Solving Large Sparse Systems of Equations in Econometric Models

Comparative studies of Gauss-Seidel and Newton-type algorithms for solving large sparse systems of equations are reported by Népomiastchy and Ravelli (1978), Gabay et al. (1980) and Norman et al. (1983). The first two favour Newton's method, the third favours Gauss-Seidel. Apart from working on different test models, their setups differ in the implementation of both schemes. This paper studies the performance of both methods on ten different econometric models of varying size and complexity. First the choice of implementation (equation reordering, updating rules for Newton's Jacobian) is studied on a relatively small model. Qualitative and quantitative feedback criteria are considered, and an efficient reordering algorithm is discussed. On the ten models considered, the selected Newton method is almost uniformly cheaper, generally reducing the number of iterations by more than 30 percent A final section draws attention to the possible extra gains of Newton's method in evaluating multipliers for policy analysis