Inexact Newton methods for model simulation

Abstract

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.

Keywords:

• inexact Newton methods
• globalization strategy
• preconditioners
• forward-looking models
• matrix-free

2010 AMS Subject Classifications :

• 65H10
• 90C06

Acknowledgements

Work supported in part by INDAM-GNCS grant ‘Progetti 2010’, ‘Analisi e risoluzione iterativa di sistemi lineari di grandi dimensioni in problemi di ottimizzazione’, and by grant PRIN 20083KLJEZ, MIUR, Roma, Italia. The authors are grateful for the helpful comments made by the referee on the original manuscript.