Simulating Continuous-Time Infinite Horizon Optimization Models: A Simple Method and Applications

Abstract

We propose the relaxation algorithm as a simple and powerful method for simulating the transition process in growth models. This method has a number of important advantages: First, it can easily deal with a wide range of dynamic systems including stiff differential equations and systems giving rise to a continuum of stationary equilibria. Second, the application of the procedure is fairly user friendly. The only input required is the dynamic system. Third, the variant of the relaxation algorithm we propose exploits the infinite time horizon, which usually underlies optimal control problems in economics, in a natural manner. Fourth, the algorithm can solve preannounced or anticipated parameter changes in an easy and intuitive way, which makes it very useful for policy analysis, e.g. in a dynamic General Equilibrium context. As an illustrative application, we compute the transition process of the Jones (1995) and the Lucas (1988) models. In addition, we solve the Ramsey-Cass-Koopmans model for a shock consisting of anticipated parameter changes. Finally, we construct a General Equilibrium model with heterogenous households to demonstrate the potential of the relaxation algorithm. The model is calibrated to Jordanian data and employed to solve different scenarios of trade liberalization between Jordan and the European Union. This model exhibits many of the attributes that makes the application of usual procedures highly inefficient or even impossible.