A Geometric Description of a Macroeconomic Model with a Center Manifold
AbstractThis 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 Cabr, Fontich and de la Llave , and the semianalytical algorithms proposed by Sim , and those of Gomis-Porqueras and Haro . 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, 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.
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Bibliographic InfoPaper provided by Barcelona Graduate School of Economics in its series Working Papers with number 364.
Date of creation: Oct 2008
Date of revision:
Invariant manifold; Center Manifold; Global Dynamics;
Other versions of this item:
- Gomis-Porqueras, Pere & Haro, Àlex, 2009. "A geometric description of a macroeconomic model with a center manifold," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(6), pages 1217-1235, June.
- E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
- E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
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