Abstract
This paper presents a new solution method for dynamic equilibrium models. The proposed method approximates the solution by polynomials that zero the residual function and its derivatives at a given point x0. It is essentially a projection-type algorithm, but is significantly faster than standard projection, since the problem is highly sparse and can be easily solved by a Newton solver. The obtained solution is accurate locally in the neighbourhood of x_0. 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. As an illustration, the paper solves a multi-country growth model and simulates the Solow convergence from an initial point of high cross-country inequality.
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