicas)

Abstract

We present in this paper some new results on the strong incompatibility between chaos and patience in a macroeconomic model of capital accumulation. These results are explicit and non-trivial applications of the general theorem proven in Guerrero-Luchtenberg (2000), in which the statement (theorem 2) ‘chaos vanishes as the discount factor tends to one’, is formally presented. Here, we show precisely how this statement applies to some important indicators of chaos not analyzed before. Furthermore, we will show that, for a given family of optimal growth models, there is a bound on the discount factor such that any type of chaos is negligible.

Suggested Citation

  • 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.
  • Handle: RePEc:emx:esteco:v:19:y:2004:i:1:p:45-60
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    References listed on IDEAS

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    1. Nishimura, Kazuo & Yano, Makoto, 1996. "On the Least Upper Bound of Discount Factors That Are Compatible with Optimal Period-Three Cycles," Journal of Economic Theory, Elsevier, vol. 69(2), pages 306-333, May.
    2. 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.
    3. Guerrero-Luchtenberg, C.L., 2000. "A uniform neighborhood turnpike theorem and applications," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 329-357, November.
    4. 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.
    5. 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.
    6. McKenzie, Lionel W., 2005. "Optimal economic growth, turnpike theorems and comparative dynamics," Handbook of Mathematical Economics,in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 2, volume 3, chapter 26, pages 1281-1355 Elsevier.
    7. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
    8. Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, vol. 12(1), pages 11-30, February.
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