GLOBALLY INDETERMINATE GROWTH PATHS IN THE LUCAS MODEL OF ENDOGENOUS GROWTH. (4th April 2021)

• Record Type: Journal Article
• Authors: Bella, Giovanni; Mattana, Paolo; Venturi, Beatrice
• Is Part Of: Macroeconomic dynamics. Volume 25:Number 3(2021)
• Page Start: 693
• Page End: 704
• Publication Date: 2021-04-04
• Subjects: Lucas Model, -- Homoclinic Orbit to Real Saddle, -- Global Indeterminacy; Macroeconomics -- Periodicals; 339.05
• DOI: 10.1017/S1365100519000373
• Languages: English
• ISSNs: 1365-1005

Abstract

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.