Negatives in symmetric input–output tables: the impossible quest for the Holy Grail

Abstract

In the Supply-Use (or Make-Use) input–output models, “product-technology” (PT) or “fixed-industry-sales-structure” (FISS) assumptions are more widely adopted (SNA, Eurostat) for deriving symmetric input–output tables (SIOT) than “industry-technology” or “fixed-product-sales-structure” assumptions, but generate negatives in the SIOT. A SIOT deduced from the Supply-Use model is considered as satisfactory as soon as it contains no more negatives; scholars have focused on the negatives in the SIOT and on how to remove them. However, as a SIOT may include no negatives even if there are some negatives in the inverse Supply matrix, we have completely reversed the reasoning. A counter-example demonstrates that computing the inverse Supply matrix, as imposed by PT or FISS assumptions, is mathematically a nonsense operation even when the symmetric input–output tables do not include any negative; this result is new. Hence, deriving a SIOT under PT or FISS assumption must be rejected. Three applications are provided: Austria 2000 and 2005 and USA 2007.