IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v25y2005i1p91-108.html
   My bibliography  Save this article

Hopf bifurcation and chaos in macroeconomic models with policy lag

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077904006411
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2004.09.075?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
    2. Ioannides, Yannis M. & Taub, Bart, 1992. "On dynamics with time-to-build investment technology and non-time-separable leisure," Journal of Economic Dynamics and Control, Elsevier, vol. 16(2), pages 225-241, April.
    3. Mackey, Michael C., 1989. "Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors," Journal of Economic Theory, Elsevier, vol. 48(2), pages 497-509, August.
    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. 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.

    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. 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.
    2. Ghassan Dibeh, 2001. "Time Delays and Business Cycles: Hilferding's model revisited," Review of Political Economy, Taylor & Francis Journals, vol. 13(3), pages 329-341.
    3. Kitagawa, Akiomi & Shibata, Akihisa, 2001. "Long gestation in an overlapping generations economy: endogenous cycles and indeterminacy of equilibria," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 99-127, February.
    4. Ralph Winkler, 2008. "Optimal compliance with emission constraints: dynamic characteristics and the choice of technique," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 39(4), pages 411-432, April.
    5. De Cesare, Luigi & Sportelli, Mario, 2005. "A dynamic IS-LM model with delayed taxation revenues," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 233-244.
    6. De Cesare, Luigi & Sportelli, Mario, 2022. "A non-linear approach to Kalecki’s investment cycle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 57-70.
    7. Ulrich Brandt-Pollmann & Ralph Winkler & Sebastian Sager & Ulf Moslener & Johannes Schlöder, 2008. "Numerical Solution of Optimal Control Problems with Constant Control Delays," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 181-206, March.
    8. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Working Papers hal-03145949, HAL.
    9. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics.
    10. Gori, Luca & Guerrini, Luca & Sodini, Mauro, 2015. "A continuous time Cournot duopoly with delays," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 166-177.
    11. Heinzel, Christoph & Winkler, Ralph, 2006. "Gradual versus structural technological change in the transition to a low-emission energy industry: How time-to-build and differing social and individual discount rates influence environmental and tec," Dresden Discussion Paper Series in Economics 09/06, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    12. Cui, Dan & Wei, Xiang & Wu, Dianting & Cui, Nana & Nijkamp, Peter, 2019. "Leisure time and labor productivity: A new economic view rooted from sociological perspective," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 13, pages 1-24.
    13. Chambers, Marcus J., 1998. "The estimation of systems of joint differential-difference equations," Journal of Econometrics, Elsevier, vol. 85(1), pages 1-31, July.
    14. Richard Hartl & Peter Kort, 2010. "Delay in finite time capital accumulation," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(4), pages 465-475, December.
    15. Paul Zak, 1999. "Kaleckian Lags in General Equilibrium," Review of Political Economy, Taylor & Francis Journals, vol. 11(3), pages 321-330.
    16. Olivia BUNDAU & Mihaela NEAMTU, 2009. "The Analysis of an Economic Growth Model with Tax Evasion and Delay," Timisoara Journal of Economics, West University of Timisoara, Romania, Faculty of Economics and Business Administration, vol. 2(1(5)), pages 13-18.
    17. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    18. Ralph Winkler, 2008. "Optimal control of pollutants with delayed stock accumulation," CER-ETH Economics working paper series 08/91, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    19. d’Albis, Hippolyte & Augeraud-Veron, Emmanuelle & Venditti, Alain, 2012. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 295-308.
    20. Christoph Heinzel & Ralph Winkler, 2011. "Distorted Time Preferences and Time-to-Build in the Transition to a Low-Carbon Energy Industry," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 49(2), pages 217-241, June.

    More about this item

    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:eee:chsofr:v:25:y:2005:i:1:p:91-108. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.