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Stability Analysis of Continuous-Time Macroeconometric Systems

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Author Info

  • Barnett William A.

    (Washington University in St. Louis)

  • He Yijun

    (Washington University in St. Louis)

Abstract

There has been increasing interest in continuous-time macroeconometric models. This research investigates stability of the Bergstrom, Nowman, and Wymer continuous-time model of the U.K. when system parameters change. This particularly well-regarded continuous-time macroeconometric model is chosen to assure the empirical and potential policy relevance of the results. Stability analysis is important with this model for understanding the dynamic properties of the system and for determining which parameters are the most important to those dynamic properties. The main objective of this paper is to determine the boundaries of parameters at which instability occurs. Two types of boundaries are found: the transcritical bifurcation boundary and the Hopf bifurcation boundary, corresponding to two different ways that instability occurs when parameter values cross the bifurcation boundary.The existence of the Hopf bifurcation boundary is particularly useful, since Hopf bifurcation may provide explanations for some cyclical phenomena in macroeconomy. Numerical algorithms are designed to locate the stability boundaries, which are displayed in three-dimensional diagrams. A notable and perhaps surprising fact is that both types of bifurcations can coexist with this well-regarded U.K. model--in the same neighborhood of the parameter space.

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File URL: http://www.degruyter.com/view/j/snde.1999.3.4/snde.1999.3.4.1047/snde.1999.3.4.1047.xml?format=INT
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Bibliographic Info

Article provided by De Gruyter in its journal Studies in Nonlinear Dynamics & Econometrics.

Volume (Year): 3 (1999)
Issue (Month): 4 (January)
Pages: 1-22

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Handle: RePEc:bpj:sndecm:v:3:y:1999:i:4:n:1

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Web page: http://www.degruyter.com

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Cited by:
  1. William Barnett & Unal Eryilmaz, 2012. "Hopf Bifurcation in the Clarida, Gali, and Gertler Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201211, University of Kansas, Department of Economics, revised Sep 2012.
  2. William Barnett & Evgeniya Duzhak, 2010. "Empirical assessment of bifurcation regions within New Keynesian models," Economic Theory, Springer, vol. 45(1), pages 99-128, October.
  3. William Barnett & Evgeniya Aleksandrovna Duzhak, 2006. "Non-Robust Dynamic Inferences from Macroeconometric Models: Bifurcation Stratification of Confidence Regions," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200608, University of Kansas, Department of Economics.
  4. Jang-Ting Guo & Kevin Lansing, 1999. "Fiscal policy, increasing returns, and endogenous fluctuations," Working Papers in Applied Economic Theory 99-08, Federal Reserve Bank of San Francisco.
  5. Antinolfi, Gaetano & Keister, Todd & Shell, Karl, 2001. "Growth Dynamics and Returns to Scale: Bifurcation Analysis," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 70-96, January.
  6. Yijun He & William A. Barnett, 2004. "Singularity Bifurcation," Macroeconomics 0409024, EconWPA, revised 13 Oct 2004.
  7. Barnett, William A. & He, Susan, 2009. "Existence of Singularity Bifurcation in an Euler-Equations Model of the United States Economy: Grandmont was Right," MPRA Paper 12803, University Library of Munich, Germany.
  8. Pu Chen & Carl Chiarella & Peter Flaschel & Willi Semmler, 2006. "The feedback channels in macroeconomics: analytical foundations for structural econometric model building," Central European Journal of Operations Research, Springer, vol. 14(3), pages 261-288, September.
  9. William A. Barnett & Yijun He, 2002. "Bifurcations in Macroeconomic Models," Macroeconomics 0210006, EconWPA.
  10. William Barnett & Morgan Rose, 2005. "Joseph Schumpeter and Modern Nonlinear Dynamics," Method and Hist of Econ Thought 0504001, EconWPA.

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