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Fading Memory Learning in the Cobweb Model with Risk Averse Heterogeneous Producers

  • Peiyuan Zhu
  • Carl Chiarella
  • Tony He

This paper studies the dynamics of the traditional cobweb model with risk averse heterogeneous producers who seek to learn the distribution of asset prices using a geometric decay processes (GDP) - the expected mean and variance are estimated as a geometric weighted average of past observations - with either finite or infinite fading memory. With constant absolute risk aversion, the dynamics of the model can be characterized with respect to the length of memory window and the memory decay rate of the learning GPD. The dynamics of such heterogeneous learning processes and capability of producers' learning are discussed. It is found that the learning memory decay rate of the GDP of heterogeneous producers plays a complicated role on the pricing dynamics of the nonlinear cobweb model. In general, an increase of the memory decay rate plays stabilizing role on the local stability of the steady state price when the memory is infinite, but this role becomes less clear when the memory is finite. It shows a double edged effect of the heterogeneity on the dynamics. It is shown that (quasi)periodic solutions and strange (or even chaotic) attractors can be created through Neimark-Hopf bifurcation when the memory is infinite and through flip bifucation as well when the memory is finite.

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2003 with number 31.

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Date of creation: 01 Aug 2003
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Handle: RePEc:sce:scecf3:31
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  1. M. Burton, 1993. "Some Illustrations Of Chaos In Commodity Models," Journal of Agricultural Economics, Wiley Blackwell, vol. 44(1), pages 38-50.
  2. 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.
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  17. 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.
  18. Day, R H, 1992. "Complex Economic Dynamics: Obvious in History, Generic in Theory, Elusive in Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S9-23, Suppl. De.
  19. Evans, George W. & Honkapohja, Seppo, 1999. "Learning dynamics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 7, pages 449-542 Elsevier.
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