Cobweb
A COBWEB MODEL WITH RANDOM EXPECTATIONS
Serena Brianzoni, Università degli studi di Macerata
Cristiana Mammana, Università degli studi di Macerata
Elisabetta Michetti, Università degli studi di Macerata
Francesco Zirilli, Università di Roma ‘La Sapienza’
EXTENDED ABSTRACT
1. Introduction
The cobweb model is a dynamical system that describes price fluctuations as a result of the interaction between demand function depending on current price and supply function depending on expected price.
A classic definition of the cobweb model is the one given by Ezekiel (1938) who proposed a linear model with deterministic static expectation. The least convincing elements of the initial formulation is the linearity of the functions describing the market and its simple expectations. For these reasons several efforts have been made over time to improve the original model. In a number of works nonlinearities have been introduced in the cobweb model (see Holmes and Manning (1988)) while other authors considered different kinds of price expectations (see, among others, Nerlove (1958), Chiarella (1988), Hommes (1994),
Gallas and Nusse (1996)). More recently in Mammana and Michetti (2003, 2004) an infinite memory learning mechanism has been introduced in the nonlinear cobweb model.
In this work we consider a stochastic nonlinear cobweb model that generalizes the model of Jensen and Urban (1984) assuming that the representative entrepreneur chooses between two different predictors in order to formulate his expectations:
•
backward predictor: the expectation of future price is the arithmetical mean of past observations with decreasing weights, according to a geometrical progression of ρ region;1
•
forward predictor: the formation mechanism of this expectation takes into account the market equilibrium price while considering that the current price will converge to it only in the long run.
The representative entrepreneur chooses the backward predictor with probability q
( 0 < q < 1 ) and
Serena Brianzoni, Università degli studi di Macerata
Cristiana Mammana, Università degli studi di Macerata
Elisabetta Michetti, Università degli studi di Macerata
Francesco Zirilli, Università di Roma ‘La Sapienza’
EXTENDED ABSTRACT
1. Introduction
The cobweb model is a dynamical system that describes price fluctuations as a result of the interaction between demand function depending on current price and supply function depending on expected price.
A classic definition of the cobweb model is the one given by Ezekiel (1938) who proposed a linear model with deterministic static expectation. The least convincing elements of the initial formulation is the linearity of the functions describing the market and its simple expectations. For these reasons several efforts have been made over time to improve the original model. In a number of works nonlinearities have been introduced in the cobweb model (see Holmes and Manning (1988)) while other authors considered different kinds of price expectations (see, among others, Nerlove (1958), Chiarella (1988), Hommes (1994),
Gallas and Nusse (1996)). More recently in Mammana and Michetti (2003, 2004) an infinite memory learning mechanism has been introduced in the nonlinear cobweb model.
In this work we consider a stochastic nonlinear cobweb model that generalizes the model of Jensen and Urban (1984) assuming that the representative entrepreneur chooses between two different predictors in order to formulate his expectations:
•
backward predictor: the expectation of future price is the arithmetical mean of past observations with decreasing weights, according to a geometrical progression of ρ region;1
•
forward predictor: the formation mechanism of this expectation takes into account the market equilibrium price while considering that the current price will converge to it only in the long run.
The representative entrepreneur chooses the backward predictor with probability q
( 0 < q < 1 ) and
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