Relevance of an accuracy control module - implementation into an economic modelling software

Buda, Rodolphe (2005): Relevance of an accuracy control module - implementation into an economic modelling software.

Abstract

Economic modelers or econometricians know that they have to control the accuracy of the computations, to get their results safe. Unfortunately, even if a few softwares allow to control it (especially in using an interval arithmetic), most of them are presented like black boxes, from an arithmetical point of view. We have tried, in this paper, to provide the point of view of a macroeconomic modelling software’s builder. After having recalled the accuracy problem and its solutions (algebraic and arithmetical), we'll present the GNOMBR software we have developed, based on multiple precision arithmetic methods. Then we'll present an application to an input-output model. Then we'll give elements to conclude to the relevance of this technique.

• Item Type: MPRA Paper
• Language: English
• Keywords: Modelling software ; Floating point arithmetic ; Accuracy Results Control ; Arithmetic Accuracy Computer
• Subjects: C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C82 - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data ; Data Access; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C87 - Econometric Software; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C88 - Other Computer Software

References

Alefeld G. & J.Herzberger, Introduction to Interval Computations, New York, Academic Press, 1983.

Avizienis A., "Signed Digit Number Representations for Fast Parallel Arithmetic", IRE Transactions on Electronic Computers, N°10, 1961, pp.389-400.

Berstel J., J.E.Pin & M.Pocchiola, Mathématiques et informatique - tome 2 Combinatoire et arithmétique, Paris, Ediscience international, Informatique, 1991, 257 p. + Programmes.

Buda R., "Présentation d’un outil de contrôle de la précision des calculs en modélisation macro-économétrique", Document de travail GAMA, Université de Paris X-Nanterre, août, 1996, 21 p. + Le logiciel GNOMBR.

Buda R., "SIMUL - Manuel de références et guide d’utilisation version 3.1", Document de travail GAMA, Université de Paris X-Nanterre, 1999, 60 p. + Le logiciel SIMUL.

Buda R., "Les algorithmes de la modélisation - une présentation critique pour la modélisation économique", Document de travail Modem N°01-44, Université de Paris X-Nanterre, juil., 2001, 97 p.

Daumas M. & J.M.Muller (Eds), Qualité des calculs sur ordinateur - vers des arithmétiques plus fiables ?, Paris, Masson, Informatique, 1997, 164 p.

Dumontet J., Vignes J., "Algorithme de dérivation numérique", RAIRO, Vol.1, 1989.

Jerrell M.E., "Interval Arithmetic for Input-Output Models with Inexact Data", Computational Economics, 1997, 10(1), pp.89-100.

Knuth D.E., The Art of Programming - tome 2, Seminumerical Algorithms, (Third ed.), Reading (Mass.), Addison-Wesley, 1997, 762 p.

Kulisch U., "Advanced Arithmetic for the Digital Computer, Design of Arithmetic Units", Electronic Notes in Theoretical Computer Science, 24 , Apr. 2000.a, 63 p.

Kulish U., "Interval Arithmetic in Forte Fortran", Technical White Paper Sun Microsystems, Palo Alto, 2000.b, 54 p.

Kulisch U.,W.M.Miranker, Computer Arithmetic in Theory and Practice, New York, Academic Press, 1981.

La Porte M., Vignes J., Algorithmiques numériques - Tome 1, Paris, Techniq, 1974, 226 p.

Maillé M., "Some Methods to Estimate Accuracy of Measurements or Numerical Computations", Processing of Mathematics for Computer, Congress AFCET, 1982.

Morgenstern O., On the Accuracy of Economic Observations, Princeton, Princeton University Press, 1950.

Moore R.E., Interval Analysis, Prentice-Hall, Englewood Cliffs (N.J.), 1966.

Muller J.M., Arithmétiques des ordinateurs - opérateurs et fonctions élémentaires, Paris, Masson, Études et recherches en informatique, 1989, 214 p.

Pichat M. & J.Vignes, Ingéniérie du contrôle de la précision des calculs sur ordinateurs, Paris, Technip, Informatique, 1993, 233 p. + Programmes.

Sofronioua M. & G.Spaletta, "Precise numerical computation", Journal of Logic and Algebraic Programming, 64(1), Jul., 2005, pp.113-134.

Taylor J., An Introduction to Error Analysis - : The Study of Uncertainties in Physical Measurements, Enfield (New Hampshire), University Science Books, 1996, 327 p.

Wirth N., Algorithmes et structures de données, Paris, Eyrolles, 1987, 320 p.