Stability analysis of Uzawa-Lucas endogenous growth model
This paper analyzes, within its feasible parameter space, the dynamics of the Uzawa-Lucas endogenous growth model. The model is solved from a centralized social planner perspective as well as in the model’s decentralized market economy form. We examine the stability properties of both versions of the model and locate Hopf and transcritical bifurcation boundaries. In an extended analysis, we investigate the existence of Andronov-Hopf bifurcation, branch point bifurcation, limit point cycle bifurcation, and period doubling bifurcations. While these all are local bifurcations, the presence of global bifurcation is confirmed as well. We find evidence that the model could produce chaotic dynamics, but our analysis cannot confirm that conjecture. 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.
|Date of creation:||27 May 2013|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- William Barnett & Evgeniya Duzhak, 2010.
"Empirical assessment of bifurcation regions within New Keynesian models,"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 99-128, October.
- William Barnett & Evgeniya Aleksandrovna Duzhak, 2008. "Empirical Assessment of Bifurcation Regions within New Keynesian Models," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200811, University of Kansas, Department of Economics, revised Oct 2008.
- Barnett, William A. & Duzhak, Evgeniya A., 2008. "Empirical assessment of bifurcation regions within new Keynesian models," MPRA Paper 11249, University Library of Munich, Germany.
- Arnold, Lutz G., 2000. "Stability of the Market Equilibrium in Romer's Model of Endogenous Technological Change: A Complete Characterization," Journal of Macroeconomics, Elsevier, vol. 22(1), pages 69-84, January.
- Barnett, William A. & Eryilmaz, Unal, 2013. "Hopf bifurcation in the Clarida, Gali, and Gertler model," Economic Modelling, Elsevier, vol. 31(C), pages 401-404.
- Barnett, William A. & Eryilmaz, Unal, 2012. "Hopf bifurcation in the Clarida, Gali, and Gertler model," MPRA Paper 40668, University Library of Munich, Germany.
- William Barnett & Unal Eryilmaz, 2012. "Hopf Bifurcation in the Clarida, Gali, and Gertler Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201211, University of Kansas, Department of Economics, revised Sep 2012.
- Mondal, Debasis, 2008. "Stability analysis of the Grossman-Helpman model of endogenous product cycles," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 1302-1322, September.
- Barnett, William A. & He, Yijun, 2002. "Stabilization Policy As Bifurcation Selection: Would Stabilization Policy Work If The Economy Really Were Unstable?," Macroeconomic Dynamics, Cambridge University Press, vol. 6(05), pages 713-747, November. Full references (including those not matched with items on IDEAS)