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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, generalizing the example of Brock and Hommes (1997). We examine situations where the agents form expectations by using either rational expectations, or a type 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 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 Centre for Dynamic Macroeconomic Analysis in its series CDMA Working Paper Series with number 200706.

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Date of creation: 15 Jan 2007
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Handle: RePEc:san:cdmawp:0706

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Keywords: Bounded rationality; Cobweb model; Flip bifurcation; Neimark-Sacker bifurcation.;

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References

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  1. 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.
  2. 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.
  3. Xue-Zhong (Tony) He & Carl Chiarella, 2001. "Asset Price and Wealth Dynamics under Heterogeneous Expectations," CeNDEF Workshop Papers, January 2001 5A.2, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  4. 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.
  5. repec:att:wimass:9506 is not listed on IDEAS
  6. William A. Brock & Cars H. Hommes, 1995. "Rational Routes to Randomness," Working Papers 95-03-029, Santa Fe Institute.
  7. Woodford, Michael, 2000. "An Interview With William A. Brock," Macroeconomic Dynamics, Cambridge University Press, vol. 4(01), pages 108-138, March.
  8. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
  9. repec:cup:macdyn:v:4:y:2000:i:1:p:108-38 is not listed on IDEAS
  10. Reiner Franke & Tim Nesemann, 1999. "Two destabilizing strategies may be jointly stabilizing," Journal of Economics, Springer, vol. 69(1), pages 1-18, February.
  11. 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.
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Cited by:
  1. Michele Berardi, 2008. "Fundamentalists vs. chartists: learning and predictor choice dynamics," Centre for Growth and Business Cycle Research Discussion Paper Series 104, Economics, The Univeristy of Manchester.
  2. 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.
  3. Dieci, Roberto & Westerhoff, Frank, 2010. "Interacting cobweb markets," Journal of Economic Behavior & Organization, Elsevier, vol. 75(3), pages 461-481, September.
  4. 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.
  5. 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.

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