TITLE: 
A geometric description of a macroeconomic model with a center manifold 

AUTHORS: 

Pere Gomis-Porqueras, 
Department of Economics
University of Miami
E-mail: gomis@miami.edu

Alex Haro
Departament de Matematica Aplicada i Analisi
Universitat de Barcelona
E-mail: alex@maia.ub.es

NOTE: To appear in Journal of Economic Dynamics and Control (submitted in 2004). 


ABSTRACT: 
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 Cabre, Fontich and de la Llave, the semianalytical algorithms
proposed by Simo, and those of Gomis-Porqueras and Haro in a previous paper.
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 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, Bullard and Smith. 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.