Additive Structural Decomposition Analysis and Index Number Theory: An Empirical Application of the Montgomery Decomposition
Additive Structural Decomposition Analysis and Index Number Theory: An Empirical Application of the Montgomery Decomposition
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DOI：
10.1080/09535310801892066
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发表时间：
2008-03
影响因子：
2.5
通讯作者：
P. M. C. De Boer
中科院分区：
文献类型：
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作者：
P. M. C. De Boer
近年来，该期刊上发表了大量关于结构分解分析的实证文章，其目的是将变量的总体变化分解为其r个因子。常用的方法是对两个极坐标分解求平均值和对所有r！初等分解（Dietzenbacher and Los, 1998, D&L）。我们建议使用“理想”蒙哥马利分解，这意味着它满足指数理论中施加的因子反转的要求。与前面提到的方法相比，我们更喜欢它。两个极坐标分解的平均值不是“理想的”，因此结果取决于因子的排序。所有初等分解的平均值是“理想的”，但随着因子数量的增加，需要计算越来越多的分解。通过对四因素D&L的实例分析表明，三种方法得到的结果较为接近。
ABSTRACT In recent years, a large number of empirical articles on structural decomposition analysis, which aims at disentangling an aggregate change in a variable into its r factors, has been published in this journal. Commonly used methods are the average of the two polar decompositions and the average of all r! elementary decompositions (Dietzenbacher and Los, 1998, D&L). We propose to use instead the ‘ideal’ Montgomery decomposition, which means that it satisfies the requirement of factor reversal imposed in index number theory. We prefer it to the methods previously mentioned. The average of the two polar decompositions is not ‘ideal’, so that the outcome depends on the ordering of the factors. The average of all elementary decompositions is ‘ideal’, but requires the computation of an ever increasing number of decompositions when the number of factors increases. Application to the example of D&L (four factors) shows that the three methods yield results that are close to each other.