IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v104y2017icp452-460.html
   My bibliography  Save this article

Homoclinic bifurcation and the Belyakov degeneracy in a variant of the Romer model of endogenous growth

Author

Listed:
  • Bella, Giovanni

Abstract

This paper explores the possibility of complex dynamics in a variant of the [29] model of endogenous growth. In particular, we derive the exact parametric configuration that allows for the emergence of a double-pulse homoclinic orbit, and the rise of globally indeterminate solutions, in the same area where local determinacy was found. Our results confirm that irregular patterns and oscillating solutions can be obtained along a subsidiary homoclinic orbit at which the periodic loop starts to double, so that the system might perpetually oscillate around the long run equilibrium, being thus confined in a stationary trapping region outside the neighborhood of the steady state. The economic implications of these results are finally discussed.

Suggested Citation

  • Bella, Giovanni, 2017. "Homoclinic bifurcation and the Belyakov degeneracy in a variant of the Romer model of endogenous growth," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 452-460.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:452-460
    DOI: 10.1016/j.chaos.2017.08.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917303569
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.08.025?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Bella, Giovanni & Mattana, Paolo, 2014. "Global indeterminacy of the equilibrium in the Chamley model of endogenous growth in the vicinity of a Bogdanov–Takens bifurcation," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 69-79.
    2. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
    3. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
    4. Slobodyan, Sergey, 2007. "Indeterminacy and stability in a modified Romer model," Journal of Macroeconomics, Elsevier, vol. 29(1), pages 169-177, March.
    5. Jess Benhabib & Qinglai Meng & Kazuo Nishimura, 2012. "Indeterminacy Under Constant Returns to Scale in Multisector Economies," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 403-412, Springer.
    6. Boldrin, Michele & Nishimura, Kazuo & Shigoka, Tadashi & Yano, Makoto, 2001. "Chaotic Equilibrium Dynamics in Endogenous Growth Models," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 97-132, January.
    7. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    8. Mitra, Tapan & Nishimura, Kazuo, 2001. "Discounting and Long-Run Behavior: Global Bifurcation Analysis of a Family of Dynamical Systems," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 256-293, January.
    9. Paolo Mattana & Kazuo Nishimura & Tadashi Shigoka, 2012. "Homoclinic Bifurcation and Global Indeterminacy of Equilibrium in a Two-Sector Endogenous Growth Model," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 427-451, Springer.
    10. Jess Benhabib & Stephanie Schmitt-Grohé & Martín Uribe, 2002. "Chaotic Interest-Rate Rules," American Economic Review, American Economic Association, vol. 92(2), pages 72-78, May.
    11. Kiminori Matsuyama, 1999. "Growing Through Cycles," Econometrica, Econometric Society, vol. 67(2), pages 335-348, March.
    12. Brito, Paulo & Venditti, Alain, 2010. "Local and global indeterminacy in two-sector models of endogenous growth," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 893-911, September.
    13. Matsuyama, Kiminori, 2001. "Growing through Cycles in an Infinitely Lived Agent Economy," Journal of Economic Theory, Elsevier, vol. 100(2), pages 220-234, October.
    14. 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.
    15. Benhabib, Jess & Farmer, Roger E. A., 1996. "Indeterminacy and sector-specific externalities," Journal of Monetary Economics, Elsevier, vol. 37(3), pages 421-443, June.
    16. Angelo Antoci & Marcello Galeotti & Paolo Russu, 2014. "Global analysis and indeterminacy in a two-sector growth model with human capital," International Journal of Economic Theory, The International Society for Economic Theory, vol. 10(4), pages 313-338, December.
    17. Jess Benhabib & Kazuo Nishimura & Tadashi Shigoka, 2008. "Bifurcation and sunspots in the continuous time equilibrium model with capacity utilization," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(2), pages 337-355, June.
    18. Gardini, Laura & Sushko, Iryna & Naimzada, Ahmad K., 2008. "Growing through chaotic intervals," Journal of Economic Theory, Elsevier, vol. 143(1), pages 541-557, November.
    19. Feng, Jingjing & Zhang, Qichang & Wang, Wei, 2012. "Chaos of several typical asymmetric systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 950-958.
    20. Khan, M. Ali & Mitra, Tapan, 2005. "On topological chaos in the Robinson-Solow-Srinivasan model," Economics Letters, Elsevier, vol. 88(1), pages 127-133, July.
    21. Benhabib, Jess & Perli, Roberto & Xie, Danyang, 1994. "Monopolistic competition, indeterminacy and growth," MPRA Paper 37411, University Library of Munich, Germany, revised 1994.
    22. Mitra, Tapan, 2001. "A Sufficient Condition for Topological Chaos with an Application to a Model of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 133-152, January.
    23. Nishimura, Kazuo & Sorger, Gerhard & Yano, Makoto, 1994. "Ergodic Chaos in Optimal Growth Models with Low Discount Rates," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(5), pages 705-717, August.
    24. Mitra, Tapan & Nishimura, Kazuo, 2001. "Introduction to Intertemporal Equilibrium Theory: Indeterminacy, Bifurcations, and Stability," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 1-12, January.
    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. Alexeeva, Tatyana A. & Kuznetsov, Nikolay V. & Mokaev, Timur N., 2021. "Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

    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. Bella, Giovanni & Mattana, Paolo & Venturi, Beatrice, 2017. "Shilnikov chaos in the Lucas model of endogenous growth," Journal of Economic Theory, Elsevier, vol. 172(C), pages 451-477.
    2. Bella, Giovanni & Mattana, Paolo, 2014. "Global indeterminacy of the equilibrium in the Chamley model of endogenous growth in the vicinity of a Bogdanov–Takens bifurcation," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 69-79.
    3. Orlando Gomes, 2007. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing, vol. 33(6), pages 437-468, January.
    4. Orlando Gomes, 2006. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing, vol. 33(6), pages 437-468, November.
    5. Orlando Gomes, 2006. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing Limited, vol. 33(6), pages 437-468, November.
    6. Tarek Coury & Yi Wen, 2009. "Global indeterminacy in locally determinate real business cycle models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 49-60, March.
    7. Angelo Antoci & Marcello Galeotti & Paolo Russu, 2014. "Global analysis and indeterminacy in a two-sector growth model with human capital," International Journal of Economic Theory, The International Society for Economic Theory, vol. 10(4), pages 313-338, December.
    8. repec:ipg:wpaper:2014-461 is not listed on IDEAS
    9. Rangan Gupta & Lardo Stander, 2014. "Endogenous Fluctuations in an Endogenous Growth Model with Inflation Targeting," Working Papers 201432, University of Pretoria, Department of Economics.
    10. Orlando Gomes, 2006. "Local Bifurcations and Global Dynamics in a Solow-type Endogenous Business Cycles Model," Annals of Economics and Finance, Society for AEF, vol. 7(1), pages 91-127, May.
    11. Park, Hyun, 2020. "Indeterminate equilibrium growth with product and R&D spillovers," Economic Modelling, Elsevier, vol. 86(C), pages 286-298.
    12. Tarek Coury & Yi Wen, 2007. "Global indeterminacy in locally determinate RBC models," Working Papers 2007-029, Federal Reserve Bank of St. Louis.
    13. Gupta, Rangan & Stander, Lardo, 2018. "Endogenous fluctuations in an endogenous growth model: An analysis of inflation targeting as a policy," The Quarterly Review of Economics and Finance, Elsevier, vol. 69(C), pages 1-8.
    14. Maxime Menuet & Alexandru Minea & Patrick Villieu, 2019. "Endogenous fluctuations and the balanced-budget rule: taxes versus spending-based adjustment," Post-Print halshs-02318369, HAL.
    15. Asano, Takao & Yokoo, Masanori, 2019. "Chaotic dynamics of a piecewise linear model of credit cycles," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 9-21.
    16. Deng, Liuchun & Khan, M. Ali, 2018. "On growing through cycles: Matsuyama’s M-map and Li–Yorke chaos," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 46-55.
    17. Carboni, Oliviero A. & Russu, Paolo, 2013. "Linear production function, externalities and indeterminacy in a capital-resource growth model," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 422-428.
    18. Maxime Menuet & Alexandru Minea & Patrick Villieu, 2019. "The Peril of Fiscal Rules," Post-Print hal-02314996, HAL.
    19. Maxime MENUET & Alexandru MINEA & Patrick VILLIEU, 2017. "Public Debt, Endogenous Growth Cycles and Indeterminacy," LEO Working Papers / DR LEO 2467, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    20. Schaal, Edouard & Taschereau-Dumouchel, Mathieu, 2023. "Herding through booms and busts," Journal of Economic Theory, Elsevier, vol. 210(C).
    21. Gomes, Orlando, 2015. "Optimal resource allocation in a representative investor economy," Economic Modelling, Elsevier, vol. 50(C), pages 72-84.

    More about this item

    Keywords

    Romer model; Belyakov point degeneracy; Double-pulse homoclinic orbit; Global indeterminacy;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

    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:104:y:2017:i:c:p:452-460. 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.