A geometric description of a macroeconomic model with a center manifold
This paper presents a unified framework of different algorithms to numerically compute high order expansions of invariant manifolds associated to a steady state of a dynamical system. The framework is inspired in the parameterization method of Cabré et al. [2003. The parameterization method for invariant manifolds. I. Manifolds associated to non-resonant subspaces. Indiana University Mathematics Journal 52(2), 283-328], and the semianalytical algorithms proposed by Simó [1990. On the analytical and numerical approximation of invariant manifolds. In: Benest, D., Froeschlé, C. (Eds.), Les Méthodes Modernes de la Mecánique Céleste (Course given at Goutelas, France, 1989), Editions Frontières, Paris, pp. 285-329], and those of Gomis-Porqueras and Haro [2003. Global dynamics in macroeconomics: an overlapping generations example. Journal of Economic Dynamics and Control 27, 1941-1959]. Within this methodology, one can compute high order approximations of stable, unstable and center manifolds. In this last case the use of high order approximations (not just linear) are crucial in understanding the dynamic properties of the model near the steady state. To illustrate the algorithms we consider a model economy introduced by Azariadis et al. [2001. Public and private circulating liabilities. Journal of Economic Theory 99, 59-116]. Besides its intrinsic importance, this four-dimensional macroeconomic model is an ideal testing ground because it delivers steady states with stable and unstable manifolds (of dimensions 1 or 2), and each of them has also a one-dimensional center manifold. Moreover, the numerical computations lead to a further theoretical study of the dynamical system completing some of the results in the original paper.
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
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.:
- Gomis-Porqueras, Pere & Haro, Alex, 2003.
"Global dynamics in macroeconomics: an overlapping generations example,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 27(11), pages 1941-1959.
- Gomis-Porqueras, Pere & Haro, Alex, 2003. "Global dynamics in macroeconomics: an overlapping generations example," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11-12), pages 1941-1959, September.
- Boldrin, Michele & Rustichini, Aldo, 1994.
"Growth and Indeterminacy in Dynamic Models with Externalities,"
Econometric Society, vol. 62(2), pages 323-342, March.
- Michele Boldrin & Aldo Rustichini, 2010. "Growth and Indeterminacy in Dynamic Models with Externalities," Levine's Working Paper Archive 1382, David K. Levine.
- Grandmont, Jean-Michel, 1985.
"On Endogenous Competitive Business Cycles,"
Econometric Society, vol. 53(5), pages 995-1045, September.
- Gomis-Porqueras, Pere & Haro, Alex, 2007.
"Global bifurcations, credit rationing and recurrent hyperinflations,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 31(2), pages 473-491, February.
- Pere Gomis-Porqueras & Àlex Haro, 2005. "Global Bifurcations, Credit Rationing and Recurrent Hyperinflations," Working Papers 239, Barcelona Graduate School of Economics.
When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:33:y:2009:i:6:p:1217-1235. 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: (Dana Niculescu)
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.