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GLOBALLY INDETERMINATE GROWTH PATHS IN THE LUCAS MODEL OF ENDOGENOUS GROWTH

Published online by Cambridge University Press:  04 September 2019

Giovanni Bella ,
Paolo Mattana  and
Beatrice Venturi
Giovanni Bella*
Affiliation:
University of Cagliari
Paolo Mattana
Affiliation:
University of Cagliari
Beatrice Venturi
Affiliation:
University of Cagliari
*
Address correspondence to: Giovanni Bella, Department of Economics and Business, University of Cagliari, Via S. Ignazio 17, 09123 Cagliari (Italy). e-mail: [email protected]. Phone: +390706753340. Fax: +39070660929.
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Abstract

This paper shows that global indeterminacy may characterize the three-dimensional vector field implied by the Lucas [(1988) Journal of Monetary Economics 22, 3–42] endogenous growth model. To achieve this result, we demonstrate the emergence of a family of homoclinic orbits connecting the steady state to itself in backward and forward time, when the stable and unstable manifolds are locally governed by real eigenvalues. In this situation, we prove that if the saddle quantity is negative, and other genericity conditions are fulfilled, a stable limit cycle bifurcates from the homoclinic orbit. Orbits originating in a tubular neighborhood of the homoclinic orbit are then bound to converge to this limit cycle, creating the conditions for the onset of global indeterminacy. Some economic intuitions related to this phenomenon are finally explored.

Keywords

Lucas ModelHomoclinic Orbit to Real SaddleGlobal Indeterminacy
Type
Articles
Information
Macroeconomic Dynamics , Volume 25 , Issue 3 , April 2021 , pp. 693 - 704
Copyright
© Cambridge University Press 2019

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