Additive Structural Decomposition Analysis and Index Number Theory: An Empirical Application of the Montgomery Decomposition

Paul De Boer
2008 Economic Systems Research  
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!, none 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
more » ... his 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. *The author is indebted to Erik Dietzenbacher and Piet Verbiest for comments and advice on an earlier version of this paper, and to Bart Los for putting the data sets at his disposal. Bert Balk, last but not least, is acknowledged for his suggestion to apply the solution of Montgomery to structural decomposition analysis.
doi:10.1080/09535310801892066 fatcat:ezxtnqncrfbsblgsvzkohlwp7u