A new alternative for matrix balancing under conflicting information

Abstract

Balancing input–output tables using iterative proportional fitting techniques can be prevented due to conflicting information. What is to be done in such cases? Literature suggests a wide variety of alternative methods. Within iterative proportional fitting techniques, modifying the constraint set to circumvent conflicting information problems has been suggested as a promising avenue. Following this approach, we identify some opportunities for improvement not yet been addressed. As a result of this research, we present an iterative proportional fitting variant. Our algorithm uses information contained in the matrix to be balanced for dynamically modifying our constraint set. We ensure economically meaningful solutions, avoiding unsought sign flips. We also respect all macroeconomic aggregates. To illustrate our findings, we provide an empirical example based on the supply-use tables for the region of Galicia (Northwest Spain). Results suggest that our methodological proposal can yield estimates almost as accurate as other alternatives while avoiding undesired outcomes.

KEYWORDS:

• Input–output
• RAS
• conflicting information

JEL Codes:

• C67
• C61
• C65

Acknowledgements

We would like to thank professors André Carrascal Incera, Esteban Fernández Vázquez, Geoffrey J.D. Hewings and Carmen Ramos Carvajal for their valuable comments and suggestions. We are also grateful to the four referees involved in the peer review process. However, the authors account for all possible mistakes contained in this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 In this section, notation used in the quoted contributions has been adapted for coherency purposes.

2 Matrices are denoted in upper-case bold font; vectors in lower-case bold font and scalars are denoted in italic font. Vectors are columns by definition. Superscript indicates transposition. Subscript • is used to note sum across a specific dimension. A circumflex, $\hat{x}$, indicates that the vector has been transformed into a square diagonal matrix, i.e. one with elements on the main diagonal and zeros elsewhere. For clarity purposes, we substitute circumflex by ‘diag’ to denote a square diagonal matrix involving a composite vector. A vector of ones is denoted by i.

3 All data used in cases II and III can be retrieved from: https://www.ige.eu/web/mostrar_actividade_estatistica.jsp?idioma=gl&codigo=0307007003

4 For example, the main production of an industry could be the one chosen for the underconstrained scaling, letting the secondary products to adjust biproportionally.