A Dynamic IS-LM Model with Adaptive Expectations

We analyze the stability of a discrete-time dynamic model with an IS-LM structure. We assume that the Aggregate Supply function is of Lucas type, and the monetary policy rule is of Friedman type. The mechanism of expectations formation is assumed to be of adaptive type (Friedman-Cagan). In its final form, the model contains two state variables, namely money supply and expected inflation. From the mathematical point of view, it is an affine discrete-time system, whose stability properties are analyzed in the paper. We deduce sufficient conditions concerning the "learning coefficient" involved in the Friedman-Cagan type of forecast equation, so that the model is stable.