Balance issues in input–output analysis: A comment on physical inhomogeneity, aggregation bias, and coproduction

Recently, Merciai and Heijungs (2014) demonstrated that monetary input–output (IO) analysis can lead to system descriptions that do not conserve mass when the assumption of homogeneous prices is violated. They warn that this violation of basic balance laws can lead to biased estimates of environmental impacts, and they therefore recommend performing IO analysis in a physically accounted framework. We take a broader scope on this issue and present price inhomogeneity as a special case of product mix inhomogeneity. We demonstrate that even a fully physically accounted IO analysis or lifecycle assessment will violate balance laws if it suffers from inhomogeneous aggregation. The core issue is not whether a system is described using monetary or physical units, but rather whether product groups are too aggregated to allow for the concurrent respect of energy, mass, financial and elemental balances. We further analyze the link between the violation of physical balances and the introduction of biases. We find that imbalances are neither a necessary nor a sufficient condition for the presence of systematic errors in environmental pressure estimates. We suggest two ways to leverage the additional explanatory power of multi-unit inventory tables to reduce instances of imbalances and aggregation biases.