IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v32y2008i3p939-955.html
   My bibliography  Save this article

Chaotic equilibria in models with backward dynamics

Author

Listed:
  • Kennedy, Judy A.
  • Stockman, David R.

Abstract

Some economic models like the cash-in-advance model of money or overlapping generations model have the property that the dynamical system characterizing equilibria in the model are multi-valued going forward in time, but single-valued going backward in time, i.e., the model or dynamical system has backward dynamics. In such instances, what does it mean for a dynamical system (set-valued) to be chaotic? Furthermore, under what conditions are such dynamical systems chaotic? In this paper, we provide a definition of chaos that is in the spirit of Devaney for a dynamical system with backward dynamics. We utilize the theory of inverse limits to provide necessary and sufficient conditions for such a dynamical system to be chaotic.

Suggested Citation

  • Kennedy, Judy A. & Stockman, David R., 2008. "Chaotic equilibria in models with backward dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 939-955, March.
    • Handle: RePEc:eee:dyncon:v:32:y:2008:i:3:p:939-955
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(07)00106-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Michener, Ronald & Ravikumar, B., 1998. "Chaotic dynamics in a cash-in-advance economy," Journal of Economic Dynamics and Control, Elsevier, vol. 22(7), pages 1117-1137, May.
    2. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    3. Christiano, Lawrence J. & G. Harrison, Sharon, 1999. "Chaos, sunspots and automatic stabilizers," Journal of Monetary Economics, Elsevier, vol. 44(1), pages 3-31, August.
    4. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    5. Medio, Alfredo & Raines, Brian, 2007. "Backward dynamics in economics. The inverse limit approach," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1633-1671, May.
    6. Medio,Alfredo & Gallo,Giampaolo, 1995. "Chaotic Dynamics," Cambridge Books, Cambridge University Press, number 9780521484619, January.
    7. Lucas, Robert E, Jr & Stokey, Nancy L, 1987. "Money and Interest in a Cash-in-Advance Economy," Econometrica, Econometric Society, vol. 55(3), pages 491-513, May.
    8. David Stockman & Judy Kennedy & James Yorke, 2006. "Inverse Limits and Models with Backward Dynamics," Working Papers 06-12, University of Delaware, Department of Economics.
    9. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
    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. Gardini, Laura & Hommes, Cars & Tramontana, Fabio & de Vilder, Robin, 2009. "Forward and backward dynamics in implicitly defined overlapping generations models," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 110-129, August.
    2. David Stockman & Judy Kennedy & James Yorke, 2006. "Inverse Limits and Models with Backward Dynamics," Working Papers 06-12, University of Delaware, Department of Economics.
    3. Kennedy, Judy & Stockman, David R. & Yorke, James A., 2008. "The inverse limits approach to chaos," Journal of Mathematical Economics, Elsevier, vol. 44(5-6), pages 423-444, April.
    4. Airaudo, Marco, 2016. "Endogenous Stock Price Fluctuations with Dynamic Self-Control Preferences," School of Economics Working Paper Series 2016-2, LeBow College of Business, Drexel University.
    5. Nika Lazaryan & Thomas A. Lubik, 2019. "Global dynamics in a search and matching model of the labor market," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(2), pages 461-497, September.
    6. Nika Lazaryan & Thomas A. Lubik, 2017. "Global Dynamics in a Search and Matching Model of the Labor Market," Working Paper 17-12, Federal Reserve Bank of Richmond.
    7. Jess Benhabib & Jianjun Miao & Pengfei Wang, 2016. "Chaotic banking crises and regulations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(2), pages 393-422, February.
    8. David R. Stockman, 2008. "Uniform Measures On Inverse Limit Spaces," Working Papers 08-25, University of Delaware, Department of Economics.
    9. Grandmont, Jean-Michel, 2008. "Nonlinear difference equations, bifurcations and chaos: An introduction," Research in Economics, Elsevier, vol. 62(3), pages 122-177, September.
    10. Timsina, Archana Neupane & Mireles James, J.D., 2022. "Parameterized stable/unstable manifolds for periodic solutions of implicitly defined dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    11. Deng, Liuchun & Khan, M. Ali, 2018. "On growing through cycles: Matsuyama’s M-map and Li–Yorke chaos," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 46-55.
    12. David R. Stockman & Judy Kennedy & Brian Raines, 2007. "Expected Utility in Models with Chaos," Working Papers 07-16, University of Delaware, Department of Economics.
    13. Walter Briec & Laurence Lasselle, 2013. "On the Use of the Renormalization Procedure to Estimate the Bifurcation Parameters in Nonlinear Dynamic Models," Computational Economics, Springer;Society for Computational Economics, vol. 41(4), pages 557-574, April.
    14. Alves, P.R.L. & Duarte, L.G.S. & da Mota, L.A.C.P., 2017. "A new characterization of chaos from a time series," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 323-326.

    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. David R. Stockman, 2008. "Uniform Measures On Inverse Limit Spaces," Working Papers 08-25, University of Delaware, Department of Economics.
    2. Kennedy, Judy & Stockman, David R. & Yorke, James A., 2008. "The inverse limits approach to chaos," Journal of Mathematical Economics, Elsevier, vol. 44(5-6), pages 423-444, April.
    3. Medio, Alfredo & Raines, Brian, 2007. "Backward dynamics in economics. The inverse limit approach," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1633-1671, May.
    4. David R. Stockman & Judy Kennedy & James A. Yorke, 2005. " Inverse Limits and Models with Ill-Defined Forward Dynamics," Working Papers 05-06, University of Delaware, Department of Economics.
    5. David Stockman & Judy Kennedy & James Yorke, 2006. "Inverse Limits and Models with Backward Dynamics," Working Papers 06-12, University of Delaware, Department of Economics.
    6. David R. Stockman & Judy Kennedy & Brian Raines, 2007. "Expected Utility in Models with Chaos," Working Papers 07-16, University of Delaware, Department of Economics.
    7. Tarek Coury & Yi Wen, 2009. "Global indeterminacy in locally determinate real business cycle models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 49-60, March.
    8. Hippolyte D'Albis & Emmanuelle Augeraud-Veron, 2008. "Endogenous Retirement and Monetary Cycles," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(4), pages 214-229.
    9. Michener, Ronald & Ravikumar, B., 1998. "Chaotic dynamics in a cash-in-advance economy," Journal of Economic Dynamics and Control, Elsevier, vol. 22(7), pages 1117-1137, May.
    10. Calvet, Laurent E., 2001. "Incomplete Markets and Volatility," Journal of Economic Theory, Elsevier, vol. 98(2), pages 295-338, June.
    11. Tvede Mich, 2009. "Fluctuations in Overlapping Generations Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-19, May.
    12. 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.
    13. Simonovits, Andras, 1999. "Are there cycles in realistic overlapping cohorts models?," Structural Change and Economic Dynamics, Elsevier, vol. 10(2), pages 261-275, June.
    14. Stockman, David R., 2010. "Balanced-budget rules: Chaos and deterministic sunspots," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1060-1085, May.
    15. Grandmont, Jean-Michel, 2008. "Nonlinear difference equations, bifurcations and chaos: An introduction," Research in Economics, Elsevier, vol. 62(3), pages 122-177, September.
    16. Molnar, Gyorgy & Simonovits, Andras, 1998. "Expectations, (in)stability and (in)viability in realistic overlapping cohorts models," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 303-332, September.
    17. Orlando Gomes, 2007. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing, vol. 33(6), pages 437-468, January.
    18. Stockman, David R., 2009. "Chaos and sector-specific externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 2030-2046, December.
    19. Fukuda, Shin-ichi, 2004. "Extraneous shocks and international linkage of business cycles in a two-country monetary model," Journal of Economic Behavior & Organization, Elsevier, vol. 54(3), pages 389-409, July.
    20. Gardini, Laura & Hommes, Cars & Tramontana, Fabio & de Vilder, Robin, 2009. "Forward and backward dynamics in implicitly defined overlapping generations models," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 110-129, August.

    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:dyncon:v:32:y:2008:i:3:p:939-955. 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.elsevier.com/locate/jedc .

    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.