Bifurcation Analysis of an Endogenous Growth Model

William Barnett and Taniya Ghosh

No 201306, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics

Abstract: This paper analyzes the dynamics of a variant of Jones (2002) semi-endogenous growth model within the feasible parameter space. We derive the long run growth rate of the economy and do a detailed bifurcation analysis of the equilibrium. We show the existence of codimension-1 bifurcations (Hopf, Branch Point, Limit Point of Cycles, and Period Doubling) and codimension-2 (Bogdanov-Takens and Generalized Hopf) bifurcations within the feasible parameter range of the model. It is important to recognize that bifurcation boundaries do not necessarily separate stable from unstable solution domains. Bifurcation boundaries can separate one kind of unstable dynamics domain from another kind of unstable dynamics domain, or one kind of stable dynamics domain from another kind (called soft bifurcation), such as bifurcation from monotonic stability to damped periodic stability or from damped periodic to damped multiperiodic stability. There are not only an infinite number of kinds of unstable dynamics, some very close to stability in appearance, but also an infinite number of kinds of stable dynamics. Hence subjective prior views on whether the economy is or is not stable provide little guidance without mathematical analysis of model dynamics. When a bifurcation boundary crosses the parameter estimatesí confidence region, robustness of dynamical inferences from policy simulations are compromised, when conducted, in the usual manner, only at the parametersí point estimates.

Keywords: bifurcation; endogenous growth; Jones growth model; Hopf; inference robustness; dynamics; stability. (search for similar items in EconPapers)
Pages: 22 pages
Date: 2013-10, Revised 2013-10
New Economics Papers: this item is included in nep-dge
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Citations: View citations in EconPapers (8)

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Related works:
Journal Article: Bifurcation analysis of an endogenous growth model (2013)
Working Paper: Bifurcation Analysis of an Endogenous Growth Model (2013)
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