IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v63y2003i6p505-527.html
   My bibliography  Save this article

Hicks’ trade cycle revisited: cycles and bifurcations

Author

Listed:
  • Gallegati, M.
  • Gardini, L.
  • Puu, T.
  • Sushko, I.

Abstract

In the Trade Cycle, Hicks introduced the idea that endogenous fluctuations could be coupled with a growth process via nonlinear processes. To argue for this hypothesis, Hicks used a piecewise-linear model. This paper shows the need for a reinterpretation of Hicks’ contribution in the light of a more careful mathematical investigation. In particular, it will be shown that only one bound is needed to have non explosive outcome if the equilibrium point is an unstable focus. It will also be shown that when the fixed point is unstable the attracting set has a particular structure: It is a one-dimensional closed invariant curve, made up of a finite number of linear pieces, on which the dynamics are either periodic or quasi-periodic. The conditions under which the model produces periodic or quasi-periodic trajectories and the related bifurcations as a function of the main economic parameters are determined.

Suggested Citation

  • Gallegati, M. & Gardini, L. & Puu, T. & Sushko, I., 2003. "Hicks’ trade cycle revisited: cycles and bifurcations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(6), pages 505-527.
    • Handle: RePEc:eee:matcom:v:63:y:2003:i:6:p:505-527
    DOI: 10.1016/S0378-4754(03)00060-0
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475403000600
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/S0378-4754(03)00060-0?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. Arnold Heertje & Peter Heemeijer, 2002. "On the Origin of Samuelson's Multiplier-Accelerator Model," History of Political Economy, Duke University Press, vol. 34(1), pages 207-218, Spring.
    2. Hommes, Cars H., 1995. "A reconsideration of Hicks' non-linear trade cycle model," Structural Change and Economic Dynamics, Elsevier, vol. 6(4), pages 435-459, December.
    3. James J. Duesenberry, 1950. "Hicks on the Trade Cycle," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 64(3), pages 464-476.
    4. Hommes, Cars H., 1993. "Periodic, almost periodic and chaotic behaviour in Hicks' non-linear trade cycle model," Economics Letters, Elsevier, vol. 41(4), pages 391-397.
    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. Tramontana, Fabio & Gardini, Laura & Puu, Tönu, 2009. "Cournot duopoly when the competitors operate multiple production plants," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 250-265, January.
    2. Puu, Tonu & Gardini, Laura & Sushko, Irina, 2005. "A Hicksian multiplier-accelerator model with floor determined by capital stock," Journal of Economic Behavior & Organization, Elsevier, vol. 56(3), pages 331-348, March.
    3. Zhusubaliyev, Zhanybai T. & Soukhoterin, Evgeniy & Mosekilde, Erik, 2007. "Quasiperiodicity and torus breakdown in a power electronic dc/dc converter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(6), pages 364-377.

    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. Serena Sordi & Alessandro Vercelli, "undated". "Financial Fragility and Economic Fluctuations: Numerical Simulations and Policy Implications," Modeling, Computing, and Mastering Complexity 2003 20, Society for Computational Economics.
    2. Puu, Tonu, 2007. "The Hicksian trade cycle with floor and ceiling dependent on capital stock," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 575-592, February.
    3. Matsumoto, Akio, 2009. "Note on Goodwin's 1951 nonlinear accelerator model with an investment delay," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 832-842, April.
    4. Muñoz-Guillermo, María, 2021. "Revisiting the business cycle model with cubic nonlinear investment function," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Saura, Dulce & Vazquez, Francisco J. & Vegas, Jose M., 1998. "Non-chaotic oscillations in some regularized Hicks models A restatement of the ceiling and floor conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 22(5), pages 667-678, May.
    6. Tramontana, Fabio & Gardini, Laura & Agliari, Anna, 2011. "Endogenous cycles in discontinuous growth models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1625-1639.
    7. Frank H. Westerhoff, 2008. "Heuristic Expectation Formation And Business Cycles: A Simple Linear Model," Metroeconomica, Wiley Blackwell, vol. 59(1), pages 47-56, February.
    8. Tramontana, F. & Gardini, L. & Ferri, P., 2010. "The dynamics of the NAIRU model with two switching regimes," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 681-695, April.
    9. Robert Calvert Jump & Engelbert Stockhammer, 2023. "Building blocks of a heterodox business cycle theory," Journal of Post Keynesian Economics, Taylor & Francis Journals, vol. 46(2), pages 334-358, April.
    10. Matsumoto, Akio & Szidarovszky, Ferenc, 2010. "Continuous Hicksian trade cycle model with consumption and investment time delays," Journal of Economic Behavior & Organization, Elsevier, vol. 75(1), pages 95-114, July.
    11. Iryna Sushko & Laura Gardini & Kiminori Matsuyama, 2014. "Chaos in a Model of Credit Cycles with Good and Bad Projects," Working Papers 1405, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2014.
    12. Di Matteo, Massimo & Filippi, Francesco & Sordi, Serena, 2006. "`The confessions of an unrepentant model builder': Rummaging in Goodwin's Archive," Structural Change and Economic Dynamics, Elsevier, vol. 17(4), pages 400-414, December.
    13. Westerhoff Frank H., 2006. "Nonlinear Expectation Formation, Endogenous Business Cycles and Stylized Facts," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(4), pages 1-17, December.
    14. Puu, Tonu & Gardini, Laura & Sushko, Irina, 2005. "A Hicksian multiplier-accelerator model with floor determined by capital stock," Journal of Economic Behavior & Organization, Elsevier, vol. 56(3), pages 331-348, March.
    15. Barbara Dluhosch, 2011. "European Economics at a Crossroads, by J. Barkley Rosser, Jr., Richard P. F. Holt, and David Colander," Journal of Regional Science, Wiley Blackwell, vol. 51(3), pages 629-631, August.
    16. George Kapetanios, 2003. "Threshold models for trended time series," Empirical Economics, Springer, vol. 28(4), pages 687-707, November.
    17. Schmitt, Noemi & Tuinstra, Jan & Westerhoff, Frank, 2017. "Side effects of nonlinear profit taxes in an evolutionary market entry model: Abrupt changes, coexisting attractors and hysteresis problems," Journal of Economic Behavior & Organization, Elsevier, vol. 135(C), pages 15-38.
    18. Cavalli, Fausto & Naimzada, Ahmad K. & Pecora, Nicolò, 2019. "Complex interplay between monetary and fiscal policies in a real economy model," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 318-330.
    19. Sordi, Serena & Vercelli, Alessandro, 2006. "Financial fragility and economic fluctuations," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 543-561, December.
    20. K. Vela Velupillai, 2008. "JAPANESE CONTRIBUTIONS TO NONLINEAR CYCLE THEORY IN THE 1950s," The Japanese Economic Review, Japanese Economic Association, vol. 59(1), pages 54-74, March.

    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:matcom:v:63:y:2003:i:6:p:505-527. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.