Global Dynamics In Macroeconomics: A General Equilibrium Example
The interest and study of global dynamics in macroeconomics is fairly recent. However, there has bee an increasing number of articles addressing the issue. In order to investigate the global dynamics of an economy, we introduce some mathematical techniques used in the dynamical systems literature. These techniques are similar in spirit to Judd's perturbation and projection methods. One of the advantages of considering a global analysis is that we can determine the quality of the local approximation. Furthermore, a global analysis can capture new dynamical phenomena like wandering cycles and Homoclinic points that are not observed when performing a local analysis.The techniques presented in this paper can fully characterize the shape of the stable and unstable manifolds of a given dynamical system. Once we impose the corresponding invariant conditions, the problem can be reduced to the description of a manifold in R^n. There are two basic methods of describing the shape of a manifold in R^n. On the one hand, we can think the manifold in terms of a graph in R^n. Or we can interpret the manifold as being defined as a result of a particular parameterization in R^n. In order to illustrate these techniques, we present a general equilibrium model under two different policy regimes demonstrating that the local and global dynamics of an economic system can be substantially different.
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