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Global Dynamics In Macroeconomics: A General Equilibrium Example

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  • Pedro Gomis-Porqueras

    (University of Texas at Austin)

Abstract

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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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2000 with number 217.

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Date of creation: 05 Jul 2000
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Handle: RePEc:sce:scecf0:217

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Postal: CEF 2000, Departament d'Economia i Empresa, Universitat Pompeu Fabra, Ramon Trias Fargas, 25,27, 08005, Barcelona, Spain
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  1. Jess Gaspar & Kenneth L. Judd, 1997. "Solving Large Scale Rational Expectations Models," NBER Technical Working Papers 0207, National Bureau of Economic Research, Inc.
  2. Judd, Kenneth L. & Guu, Sy-Ming, 1997. "Asymptotic methods for aggregate growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 1025-1042, June.
  3. Stacey L. Schreft & Bruce D. Smith, 1997. "The evolution of cash transactions: some implications for monetary policy," Financial Services working paper 97-04, Federal Reserve Bank of Cleveland.
  4. Yokoo, Masanori, 2000. "Chaotic dynamics in a two-dimensional overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 909-934, June.
  5. Diamond, Douglas W & Dybvig, Philip H, 1983. "Bank Runs, Deposit Insurance, and Liquidity," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 401-19, June.
  6. Smale, Stephen, 1976. "Dynamics in General Equilibrium Theory," American Economic Review, American Economic Association, vol. 66(2), pages 288-94, May.
  7. Townsend, Robert M, 1987. "Economic Organization with Limited Communication," American Economic Review, American Economic Association, vol. 77(5), pages 954-71, December.
  8. Bischi, Gian Italo & Gardini, Laura & Kopel, Michael, 2000. "Analysis of global bifurcations in a market share attraction model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 855-879, June.
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