Multi-level comparisons of input–output tables using cross-entropy indicators

We introduce a cross-entropy (CE) indicator to quantify the extent to which two input–output tables or two tables with results based on input–output analysis differ from each other. Our work deploys a unique feature of the CE indicator: it can be decomposed, allowing for matrix comparisons at various levels within one coherent framework. To illustrate the power of this approach, we apply the technique to five multi-region input–output (MRIO) tables for 2011, derived from the Eora, EXIOBASE, GTAP, OECD and WIOD databases. We make pairwise comparisons between MRIOs and between global value chain (GVC) computations based on these MRIOs. We find that answers to questions related to broader aggregates are generally quite similar, but that answers to questions at the level of single industries can be rather different across MRIOs.