Solving Large Sparse Systems of Equations in Econometric Models

Journal of Forecasting, Vol. 6, No. 3, pages 167-180, 1987

Posted: 29 May 2007

See all articles by Giampiero M. Gallo

Giampiero M. Gallo

Corte dei Conti - Italian Court of Audits; University of Bologna - Rimini Center for Economic Analysis (RCEA); Universita' di Firenze - Dipartimento di Statistica, Informatica, Applicazioni "G.Parenti"

Henk Don

CPB Netherlands Bureau of Economic Policy Analysis

Abstract

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.

Keywords: Solution algorithms, Feedback, Newton's method, Equation reordering, Econometric models

Suggested Citation

Gallo, Giampiero M. and Don, Henk, Solving Large Sparse Systems of Equations in Econometric Models. Journal of Forecasting, Vol. 6, No. 3, pages 167-180, 1987, Available at SSRN: https://ssrn.com/abstract=989206

Giampiero M. Gallo (Contact Author)

Corte dei Conti - Italian Court of Audits ( email )

viale Mazzini
Roma, Roma 00195
Italy

University of Bologna - Rimini Center for Economic Analysis (RCEA) ( email )

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Italy

Universita' di Firenze - Dipartimento di Statistica, Informatica, Applicazioni "G.Parenti" ( email )

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Florence, 50134
Italy
0039 055 2751 591 (Phone)
0039 055 4223560 (Fax)

HOME PAGE: http://www.disia.unifi.it/gallog

Henk Don

CPB Netherlands Bureau of Economic Policy Analysis ( email )

P.O. Box 80510
2508 GM The Hague, 2585 JR
Netherlands

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