The Dynamics of the Cobweb when Producers are Risk Averse Learners
|Author(s):||Carl Chiarella & Xue-Zhong He|
|Date of publication:||September 1999|
|Working paper number:||90|
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.
|Paper:||Download (Format: PDF, Size: 809 Kb)|
|Comments:||Published as: Chiarella, C. and He, X., 2000, "The Dynamics of the Cobweb When Producers are Risk Averse Learners", In Engelbert J. Dockner, Richard F. Hartl, Mikulas Luptačik and Gerhard Sorger (eds) Optimization, Dynamics, and Economic Analysis: Essays in Honor of Gustav Feichtinger, 86-100.|
Chiarella, C. and He, X., 2003, "Dynamics of Beliefs and Learning Under aL-Processes - The Heterogeneous Case", Journal of Economic Dynamics and Control, 27(3), 503-531.
Chiarella, C., He, X., Hung, H. and Zhu, P., 2006, "An Analysis of the Cobweb Model with Boundedly Rational Heterogeneous Producers", Journal of Economic Behvior and Organization, 60(4), 750-768.
Chiarella, C., He, X. and Zhu, P., 2003. "Fading Memory Learning in the Cobweb Model with Risk Averse Heterogeneous Producers", Research Paper: 108, Quantitative Finance Research Centre, University of Technology, Sydney.
Dudek, M. K., 2005. "Expectation Formation and Endogenous Fluctuations in Aggregate Demand", Computing in Economics and Finance 2005 263, Society for Computational Economics.