Structural decomposition analysis and index number theory: an empirical application of the Montgomery decomposition.

Abstract In recent years a large number of empirical articles on structural decomposition analysis, which aims at disentangling an aggregate change into its factors, has been published in Economic Systems Research. Dietzenbacher and Los (D&L) proved that in case of n factors the number of possible decompositions is equal to n!, non of which satisfies time reversal. Averages of decompositions satisfy this requirement, such as the average of all decompositions. In index number theory this problem is known as the decomposition of an aggregate change into symmetric factors (usually two: price and quantity). Balk proposes to generalize the Montgomery decomposition, which obeys time reversal, to three factors. In this paper we apply this solution to a more intricate decomposition into four factors, viz. the example analyzed by D&L. We show that for most sectors the results of the Montgomery decomposition are remarkably close to those of the average of the 24 decompositions.