Learning, Estimation, And The Stability Of Rational Expectations

This paper is an investigation of the stability of the rational expectations equilibrium of a simple asset market model, in a situation where a group of dealers are learning by estimating the relationship between the price and return on the asset by ordinary least squares, and using their estimates in predicting the return from the price. The model which is being estimated is a well specified model of the rational expectations equilibrium, but a mis-specified model of the situation in which the dealers are learning. Two learning methods are studied; in the first the estimates reach their probability limits before a new forecasting rule is adopted, in the second the forecasting rule is modified each time a new data point is observed. The stability of the rational expectations equilibrium under both these learning rules depends upon a parameter k, which is a function of the proportion of demand which originates from the dealers who are learning and the regression coefficient of return on price in the rational expectations equilibrium. The conditions for global stability of the equilibrium are -1 < k < 1 under the first learning method and k > -1 under the second.