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Singularity Bifurcation

  • Yijun He

    (Washington State University)

  • William A. Barnett

    (University of Kansas)

Euler equation models represent an important class of macroeconomic systems. Our ongoing research (He and Barnett (2003)) on the Leeper and Sims (1994) Euler equations macroeconometric model is revealing the existence of singularity-induced bifurcations, when the model’s parameters are within a confidence region about the parameter estimates. Although known to engineers, singularity bifurcation has not previously been seen in the economics literature. Knowledge of the nature of singularity-induced bifurcations is likely to become important in understanding the dynamics of modern macroeconometric models. This paper explains singularity-induced bifurcation, its nature, and its identification and contrasts this class of bifurcations with the more common forms of bifurcation we have previously encountered within the parameter space of the Bergstrom and Wymer (1976) continuous time macroeconometric model of the UK economy. (See, e.g., Barnett and He (1999, 2002)).

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Paper provided by EconWPA in its series Macroeconomics with number 0409024.

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Length: 42 pages
Date of creation: 28 Sep 2004
Date of revision: 13 Oct 2004
Handle: RePEc:wpa:wuwpma:0409024
Note: Type of Document - pdf; pages: 42
Contact details of provider: Web page: http://128.118.178.162

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  1. Eric M. Leeper & Christopher A. Sims, 1994. "Toward a Modern Macroeconomic Model Usable for Policy Analysis," NBER Chapters, in: NBER Macroeconomics Annual 1994, Volume 9, pages 81-140 National Bureau of Economic Research, Inc.
  2. repec:cup:macdyn:v:6:y:2002:i:5:p:713-47 is not listed on IDEAS
  3. William A. Barnett & Yijun He & ., 1999. "Stabilization Policy as Bifurcation Selection: Would Keynesian Policy Work if the World Really were Keynesian?," Macroeconomics 9906008, EconWPA.
  4. Engelbert Dockner & Gustav Feichtinger, 1991. "On the optimality of limit cycles in dynamic economic systems," Journal of Economics, Springer, vol. 53(1), pages 31-50, February.
  5. Barnett, William A. & He, Yijun, 2002. "Stabilization Policy As Bifurcation Selection: Would Stabilization Policy Work If The Economy Really Were Unstable?," Macroeconomic Dynamics, Cambridge University Press, vol. 6(05), pages 713-747, November.
  6. Michele Boldrin & Michael Woodford, 1988. "Equilibruim Models Displaying Endogenous Fluctuations and Chaos: A Survey," UCLA Economics Working Papers 530, UCLA Department of Economics.
  7. William A. Barnett & Jane Binner & W. Erwin Diewert, 2005. "Functional Structure and Approximation in Econometrics (book front matter)," Econometrics 0511006, EconWPA.
  8. Venkatesh Bala, 1997. "A pitchfork bifurcation in the tatonnement process," Economic Theory, Springer, vol. 10(3), pages 521-530.
  9. Bala, Venkatesh & Majumdar, Mukul, 1992. "Chaotic Tatonnement," Economic Theory, Springer, vol. 2(4), pages 437-45, October.
  10. William A. Barnett & Yijun He, 2004. "New Phenomena Identified in a Stochastic Dynamic Macroeconometric Model: A Bifurcation Perspective," Computing in Economics and Finance 2004 145, Society for Computational Economics.
  11. Luenberger, David G & Arbel, Ami, 1977. "Singular Dynamic Leontief Systems," Econometrica, Econometric Society, vol. 45(4), pages 991-95, May.
  12. Benhabib, Jess & Nishimura, Kazuo, 1979. "The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth," Journal of Economic Theory, Elsevier, vol. 21(3), pages 421-444, December.
  13. Herbert E. Scarf, 1959. "Some Examples of Global Instability of the Competitive Equilibrium," Cowles Foundation Discussion Papers 79, Cowles Foundation for Research in Economics, Yale University.
  14. Barnett William A. & He Yijun, 1999. "Stability Analysis of Continuous-Time Macroeconometric Systems," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(4), pages 1-22, January.
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