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Existence and implications of a pitchfork-Hopf bifurcation in a continuous-time two-sector growth model

Author

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  • Giovanni Bella

    (University of Cagliari)

  • Paolo Mattana

    (University of Cagliari)

  • Beatrice Venturi

    (University of Cagliari)

Abstract

This paper shows that the dynamics of the Lucas (J Monet Econ, 22:3–42, 1988) endogenous growth model with flow externalities may give rise to a 2-torus, a compact three-dimensional manifold enclosed by a two-dimensional surface. The implications of this result are relevant for many fields of economic theory. It is first of all clear that if we choose to initialize the dynamics in the basin of attraction of this trapping region, a continuum of perfect foresight solutions may be observed. A simple econometric exercise, linking the physical-to-human capital ratio (state variable) to the 5-years forward variance of the growth rate of an unbalanced sample of 183 countries, seems to provide empirical backing for the phenomenon. Other important consequences, relevant from the point of view of endogenous cycles theory, are also scrutinized in the paper.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jeicoo:v:17:y:2022:i:1:d:10.1007_s11403-021-00331-8
    DOI: 10.1007/s11403-021-00331-8
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    References listed on IDEAS

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    Cited by:

    1. Marco Desogus & Beatrice Venturi, 2023. "Stability and Bifurcations in Banks and Small Enterprises—A Three-Dimensional Continuous-Time Dynamical System," JRFM, MDPI, vol. 16(3), pages 1-20, March.

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    More about this item

    Keywords

    2-tori dynamics; Global indeterminacy; Endogenous oscillations; Basins of attraction;
    All these keywords.

    JEL classification:

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

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