On Lipschitz continuity of the iterated function system in a stochastic optimal growth model
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 45 (2009)
Issue (Month): 1-2 (January)
Contact details of provider:
Web page: http://www.elsevier.com/locate/jmateco
Stochastic optimal growth Iterated function system Invariant measure Lipschitz property Contraction property No overlap property Generalized topological Cantor set Singular invariant distribution;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, Elsevier, vol. 11(3), pages 329-339, December.
- 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.
- 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.
- 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.
- 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.
- 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.
- Gardini, L. & Hommes, C.H. & Tramontana, F. & de Vilder, R., 2009. "Forward and Backward Dynamics in implicitly defined Overlapping Generations Models," CeNDEF Working Papers, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance 09-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- Laura Gardini & Cars Hommes & Fabio Tramontana & Robin de Vilder, 2008. "Forward and Backward Dynamics in Implicitly Defined Overlapping Generations Models," Working Papers, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini 0806, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.