Adaptive Rational Expectations in Models of Monetary Dynamics

Carl Chiarella and Alexander Khomin - University of Technology, Sydney

The stability of the basic model of monetary dynamics under perfect foresight (e.g. Sargent and Wallace [1973], Calvo [1977]) poses a saddle point instability problem. This behavior is inherited by a wide range of models employing the perfect foresight or rational expectation assumption. The traditional solution to this problem has been to employ the so-called jump variable technique by which certain economic quantities jump instantaneously (but in an unexplained way) so as to place the economy on a manifold which is stable to its equilibrium. Whilst use of this technique is widespread it is not used without some misgivings as evidenced for example of the oft-quoted comment in Blanchard (1981).

It was shown in Chiarella (1986, 1990) that use of the jump variable technique can be obviated by introducing a nonlinear money demand function (which has different elasticities close to equilibrium and away from equilibrium) and adopting adaptive expectations with perfect foresight being treated as a limiting case as speed of expectations adjustment goes to infinity. The resulting model exhibits stable limit cycle behavior so that a stable attractor is approached from any initial value. In the perfect foresight limit the limit cycle becomes a relaxation cycle. The above scenario may be perceived as being too dependent on the change in the elasticity of money demand close to and away from equilibrium. In this paper we retain the assumption of constant elasticity of money demand and instead model expectations according to the adaptively rational expectations scheme of Brock and Hommes (1995). According to this scheme we take expectations as a weighted sum of two predictors. One which his stabilizing but costly the other free (or less costly) but destabilizing. The weights applied to these predictors evolve dynamically as the economy evolves. As the error in expectations grow (and the system becomes more unstable) greater weight is placed on the costly (stabilizing) predictor. When the system moves closer to equilibrium (and prediction error declines) greater weight is placed on the cheaper predictor which again eventually destabilizes the system. The complex dynamic to which this mechanism gives rise is investigated form a number of perspectives, eigenvalue analysis, computer simulations etc. We also briefly explore the implications of this expectations mechanism far more completely specified Keynesian models of monetary dynamics of the type considered by Chiarella and Flaschel(1996).

Scheduled for Session 5.3 Techniques In Economic Dynamics