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-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.

In this paper we investigate theoretically the numerical bias due to the truncation of structurally infinite time forward-looking models, by the means of various terminal conditions. On a general multivariate optimal growth model, we first analytically confirm some well-known heuristic properties for certain extreme spectral cases. However, we show that the heuristic findings stated in the literature, relying on intermediate spectral configurations, lack theoretical basis as that they omit, among other relevant features, the crucial role of initial conditions: in this case, comparison criteria exclusively based on spectral considerations lack theoretical sense. Numerical evidence is proposed to illustrate this point and other related empirical findings are presented. Citation Copyright 1997 by Kluwer Academic Publishers.

In this paper we present a theoretically founded procedure in order to check for saddlepoint stability of rational expectations models. The proposed device uses some specific perturbed finite time approximations of the models and allows for an explicit theoretical foundation. Numerical evidence are presented to study the feasibility of the procedure regarding to the scales and the spectra of the models. In particular, it is shown how to apply it on nonlinear models in connection with relaxation resolution algorithms. Actually, this paper gives theoretical basis to the heuristic sensitivity tests traditionally conducted for saddlepoint stability assessment. Citation Copyright 1996 by Kluwer Academic Publishers.