add to this an alternative level of service share in final demand; and in the final step we further
add an alternative mix of manufacturing industries.
An example from a cross-sectional comparison will clarify (for comparison over time the
country suffixes are replaced by time suffixes). The objective is to compare the employment
effect in the US of a different final demand mix, for instance for Germany (G). The final demand
vector for the US can be partitioned into two parts, final demand for Manufactures and final
demand for Services
FD M
US
FD S
US
where the upper part of the vector contains the set of
Manufacturing industries (denoted by M) while the lower part contains the Service industries
(denoted by S). Total final demand for US products is then the element-by-element sum across
the two sub-vectors, FDUS = FDUMS + FDUSS . In the first step we change only the Service mix,
adopting the Service mix from Germany, while leaving total final demand and the Service share
unchanged. Denoting the generic industry by i the alternative final demand vector for step 1
AFD1 is:
( A
AFD1M = FDMS1
i US,i
AFD1 =
FDG
AFD1iS = G,i FDUSS
iFDS US
FDUSS AFD1S
FDUS FDUS
[3]
where FDUSS denotes final demand for Services in the US. In ADF1 US demand for Services
takes the German mix while retaining its US share in final demand.
The second step allows a change in the Services share in final demand:
18
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