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The Dynamics of the Cobweb when Producers are Risk Averse Learners

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In this paper we investigate the dynamics of the traditional cobweb model where producres are risk averse and seek to learn the distribution of asset prices. We consider the subjective estimates of the statistical distribution of the market prices based on L-step backward time series of market clearing prices. With constant absolute risk aversion, the cobweb model becomes nonlinear. Sufficient conditions on the local stability of the unique positive equilibrium of the nonlinear model are derived and, consequently, we show that the local stability region is proportional to the lag length L. When the equilibrium loses its local stability, we show that, for L = 2, the model has a strong 1:3 resonance bifurcation and a family of fixed points of order 3 becomes unstable on both sides of criticality. For general lag lengths, numerical simulations suggest that the model displays a variety of complex dynamics.

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  • Carl Chiarella & Xue-Zhong He, 1999. "The Dynamics of the Cobweb when Producers are Risk Averse Learners," Working Paper Series 90, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    • Handle: RePEc:uts:wpaper:90
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    File URL: http://www.finance.uts.edu.au/research/wpapers/wp90.pdf
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    References listed on IDEAS

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    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. Chiarella, Carl, 1988. "The cobweb model: Its instability and the onset of chaos," Economic Modelling, Elsevier, vol. 5(4), pages 377-384, October.
    3. Holmes, James M. & Manning, Richard, 1988. "Memory and market stability : The case of the cobweb," Economics Letters, Elsevier, vol. 28(1), pages 1-7.
    4. Jensen, Roderick V. & Urban, Robin, 1984. "Chaotic price behavior in a non-linear cobweb model," Economics Letters, Elsevier, vol. 15(3-4), pages 235-240.
    5. Boussard, Jean-Marc, 1996. "When risk generates chaos," Journal of Economic Behavior & Organization, Elsevier, vol. 29(3), pages 433-446, May.
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    Cited by:

    1. Maciej K. Dudek, 2004. "Expectation Formation and Endogenous Fluctuations in Aggregate Demand," Econometric Society 2004 Latin American Meetings 103, Econometric Society.
    2. Chiarella, Carl & He, Xue-Zhong & Hommes, Cars, 2006. "A dynamic analysis of moving average rules," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1729-1753.
    3. Xue-Zhong He, 2004. "Dynamics of Beliefs and Learning Under aL-Processes—The Homogeneous Case," International Symposia in Economic Theory and Econometrics, in: Economic Complexity, pages 363-390, Emerald Group Publishing Limited.
    4. Carl Chiarella & Xue-Zhong He & Peiyuan Zhu, 2003. "Fading Memory Learning in the Cobweb Model with Risk Averse Heterogeneous Producers," Research Paper Series 108, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Chiarella, Carl & He, Xue-Zhong & Hung, Hing & Zhu, Peiyuan, 2006. "An analysis of the cobweb model with boundedly rational heterogeneous producers," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 750-768, December.
    6. Chiarella, Carl & He, Xue-Zhong, 2003. "Dynamics of beliefs and learning under aL-processes -- the heterogeneous case," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 503-531, January.

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