Numerical Analysis of Some Innovation-Adoption Models with State-Dependent Lags

In this paper, we introduce adoption/gestation lags in some standard growth models with a vintage capital structure. The diffusion of innovations is not immediate, and this can be modeled using adoption lags. Adoption lags are specified according to Nelson and Phelps (1966), AER. In particular, adoption lags are taken state-dependent: they are indeed modeled as functions of some proxies of the aggregate human capital of the economies under consideration. We show that the modified models can be written as systems of delay differential equations or integro-delay differential equations. By construction, the delays are state-dependent. To solve the models, we use a version of the methods of steps. Concretely, we use the ARCHI code written by Paul for state-dependent delays systems. Particular attention has been paid to the ability of this code to handle non-differentiabilities in the solution paths, a feature inherent to vintage capital models.