A state space approach to the estimation of price expectations

One of the most pervasive forms of the unobservable variable problem in econometrics is the appearance of expectational variables in any carefully motivated theory of economic behavior. Some theory of expectation formation must lie at the base of all but the most tautological theories of individual decision making. This fact has long been recognized by economists and the common approach to dealing with it has been to model expectations as a deterministic function of the past values of the variable being considered. This paper suggests a procedure for estimating expectations as the unobservable states of a dynamic system. The approach used combines output correlation methods with the Kalman filter to obtain estimates of the price expectations. These techniques have been widely used in the control theory literature to address unobservable problems in engineering applications although certain modifications are necessary to make them fully applicable in an econometric environment.