Rational Expectations in Stationary Linear Models

Abstract

Linear time series models have come to dominate the macroeconomic literature on rational expectations and equilibrium business cycle theory. But the explicit solution of such models has generally required strong restrictions upon the exogenous process of stochastic shocks (e.g., temporal independence) as well as upon the values of various demand and supply elasticities. This paper exhibits a solution technique, the method of z-transforms, which does not require one to impose such restrictions. The value of this method is illustrated by applying it to completely characterize the symmetric, stationary, rational expectations equilibria of a naive linear model of land speculation. This approach also permits systematic study of the informationally asymmetric equilibria of the model. THIS PAPER develops a method for analyzing rational expectations (RE) equilibria in linear economic models. The methods I shall discuss usually enable one to determine whether or not a given model has a RE equilibrium and, if one exists, to exhibit an explicit expression for the stochastic process of equilibrium prices. The techniques apply to linear models driven by stationary processes of exogenous random shocks.