We examine techniques for the analytical and numerical
solution of state-dependent differential-difference equations. Such equations
occur in the continuous-time modelling of vintage capital growth models,
which form an important class of models in modern economic growth theory.
The theoretical treatment of non-state-dependent differential equations
in economics was discussed by Benhabib and Rustichini (1991). In general,
though, the state dependence of a model prevents its analytical solution
in all but the simplest of cases. We review a numerical method for solving
state-dependent models, using simple examples to illustrate our discussion.
In addition, we apply this numerical method to the Solow vintage capital