Given value added in each sector it is possible using an exogenously provided input/output matrix (A) to determine the level of gross production in each sector. We will see below, however, that the A-matrix is actually computed as a function of GDP per capita—the model interpolates among multiple A-matrices for various levels of GDP per capita in a procedure originally developed for the GLOBUS model (Hughes 1987).

Given gross production and the A-matrix we can compute intersectoral flows (INTS).

Production available for final demand (PFD) is the residual of gross production minus the sum delivered to all columns.

GDP per capita-linked generic A-matrices are created in the pre-processor of IFs. To build them the IFs project turned to the IO matrices collected in the Global Trade Analysis Project. That database includes extensive data, including IO matrices, for 127 regions/individual countries across 57 sectors in GTAP 8 (every version tends to increase geographic coverage). With origins in 1992 of the now global project at the agricultural economics department of Purdue, GTAP heavily represents agricultural sectors. Narayanan, Aguilar and McDougall (2012) documented GTAP 8 (see also earlier versions including Dimaranan and McDougall (2002) for GTAP 5).

The pre-processor of IFs (Hughes and Irfan 2006) processes the IO matrices of GTAP to create those needed by IFs. One aspect of that involves collapsing the sectors to those of IFs (currently 6) using a concordance table. Even more importantly, however, the pre-processor generates from the most recent GTAP files within IFs a set of nine generic IO matrices to represent the average technical coefficient pattern of countries at different levels of GDP per capita. The generic matrices are calculated as unweighted averages of matrices for all countries with GDPs per capita in categories established by lower-end breakpoints of $0, $175, $375, $750, $1,500, $3,000, $6,000, $12,000, and $24,000.

The assumption behind the generic IO matrices is that countries at different GDP per capita levels typically use different types of technology. The resultant IO matrices bear this out in ways that seem intuitively plausible. For example, Tables 3.1 and 3.2 show (using earlier data from GTAP 5) the technical coefficient matrices for extreme levels of GDP/capita, below $100 and above $24,000, respectively. Note, for instance, how much lower a share of manufactures goes into the agricultural sector in the richest countries relative to the poorest, and how much more of the IC sector goes back into the IC sector in richer countries.

These generic matrices are used for two purposes. First, they are used for estimating values for countries of IFs that are NOT in the GTAP data set. Second, they are used in the actual dynamic calculations of the model. As countries rise in GDP/capita, interpolations between matrices above and below their level allow us to gradually change the matrix representing each country.

GTAP also provides data on return to four factors of production in each sector: land, unskilled labor, skilled labor, and capital. These returns represent value added and are very important data for the value added blocks of the SAM. The pre-processor also collapses these values into the (six) sectors of IFs and computes generic shares of the factors in value added by GDP per capita category, using the same unweighted average technique used for the IO coefficients. Once again the generic value-added shares are used both to fill country holes in the GTAP data set and to provide a basis for dynamically representing changes in those shares as countries develop.

The changes across the levels of GDP/capita appear reasonable. Note, for instance, the general shift of return to skilled from unskilled labor and the increase in returns to labor in total for the manufacturing and ICT sectors (at the expense of capital and other inputs).

The equations for value added and income in household categories can be found in the discussion of households as agents. Although the GTAP data by no means provide everything that was needed for the generation of universal SAMs, the project is aware of the utility of SAMs (Brockmeier and Arndt 2002) and provided several primary data inputs that serve our purposes.

Further, the GTAP data and the GDP per capita threshold approach is used in the pre-processor to compute a generic table for labor demand coefficients by sector, distinguishing skilled and unskilled labor. These are stored in the IOLaborCoefs table of IFs.mdb and are available for the computation of labor demand in the economic model.