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Center Manifold, Stability, and Bifurcations in Continuous Time Macroeconometric Systems

Author

Listed:
  • William A. Barnett

    (Washington University in St. Louis)

  • Yijun He

    (Washington University in St. Louis)

Abstract

This paper is a follow-on to our earlier paper, "Bifurcations in Continuous-Time Macroeconomic Systems." In this paper, we determine the stability properties of the UK continuous time macroeconometric model on its bifurcation boundaries and we test the null hypothesis that the model's parameters are inside the model's unstable region. We then attach to the model Bergstrom's recommended stabilization policy rule. We find that for most settings of his policy rule's parameters, the model's stable region becomes smaller. Hence the policy may be counter- productive. To the degree that "stabilization policy" is interesting, its intent must be to stabilize a system that is not stable. This is bifurcation. Hence stabilization policy only can be understood as bifurcation selection. We find that selection of a policy that will produce successful bifurcation from the model's unstable region to its stable region is much more difficult than previously believe. If in fact the economy is unstable without policy, the selection of successful stabilization policy is an exercise in a very difficult area of complex dynamics. Since Berstrom is one of the originators of the Bergstrom-Wymer-Nowman model, Bergstrom's choice of stabilization policy cannot be viewed as uninformed. We do find that a policy produced from optimal control theory is capable of bifurcating the system successfully from its unstable region to the stable region. But the form of the resulting policy rule is far too complicated to be of practical use. In addition, such a policy, even if implemented, cannot reasonably be viewed as robust to model specification error, since issues regarding the Lucas critique and time inconsistency (Kydland and Prescott) suggest the need for caution in any assumption of robustness to specification error, when such experiments condition upon a structural model.

Suggested Citation

  • William A. Barnett & Yijun He, 1999. "Center Manifold, Stability, and Bifurcations in Continuous Time Macroeconometric Systems," Macroeconomics 9901002, EconWPA.
  • Handle: RePEc:wpa:wuwpma:9901002
    Note: Type of Document - pdf and ps zip; prepared on UNIX Sparc, pdf and ps; pages: 29 ; figures: included. Using the UK continuous time macroeconometric model, we explore its stability properties, its bifurcation boundaries, and its properties under stabilization policy. Earlier work by Grandmont and others has shown that complex dynamics of various forms can be produced by simple models that have no policy relevancy. We use the UK continuous time macroeconometric model to permit similar analysis with a model that has policy relevancy.
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    References listed on IDEAS

    as
    1. Nieuwenhuis, Herman J. & Schoonbeek, Lambert, 1997. "Stability and the structure of continuous-time economic models," Economic Modelling, Elsevier, vol. 14(3), pages 311-340, July.
    2. Barnett, William A. & Gallant, A. Ronald & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1997. "A single-blind controlled competition among tests for nonlinearity and chaos," Journal of Econometrics, Elsevier, vol. 82(1), pages 157-192.
    3. Barnett, William A. & Serletis, Apostolos & Serletis, Demitre, 2015. "Nonlinear And Complex Dynamics In Economics," Macroeconomic Dynamics, Cambridge University Press, vol. 19(08), pages 1749-1779, December.
    4. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    5. 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.
    6. Goenka, Aditya & Kelly, David L. & Spear, Stephen E., 1998. "Endogenous Strategic Business Cycles," Journal of Economic Theory, Elsevier, vol. 81(1), pages 97-125, July.
    7. Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, vol. 66(4), pages 741-782, July.
    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. Bergstrom, A. R. & Nowman, K. B. & Wymer, C. R., 1992. "Gaussian estimation of a second order continuous time macroeconometric model of the UK," Economic Modelling, Elsevier, vol. 9(4), pages 313-351, October.
    11. Bergstrom, A. R. & Nowman, K. B. & Wandasiewicz, S., 1994. "Monetary and fiscal policy in a second-order continuous time macroeconometric model of the United Kingdom," Journal of Economic Dynamics and Control, Elsevier, vol. 18(3-4), pages 731-761.
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    Keywords

    bifurcation stabilization policy instability;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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