Structural Decomposition Techniques: Sense and Sensitivity

Structural decomposition techniques are widely used to break down the growth in some variable into the changes in its determinants. In this paper, we discuss the problems caused by the existence of a multitude of equivalent decomposition forms which are used to measure the contribution of a specific determinant. Although it is well known that structural decompositions are not unique, the extent of the problem and its consequences seem to have been largely neglected. In an empirical analysis for The Netherlands between 1986 and 1992, results are calculated for 24 equivalent decomposition forms. The outcomes exhibit a large degree of variability across the different forms. We also examine the two approaches that have been used predominantly in the literature. The average of the two so-called polar decompositions appears to be remarkably close to the average of the full set of 24 decompositions. The approximate decomposition with mid-point weights appears to be almost exact. Although this last alternative might seem a solution to the problem of the marked sensitivity, in fact, it only conceals the problem.