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
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 estimates’ confidence region, robustness of dynamical inferences from policy simulations are compromised, when conducted, in the usual manner, only at the parameters’ 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
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8) Track citations by RSS feed
Downloads: (external link)
Journal Article: Bifurcation analysis of an endogenous growth model (2013)
Working Paper: Bifurcation Analysis of an Endogenous Growth Model (2013)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:kan:wpaper:201306
Access Statistics for this paper
More papers in WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics Contact information at EDIRC.
Bibliographic data for series maintained by Professor Zongwu Cai ().