The Rational Expectations Hypothesis in Linear Stationary Models: A New Formulation of Single-Equation Models

Abstract

In this chapter a new formulation of the rational expectations (RE) hypothesis in linear stationary models composed of a single equation is presented. Using the martingale difference approach (see, e.g., Broze et al., 1985; and Broze and Szafarz, 1991), the familiar Cagan’s (1956) hyper-inflation model is revisited in Section 7.2. Then it is generalized to include an exogenous term with an intercept and a disturbance term, an m-period ahead future expectation, several future expectations, K−1 exogenous variables and, finally, lagged values of the endogenous and exogenous variables (sections 7.3–7.7). In Cagan type model, the expectation of the future endogenous variable and the current value of this variable are determined simultaneously. In many situations, however, the expectation is formed before the current endogenous variable realizes and it is based on the past values of the endogenous and exogenous variables. This is the case, for instance, in Taylor’s (1977) macroeconomic model which is first presented and then extended along the lines sketched above (Section 7.8 through 7.11). Then Section 7.12 examines a model encompassing both the Cagan and Taylor type model as special cases. To see if the results obtained in this chapter crucially depend on the presence of future expectations, the classical Muth’s (1961) model with the expectation of the current endogenous variable is considered. The final generalization with current and future expectations is carried out in Section 7.13. The main conclusions are summarized in the final section.