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Inexact Newton methods for model simulation. (English) Zbl 1238.91009

Summary: 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.

MSC:

91-08 Computational methods for problems pertaining to game theory, economics, and finance
65H10 Numerical computation of solutions to systems of equations
65F08 Preconditioners for iterative methods
91B64 Macroeconomic theory (monetary models, models of taxation)

Software:

Matlab; STRSCNE
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References:

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