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A Chaotic Map Arising in the Theory of Endogenous Growth

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  • Michele Boldrin
  • Nicola Perisco

Abstract

Growth theorists have almost always adopted the assumption of balanced growth in their investigations of development phenomena. In reality countries growth rates oscillate, sometimes wildly, around some average value. The latter is often taken to represent the balanced rate to which the development dynamics spontaneously tends to return after each perturbation. In this paper we try a different interpretation: the growth rate of capital stock in a developing economy oscillates within some bounded interval of feasible values and the balanced growth is in fact unstable. These oscillations may be persistent and endogenously determined by the accumulation process itself and they generate a non-trivial, invariant distribution of growth rates. We study a class of two-sector models displaying this feature in the prescence of a positive external effect. The qualitative properties of a specific example are analyzed by means of analytical and numerical methods. Our simulations reveal that, while the artificial economy is certainly able to display rather impressive endogenous growth cycles, they occur only when the external effects is unreasonably strong. Similarly to previous tentatives of modeling endogenous oscillations by means a chaotic map, we suceed at the theoretical level but fail short of reproducing some crucial empirical properties of the growth cycles experienced by modern market economies.

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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1071.

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Date of creation: Nov 1993
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Handle: RePEc:nwu:cmsems:1071

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Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 309-327, November.
  2. Michele Boldrin & Aldo Rustichini, 2010. "Growth and Indeterminacy in Dynamic Models with Externalities," Levine's Working Paper Archive 1382, David K. Levine.
  3. Brock, William A., 1975. "A simple perfect foresight monetary model," Journal of Monetary Economics, Elsevier, vol. 1(2), pages 133-150, April.
  4. Michele Boldrin, 1988. "Paths of Optimal Accumulation in Two-Sector Models," UCLA Economics Working Papers 464, UCLA Department of Economics.
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Cited by:
  1. Takahashi, Harutaka & Sakagami, Tomoya, 1998. "Transitional dynamics of economic integration and endogenous growth," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 543-555, January.
  2. Shigoka, Tadashi, 1997. "On the nonstationary sunspot equilibria generated by an unbounded growth model," Japan and the World Economy, Elsevier, vol. 9(2), pages 261-277, May.
  3. Venditti, A., 1996. "Indeterminancy and Endogenous Fluctuations in Two-Sector Growth Models with Externalities," G.R.E.Q.A.M. 96a04, Universite Aix-Marseille III.

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