Barnett, William and Ghosh, Taniya (2013): Bifurcation Analysis of an Endogenous Growth Model.

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Abstract
This paper analyzes the dynamics of a variant of Jones (2002) semiendogenous 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 codimension1 bifurcations (Hopf, Branch Point, Limit Point of Cycles, and Period Doubling) and codimension2 (BogdanovTakens 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.
Item Type:  MPRA Paper 

Original Title:  Bifurcation Analysis of an Endogenous Growth Model 
Language:  English 
Keywords:  bifurcation, endogenous growth, Jones growth model, Hopf, inference robustness, dynamics, stability. 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C53  Forecasting and Prediction Methods ; Simulation Methods C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62  Existence and Stability Conditions of Equilibrium C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63  Computational Techniques ; Simulation Modeling E  Macroeconomics and Monetary Economics > E1  General Aggregative Models 
Item ID:  50131 
Depositing User:  William A. Barnett 
Date Deposited:  24. Sep 2013 01:39 
Last Modified:  24. Sep 2013 02:03 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/50131 