Advanced Search
MyIDEAS: Login to save this paper or follow this series

Stability Analysis of Uzawa-Lucas Endogenous Growth Model

Contents:

Author Info

  • William Barnett

    (Department of Economics, The University of Kansas)

  • Taniya Ghosh

    (Indira Gandhi Institute of Development Research, Reserve Bank of India, Mumbai)

Abstract

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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www2.ku.edu/~kuwpaper/2009Papers/201304.pdf
Download Restriction: no

Bibliographic Info

Paper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 201304.

as in new window
Length: 26 pages
Date of creation: May 2013
Date of revision: May 2013
Handle: RePEc:kan:wpaper:201304

Contact details of provider:
Postal: 415 Snow Hall, Lawrence, KS 66045
Phone: (785) 864-3501
Fax: (785) 864-5270
Email:
Web page: http://www2.ku.edu/~kuwpaper/
More information through EDIRC

Related research

Keywords: bifurcation; endogenous growth; Lucas-Uzawa model; Hopf; inference robustness; dynamics; stability.;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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.:
as in new window
  1. William Barnett & Unal Eryilmaz, 2012. "Hopf Bifurcation in the Clarida, Gali, and Gertler Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS, University of Kansas, Department of Economics 201211, University of Kansas, Department of Economics, revised Sep 2012.
  2. William Barnett & Evgeniya Duzhak, 2010. "Empirical assessment of bifurcation regions within New Keynesian models," Economic Theory, Springer, Springer, vol. 45(1), pages 99-128, October.
  3. Mondal, Debasis, 2008. "Stability analysis of the Grossman-Helpman model of endogenous product cycles," Journal of Macroeconomics, Elsevier, Elsevier, vol. 30(3), pages 1302-1322, September.
  4. Arnold, Lutz G., 2000. "Stability of the Market Equilibrium in Romer's Model of Endogenous Technological Change: A Complete Characterization," Journal of Macroeconomics, Elsevier, Elsevier, vol. 22(1), pages 69-84, January.
  5. 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, Cambridge University Press, vol. 6(05), pages 713-747, November.
Full references (including those not matched with items on IDEAS)

Citations

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:kan:wpaper:201304. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Jianbo Zhang).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.