A reliable and computationally efficient algorithm for imposing the saddle point property in dynamic models

摘要

(Anderson and Moore, 1983; Anderson and Moore, 1985) describe a powerful method for solving linear saddle point models. The algorithm has proved useful in a wide array of applications including analyzing linear perfect foresight models, providing initial solutions and asymptotic constraints for nonlinear models. Although widely used at the Federal Reserve, few outside the central bank know about or have used the algorithm. This paper attempts to present the current algorithm in a more accessible format in the hope that economists outside the Federal Reserve may also find it useful. In addition, over the years there have been many undocumented changes in approach that have improved the efficiency and reliability of algorithm. This paper describes the present state of development of this set of tools. This paper analyzes a general linear saddle point model with a unique steady state and a unique solution converging to that steady state for any set of temporally predetermined variables. We prove that any such model has a reduced form relating the solution sequence entirely to its history, and we present an efficient procedure for computing the reduced form coefficients. The procedure is a generalization of the familiar saddlepoint analysis, and it is straightforward to program. The procedure consists of efficient library routines for matrix rank determination and invariant space calculation embedded in a simple control structure. The algorithm solves linear probles with dozens of lags and leads and hundreds of equations in seconds. The technique works well for both symbolic algebra and numerical computation.