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Stability And Cycles In A Cobweb Model With Heterogeneous Expectations

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  • LASSELLE, LAURENCE
  • SVIZZERO, SERGE
  • TISDELL, CLEM

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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Suggested Citation

  • Lasselle, Laurence & Svizzero, Serge & Tisdell, Clem, 2005. "Stability And Cycles In A Cobweb Model With Heterogeneous Expectations," Macroeconomic Dynamics, Cambridge University Press, vol. 9(05), pages 630-650, November.
  • Handle: RePEc:cup:macdyn:v:9:y:2005:i:05:p:630-650_05
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    1. repec:cup:macdyn:v:4:y:2000:i:1:p:108-38 is not listed on IDEAS
    2. Woodford, Michael, 2000. "An Interview With William A. Brock," Macroeconomic Dynamics, Cambridge University Press, vol. 4(01), pages 108-138, March.
    3. 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.
    4. 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.
    5. C. Chiarella & X-Z. He, 2001. "Asset price and wealth dynamics under heterogeneous expectations," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 509-526.
    6. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    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. 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.
    9. William A. Brock & Cars H. Hommes, 1995. "Rational Routes to Randomness," Working Papers 95-03-029, Santa Fe Institute.
    10. 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. Christophe Gouel, 2012. "Agricultural Price Instability: A Survey Of Competing Explanations And Remedies," Journal of Economic Surveys, Wiley Blackwell, vol. 26(1), pages 129-156, February.
    2. Hommes, C.H., 2005. "Heterogeneous Agent Models in Economics and Finance, In: Handbook of Computational Economics II: Agent-Based Computational Economics, edited by Leigh Tesfatsion and Ken Judd , Elsevier, Amsterdam 2006," CeNDEF Working Papers 05-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    3. Schmitt, Noemi & Westerhoff, Frank, 2015. "Managing rational routes to randomness," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 157-173.
    4. Schmitt, Noemi & Westerhoff, Frank, 2015. "Evolutionary competition and profit taxes: market stability versus tax burden," BERG Working Paper Series 104, Bamberg University, Bamberg Economic Research Group.
    5. 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.
    6. 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.
    7. 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.
    8. Dieci, Roberto & Westerhoff, Frank, 2010. "Interacting cobweb markets," Journal of Economic Behavior & Organization, Elsevier, vol. 75(3), pages 461-481, September.
    9. 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.
    10. ., 2013. "Market impediments, restrained reactions and market dynamics," Chapters,in: Competition, Diversity and Economic Performance, chapter 9, pages 183-201 Edward Elgar Publishing.
    11. 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.

    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - 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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