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Singularity bifurcations

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  • He, Yijun
  • Barnett, William A.

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Macroeconomics.

Volume (Year): 28 (2006)
Issue (Month): 1 (March)
Pages: 5-22

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Handle: RePEc:eee:jmacro:v:28:y:2006:i:1:p:5-22

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Web page: http://www.elsevier.com/locate/inca/622617

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References

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  1. 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.
  2. 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.
  3. Eric M. Leeper & Christopher A. Sims, 1994. "Toward a modern macroeconomic model usable for policy analysis," Working Paper 94-5, Federal Reserve Bank of Atlanta.
  4. Bala, Venkatesh & Majumdar, Mukul, 1992. "Chaotic Tatonnement," Economic Theory, Springer, vol. 2(4), pages 437-45, October.
  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. Boldrin, Michele & Woodford, Michael, 1990. "Equilibrium models displaying endogenous fluctuations and chaos : A survey," Journal of Monetary Economics, Elsevier, vol. 25(2), pages 189-222, March.
  7. 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.
  8. 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.
  9. 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.
  10. 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 201228, University of Kansas, Department of Economics, revised Sep 2012.
  11. repec:cup:macdyn:v:6:y:2002:i:5:p:713-47 is not listed on IDEAS
  12. William A. Barnett & Jane Binner & W. Erwin Diewert, 2005. "Functional Structure and Approximation in Econometrics (book front matter)," Econometrics 0511006, EconWPA.
  13. Luenberger, David G & Arbel, Ami, 1977. "Singular Dynamic Leontief Systems," Econometrica, Econometric Society, vol. 45(4), pages 991-95, May.
  14. Venkatesh Bala, 1997. "A pitchfork bifurcation in the tatonnement process," Economic Theory, Springer, vol. 10(3), pages 521-530.
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Cited by:
  1. Barnett, William A. & Eryilmaz, Unal, 2013. "Hopf bifurcation in the Clarida, Gali, and Gertler model," Economic Modelling, Elsevier, vol. 31(C), pages 401-404.
  2. 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, vol. 27(6), pages 1345-1354, November.
  3. 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.
  4. Sanjibani Banerjee & William Barnett & Evgeniya Duzhak & Ramu Gopalan, 2011. "Bifurcation Analysis of Zellner's Marshallian Macroeconomic Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201102, University of Kansas, Department of Economics, revised Apr 2011.

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