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Hopf bifurcation and chaos in macroeconomic models with policy lag

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  • Liao, Xiaofeng
  • Li, Chuandong
  • Zhou, Shangbo

Abstract

In this paper, we consider the macroeconomic models with policy lag, and study how lags in policy response affect the macroeconomic stability. The local stability of the nonzero equilibrium of this equation is investigated by analyzing the corresponding transcendental characteristic equation of its linearized equation. Some general stability criteria involving the policy lag and the system parameter are derived. By choosing the policy lag as a bifurcation parameter, the model is found to undergo a sequence of Hopf bifurcation. The direction and stability of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. Moreover, we show that the government can stabilize the intrinsically unstable economy if the policy lag is sufficiently short, but the system become locally unstable when the policy lag is too long. We also find the chaotic behavior in some range of the policy lag.

Suggested Citation

  • Liao, Xiaofeng & Li, Chuandong & Zhou, Shangbo, 2005. "Hopf bifurcation and chaos in macroeconomic models with policy lag," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 91-108.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:1:p:91-108
    DOI: 10.1016/j.chaos.2004.09.075
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    1. Neamţu, Mihaela & Opriş, Dumitru & Chilaˇrescu, Constantin, 2007. "Hopf bifurcation in a dynamic IS–LM model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 519-530.
    2. Tamara Merkulova & Tatyana Bitkova & Kateryna Kononova, 2016. "Tax Factors of Sustainable Development: System Dynamics Approach towards Tax Evasion Analyses," RIVISTA DI STUDI SULLA SOSTENIBILITA', FrancoAngeli Editore, vol. 2016(1), pages 35-47.
    3. Neamtu, Mihaela & Opris, Dumitru & Chilarescu, Constantin, 2005. "Hopf bifurcation in a dynamic IS-LM model with time delay," MPRA Paper 13270, University Library of Munich, Germany.
    4. Wei Li & Baichuan Xiang & Rongxia Zhang & Guomin Li & Zhihao Wang & Bin Su & Tossou Mahugbe Eric, 2022. "Impact of Resource-Based Economic Transformation Policy on Sulfur Dioxide Emissions: A Case Study of Shanxi Province," Sustainability, MDPI, vol. 14(14), pages 1-22, July.
    5. Wang, Qiubao & Li, Dongsong & Liu, M.Z., 2009. "Numerical Hopf bifurcation of Runge–Kutta methods for a class of delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3087-3099.
    6. Liao, Xiaofeng & Ran, Jiouhong, 2007. "Hopf bifurcation in love dynamical models with nonlinear couples and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 853-865.
    7. Liu, Xiaoming & Liao, Xiaofeng, 2009. "Necessary and sufficient conditions for Hopf bifurcation in tri-neuron equation with a delay," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 481-490.
    8. G. Rigatos & P. Siano & M. Abbaszadeh & T. Ghosh, 2021. "Nonlinear optimal control of coupled time-delayed models of economic growth," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 375-399, June.
    9. Sportelli, Mario & De Cesare, Luigi, 2019. "Fiscal policy delays and the classical growth cycle," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 9-31.

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