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Bifurcations in Macroeconomic Models

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Author Info

  • William A. Barnett

    (University of Kansas)

  • Yijun He

    (Washington State University)

Abstract

Grandmont (1985) found that the parameter space of even the simplest, most classical models is stratified into bifurcation regions. But in such classical models all policies are Ricardian equivalent and all solutions are Pareto optimal. As a result he was not able to reach conclusions about policy relevance of his dramatic discovery. Barnett and He (1999,2002) subsequently found transcritical, codimension two, and Hopf bifurcation boundaries within the parameter space of the policy relevant Bergstrom and Wymer continuous time dynamic macroeconometric model of the UK economy. Because of the Lucas critique, there is increasing interest in Euler equation models with GMM estimated deep parameters. He and Barnett’s (2002) analysis of the Leeper and Sims (1994) Euler equations macroeconometric model revealed the existence of singularity-induced bifurcation within the model's parameter space. Although known in engineering, singularity-induced bifurcations have not previously been encountered in economics. The purpose of the paper is to introduce the bifurcation phenomena that we have encountered in the analysis of macroeconometric models. We include and emphasize the concept of singularity-induced bifurcation and its relationship with other forms of bifurcation. We do so for the benefit of economists who might encounter singularity bifurcation in the future, as we believe is likely with other Euler equation models similarly parameterized with deep parameters.

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Bibliographic Info

Paper provided by EconWPA in its series Macroeconomics with number 0210006.

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Date of creation: 30 Oct 2002
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Handle: RePEc:wpa:wuwpma:0210006

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Web page: http://128.118.178.162

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Keywords: bifurcation macroeconomics dynamics nonlinearity;

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References

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  1. 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.
  2. William A. Barnett & Yijun He & ., 1999. "Stabilization Policy as Bifurcation Selection: Would Keynesian Policy Work if the World Really were Keynesian?," Macroeconomics 9906008, EconWPA.
  3. 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.
  4. Venkatesh Bala, 1997. "A pitchfork bifurcation in the tatonnement process," Economic Theory, Springer, vol. 10(3), pages 521-530.
  5. Luenberger, David G & Arbel, Ami, 1977. "Singular Dynamic Leontief Systems," Econometrica, Econometric Society, vol. 45(4), pages 991-95, May.
  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. repec:cup:macdyn:v:6:y:2002:i:5:p:713-47 is not listed on IDEAS
  8. 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.
  9. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
  10. 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.
  11. Bala, Venkatesh & Majumdar, Mukul, 1992. "Chaotic Tatonnement," Economic Theory, Springer, vol. 2(4), pages 437-45, October.
  12. 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.
  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.
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Citations

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Cited by:
  1. 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.
  2. William Barnett & Evgeniya Aleksandrovna Duzhak, 2008. "Empirical Assessment of Bifurcation Regions within New Keynesian Models," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200811, University of Kansas, Department of Economics, revised Oct 2008.
  3. Barnett, William A. & Duzhak, Evgeniya, 2006. "Non-Robust Dynamic Inferences from Macroeconometric Models: Bifurcation Stratification of Confidence Regions," MPRA Paper 402, University Library of Munich, Germany.
  4. Stéphane Hallegatte & Michael Ghil & Patrice Dumas & Jean-Charles Hourcade, 2008. "Business Cycles, Bifurcations and Chaos in a Neo-Classical Model with Investment Dynamics," Post-Print halshs-00007196, HAL.

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