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Nonlinear and Complex Dynamics in Economics

Author

Listed:
  • William Barnett

    (Department of Economics, University of Kansas)

  • Apostolos Serletis

    (Department of Economics, University of Calgary)

  • Demitre Serletis

    (Neurological Institute, Epilepsy Center)

Abstract

This paper is an up-to-date survey of the state-of-the-art in dynamical systems theory relevant to high levels of dynamical complexity, characterizing chaos and near chaos, as commonly found in the physical sciences. The paper also surveys applications in economics and finance. This survey does not include bifurcation analyses at lower levels of dynamical complexity, such as Hopf and transcritical bifurcations, which arise closer to the stable region of the parameter space. We discuss the geometric approach (based on the theory of differential/difference equations) to dynamical systems and make the basic notions of complexity, chaos, and other related concepts precise, having in mind their (actual or potential) applications to economically motivated questions. We also introduce specific applications in microeconomics, macroeconomics, and finance, and discuss the policy relevancy of chaos.

Suggested Citation

  • William Barnett & Apostolos Serletis & Demitre Serletis, 2012. "Nonlinear and Complex Dynamics in Economics," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201238, University of Kansas, Department of Economics, revised Sep 2012.
    • Handle: RePEc:kan:wpaper:201238
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    Cited by:

    1. Barnett, William A. & Serletis, Apostolos & Serletis, Demitre, 2015. "Nonlinear And Complex Dynamics In Economics," Macroeconomic Dynamics, Cambridge University Press, vol. 19(8), pages 1749-1779, December.
    2. Apostolos Serletis & Khandokar Istiak, 2018. "Broker-dealer Leverage and the Stock Market," Open Economies Review, Springer, vol. 29(2), pages 215-222, April.
    3. Miguel Henry & George Judge, 2019. "Permutation Entropy and Information Recovery in Nonlinear Dynamic Economic Time Series," Econometrics, MDPI, vol. 7(1), pages 1-16, March.
    4. Libo Xu & Apostolos Serletis, 2019. "Communication frictions, sentiments, and nonlinear business cycles," International Journal of Economic Theory, The International Society for Economic Theory, vol. 15(2), pages 137-152, June.
    5. Fredj Jawadi & Hachmi Ben Ameur & Stephanie Bigou & Alexis Flageollet, 2022. "Does the Real Business Cycle Help Forecast the Financial Cycle?," Computational Economics, Springer;Society for Computational Economics, vol. 60(4), pages 1529-1546, December.
    6. Haider, Adnan & Hanif, Muhammad Nadeem, 2007. "Inflation Forecasting in Pakistan using Artificial Neural Networks," MPRA Paper 14645, University Library of Munich, Germany.
    7. Gomes, Orlando, 2013. "Information stickiness on general equilibrium and endogenous cycles," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 7, pages 1-43.
    8. Orlando Gomes, 2007. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing, vol. 33(6), pages 437-468, January.
    9. Vivaldo M. Mendes & Diana A. Mendes, 2007. "Controlling Endogenous Cycles in an OLG Economy by the OGY Method," Working Papers Series 1 ercwp0808, ISCTE-IUL, Business Research Unit (BRU-IUL).
    10. Orlando Gomes, 2024. "The emergence of chaos in productivity distribution dynamics," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(2), pages 565-596, December.
    11. Nakamura, Emi, 2005. "Inflation forecasting using a neural network," Economics Letters, Elsevier, vol. 86(3), pages 373-378, March.
    12. Serletis, Apostolos & He, Mingyu & Chowdhury, M.M. Islam, 2023. "Chaos in long-maturity real rates," Economics Letters, Elsevier, vol. 225(C).
    13. Barnett William A. & Jawadi Fredj & Ftiti Zied, 2020. "Causal relationships between inflation and inflation uncertainty," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(5), pages 1-26, December.
    14. Ingrid Kubin & Laura Gardini, 2022. "On the significance of borders: the emergence of endogenous dynamics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 41-62, January.
    15. Orlando Gomes, 2006. "Endogenous Business Cycles in the Ramsey Growth Model," Zagreb International Review of Economics and Business, Faculty of Economics and Business, University of Zagreb, vol. 9(2), pages 13-36, November.
    16. Orlando Gomes, 2006. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing Limited, vol. 33(6), pages 437-468, November.
    17. Orlando Gomes, 2006. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing, vol. 33(6), pages 437-468, November.
    18. William A. Barnett & Yijun He, 1999. "Center Manifold, Stability, and Bifurcations in Continuous Time Macroeconometric Systems," Macroeconomics 9901002, University Library of Munich, Germany.
    19. Vivaldo M. Mendes & Diana A. Mendes, 2006. "Active Interest Rate Rules and the Role of Stabilization Policy R&D Tax Credits," Working Papers Series 1 ercwp0208, ISCTE-IUL, Business Research Unit (BRU-IUL).
    20. Orzeszko, Witold, 2008. "The new method of measuring the effects of noise reduction in chaotic data," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1355-1368.
    21. Andreas Psimopoulos, 2020. "Forecasting Economic Recessions Using Machine Learning:An Empirical Study in Six Countries," South-Eastern Europe Journal of Economics, Association of Economic Universities of South and Eastern Europe and the Black Sea Region, vol. 18(1), pages 40-99.
    22. Tang, Qihe & Tong, Zhiwei & Yang, Yang, 2021. "Large portfolio losses in a turbulent market," European Journal of Operational Research, Elsevier, vol. 292(2), pages 755-769.

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    More about this item

    Keywords

    Complexity; Chaos; Endogenous business cycles;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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