The Employment Impact of Differences in Dmand and Production

Both decompositions are correct, but the weight, and hence importance, of the different
components could differ significantly in the two formulations. Since all are formally correct, one
would ideally compute all possible decompositions and then average across these. There are
two special cases, as follows:

∆n=∆nB⁹⁰F⁹⁰ +N⁷⁰∆BF⁹⁰ +n⁷⁰B⁷⁰∆F  [A]

alternatively, the same difference in employment can be decomposed as follows:

∆n=∆nB⁷⁰F⁷⁰+n⁹⁰∆BF⁷⁰+n⁹⁰B⁹⁰∆F   [B]

These two decompositions are known as the “polar decompositions”. The two decompositions
are equivalent; and there is no theoretical reason to prefer one to the other. However,
Dietzenbacher and Los (1998) show that the average effect of each component across all
possible decompositions is virtually identical to the average between the two polar
decompositions;

∆ n = 2(∆NB⁹⁰ F⁹⁰ + n ⁷⁰∆BF⁹⁰ + N⁷⁰ B ∆F ) + 2(∆ nB⁷⁰ F⁷⁰ + N ⁹⁰∆BF⁷⁰ + N⁹⁰ B ⁹⁰∆F )

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