Page 55 - Special Topic Session (STS) - Volume 2

STS452 Joseph M.
output of any given sector. The decomposition within the input–output
analysis framework provides a facility to discern the length of the production
chain, degree of the distribution of the production process globally
(production sharing), and position of an economy or sector in the production
sequence of a commodity. Crucially, by identifying and quantifying the
contribution (value added) of each economy or sector in the production of a
commodity, the value added decomposition permits the measurement of the
benefits accruing to the sector or economy as a result of participating in the
production, and trade, of the commodity. In terms of standard System of
National Accounts concepts, the net benefit (or income or value) accruing to
an economy or sector in order for it to be counted in as part of GDP is the
value added. The value added approach can succinctly be encapsulated in the
input–output framework tracing both the sector or economy contribution to
the full set of production processes (forward linkages) and contributions of all
the sectors or economies to the production process of a given sector
(backward linkages). An abstract technical coefficient matrix and its Leontief
inverse are presented in Figure 4.2. To recapitulate, each term in the Leontief
inverse, or total requirements matrix, of the technical coefficient matrix of an
economy shows how much of sector i’s output is needed to meet the
economy’s productive, direct and indirect, requirements to supply one unit
value of the final demand, including exports, for the output of sector j. The
column j thus gives the total requirements by the producing sector for all the
intermediates needed to produce output Xj of sector j in order to meet an
additional unit value of the final demand for the product of sector j. Row i
shows the total amount of the output of sector i needed, directly and
indirectly, by the economy to meet the final demand for the product of each
sector j. Since each element in the matrix is given in terms of output of sector
i, it can be converted into value added terms by multiplying it by the
proportion of value added, Vi, embedded in the products as shown in Figure
4.3. However, as discussed above, the total value added, even at the sector
level, translates into final use or final demand. Thus, the column sum of the
value added embedded in each term of the total requirement matrix is equal
to the final demand for a sector’s output, which is unity by definition.
Extending this mathematical formulation and multiplying the total
requirement matrix of value added (VB) by the matrix of actual level of final
demand for each sector’s product Y results in a matrix (VBY) that provides a
framework for decomposing the final demand of a sector’s product into
various, economy-sector-specific, value added components (Figure 4.4).

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