The Employment Impact of Differences in Dmand and Production

Following Momigliano and Siniscalco (1982), the vector of final demand F is to be transformed
into a block diagonal matrix whose elements (on the main diagonal) are the final demand
directed to a given block (either services or manufacturing):

GO¹¹  GO¹²  _ B¹¹  B²¹  F¹  0

GO²¹  GO²² = B¹²  B²²   0   F²

The GO matrix now represents a set of vertically integrated sectors (Pasinetti, 1973). GO¹¹
denotes the manufacturing (sector 1) output needed to sustain final demand directed to
manufacturing. GO²¹ represents the service (sectpr 2) output needed to support manufacturing
final demand (directly and indirectly). GO¹² represents the amount of manufacturing output
needed to support final demand for the service industries, and finally GO²² represents the
service output needed to support service final demand.

The matrix GO can be converted into employment units by applying the relevant labour
productivity measure. This is summarized in the labour requirement matrix N (m+s, m+s),
which provides the number of workers required per unit of gross output produced. This is a
diagonal matrix, with generic element on the main diagonal expressed as njj=Nj/GOj, where Nj is
the employment in industry j; off-diagonal elements are zero. Pre-multiplying by the labour
requirement matrix gives the employment matrix N:

The employment matrix N has several useful features. Its elements are expressed in the same
unit of measurement - number of workers -and can therefore be summed.¹⁷ The total of the
number of workers down the columns (N¹²+N²¹) reflects the employment directly and indirectly

Furthermore, the labour requirement matrix N can be derived from input-output tables at both current and
constant prices. The elements of the Leontief inverse B are pure numbers; final demand and gross output are both
in the same prices, thus cancelling out the price basis (see Appendix 3).

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