A dynamical systems model of price bubbles and cycles

Abstract

Various markets exhibit growth and collapse in prices that are sometimes called bubbles, and cycles if the phenomenon repeats. Rational expectations models have been proposed to explain these phenomena; however, such models suffer from a number of criticisms, including lack of experimental support. Moreover, they assume unbiased forecasts without explaining how the investors form their forecasts. In this paper, we provide a model of asset price forecasts and market prices that can be calibrated with experimental data and that can capture various behavioural characteristics of investors such as confidence and panic. We study the resulting dynamical system and show that asset price bubbles may result from seemingly reasonable forecasts and decisions of investors. The model attempts to provide insight into the qualitative connection between investors’ forecasting behaviour and the formation of bubbles and cycles. We present results on the convergence of the process to a fixed point, or to an attractor that describes a price cycle, or to long-run behaviour that seems unpredictable, and we consider where in the cycles most time is spent.