By Juan Carlos Parra-Alvarez
This paper evaluates the accuracy of a set of techniques that approximate the solution of continuous-time DSGE models. Using the neoclassical growth model I compare linear-quadratic, perturbation and projection methods. All techniques are applied to the HJB equation and the optimality conditions that define the general equilibrium of the economy. Two cases are studied depending on whether a closed form solution is available. I also analyze how different degrees of non-linearities affect the approximated solution. The results encourage the use of perturbations for reasonable values of the structural parameters of the model and suggest the use of projection methods when a high degree of accuracy is required.
Continuous-time DSGE models are not very popular but do have some interest applications. While there is an extensive literature looking at solution methods for discrete-time models that is looking a computing performance and precisions, that literature is much scarcer for the continuous-time kind. That paper is a good start.