Numerical Solution of an Endogenous Growth Model with Threshold Learning

Baoline Chen - Rutgers University

This paper describes an application of numerical methods to solve a continuous time non-linear optimal growth model with technology adoption, and the model involves a non-convex production function due to a threshold level of knowledge required to operate the 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-Laugerre quadrature for computing discounted utility over an infinite horizon; ii) Fourth-Order Runge-Kutta method for solving differential equation; 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 extroplation for approximating the gradient vector.

Key words: Numerical optimization, non-linear optimal growth, non-convexity

JEL classification: O4, O3, D9, C6

Scheduled for Session 2.2 Modeling Economic Dynamics And Adjustment Costs