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Self-Similar Measures in Multi-Sector Endogenous Growth Models

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  • Davide La Torre

    ()

  • Simone, Marsiglio

    ()

  • Mendivil, Franklin

    ()

  • Privileggi, Fabio

    () (University of Turin)

Abstract

We analyze two types of stochastic discrete time multi-sector endogenous growth models, namely a basic Lucas-Uzawa (1988) model and an extended three-sector version as in La Torre and Marsiglio (2010). As in the case of sustained growth the optimal dynamics of the state variables are not stationary, we focus on the dynamics of the capital ratio variables, and we show that, through appropriate log-transform ations, they can be converted into affine iterated function systems converging to an invariant distribution supported on some fractal set. This proves that also the steady state of endogenous growth models i.e., the stochastic balanced growth path equilibrium—might have a fractal nature. We also provide some sufficient conditions under which the associated self-similar measures turn out to be either singular or absolutely continuous (for the three-sector model we only consider the singularity).

Suggested Citation

  • Davide La Torre & Simone, Marsiglio & Mendivil, Franklin & Privileggi, Fabio, 2015. "Self-Similar Measures in Multi-Sector Endogenous Growth Models," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201509, University of Turin.
  • Handle: RePEc:uto:dipeco:201509
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    References listed on IDEAS

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    1. Simone Marsiglio, 2012. "Economic Growth: Technical Progress, Population Dynamics and Sustainability," Rivista italiana degli economisti, Società editrice il Mulino, issue 1, pages 151-158.
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    4. 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.
    5. 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 157, Institute of Public Policy and Public Choice - POLIS.
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    Cited by:

    1. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2020. "Public Debt Dynamics under Ambiguity by Means of Iterated Function Systems on Density Functions," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202009, University of Turin.
    2. Simone Marsiglio & Privileggi, Fabio, 2020. "Three Dimensional Fractal Attractors in a Green Transition Economic Growth Model," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202019, University of Turin.
    3. La Torre, Davide & Marsiglio, Simone & Privileggi, Fabio, 2018. "Fractal Attractors in Economic Growth Models with Random Pollution Externalities," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201801, University of Turin.
    4. Torre, Davide La & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2019. "A stochastic economic growth model with health capital and state-dependent probabilities," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 81-93.
    5. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2016. "Fractal Attractors and Singular Invariant Measures in Two-Sector Growth Models with Random Factor Shares," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201620, University of Turin.

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