Global analysis and indeterminacy of atwo sector endougenous growth model

BELLA, GIOVANNI;MATTANA, PAOLO;VENTURI, BEATRICE

2014-01-01

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Abstract

In this paper we prove analytically the existence of a homoclinic orbit in a well known modified version of Romer's model, ( see Slobodyan S., 2006) a system with a single equilibrium point, and there the existence of chaos. More in detail, by the undetermined coefficient method, we analytically demonstrate that there exists a homoclinic orbit of a Shilnikov type that connects the single equilibrium point (see, Shang D., Han M., 2005). Furthermore, on the basis of the Shilnikov Theorem assumptions, we find that Smale horseshoe occurs both theoretically and numerically. The economic implications of this analysis are finally discussed. (see also Mattana P. and Venturi B., 1999; D. Fiaschi and S. Sordi , 2002; De Cesare L. and Sportelli M., 2005; Cai J., 2005; Neri U. and Venturi B., 2007; Bella G., Mattana P., Venturi B., 2013). The nature of the growth paths in this chaotic regime might depend on the initial conditions, and looked noisy, like the simple function of a stochastic process. Finally, chaos has interesting implications for the rational expectations. If the economy happens to be in the chaotic regime, then, even if economic agents know perfectly how the economy functions, they are unable to predict its complete behavior. Keywords: Endogenous Growth, Optimality condition, Homoclinic orbits, Shilnikov Theorem.