IDEAS home Printed from https://ideas.repec.org/p/uto/dipeco/201620.html
   My bibliography  Save this paper

Fractal Attractors and Singular Invariant Measures in Two-Sector Growth Models with Random Factor Shares

Author

Listed:

Abstract

We analyze a multi-sector growth model subject to random shocks affecting the two sector-specific production functions twofold: the evolution of both productivity and factor shares is the result of such exogenous shocks. We determine the optimal dynamics via Euler-Lagrange equations, and show how these dynamics can be described in terms of an iterated function system with probability. We also provide conditions that imply the singularity of the invariant measure associated with the fractal attractor. Numerical examples show how specific parameter configurations might generate distorted copies of the Barnsley’s fern attractor.

Suggested Citation

  • 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.
    • Handle: RePEc:uto:dipeco:201620
    as

    Download full text from publisher

    File URL: http://www.est.unito.it/do/home.pl/Download?doc=/allegati/wp2016dip/wp_20_2016.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mitra, Tapan & Privileggi, Fabio, 2006. "Cantor type attractors in stochastic growth models," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 626-637.
    2. Growiec, Jakub & McAdam, Peter & Mućk, Jakub, 2018. "Endogenous labor share cycles: Theory and evidence," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 74-93.
    3. Leonard J. Mirman & Kevin Reffett & Marc Santugini, 2016. "On learning and growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(4), pages 641-684, April.
    4. 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.
    5. 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.
    6. Simone Marsiglio & Alberto Ansuategi & Maria Carmen Gallastegui, 2016. "The Environmental Kuznets Curve and the Structural Change Hypothesis," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 63(2), pages 265-288, February.
    7. Dirk Bethmann, 2013. "Solving Macroeconomic Models with Homogeneous Technology and Logarithmic Preferences," Australian Economic Papers, Wiley Blackwell, vol. 52(1), pages 1-18, March.
    8. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
    9. 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.
    10. Fabio Privileggi, 1995. "A characterization for solutions of stochastic discrete time optimization models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 18(2), pages 165-180, September.
    11. Stephen Nickell & Stephen Redding & Joanna Swaffield, 2008. "The Uneven Pace of Deindustrialisation in the OECD," The World Economy, Wiley Blackwell, vol. 31(9), pages 1154-1184, 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. Dirk Bethmann, 2007. "A Closed-form Solution of the Uzawa-Lucas Model of Endogenous Growth," Journal of Economics, Springer, vol. 90(1), pages 87-107, January.
    14. 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.
    15. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    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 & 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. 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. Guido Cozzi & Fabio Privileggi, 2009. "The fractal nature of inequality in a fast growing world: new version," Working Papers 2009_30, Business School - Economics, University of Glasgow.
    8. La Torre, Davide & Marsiglio,Simone & Mendivil, Franklin & Privileggi, Fabio, 2023. "Stochastic Optimal Growth through State-Dependent Probabilities," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202312, University of Turin.
    9. Mitra, Tapan & Privileggi, Fabio, 2006. "Cantor type attractors in stochastic growth models," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 626-637.
    10. 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.
    11. Lars J. Olson & Santanu Roy, 2006. "Theory of Stochastic Optimal Economic Growth," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 11, pages 297-335, Springer.
    12. 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.
    13. Shilei Wang, 2015. "The Iterative Nature of a Class of Economic Dynamics," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 9(3), pages 155-168, December.
    14. Davide Torre & Simone Marsiglio & Franklin Mendivil & Fabio Privileggi, 2024. "Stochastic disease spreading and containment policies under state-dependent probabilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 127-168, February.
    15. 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.
    16. Tomoo Kikuchi & George Vachadze, 2018. "Minimum investment requirement, financial market imperfection and self-fulfilling belief," Journal of Evolutionary Economics, Springer, vol. 28(2), pages 305-332, April.
    17. Guido Cozzi & Fabio Privileggi, 2007. "The Fractal Nature of Inequality in a Fast Growing World," Working Papers 2007_45, Business School - Economics, University of Glasgow.
    18. Simone Marsiglio & Fabio Privileggi, 2021. "On the economic growth and environmental trade-off: a multi-objective analysis," Annals of Operations Research, Springer, vol. 296(1), pages 263-289, January.
    19. Stefano Bosi & Carmen Camacho & Thai Ha-Huy, 2023. "On the uniqueness of the optimal path in a discrete-time model à la Lucas (1988)," PSE Working Papers halshs-03920386, HAL.
    20. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:uto:dipeco:201620. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Piero Cavaleri or Marina Grazioli (email available below). General contact details of provider: https://edirc.repec.org/data/detorit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.