IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpma/9805018.html
   My bibliography  Save this paper

Bifurcations in Continuous-Time Macroeconomic Systems

Author

Listed:
  • 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.
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/mac/papers/9805/9805018.ps.gz
    Download Restriction: no

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/mac/papers/9805/9805018.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. William A. Barnett & Yijun He & ., 1999. "Stabilization Policy as Bifurcation Selection: Would Keynesian Policy Work if the World Really were Keynesian?," Macroeconomics 9906008, University Library of Munich, Germany.
    2. He, Yijun & Barnett, William A., 2006. "Existence of bifurcation in macroeconomic dynamics: Grandmont was right," MPRA Paper 756, University Library of Munich, Germany.
    3. 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.
    4. William A. Barnett & Yijun He, 1999. "Center Manifold, Stability, and Bifurcations in Continuous Time Macroeconometric Systems," Macroeconomics 9901002, University Library of Munich, Germany.
    5. Kieran P. Donaghy, 1998. "Incomes Policies Revisited," Working Papers 46, Sapienza University of Rome, CIDEI.
    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.
    7. Federici, Daniela & Saltari, Enrico, 2018. "Elasticity Of Substitution And Technical Progress: Is There A Misspecification Problem?," Macroeconomic Dynamics, Cambridge University Press, vol. 22(1), pages 101-121, January.
    8. William Barnett & Evgeniya Duzhak, 2010. "Empirical assessment of bifurcation regions within New Keynesian models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 99-128, October.
    9. Barnett, William A. & Duzhak, Evgeniya Aleksandrovna, 2008. "Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3817-3825.
    10. Chambers, MJ & McCrorie, JR & Thornton, MA, 2017. "Continuous Time Modelling Based on an Exact Discrete Time Representation," Economics Discussion Papers 20497, University of Essex, Department of Economics.
    11. Wymer, Clifford R. & Saltari, Enrico & Federici, Daniela, 2019. "Endogenizing The Ict Sector: A Multisector Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 23(S1), pages 25-58, September.
    12. Barnett, William A. & Chen, Guo, 2015. "Bifurcation of Macroeconometric Models and Robustness of Dynamical Inferences," Foundations and Trends(R) in Econometrics, now publishers, vol. 8(1-2), pages 1-144, September.
    13. William Barnett & Morgan Rose, 2005. "Joseph Schumpeter and Modern Nonlinear Dynamics," Method and Hist of Econ Thought 0504001, University Library of Munich, Germany.
    14. Enrico Saltari & Clifford Wymer & Daniela Federici & Marilena Giannetti, 2011. "The impact of ICT on the Italian productivity dynamics," Working Papers in Public Economics 149, University of Rome La Sapienza, Department of Economics and Law.
    15. Roderick McCrorie, J., 2001. "Interpolating exogenous variables in continuous time dynamic models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(9), pages 1399-1427, September.
    16. Jewitt, Giles & Roderick McCrorie, J., 2005. "Computing estimates of continuous time macroeconometric models on the basis of discrete data," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 397-416, April.
    17. Saltari Enrico & Wymer Clifford R. & Federici Daniela & Giannetti Marilena, 2012. "Technological Adoption with Imperfect Markets in the Italian Economy," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(2), pages 1-30, April.
    18. Goldberg, Michael D., 2000. "On empirical exchange rate models: what does a rejection of the symmetry restriction on short-run interest rates mean?," Journal of International Money and Finance, Elsevier, vol. 19(5), pages 673-688, October.
    19. Nastac, Iulian & Dobrescu, Emilian & Pelinescu, Elena, 2007. "Neuro-Adaptive Model for Financial Forecasting," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 4(3), pages 19-41, September.
    20. Joanne S. McGarry & Marcus J. Chambers, 2004. "Party formation and coalitional bargaining in a model of proportional representation," Discussion Papers 04-07, Department of Economics, University of Birmingham.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpma:9805018. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.