Stable Solutions to Homogeneous Difference : Differential Equations with Constant Coefficients

In economic reality, 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. 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. We will also demonstrate the applicability of our concepts to economic modelling.