Inexact Newton methods for model simulation

Robust and efficient solution techniques for solving macroeconometric models are increasingly becoming a key factor in developing models employed by policy-making institutions for policy simulations and forecasting. Traditionally, when solved in the presence of forward-looking variables, these models are nonlinear, large-scale and sparse and give rise to large and highly structured nonlinear systems. This paper proposes a Newton-GMRES method obtained tuning up the basic algorithm by properly choosing the forcing terms sequence and the preconditioning strategy. In addition, the Newton–GMRES method is wrapped into a globalization strategy based on a nonmonotone linesearch technique in order to enlarge its convergence basin and to enhance its robustness. The combination of these ingredients yields a reliable method with low memory requirements. Numerical experiments using the MULTIMOD model and a basic real business cycle model are presented. A Matlab code based on this approach is provided.