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Stability and Cycles in a Cobweb Model with Heterogeneous Expectations

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Author Info
Laurence LASSELLE
Serge SVIZZERO
Clem TISDELL

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Abstract

We investigate the dynamics of a cobweb model with heterogeneous beliefs, generalising the example of Brock and Hommes (1997). We examine situations where the agents form expectations by using either perfect foresight, or a form of adaptive expectations with limited memory defined from the last two prices. We specify conditions that generate cycles. These conditions depend on a set of factors that includes the proportion of rational agents, the intensity of switching between beliefs, and the adaption parameter. We show that both Flip bifurcation and Neimark-Sacker bifurcation can occur as primary bifurcation when the steady state is unstable.

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Paper provided by European University Institute in its series Economics Working Papers with number ECO2004/03.

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Date of creation: 2004
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Handle: RePEc:eui:euiwps:eco2004/03

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Related research
Keywords: bounded rationality; cobweb model; flip bifurcation; neimark-sacker bifurcation; rational expectations;

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Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Carl Chiarella & Xue-Zhong He, 2001. "Asset Price and Wealth Dynamics Under Heterogeneous Expectations," Research Paper Series 56, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
    Other versions:
  2. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
  3. Lasselle, Laurence & Serge Svizzero & Clem Tisdell, 2003. "Heterogeneous Expectations, Dynamics, and Stability of Markets," Royal Economic Society Annual Conference 2003 130, Royal Economic Society. [Downloadable!]
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  4. repec:att:wimass:19956 is not listed on IDEAS
  5. Reiner Franke & Tim Nesemann, 1999. "Two destabilizing strategies may be jointly stabilizing," Journal of Economics, Springer, vol. 69(1), pages 1-18, February. [Downloadable!] (restricted)
  6. repec:cup:macdyn:v:4:y:2000:i:1:p:108-38 is not listed on IDEAS
  7. repec:att:wimass:199530 is not listed on IDEAS
  8. Woodford, Michael, 2000. "An Interview With William A. Brock," Macroeconomic Dynamics, Cambridge University Press, vol. 4(01), pages 108-138, March. [Downloadable!]
  9. Goeree, Jacob K. & Hommes, Cars H., 2000. "Heterogeneous beliefs and the non-linear cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 761-798, June. [Downloadable!] (restricted)
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  10. Branch, William A., 2002. "Local convergence properties of a cobweb model with rationally heterogeneous expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 63-85, November. [Downloadable!] (restricted)
  11. Hommes, Cars H., 1998. "On the consistency of backward-looking expectations: The case of the cobweb," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 333-362, January. [Downloadable!] (restricted)
  12. William A. Brock & Cars H. Hommes, 1995. "Rational Routes to Randomness," Working Papers 95-03-029, Santa Fe Institute.
  13. Hommes, C.H., 1999. "Cobweb Dynamics under Bounded Rationality," CeNDEF Working Papers 99-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
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