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Self-Similar Measures in Multi-Sector Endogenous Growth Models

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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).

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  • 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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    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. 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.
    5. Davide La Torre & Simone Marsiglio & Fabio Privileggi, 2024. "Infectious diseases and social distancing under state-dependent probabilities," Annals of Operations Research, Springer, vol. 337(3), pages 993-1008, June.
    6. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2021. "Generalized Fractal Transforms with Condensation: a Macroeconomic-Epidemiological Application," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202107, University of Turin.
    7. 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.

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