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Stability And Cycles In A Cobweb Model With Heterogeneous Expectations

Author

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

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(5), pages 630-650, November.
    • Handle: RePEc:cup:macdyn:v:9:y:2005:i:05:p:630-650_05
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    References listed on IDEAS

    as
    1. Hommes, Cars H., 1991. "Adaptive learning and roads to chaos : The case of the cobweb," Economics Letters, Elsevier, vol. 36(2), pages 127-132, June.
    2. Woodford, Michael, 2000. "An Interview With William A. Brock," Macroeconomic Dynamics, Cambridge University Press, vol. 4(1), 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. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    5. 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.
    6. 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.
    7. Clem Tisdell, 1996. "Bounded Rationality and Economic Evolution," Books, Edward Elgar Publishing, number 960.
    8. Laurence Lasselle & Serge Svizzero & Clement Allan Tisdell, 2003. "Heterogeneous Expectations, Dynamics, and Stability of Markets," Post-Print hal-02163226, HAL.
    9. Laurence Lasselle & Serge Svizzero & Clement Allan Tisdell, 2003. "Heterogeneous Expectations, Dynamics, and Stability of Markets," Post-Print hal-02163226, HAL.
    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.
    12. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    13. Frankel, Jeffrey A & Froot, Kenneth A, 1990. "Chartists, Fundamentalists, and Trading in the Foreign Exchange Market," American Economic Review, American Economic Association, vol. 80(2), pages 181-185, May.
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    Citations

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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, 2018. "Evolutionary Competition And Profit Taxes: Market Stability Versus Tax Burden," Macroeconomic Dynamics, Cambridge University Press, vol. 22(8), pages 2007-2031, December.
    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. Dieci, Roberto & Mignot, Sarah & Westerhoff, Frank, 2022. "Production delays, technology choice and cyclical cobweb dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    10. 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.
    11. Clement A. Tisdell, 2017. "Bounded Rationality, Satisficing and the Evolution of Economic Thought," Economic Theory, Applications and Issues Working Papers 264873, University of Queensland, School of Economics.
    12. ., 2013. "Market impediments, restrained reactions and market dynamics," Chapters, in: Competition, Diversity and Economic Performance, chapter 9, pages 183-201, Edward Elgar Publishing.
    13. 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.
    14. Guo Feng & Liu Chong & Shi Qingling, 2019. "Smart or stupid depends on who is your counterpart: a cobweb model with heterogeneous expectations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(5), pages 1-17, December.
    15. Clement A. Tisdell, 2018. "Diversity In Economic Decision-Making And Behaviour: A New Brief Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 22(1), pages 351-368, December.

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    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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