STABLE SOLUTIONS TO HOMOGENEOUS DIFFERENCE-DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS: ANALYTICAL INSTRUMENTS AND AN APPLICATION TO MONETARY THEORY

摘要

In economic systems, reactions to external shocks often come with a delay. On the other hand, agents try to anticipate future developments. Both can lead to difference-differential equations with an advancing argument. These are more difficult to handle than either difference or differential equations, but they have the merit of added realism and increased credibility. This paper generalizes a model from monetary economics by von Kalckreuth and Schroder. Working out its stability properties, we present a general method for determining the stability of any solution to a homogeneous linear difference-differential equation with constant coefficients and advancing arguments.