Analysis of the Stability in an Economy with Sectoral Imbalances

Authors

  • Xesús Pereira López Departamento de Economía Cuantitativa Universidad de Santiago de Compostela
  • José Luis Quiñoá López Departamento de Economía Cuantitativa Universidad de Santiago de Compostela
  • Melchor Fernández Fernández Departamento de Fundamentos del Análisis Económico Universidad de Santiago de Compostela

DOI:

https://doi.org/10.46661/revmetodoscuanteconempresa.2228

Keywords:

Input-output, valores negativos, estabilidad económica, input-output, negative values, economic stability

Abstract

The presence of negative values in the primary inputs vector in the input output framework has been considered as a limitation to the development of multi-sectoral linear models. It is true that, when this circumstance happens, the industries that are related appear unbalanced, however, the whole economic system could be stable within a short time. In this paper we demonstrate that this fact does not imply an error in the construction of the input-output tables nor involves unavoidable modifications to facilitate its use in modelling. It will be shown how non-negatives solutions can appear without taking into account the classic Hawkins-Simon condition. In other words, in this paper we examine until which extent sectoral imbalances do not put in danger the viability of the whole economic system under study. In line with this, we introduce several tools, as theorems, in order to see in which cases non-negatives Leontief's inverses can exist that enable the development and solution of supply and demand input-output models. It is also considered the possible economic interpretations of the different instrumental matrices used in the described analysis.

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References

Barrios, J.; González, C.; Moreno, J.C. (2006) Álgebra Matricial para Economía y Empresa, Madrid, Delta Publicaciones.

Bidard, C. (2007) “The Weak Hawkins-Simon Condition”, Electronic Journal of Linear Algebra, 16, pp. 44–59.

Bourbaki, N. (1967) Thèories Spectrales: Éléments de Mathématique, Paris, Hermann.

Debnath, L.; Mikusinski, P. (2005) Introduction to Hilbert Spaces with Applications, San Diego, Elsevier Academic Press (3rd Editon).

Eurostat (1996) European System of National and Regional Accounts: ESA 1995, Luxemburgo, Statistical Office.

Frobenius, G. (1912) Über Matrizen aus nicht Negativen Elementen, Berlin, Sitzungsberg. Königlich Preußische Akademie der Wissenschaften, pp. 456–477.

Fujimoto, T.; Ranade, R. (2004) “Two characterizations of inverse-positive matrices: The Hawkins-Simon Condition and the Chatelier-Braun Principle”, Electronic Journal of Linear Algebra, 11, pp. 59–65.

Fujita, Y. (2008) “A Reconsideration of a Correct Economic Interpretation of the Hawkins-Simon Condition”, Fukuoka University Review of Economics, 53 (1-2), pp. 11–15.

Hawkins, D.; Simon, H.A. (1949) “Note: Some Conditions of Macro-Economic Stability”, Econometrica, 17, pp. 245–248.

Jungers, R. (2008) Thesis: Infinite Matrix Products from the Joint Spectral Radius to Combinatorics, Louvain, Université Catholique de Louvain.

Lady, G. (1996) “Detecting Stable Matrices”, Annuals of Mathematics and Artificial Intelligence, 17, pp. 29–36.

McKenzie, L.W. (1960) “Stability of Equilibrium and the Value of Excess Demand”, Econometrica, 28, pp. 606–617.

Miller, R.E.; Blair, P.D. (2009) Input-Output Analysis: Foundations and Extensions. 2nd ed. Cambridge University Press, Cambridge.

Morillas, A. (1982) “El Modelo de Leontief (Input-Output): Formulación y Limitaciones”, Cuadernos de Ciencias Económicas y Empresariales, 9 y 10, pp. 189–216.

Naciones Unidas (1999) Handbook of Input-Output Table Compilation and Analysis, Studies in Methods, Series F. 74.

Perron, O. (1907) “Zur Theorie der Matrices”, Mathematische Annalen, 64 (2), pp. 248–263.

Pulido, A.; Fontela, E. (1993): Análisis Input-Output. Modelos, Datos y Aplicaciones, Madrid, Pirámide.

Robles, L.; Sanjuán, J. (2005) “Análisis Comparativo de las Tablas Input-Output en el Tiempo”, Estadística Española, 27 (158), pp. 143–177.

Rosenblatt, D. (1957) “On Linear Models and the Graphs of Minkowski-Leontief Matrices”, Econometrica, 25, pp. 323–338.

Sánchez-Chóliz, J.; Duarte, R. (2003) “Production Chains and Linkage Indicators”, Economics Systems Research, 15 (4), pp. 481–494.

Takayama, A. (1974) Mathematical Economics, Hinsdale, III, Dryden Press.

Waugh, F.V. (1950) “Inversion of the Leontief Matrix by Power Series”, Econometrica, 18 (2), pp. 142–154.

Wood, R.J.; O'Neill, M.J. (2005) “A Faster Algorithm for Identification of an M-Matrix”, ANZIAM Journal, 46 (E), C732–C743.

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Published

2016-11-04

How to Cite

Pereira López, X., Quiñoá López, J. L., & Fernández Fernández, M. (2016). Analysis of the Stability in an Economy with Sectoral Imbalances. Journal of Quantitative Methods for Economics and Business Administration, 15, Páginas 168 a 187. https://doi.org/10.46661/revmetodoscuanteconempresa.2228

Issue

Vol. 15 (2013)

Section

Articles

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