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Singularity Bifurcations

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  • Yijun He

    (Department of Economics , Washington State University)

  • William Barnett

    (Department of Economics, The University of Kansas)

Abstract

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 University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 200412.

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Length: 44 pages
Date of creation: Oct 2004
Date of revision: Oct 2004
Handle: RePEc:kan:wpaper:200412

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  1. Michele Boldrin & Michael Woodford, 1988. "Equilibruim Models Displaying Endogenous Fluctuations and Chaos: A Survey," UCLA Economics Working Papers, UCLA Department of Economics 530, UCLA Department of Economics.
  2. Herbert E. Scarf, 1959. "Some Examples of Global Instability of the Competitive Equilibrium," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 79, Cowles Foundation for Research in Economics, Yale University.
  3. 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, Elsevier, vol. 21(3), pages 421-444, December.
  4. William A. Barnett & Jane Binner & W. Erwin Diewert, 2005. "Functional Structure and Approximation in Econometrics (book front matter)," Econometrics, EconWPA 0511006, EconWPA.
  5. repec:cup:macdyn:v:6:y:2002:i:5:p:713-47 is not listed on IDEAS
  6. Eric M. Leeper & Christopher A. Sims, 1994. "Toward a Modern Macroeconomic Model Usable for Policy Analysis," NBER Chapters, National Bureau of Economic Research, Inc, in: NBER Macroeconomics Annual 1994, Volume 9, pages 81-140 National Bureau of Economic Research, Inc.
  7. Bala, Venkatesh & Majumdar, Mukul, 1992. "Chaotic Tatonnement," Economic Theory, Springer, Springer, vol. 2(4), pages 437-45, October.
  8. William A. Barnett & Yijun He, 2004. "New Phenomena Identified in a Stochastic Dynamic Macroeconometric Model: A Bifurcation Perspective," Computing in Economics and Finance 2004, Society for Computational Economics 145, Society for Computational Economics.
  9. Venkatesh Bala, 1997. "A pitchfork bifurcation in the tatonnement process," Economic Theory, Springer, Springer, vol. 10(3), pages 521-530.
  10. 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, Cambridge University Press, vol. 6(05), pages 713-747, November.
  11. William Barnett & Yijun He, 2012. "Stabilization Policy as Bifurcation Selection: Would Keynesian Policy Work if the World Really Were Keynesian?," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS, University of Kansas, Department of Economics 201228, University of Kansas, Department of Economics, revised Sep 2012.
  12. Luenberger, David G & Arbel, Ami, 1977. "Singular Dynamic Leontief Systems," Econometrica, Econometric Society, Econometric Society, vol. 45(4), pages 991-95, May.
  13. Barnett William A. & He Yijun, 1999. "Stability Analysis of Continuous-Time Macroeconometric Systems," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 3(4), pages 1-22, January.
  14. Engelbert Dockner & Gustav Feichtinger, 1991. "On the optimality of limit cycles in dynamic economic systems," Journal of Economics, Springer, Springer, vol. 53(1), pages 31-50, February.
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Cited by:
  1. William Barnett & Evgeniya Duzhak, 2010. "Empirical assessment of bifurcation regions within New Keynesian models," Economic Theory, Springer, Springer, vol. 45(1), pages 99-128, October.
  2. William Barnett & Unal Eryilmaz, 2012. "Hopf Bifurcation in the Clarida, Gali, and Gertler Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS, University of Kansas, Department of Economics 201211, University of Kansas, Department of Economics, revised Sep 2012.
  3. Banerjee, Sanjibani & A. Barnett, William & A. Duzhak, Evgeniya & Gopalan, Ramu, 2011. "Bifurcation analysis of Zellner's Marshallian Macroeconomic Model," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 35(9), pages 1577-1585, September.
  4. Barnett, William A. & He, Susan, 2010. "Existence of singularity bifurcation in an Euler-equations model of the United States economy: Grandmont was right," Economic Modelling, Elsevier, Elsevier, vol. 27(6), pages 1345-1354, November.

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