Optimal Control of Infinite-Horizon Growth Models — A direct approach

We propose a framework to solve dynamic nonlinear infinite-horizon models like those found in the standard economic growth literature. We employ a direct method to solve the underlying optimal control problem, something novel in the economic literature. Instead of deriving the necessary optimality conditions and solving the originated ordinary differential equations, this method first discretizes and then optimizes, in effect transforming the prob- lem into a nonlinear programming problem to be optimized at each sampling instant. We incorporate the work of Fontes (2001) in order to transform the infinite-horizon problem into an equivalent finite-horizon representation of the model. This framework presents several advantages in comparison to the available alternatives that use indirect methods. First, no linearization is required, which sometimes can be erroneous. The problem can be studied in its nonlinear form. Secondly, it enables the simulation of a shock when the economy is not at its steady state, a broad assumption required by all available numerical methods. Thirdly, it allows for the easy study of anticipated shocks. It also allows for the analysis of multiple, sequential shocks. Finally, it is extremely robust and easy to use. We illustrate the application of the framework by solving the standard Ramsey-Cass-Koopsman exogenous growth model and the Uzawa-Lucas endogenous two-sector growth model.