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Bifurcations in Continuous-Time Macroeconomic Systems

Author

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  • William A. Barnett

    (Washington University in St. Louis)

  • Yijun He

    (Washington University in St. Louis)

Abstract

This research investigates bifurcation phenomena in a continuous-time model of the United Kingdom. We use the Bergstrom, Nowman, and Wymer continuous-time dynamic macroeconometric model of the UK economy. We find that bifurcations are important with this model for understanding the dynamic properties of the system and for determining which parameters are the most important to those dynamic properties. We have discovered that both saddle-node bifurcations and Hopf bifurcations indeed exist with this model within the model's region of plausible parameter settings. We find that the existence of Hopf bifurcations is particularly useful, since those bifurcations may provide explanations for some cyclical phenomena in the macroeconomy. We further design numerical algorithms to locate the bifurcation boundaries, which we display in three dimensional color bifurcation diagrams. A notable and perhaps surprising fact is that both types of bifurcation can coexist with this well-regarded UK model---in the same neighborhood of the parameter space.

Suggested Citation

  • William A. Barnett & Yijun He, 1998. "Bifurcations in Continuous-Time Macroeconomic Systems," Macroeconomics 9805018, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpma:9805018
    Note: Type of Document - Postscript Compressed; pages: 24 ; figures: included. This paper was presented by Yijun He at the annual meetings of the Society for Nonlinear Dynamics and Econometrics and has been submitted to the Society's journal, the Journal of Nonlinear Dynamics and Econometrics, which is an online journal published by MIT Press.
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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. Malcolm D. Knight & Clifford R. Wymer, 1978. "A Macroeconomic Model of the United Kingdom (Un modèle macroéconomique du Royaume-Uni) (Modelo macroeconómico del Reino Unido)," IMF Staff Papers, Palgrave Macmillan, vol. 25(4), pages 742-778, December.
    3. Gandolfo, Giancarlo & Padoan, Pietro Carlo, 1990. "The Italian continuous time model : Theory and empirical results," Economic Modelling, Elsevier, vol. 7(2), pages 91-132, April.
    4. 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.
    5. 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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    Citations

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    Cited by:

    1. Carl Chiarella & Peter Flaschel & Gangolf Groh & Carsten Köper & Willi Semmler, 1999. "Towards Applied Disequilibrium Growth Theory: VI Substitution, Money-Holdings, Wealth-Effects and Further Extensions," Working Paper Series 98, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    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. Datta, Soumya, 2013. "Robustness and Stability of Limit Cycles in a Class of Planar Dynamical Systems," MPRA Paper 50814, University Library of Munich, Germany.
    4. A. R. Bergstrom, 2001. "Stability and wage acceleration in macroeconomic models of cyclical growth," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 327-340.
    5. Carl Chiarella & Peter Flaschel, 1999. "Towards Applied Disequilibrium Growth Theory: II Intensive Form and Steady State Analysis of the Model," Working Paper Series 94, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    6. Carl Chiarella & Peter Flaschel, 1999. "Towards Applied Disequilibrium Growth Theory: I The Starting Model," Working Paper Series 93, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    7. Carl Chiarella & Peter Flaschel & Peiyuan Zhu, 2003. "Towards Applied Disequilibrium Growth Theory: IV Numerical Investigations of the Core 18D Model," Working Paper Series 96, Finance Discipline Group, UTS Business School, University of Technology, Sydney.

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    More about this item

    Keywords

    nonlinearity chaos bifurcation macroeconomics UK continuous time;

    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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