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On Lipschitz continuity of the iterated function system in a stochastic optimal growth model

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  • Mitra, Tapan
  • Privileggi, Fabio

Abstract

This paper provides qualitative properties of the iterated function system (IFS) generated by the optimal policy function for a class of stochastic one-sector optimal growth models. We obtain, explicitly in terms of the primitives of the model (i) a compact interval (not including the zero stock) in which the support of the invariant distribution of output must lie, and (ii) a Lipschitz property of the iterated function system on this interval. As applications, we are able to present parameter configurations under which (a) the support of the invariant distribution of the IFS is a generalized Cantor set, and (b) the invariant distribution is singular.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 45 (2009)
Issue (Month): 1-2 (January)
Pages: 185-198

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Handle: RePEc:eee:mateco:v:45:y:2009:i:1-2:p:185-198

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Stochastic optimal growth Iterated function system Invariant measure Lipschitz property Contraction property No overlap property Generalized topological Cantor set Singular invariant distribution;

References

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  1. Bhattacharya, Rabi & Majumdar, Mukul, 2001. "On a Class of Stable Random Dynamical Systems: Theory and Applications," Journal of Economic Theory, Elsevier, Elsevier, vol. 96(1-2), pages 208-229, January.
  2. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, Econometric Society, vol. 59(5), pages 1365-82, September.
  3. Chatterjee, Partha & Shukayev, Malik, 2008. "Note on positive lower bound of capital in the stochastic growth model," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 32(7), pages 2137-2147, July.
  4. Araujo, A, 1991. "The Once but Not Twice Differentiability of the Policy Function," Econometrica, Econometric Society, Econometric Society, vol. 59(5), pages 1383-93, September.
  5. Montrucchio, Luigi, 1987. "Lipschitz continuous policy functions for strongly concave optimization problems," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 16(3), pages 259-273, June.
  6. Mirman, Leonard J & Zilcha, Itzhak, 1976. "Unbounded Shadow Prices for Optimal Stochastic Growth Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(1), pages 121-32, February.
  7. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, Elsevier, vol. 11(3), pages 329-339, December.
  8. Mirman, Leonard J. & Zilcha, Itzhak, 1977. "Characterizing optimal policies in a one-sector model of economic growth under uncertainty," Journal of Economic Theory, Elsevier, Elsevier, vol. 14(2), pages 389-401, April.
  9. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, Elsevier, vol. 4(3), pages 479-513, June.
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Citations

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Cited by:
  1. Guido Cozzi & Fabio Privileggi, 2009. "The fractal nature of inequality in a fast growing world: new version," Working Papers, Business School - Economics, University of Glasgow 2009_30, Business School - Economics, University of Glasgow.
  2. 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, Institute of Public Policy and Public Choice - POLIS 157, Institute of Public Policy and Public Choice - POLIS.
  3. Gardini, Laura & Hommes, Cars & Tramontana, Fabio & de Vilder, Robin, 2009. "Forward and backward dynamics in implicitly defined overlapping generations models," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 71(2), pages 110-129, August.

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