Taylor Projection: A New Solution Method for Dynamic General Equilibrium Models

Abstract

This article presents a new solution method for dynamic equilibrium models. The solution is approximated by polynomials that zero the residual function and its derivatives at a given point x. The algorithm is essentially a type of projection but is significantly faster, since the problem is highly sparse and can be easily solved by a Newton solver. The obtained solution is accurate locally in the neighborhood of x. Importantly, a local solution can be obtained at any point of the state space. This makes it possible to solve models at points that are further away from the steady state.