Physical and monetary input–output analysis: What makes the difference?

A recent paper in which embodied land appropriation of exports was calculated using a physical input–output model (Ecological Economics 44 (2003) 137–151) initiated a discussion in this journal concerning the conceptual differences between input–output models using a coefficient matrix based on physical input–output tables (PIOTs) in a single unit of mass and input–output models using a coefficient matrix based on monetary input–output tables (MIOTs) extended by a coefficient vector of physical factor inputs per unit of output. In this contribution we argue that the conceptual core of the discrepancies found when comparing outcomes obtained using physical vs. monetary input–output models lies in the assumptions regarding unit prices and not in the treatment of waste as has been claimed (Ecological Economics 48 (2004) 9–17). We first show that a basic static input–output model with the coefficient matrix derived from a monetary input–output table is equivalent to one where the coefficient matrix is derived from an input–output table in physical units provided that the assumption of unique sectoral prices is satisfied. We then illustrate that the input–output tables that were used in the original publication do not satisfy the assumption of homogenous sectoral prices, even after the inconsistent treatment of waste in the PIOT is corrected. We show that substantially different results from the physical and the monetary models in fact remain. Finally, we identify and discuss possible reasons for the observed differences in sectoral prices faced by different purchasing sectors and draw conclusions for the future development of applied physical input–output analysis.