IDEAS home Printed from https://ideas.repec.org/a/bla/ijethy/v2y2006i3-4p199-216.html
   My bibliography  Save this article

Sunspots and Hopf bifurcations in continuous time endogenous growth models

Author

Listed:
  • Kazuo Nishimura
  • Tadashi Shigoka

Abstract

First we treat a three‐dimensional continuous time abstract stationary model that includes one predetermined variable and two non‐predetermined variables. We construct stationary sunspot equilibria in this model under the following two alternative conditions: (i) a steady state has two stable roots and one unstable root; and (ii) A closed orbit has a two‐dimensional manifold on which it is asymptotically stable. Next, we apply these results to the models due to Lucas and Romer that undergo Hopf bifurcations for some parameter values. We construct sunspot equilibria in these models.

Suggested Citation

  • Kazuo Nishimura & Tadashi Shigoka, 2006. "Sunspots and Hopf bifurcations in continuous time endogenous growth models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 2(3‐4), pages 199-216, September.
    • Handle: RePEc:bla:ijethy:v:2:y:2006:i:3-4:p:199-216
    DOI: 10.1111/j.1742-7363.2006.0033.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1742-7363.2006.0033.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1742-7363.2006.0033.x?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. 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. Constantin Chilarescu, 2018. "The effect of externality on the transitional dynamics: the case of Lucas model," Economics Bulletin, AccessEcon, vol. 32767(3).
    3. 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.
    4. Mauro Bambi & Alain Venditti, 2021. "Time‐varying consumption tax, productive government spending, and aggregate instability," International Journal of Economic Theory, The International Society for Economic Theory, vol. 17(2), pages 190-215, June.
    5. Pedro Rui Mazeda Gil, 2009. "Animal Spirits and the Composition of Innovation in a Lab-Equipment R&D Model," FEP Working Papers 336, Universidade do Porto, Faculdade de Economia do Porto.
    6. Pedro Gil, 2013. "Animal spirits and the composition of innovation in a lab-equipment R&D model with transition," Journal of Economics, Springer, vol. 108(1), pages 1-33, January.
    7. Giovanni Bella & Paolo Mattana & Beatrice Venturi, 2022. "Existence and implications of a pitchfork-Hopf bifurcation in a continuous-time two-sector growth model," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 259-285, January.
    8. Pedro de Mendonça, 2013. "Nonlinear Phenomena in a Growing Economy with Convex Adjustment Costs," EERI Research Paper Series EERI RP 2013/05, Economics and Econometrics Research Institute (EERI), Brussels.
    9. 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.

    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. 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.
    2. Maxime Menuet & Alexandru Minea & Patrick Villieu, 2019. "The Peril of Fiscal Rules," Post-Print hal-02314996, HAL.
    3. 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.
    4. 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.
    5. Franz Wirl, 2011. "Conditions for indeterminacy and thresholds in neoclassical growth models," Journal of Economics, Springer, vol. 102(3), pages 193-215, April.
    6. Mauro Bambi & Alain Venditti, 2021. "Time‐varying consumption tax, productive government spending, and aggregate instability," International Journal of Economic Theory, The International Society for Economic Theory, vol. 17(2), pages 190-215, June.
    7. Giovanni Bella & Paolo Mattana & Beatrice Venturi, 2013. "Kaldorian assumptions and endogenous fluctuations: a note on Schinasi’s IS–LM model," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 60(1), pages 71-81, March.
    8. 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.
    9. Savagar, Anthony & Dixon, Huw, 2020. "Firm entry, excess capacity and endogenous productivity," European Economic Review, Elsevier, vol. 121(C).
    10. 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.
    11. Antoci, Angelo & Galeotti, Marcello & Russu, Paolo, 2011. "Poverty trap and global indeterminacy in a growth model with open-access natural resources," Journal of Economic Theory, Elsevier, vol. 146(2), pages 569-591, March.
    12. Fu, Wentao & Le Riche, Antoine, 2021. "Endogenous growth model with Bayesian learning and technology selection," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 58-71.
    13. 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.
    14. 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.

    More about this item

    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:bla:ijethy:v:2:y:2006:i:3-4:p:199-216. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=1742-7355 .

    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.