Optimal Control of Infinite-Horizon Growth Models - A Direct Approach, FEP Working Paper, n. 506, 2013

Abstract

We propose a framework to solve dynamic nonlinear infinite-horizon models like thosefound in the standard economic growth literature. We employ a direct method to solve theunderlying optimal control problem, something novel in the economic literature. Instead ofderiving the necessary optimality conditions and solving the originated ordinary differentialequations, this method first discretizes and then optimizes, in effect transforming the probleminto a nonlinear programming problem to be optimized at each sampling instant. Weincorporate the work of Fontes (2001) in order to transform the infinite-horizon problem intoan equivalent finite-horizon representation of the model. This framework presents severaladvantages in comparison to the available alternatives that use indirect methods. First, nolinearization is required, which sometimes can be erroneous. The problem can be studiedin its nonlinear form. Secondly, it enables the simulation of a shock when the economy isnot 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 ofmultiple, sequential shocks. Finally, it is extremely robust and easy to use. We illustrate theapplication of the framework by solving the standard Ramsey-Cass-Koopsman exogenousgrowth model and the Uzawa-Lucas endogenous two-sector growth model.