The Commodity Technology Revisited: Theoretical Basis and an Application to Error Location in the Make-Use Framework

In this paper we provide conditions for the existence of non-negative homogeneous matrices of dimensions commodity × commodity or industry × industry in the SNA framework. These matrices are shown to satisfy all conditions underlying the commodity technology model. We point out that because the matrices exist even in the case of pure byproducts the identification of their columns as commodity specific limitational production functions is not straightforward and will require additional research on the role of fixed coefficients assumptions. In the second part of the paper we discuss a method to actually calculate these non-negative matrices via a systematic search of possible sources of inaccuracy in the basic make and use tables. The method is applied to aggregated tables for the USA, where a non-negative matrix is generated in a small number of steps. We show that the failure of present day statistical optimization methods may be due to a priori reliability estimates being off by hundreds of percent. Our main conclusion is that search methods attuned to the (labour intensive) way in which most input-output tables are compiled are most promising in error location in this field.