It follows that
x′ = v′[I - S]-1 = v′S* (3)
The typical elementrepresents the total (direct and indirect) production expansion in sector j induced by an additional unit of primary inputs in sector i.
Summingover j gives the forward linkage of sector i, as expressed in relation (2) in the main text.
Measuring Factor Intensities
The method of calculating factor intensities presented in Riedel ( 1975) is as follows:
Letbe the total (direct and indirect) labor requirements for one unit of output of sector j, calculated on the basis of interindustry relations regarding domestically produced intermediates only.
Letbe the total (direct and indirect) import requirements per unit of output of sector j.
Letbe the total (direct and indirect) labor requirements for the production of a unit of exports, where exports represent the vector of current exports of all commodities, scaled to sum to unity.
Letbe the total (direct and indirect) import requirement per unit of exports produced.
Then labor requirements per unit of output () are given by(1)
The reasoning behind relation (1) is that factor intensities reflect factor requirements in domestic production for output j plus the factor requirements of domestic production for the additional exports needed to pay for imported intermediates needed directly and indirectly for producing output j.
I wish to acknowledge helpful suggestions and comments from Ad ten Kate, Huib Poot, and Ivonia Rebelo and statistical assistance from Bart Kuijpers and Maarten de Zeeuw.