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Bifurcations in Continuous-Time Macroeconomic Systems

Author

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  • William Barnett

    (Department of Economics, The University of Kansas)

  • Yijun He

    (Washington University in St.Louis)

Abstract

There has been increasing interest in continuous-time macroeconomic models. This research investigates bifurcation phenomena in a continuous-time model of the United Kingdom. We choose a particularly well-regarded continuous-time macroeconometric model to assure the empirical and potential policy relevance of our results. In particular, 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 bifurcations can coexist with this well-regarded UK model - in the same neighborhood of the parameter space.

Suggested Citation

  • William Barnett & Yijun He, 2012. "Bifurcations in Continuous-Time Macroeconomic Systems," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201226, University of Kansas, Department of Economics, revised Sep 2012.
  • Handle: RePEc:kan:wpaper:201226
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    File URL: http://www2.ku.edu/~kuwpaper/2009Papers/201226.pdf
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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. 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.
    4. 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.
    5. 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.
    6. 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.

    More about this item

    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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