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

Giovanni Bella (), Paolo Mattana () and Beatrice Venturi ()
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Giovanni Bella: University of Cagliari
Paolo Mattana: University of Cagliari
Beatrice Venturi: University of Cagliari

Journal of Economic Interaction and Coordination, 2022, vol. 17, issue 1, No 13, 259-285

Abstract: 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.

Keywords: 2-tori dynamics; Global indeterminacy; Endogenous oscillations; Basins of attraction (search for similar items in EconPapers)
JEL-codes: C62 E32 O41 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11403-021-00331-8

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