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Expectational Consistency, Informational Lags, and the Formulation of Expectations in Continuous Time Models

Malcolm R. Gray
Stephen J. Turnovsky

Abstract

If one assumes, as is typically done in modelling continuous time systems, that: (i) a forecast is for an infinitesimally short future period; (ii) forecasters have instantaneous access to relevant information as it becomes available and have some ability to store that information; (iii) the variable being forecast is differentiable; then this paper shows how expectations must satisfy perfect myopic foresight. The implications of relaxing (i) and (ii), and thereby allowing for forecast errors, are discussed. In either case, a finite delay leading to a differential-difference equation (system) is generated. The implications of this for modelling continuous time systems are discussed and the procedure is illustrated with a simple example.