One challenge in building a globally balanced MRIO is that some portions of the system are underdetermined (values must be estimated or inferred) while other parts are overdetermined (different data sources provide conflicting values). Thus, all MRIOs are to some degree modeled. The build process used to create Eora generates a number of quality check reports. Additionally, there have been several intercomparison efforts to measure convergence across the major IO database (Eora, EXIOBASE, WIOD, GTAP, and OECD).
A special issue of Economic Systems Research contained several papers which investigated model intercomparison and the importance of sectoral (dis) aggregation in the calculation of environmental footprints. At that time, we assembled top-level results from each of the major MRIOs and prepared a comparison of results across the models. Also in that special issue we note the nice paper by Steen-Olsen et al. (2014) which clearly shows that high sector detail provides more accurate carbon footprints than more aggregate models.
For the paper Convergence Between the Eora, WIOD, EXIOBASE, and OpenEU's Consumption-Based Carbon Accounts we conducted a Monte Carlo sensitivity analysis for the calculation of the carbon footprint using Eora.
IO tables must be balanced: each sector's total outputs (row sum) must equal the sum of inputs (column sum). Given disaparate and conflicting input data, achieving a balanced table is always possible. These reports document how well each national IO table within Eora is balanced.
The GNI/GDP report shows the realized the National Accounting Balance identity for each country in each year. This identity says that Gross Domestic Production (GDP) + imports should equal Gross National Expenditure (GNE) less exports.
To build the Eora table we begin by assembling an initial table for 2000 using the best available data for that year. This is called the initial estimate. (This is not really an estimate because it is carefully assembled from the best available data, but mathmatically it is the initial estimate of what the final MRIO table will be after all other conflicting data sources are considered.) For many sections of this table, several alternative data sources exist. For example both the UN and a national statistical agency may supply slightly different IO tables. Or to take another example, a set of transactions which should balance in fact do not. These alternative data sources and balancing rules are called constraints since they constrain the value of all of the elements in the table.
This initial estimate plus set of constraints is run through optimisation software. The optimiser finds compromise values which least disturb the initial table while respecting any conflicting constraints. This page reports on the performance and effects of the optimiser.
These reports show which constraints involved have been best, and least, respected in the final solution.
The Adherence Reports show which constraints are best respected in the final result. These are the data sources with the
strongest influence on the results. Ideally, these reports should show that national agency data are well respected in relative value (multiples of standard deviation).
The Violation Reports show which constraints were least respected by the optimizer. This occurs when a data source
significantly disagrees with others. Ideally, the degree of violation is small -- that is, the difference between the True RHS (the value reported by the data source)
and the Realized RHS (the best compromise value achieved by the optimizer) is small. (RHS stands for Right-hand Side, or the vector c in the generalized optimization problem
Each of these reports is offered in both absolute value an in relative value (number of standard deviations). Start by checking the reports in absolute value terms. The reports in relative terms can be useful but can also sometimes be misleading since often the top violators in relative terms have small absolute values, and are thus of less importance to the overall results.
The constraint label format in the reports is documented in the document Eora Constraint Nomenclature
These same reports are also available for the initial estimate, that is, before the optimizer has been run:
|Adherence Report (before optimizer)|
|Violation Report (before optimizer)|
Imperfect balancing can result in Technical Coefficients (A matrix) values greater than 1. We cap these values at 1. This report showing
which values were capped at 1, and the original value, may be useful for diagnosing specific sectors where the result is of low confidence due to imperfect balancing:
Out of Bounds Technical Coefficients
Balancing success, per sector, in this country is shown in this first graph. Each dot is a sector, and the dot size is scaled according to the sector's size. Ideally all sectors are perfectly balanced, but it is normal to see the larger sectors balanced (along the horizontal line at 1) and smaller, outlier sectors less well-balanced. Also, as Eora is built using year 2000 as a "base" year, it is typical that the balance is best around that period.
Macro-economic totals (GDP, gross imports, gross exports, final demand, and balancing ratio):