Analysis of uncertainty in the Leontief model by interval arithmetic
Keywords:
System Of Interval Linear Equations, Uncertainty, Economic Modeling, Leontief Model
Abstract
This paper presents an innovative strategy to enhance the precision of economic projections through the integration of interval arithmetic into the Leontief model. We emphasise the utilisation of the Gauss-Seidel method for solving linear systems with interval coefficients. In this paper, we present a method that use the Gauss-Seidel approach to effectively solve linear systems consisting of interval coefficients. This technique enhances traditional methods by incorporating potential value intervals, in addition to exact numerical values. The result is a more precise reflection of uncertainty and a more accurate calculation of solution intervals for economic variables. We have implemented this approach in the Moroccan economic context using the Gauss-Seidel method to solve linear systems with interval coefficients. On the basis of real economic data, we have demonstrated how this technique can have a positive impact on the accuracy of output and sensitivity evaluations in the Leontief model.References
Wassily Leontief, Input-output analysis? Input-output economics, 2nd ed, oxford university press, pp 19--40, 1986.
M. Granger, and M. Henrion,Uncertainty, Cambridge University Press, 1990.
V. Beletskyy, A. Chemeris and E. Nowatskaja, Sensitivity analysis of a Leontief model, SAMO 2001, Third International Symposium on Sensitivity Analysis of Model Output, Madrid, 2001.
M. Lenzen, A generalized Input-Output multiplier Calculus for Australia, Economic System Research, Vol. 13 No. 1, 2001.
K. Ganesan, P. Veeramani, On arithmetic operations of interval numbers, International Journal of Uncertainty, Fuzziness and Knowledge - Based Systems, vol. 13, No. 6, pp. 619--631, 2005.
R.E.Moore, R. B. Kearfott and M.J.Cloud, Introduction to Interval Analysis, SIAM, 2009.
T. nirmala, D. datta, H. s. kushwaha, and K. ganesan, Inverse interval matrix : a new approach, Book title. Applied mathematical sciences, vol. 5, no. 13, 607 -- 624, 2011.
S. Ning, R. B. Kearfott, "A comparison of some methods for solving linear interval equations," SIAM Journal of Numerical Analysis, vol. 34, no. 4, pp. 1289-1305, 1997.
S. Ning, and R. B. Kearfott, A comparison of some methods for solving linear interval equations, SIAM Journal of Numerical Analysis, vol. 34, no. 4, pp. 1289--1305, 1997.
E. R. Hansen, Bounding the solution of interval linear equations, SIAM Journal of Numerical Analysis, Vol. 29, no. 5, pp. 1493--1503, 1992.
E.A Haddad, F. El-hattab, A. Ait ali, A practitioner’s guide for building the interregional input-output system for Morocco 2013, august 2017.
M.A Benhari, and M. Kaicer, Using interval arithmetic on the Leontief model, Advanced Intelligent Systems for Sustainable Development (AI2SD’2020), vol. 1, Springer, pp. 1079–-1085, 2022.
M. Granger, and M. Henrion,Uncertainty, Cambridge University Press, 1990.
V. Beletskyy, A. Chemeris and E. Nowatskaja, Sensitivity analysis of a Leontief model, SAMO 2001, Third International Symposium on Sensitivity Analysis of Model Output, Madrid, 2001.
M. Lenzen, A generalized Input-Output multiplier Calculus for Australia, Economic System Research, Vol. 13 No. 1, 2001.
K. Ganesan, P. Veeramani, On arithmetic operations of interval numbers, International Journal of Uncertainty, Fuzziness and Knowledge - Based Systems, vol. 13, No. 6, pp. 619--631, 2005.
R.E.Moore, R. B. Kearfott and M.J.Cloud, Introduction to Interval Analysis, SIAM, 2009.
T. nirmala, D. datta, H. s. kushwaha, and K. ganesan, Inverse interval matrix : a new approach, Book title. Applied mathematical sciences, vol. 5, no. 13, 607 -- 624, 2011.
S. Ning, R. B. Kearfott, "A comparison of some methods for solving linear interval equations," SIAM Journal of Numerical Analysis, vol. 34, no. 4, pp. 1289-1305, 1997.
S. Ning, and R. B. Kearfott, A comparison of some methods for solving linear interval equations, SIAM Journal of Numerical Analysis, vol. 34, no. 4, pp. 1289--1305, 1997.
E. R. Hansen, Bounding the solution of interval linear equations, SIAM Journal of Numerical Analysis, Vol. 29, no. 5, pp. 1493--1503, 1992.
E.A Haddad, F. El-hattab, A. Ait ali, A practitioner’s guide for building the interregional input-output system for Morocco 2013, august 2017.
M.A Benhari, and M. Kaicer, Using interval arithmetic on the Leontief model, Advanced Intelligent Systems for Sustainable Development (AI2SD’2020), vol. 1, Springer, pp. 1079–-1085, 2022.
Published
2025-02-07
How to Cite
benhari, mohamed amine, & MOHAMMED, K. (2025). Analysis of uncertainty in the Leontief model by interval arithmetic. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2279
Issue
Section
Research Articles
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
