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New Phenomena Identified in a Stochastic Dynamic Macroeconometric Model: A Bifurcation Perspective


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  • William A. Barnett
  • Yijun He


In this paper, we consider new bifurcation phenomena in a class of stochastic dynamic macroeconometric models as represented by the stochastic model developed by Leeper and Sims (1994). This model serves as a prototype that could be suitable for monetary policy analysis although the complexity of the model makes any attempt of analytical analysis a difficult task. Leeper and Sims model consists of differential equations with a set of algebraic constraints. Our analysis reveals that singularity occurs within a small neighborhood of estimated parameter values. Singularity boundary is determined. When the parameter values are close to the singularity boundary, one eigenvalue of the linearized part of the model rapidly moves to infinity while others remain bounded, implying nearly instantaneous response of some variables to changes of other variables. On the singularity boundary, the number of differential equations will decrease while the number of algebraic constraints will increase. Such change in the order of dynamics is a new phenomenon in macroeconometric models. We shall determine the singularity-induced bifurcation and its effect on model behavior.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 145.

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Date of creation: 11 Aug 2004
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Handle: RePEc:sce:scecf4:145

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Keywords: stability; bifurcation; macroeconometric systems;

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Cited by:
  1. He, Yijun & Barnett, William A., 2006. "Singularity bifurcations," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 5-22, March.
  2. William Barnett & Barry E. Jones & Milka Kirova & Travis D. Nesmith & Meenakshi Pasupathy1, 2004. "The Nonlinear Skeletons in the Closet," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200403, University of Kansas, Department of Economics, revised May 2004.
  3. William A. Barnett & Yijun He, 2002. "Bifurcations in Macroeconomic Models," Macroeconomics 0210006, EconWPA.


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