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Stability and Cycles in a Cobweb Model with Heterogeneous Expectations

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  • Laurence LASSELLE
  • Serge SVIZZERO
  • Clem TISDELL

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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Bibliographic Info

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

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References

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  1. repec:att:wimass:9530 is not listed on IDEAS
  2. 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.
  3. 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.
  4. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
  5. 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.
  6. 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.
  7. Reiner Franke & Tim Nesemann, 1999. "Two destabilizing strategies may be jointly stabilizing," Journal of Economics, Springer, vol. 69(1), pages 1-18, February.
  8. William A. Brock & Cars H. Hommes, 1995. "Rational Routes to Randomness," Working Papers 95-03-029, Santa Fe Institute.
  9. repec:cup:macdyn:v:4:y:2000:i:1:p:108-38 is not listed on IDEAS
  10. Woodford, Michael, 2000. "An Interview With William A. Brock," Macroeconomic Dynamics, Cambridge University Press, vol. 4(01), pages 108-138, March.
  11. 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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Cited by:
  1. Berardi, Michele, 2011. "Fundamentalists vs. chartists: Learning and predictor choice dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 776-792, May.
  2. Colucci, Domenico & Valori, Vincenzo, 2011. "Adaptive expectations and cobweb phenomena: Does heterogeneity matter?," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1307-1321, August.
  3. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186 Elsevier.
  4. Dieci, Roberto & Westerhoff, Frank, 2010. "Interacting cobweb markets," Journal of Economic Behavior & Organization, Elsevier, vol. 75(3), pages 461-481, September.
  5. Athanasiou, George & Karafyllis, Iasson & Kotsios, Stelios, 2008. "Price stabilization using buffer stocks," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1212-1235, April.

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