Efficient solution techniques for linear and non-linear rational expectations models

Abstract

Large scale non-linear econometric models are routinely used for policy analysis, forecasting and optimal control exercises. The incorporation of rational (or consistent forward looking) expectations into such models has been hindered by the lack of simple and reliable numerical solution methods. The analytical literature of rational expectations models suggests several methods of solution, but only the iterative techniques suggested by Anderson (1979) and Fair and Taylor (1983) are sufficiently general to carry over to non-linear models of any size and complexity. This paper reviews a general class of iterative algorithms of which the Anderson-Fair-Taylor technique is a special case. Convergence conditions and efficient computational forms are given for the linear case, with extensions to non-linear models. These methods are then applied to solve two large scale non-linear models of the UK economy. For the models considered, substantial reductions in computational burden are achieved by a combination of efficient solution techniques and one parameter extrapolation methods.