Numerical Solution of an Endogenous Growth Model with Threshold Learning

This paper describes an application of numerical methods to solve a continuous time non-linear optimal growth model with technology adoption. In the model, a non-convex production function arises from a threshold level of knowledge required to operate new technology. The study explains and illustrates how to compute the complete transition path of the growth model by applying in concert three broad numerical techniques in particular specialized ways, in order to maintain certain regularity conditions and restrictions of the model. The three broad techniques are: (i) Gauss-Laguerre quadrature for computing discounted utility over an infinite horizon; (ii) Fourth-Order Runge-Kutta method for solving differential equations; and (iii) the Penalty Functions method for solving the constrained optimization problem. The particular specializations involve linear interpolation for solving the optimal adoption time in the model and quasi-Newton iterations for maximizing the penalty-weighted objective function, the latter aided by grid search for determining initial values and Richardson extrapolation for approximating the gradient vector. Citation Copyright 1999 by Kluwer Academic Publishers.