Perfect foresight models and the dynamic instability problem from a higher viewpoint

Dynamic macroeconomic models incorporating perfect foresight expectations can display a dynamic instability of the saddle point type. So that unless the initial values happen to place the system on the stable arm of the saddle point, the economic variables will diverge ever more from the equilibrium. We consider the dynamic instability problem in a simple model of monetary dynamics which is non-linear and assumes adaptive expectations which are characterized by an expectations time lag. This model is shown to have a stable limit cycle. By considering perfect foresight as the limit as the expectations time lag tends to zero we are able to view the perfect foresight model from a dimension higher than that from which is it is normally viewed. We are thus able to see that the stable limit cycle continues to exist for the perfect foresight model as well. In this framework there is no longer a dynamic instability problem since whatever the intial values time paths are tending to the stable limit cycle.