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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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    4. 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.
    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. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    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. Maxime Menuet & Alexandru Minea & Patrick Villieu, 2019. "Endogenous fluctuations and the balanced-budget rule: taxes versus spending-based adjustment," Post-Print halshs-02315727, HAL.
    3. 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.
    4. Maxime Menuet & Alexandru Minea & Patrick Villieu, 2019. "The Peril of Fiscal Rules," Post-Print hal-02314996, HAL.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Franz Wirl, 2011. "Conditions for indeterminacy and thresholds in neoclassical growth models," Journal of Economics, Springer, vol. 102(3), pages 193-215, April.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Constantin Chilarescu, 2018. "The effect of externality on the transitional dynamics: the case of Lucas model," Economics Bulletin, AccessEcon, vol. 32767(3).
    17. Orlando Gomes, 2024. "The emergence of chaos in productivity distribution dynamics," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(2), pages 565-596, December.
    18. 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).
    19. 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.
    20. 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.
    21. 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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