Rectangular input-output models by Moore-Penrose inverse

Abstract

The official available data must be the primary datasource in economic studies. However, in economic modelling related with supply-use tables this aspect is ignored. In fact, as in this structure the number of products exceeds the number of industries, there is considerable information lost due to aggregations in order to get square matrices. Nevertheless, rectangular matrices can directly be modelled using generalized inverses. The main aim of this paper is to highlight the fact that it is not required to elaborate symmetric input-output tables for modelling. In spite of it, in this paper it is reminded how to construct symmetric matrices through the two main traditional hypotheses: product technology and industry technology. Finally, an empirical application is shown with the goal of highlight different alternatives in this area.