The official GDP data also contains data on total intermediate consumption by sector (a total for each column). To estimate our matrix of intermediate use, we combine these totals with the matrix of coefficients for intermediate use reported in the supply-use table. The coefficients sum to 100% for each sector (column), and thus allow us to allocate total intermediate consumption to individual sectors (rows).

The supply-use table also has details on final demand and international trade. The totals in the table are again taken directly from official GDP data for 2006, and again we update to 2007. To estimate our matrix of final demand, in which we also include both exports and imports, we combine these totals with the matrix of coefficients reported in the supply-use table. Thus, the sectoral structure of the final demand matrix in our input-output table corresponds to the structure of the supply-use table.

This completes our estimate of the input-output table. Next we analyze the data. Our analysis of the data is mainly concerned with the supply-use balance. Supply consists of domestic production and imports. Use (or demand), consists intermediate use and final demand, including exports. In a final input-output table supply must equal demand.

Table 1 shows supply-demand imbalances by sector. We report excess demand, that is demand less supply. In absolute terms, excess demand is biggest for manufacturing followed by agriculture and construction. In relative terms, excess demand is large for most sectors. Excess demand is more than 25% of total supply in 10 out of 14 sectors<sup>37</sup> .

The imbalances need to be resolved before using the data with a model. The following section develops a balancing procedure for this purpose.

The size of the imbalances suggests significant problems in the data. This calls for additional data work before adjusting the data with a balancing procedure. Unfortunately, we could not obtain additional data to improve our initial estimate of the input-output table. Instead, we assess the quality of the different parts of the data, and collect data on the structure of input-output tables for similar countries. We use the quality assessment and the auxiliary data to guide the necessary adjustments.

# **Balancing of the input-output table**

We now develop a balancing procedure that produces a balanced input-output table. All data points in the input-output table are included and may be adjusted.

The heart of the procedure is an optimization problem that in which the elements of the table are adjusted such that an objective function is minimized subject to side constraints. The objective function is of the popular form which adds the sum of the squared deviations from the initial estimates<sup>38</sup> . The side constraints include supply-use balance by sector, and a GDP accounting identity. The latter equates total GDP by measured by income with total GDP measured by expenditure.

> 37 We did a similar analysis using data from the supply-use table only (using 2006 data only and without updating to totals for 2007). The analysis revealed similar imbalances.

> 38 All of the squared deviations are scaled by the corresponding size of the original estimate to preserve the density of the input-output table.

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