Econometrica: Nov 1979, Volume 47, Issue 6

Expectational Consistency, Informational Lags, and the Formulation of Expectations in Continuous Time Models<1457:ECILAT>2.0.CO;2-5
p. 1457-1474

Malcolm R. Gray, Stephen J. Turnovsky

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.

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