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The Specification of Adaptive Expectations in Continuous Time Dynamic Economic Models

Edwin Burmeister
Stephen J. Turnovsky

Abstract

A logically consistent specification of the adaptive expectations hypothesis in continuous time is derived from an underlying discrete time model. We distinguish between (i) the time interval between predictions and (ii) the time horizon over which predictions are made. Taking limits of the expectation equation as these time intervals approach zero, we derive a mixed difference-differential equation and a mixed total-partial differential equation, respectively, describing actual changes. When these are combined with other equations in an economic model, the expectation mechanism provides a simultaneous determination of both expected and actual dynamics. New results are obtained in three separate applications: (i) the short-run stability of multi-asset markets, (ii) a heterogeneous capital goods model, and (iii) a Phillips curve model of wage-price inflation.