Fractals and Self-Similarity in Economics: the Case of a Stochastic Two-Sector Growth Model
AbstractWe study a stochastic, discrete-time, two-sector optimal growth model in which the production of the homogeneous consumption good uses a Cobb-Douglas technology, combining physical capital and an endogenously determined share of human capital. Education is intensive in human capital as in Lucas (1988), but the marginal returns of the share of human capital employed in education are decreasing, as suggested by Rebelo (1991). Assuming that the exogenous shocks are i.i.d. and affect both physical and human capital, we build specific configurations for the primitives of the model so that the optimal dynamics for the state variables can be converted, through an appropriate log-transformation, into an Iterated Function System converging to an invariant distribution supported on a generalized Sierpinski gasket.
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Bibliographic InfoPaper provided by Institute of Public Policy and Public Choice - POLIS in its series POLIS Working Papers with number 157.
Length: 16 pages
Date of creation: Jun 2011
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fractals; iterated function system; self-similarity; Sierpinski gasket; stochastic growth;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-06-18 (All new papers)
- NEP-DGE-2011-06-18 (Dynamic General Equilibrium)
- NEP-FDG-2011-06-18 (Financial Development & Growth)
- NEP-ORE-2011-06-18 (Operations Research)
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- Stefano Maria Iacus & Davide La Torre, 2002. "Approximating distribution functions by iterated function systems," Departmental Working Papers 2002-03, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
- Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
- Gardini, L. & Hommes, C.H. & Tramontana, F. & de Vilder, R., 2009.
"Forward and Backward Dynamics in implicitly defined Overlapping Generations Models,"
CeNDEF Working Papers
09-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- 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, vol. 71(2), pages 110-129, August.
- Laura Gardini & Cars Hommes & Fabio Tramontana & Robin de Vilder, 2008. "Forward and Backward Dynamics in Implicitly Defined Overlapping Generations Models," Working Papers 0806, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
- Mitra, Tapan & Privileggi, Fabio, 2009. "On Lipschitz continuity of the iterated function system in a stochastic optimal growth model," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 185-198, January.
- Nishimura, Kazuo & Yano, Makoto, 1995. "Nonlinear Dynamics and Chaos in Optimal Growth: An Example," Econometrica, Econometric Society, vol. 63(4), pages 981-1001, July.
- Mitra, Tapan & Privileggi, Fabio, 2003. "Cantor Type Invariant Distributions in the Theory of Optimal Growth under Uncertainty," Working Papers 03-09, Cornell University, Center for Analytic Economics.
- Davide LA TORRE & Franklin MENDIVIL, 2007. "Iterated function systems on multifunctions and inverse problems," Departmental Working Papers 2007-32, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
- Nishimura Kazuo & Sorger Gerhard, 1996. "Optimal Cycles and Chaos: A Survey," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(1), pages 1-20, April.
- Davide LA TORRE & Edward R. VRSCAY, 2008. "A generalized fractal transform for measure-valued images," Departmental Working Papers 2008-38, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
- Mitra, Tapan & Montrucchio, Luigi & Privileggi, Fabio, 2001.
"The Nature of the Steady State in Models of Optimal Growth Under Uncertainty,"
01-04, Cornell University, Center for Analytic Economics.
- Tapan Mitra & Luigi Montrucchio & Fabio Privileggi, 2003. "The nature of the steady state in models of optimal growth under uncertainty," Economic Theory, Springer, vol. 23(1), pages 39-71, December.
- Davide LA TORRE & Edward R. VRSCAY & Mehran EBRAHIMI & Michael F. BARNSLEY, 2008. "Measure-valued images, associated fractal transforms and the affine self-similarity of images," Departmental Working Papers 2008-45, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
- Mitra, Tapan & Privileggi, Fabio, 2005. "Cantor Type Attractors in Stochastic Growth Models," POLIS Working Papers 43, Institute of Public Policy and Public Choice - POLIS.
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