Krylov methods for solving models with forward-looking variables

Abstract

Abstract The simulation of large macroeconometric models containing forward-looking variables can become impractical when using exact Newton methods. The difficulties generally arise from the use of direct methods for the solution of the linear system in the Newton step. In such cases, nonstationary iterative methods, also called Krylov methods, provide an interesting alternative. In this paper we apply such methods to simulate a real world econometric model. Our numerical experiments confirm the interesting features of these techniques: low computational complexity and storage requirements. We also discuss a block preconditioner suitable for the particular class of models solved.