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Homoclinic Bifurcation and Global Indeterminacy of Equilibrium in a Two-Sector Endogenous Growth Model

In: Nonlinear Dynamics in Equilibrium Models

Author

Listed:
  • Paolo Mattana

    (University of Cagliari)

  • Kazuo Nishimura

    (Kyoto University)

  • Tadashi Shigoka

    (Kyoto University)

Abstract

If for a given endogenous growth model, there exists a continuum of equilibria in a small neighborhood of a balanced growth path (BGP) that continues to stay in this neighborhood, it is said that equilibrium is locally indeterminate. Here a small neighborhood of a BGP means the region in which results based on linear approximations of equilibrium dynamics on the BGP are qualitatively valid.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:sprchp:978-3-642-22397-6_18
    DOI: 10.1007/978-3-642-22397-6_18
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    References listed on IDEAS

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    1. Benhabib, Jess & Schmitt-Grohe, Stephanie & Uribe, Martin, 2001. "The Perils of Taylor Rules," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 40-69, January.
    2. 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.
    3. 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.
    4. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    5. Grandmont, Jean-Michel, 2008. "Nonlinear difference equations, bifurcations and chaos: An introduction," Research in Economics, Elsevier, vol. 62(3), pages 122-177, September.
    6. Chamley, Christophe, 1993. "Externalities and Dynamics in Models of "Learning or Doing."," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(3), pages 583-609, August.
    7. 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.
    8. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
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    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. Maxime Menuet & Alexandru Minea & Patrick Villieu, 2019. "Endogenous fluctuations and the balanced-budget rule: taxes versus spending-based adjustment," Post-Print halshs-02315727, HAL.
    4. 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.
    5. Maxime Menuet & Alexandru Minea & Patrick Villieu, 2019. "The Peril of Fiscal Rules," Post-Print hal-02314996, HAL.
    6. 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.
    7. 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.
    8. Kenji Sato & Makoto Yano, 2013. "Optimal ergodic chaos under slow capital depreciation," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 57-67, March.
    9. Zhiming Fu & Antoine Le Riche, 2022. "Public spending, monetary policy and macroeconomic instability," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(3), pages 580-608, June.
    10. Nishimura Kazuo & Shigoka Tadashi, 2019. "Hopf bifurcation and the existence and stability of closed orbits in three-sector models of optimal endogenous growth," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(4), pages 1-21, September.
    11. Antoci, Angelo & Borghesi, Simone & Galeotti, Marcello & Russu, Paolo, 2022. "Maladaptation to environmental degradation and the interplay between negative and positive externalities," European Economic Review, Elsevier, vol. 143(C).
    12. 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.
    13. Franz Wirl, 2011. "Conditions for indeterminacy and thresholds in neoclassical growth models," Journal of Economics, Springer, vol. 102(3), pages 193-215, April.
    14. Giovanni Bella & Paolo Mattana, 2018. "Global indeterminacy and equilibrium selection in a model with depletion of non-renewable resources," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 187-202, November.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

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