[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v129y2019icp81-93.html
   My bibliography  Save this article

A stochastic economic growth model with health capital and state-dependent probabilities

Author

Listed:
  • Torre, Davide La
  • Marsiglio, Simone
  • Mendivil, Franklin
  • Privileggi, Fabio
Abstract
We analyze a simple stochastic model of economic growth in which physical and health capital accumulation jointly contribute to determine long run economic growth. Health capital is subject to random shocks via the effects of behavioral changes: unpredictable changes in individuals’ attitude toward healthy behaviors may reduce the effectiveness of health services provision; this in turn, by reducing the production of new health capital, lowers economic production activities negatively affecting economic growth. Unlike the extant literature, we assume that the probability with which such random shocks occur is not constant but state-dependent. Specifically, the probability that behavioral changes will negatively impact on health capital and economic growth depends on the level of economic development, proxied by the relative abundance of health capital with respect to physical capital. We show that our model’s dynamics can be converted into an iterated function system with state-dependent probabilities which converges to an invariant self-similar measure supported on a (possibly fractal) compact attractor. We develop a numerical method to approximate the invariant distribution to illustrate its features in specific model’s parametrizations, exemplifying thus the effects of state-dependent probabilities on the model’s steady state.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:129:y:2019:i:c:p:81-93
    DOI: 10.1016/j.chaos.2019.08.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919303212
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.08.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    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. Boucekkine Raouf & Ruiz Tamarit Ramon, 2004. "Imbalance Effects in the Lucas Model: an Analytical Exploration," The B.E. Journal of Macroeconomics, De Gruyter, vol. 4(1), pages 1-19, December.
    3. Tai, Meng-Yi & Chao, Chi-Chur & Hu, Shih-Wen, 2015. "Pollution, health and economic growth," The North American Journal of Economics and Finance, Elsevier, vol. 32(C), pages 155-161.
    4. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    5. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(3), pages 739-773.
    6. North, Douglass C, 1994. "Economic Performance through Time," American Economic Review, American Economic Association, vol. 84(3), pages 359-368, June.
    7. Philippe Aghion & Peter Howitt & Fabrice Murtin, 2011. "The Relationship Between Health and Growth: When Lucas Meets Nelson-Phelps," Review of Economics and Institutions, Università di Perugia, vol. 2(1).
    8. 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.
    9. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    10. Ron Martin & Peter Sunley, 2006. "Path dependence and regional economic evolution," Journal of Economic Geography, Oxford University Press, vol. 6(4), pages 395-437, August.
    11. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
    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. Robert J. Barro, 2013. "Health and Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 14(2), pages 329-366, November.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. L. Montrucchio & F. Privileggi, 1999. "Fractal steady states instochastic optimal control models," Annals of Operations Research, Springer, vol. 88(0), pages 183-197, January.
    20. van Zon, Adriaan & Muysken, Joan, 2001. "Health and endogenous growth," Journal of Health Economics, Elsevier, vol. 20(2), pages 169-185, March.
    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. Fernandes, Leonardo H.S. & Silva, José W.L. & de Araujo, Fernando H.A., 2022. "Multifractal risk measures by Macroeconophysics perspective: The case of Brazilian inflation dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. 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.
    3. 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.
    4. 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.

    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, 2021. "Generalized Fractal Transforms with Condensation: a Macroeconomic-Epidemiological Application," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202107, University of Turin.
    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. 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. 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.
    6. 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.
    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 & 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.
    9. 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.
    10. Bloom, David E. & Canning, David & Kotschy, Rainer & Prettner, Klaus & Schünemann, Johannes, 2024. "Health and economic growth: Reconciling the micro and macro evidence," World Development, Elsevier, vol. 178(C).
    11. Matthias Firgo & Peter Mayerhofer, 2015. "Wissensintensive Unternehmensdienste, Wissens-Spillovers und regionales Wachstum. Teilprojekt 1: Wissens-Spillovers und regionale Entwicklung – Welche strukturpolitische Ausrichtung optimiert das Wach," WIFO Studies, WIFO, number 58342.
    12. Mitra, Tapan & Privileggi, Fabio, 2006. "Cantor type attractors in stochastic growth models," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 626-637.
    13. Klaus Reiner Schenk-Hopp�, "undated". "Random Dynamical Systems in Economics," IEW - Working Papers 067, Institute for Empirical Research in Economics - University of Zurich.
    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. Marcus Berliant & Ping Wang, 2005. "Dynamic Urban Models: Agglomeration and Growth," Contributions to Economic Analysis, in: Urban Dynamics and Growth: Advances in Urban Economics, pages 533-581, Emerald Group Publishing Limited.
    16. Kamihigashi, Takashi, 2007. "Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 477-500, April.
    17. 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.
    18. Thomas Ejdemo & Daniel Örtqvist, 2021. "Exploring a leading and lagging regions dichotomy: does entrepreneurship and diversity explain it?," Journal of Innovation and Entrepreneurship, Springer, vol. 10(1), pages 1-26, December.
    19. 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.
    20. Churchill, Sefa Awawoyi & Yew, Siew Ling & Ugur, Mehmet, 2015. "Effects of government education and health expenditures on economic growth: a meta-analysis," Greenwich Papers in Political Economy 14072, University of Greenwich, Greenwich Political Economy Research Centre.

    More about this item

    Keywords

    Health capital; Iterated function systems; State-dependent probabilities; Foias operator;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

    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:eee:chsofr:v:129:y:2019:i:c:p:81-93. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.