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Three Dimensional Fractal Attractors in a Green Transition Economic Growth Model

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We analyze a two-sector stochastic economic growth model of green transition with pollution externalities and foreign capital. The final good is produced by combining dirty and clean inputs, with different implications on pollution accumulation. Pollution negatively affects production capabilities and can be reduced by switching to the clean input. The clean input is produced by using the dirty input and the foreign capital received (in the form of dirty input). Random shocks make the effective economy’s ability to transition to green activities highly uncertain, eventually undermining its economic development. Such a setting gives rise to a dynamic system represented by a three dimensional affine iterated function system. We show that the economy’s steady state is represented by an invariant measure supported on a compact set, characterizing its fractal nature and showing that its attractor may be a distorted Sierpi´nski tetrahedron.

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  • 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.
    • Handle: RePEc:uto:dipeco:202019
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    1. Mitra, Tapan & Privileggi, Fabio, 2006. "Cantor type attractors in stochastic growth models," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 626-637.
    2. Hicks, Robert L. & Parks, Bradley C. & Roberts, J. Timmons & Tierney, Michael J., 2010. "Greening Aid?: Understanding the Environmental Impact of Development Assistance," OUP Catalogue, Oxford University Press, number 9780199582792.
    3. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    4. 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.
    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.
    6. Tapan Mitra & Luigi Montrucchio & Fabio Privileggi, 2003. "The nature of the steady state in models of optimal growth under uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 39-71, December.
    7. Niu, M. & Xi, L.-F., 2007. "Singularity of a class of self-similar measures," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 376-382.
    8. Kazuo Nishimura & Makoto Yano, 2012. "Non-linear Dynamics and Chaos in Optimal Growth: An Example," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 127-150, Springer.
    9. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2015. "Self-similar measures in multi-sector endogenous growth models," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 40-56.
    10. 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.
    11. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    12. L. Montrucchio & F. Privileggi, 1999. "Fractal steady states instochastic optimal control models," Annals of Operations Research, Springer, vol. 88(0), pages 183-197, January.
    13. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
    14. 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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