Differential-difference equations in economics: On the numerical solution of vintage capital growth models

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 modem economic growth theory. The theoretical treatment of non-state-dependent differential-difference 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 growth model.