Rational Asset Price Bubbles

The solution to a linear model in which supply and/or demand depends on rational expectations of future prices can involve three parts, which we denote as the fundamental component, the deterministic bubble component, and the stochastic bubble component. This paper explores the properties of these solution components, emphasizing the distinction between deterministic bubbles and stochastic bubbles, for a model of inflation and for a model of the evolution of price and quantity in the market fora storable commodity, such as gold. The analysis focuses on stochastic bubbles as a possibility peculiarly associated with models that involve rational expectations. In both the inflation model and the gold model, although the analysis points to no compelling reason to rule out rational stochastic bubbles apriori, conventional behavioral assumptions imply that anyrational bubbles that arise, whether deterministic or stochastic,are explosive. The paper discusses problems of implementing econometric tests for the existence of rational bubbles, and, as an alternative to these tests, suggests "diagnostic checking" of the stationarity properties of time series. Although these diagnostic checks do not constitute definitive hypothesis testing, we conjecture they would provide strong evidence against rational bubbles outside the context of hyperinflation.