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Shilnikov chaos in the Lucas model of endogenous growth

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  • Bella, Giovanni
  • Mattana, Paolo
  • Venturi, Beatrice

Abstract

This paper shows that chaotic dynamics and global indeterminacy may characterize the Lucas (1988) endogenous growth model in its local determinacy region of the parameter space. This is achieved by means of the Shilnikov (1965) theorem, which exploits the existence of a family of homoclinic orbits doubly asymptotic to the balanced growth path, when it is a saddle-focus. The economic implications of these results are also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jetheo:v:172:y:2017:i:c:p:451-477
    DOI: 10.1016/j.jet.2017.09.010
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    Cited by:

    1. Constantin Chilarescu, 2018. "The effect of externality on the transitional dynamics: the case of Lucas model," Economics Bulletin, AccessEcon, vol. 32767(3).
    2. Barnett, William A. & Bella, Giovanni & Ghosh, Taniya & Mattana, Paolo & Venturi, Beatrice, 2022. "Shilnikov chaos, low interest rates, and New Keynesian macroeconomics," Journal of Economic Dynamics and Control, Elsevier, vol. 134(C).
    3. Bella, Giovanni & Mattana, Paolo, 2020. "Chaos control in presence of financial bubbles," Economics Letters, Elsevier, vol. 193(C).
    4. Chatelain, Jean-Bernard & Ralf, Kirsten, 2022. "Ramsey Optimal Policy In The New-Keynesian Model With Public Debt," Macroeconomic Dynamics, Cambridge University Press, vol. 26(6), pages 1588-1614, September.
    5. Barnett, William & Bella, Giovanni & Ghosh, Taniya & Mattana, Paolo & Venturi, Beatrice, 2021. "Chaos in the UK New Keynesian Macroeconomy," MPRA Paper 109820, University Library of Munich, Germany.
    6. Antoci, Angelo & Borghesi, Simone & Galeotti, Marcello & Sodini, Mauro, 2021. "Living in an uncertain world: Environment substitution, local and global indeterminacy," Journal of Economic Dynamics and Control, Elsevier, vol. 126(C).
    7. 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).
    8. Barnett, William A. & Bella, Giovanni & Ghosh, Taniya & Mattana, Paolo & Venturi, Beatrice, 2022. "Is policy causing chaos in the United Kingdom?," Economic Modelling, Elsevier, vol. 108(C).
    9. Barnett William A. & Bella Giovanni & Mattana Paolo & Venturi Beatrice & Ghosh Taniya, 2023. "Controlling chaos in New Keynesian macroeconomics," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 27(2), pages 219-236, April.
    10. 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).
    11. Kei Hosoya, 2024. "Endogenous time preference and infrastructure-led growth with an unexpected numerical example," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 23(1), pages 3-32, January.

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    More about this item

    Keywords

    Lucas model; Shilnikov chaos; Global indeterminacy; History versus expectations;
    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

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