Stochastic Newton-like methods for computing equilibria in general equilibrium models

Abstract

Calculating an equilibrium point in general equilibrium models in many cases reduces to solving a nonlinear system of equations. Taking model parameter values as random variables with a known distribution increases the level of information provided by the model but makes computation of equilibrium points even more challenging. We propose a computationally efficient procedure based on application of the fixed Newton method for a sequence of equilibrium problems generated by simulation of parameters values. The convergence conditions of the method are derived. The numerical results presented are obtained using the neoclassic exchange model and the spatial price equilibrium model. The results show a clear difference in the quality of information obtained by solving a sequence of problems if compared with the single equilibrium problem. At the same time the proposed numerical procedure is affordable.