Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/249134 
Year of Publication: 
2021
Series/Report no.: 
Discussion Papers No. 944
Version Description: 
Updated: 8 September 2021
Publisher: 
Statistics Norway, Research Department, Oslo
Abstract: 
The weighted arithmetic mean is used in a wide variety of applications. An infinite number of possible decompositions of the weighted mean are available, and it is therefore an open question which of the possible decompositions should be applied. In this paper, we derive a decomposition of the weighted mean that is rooted in functional analysis. Our proposed decomposition is easy to employ and interpret, and we show that it satisfies the difference counterpart to the index number time reversal test. We illustrate the framework by decomposing aggregate earnings growth from 2020Q1 to 2021Q1 in Norway and compare it with some of the main decompositions proposed in the literature. We find that the wedge between the identified compositional effects from the proposed decomposition and the Bennet decomposition is substantial, and for some industries, the compositional effects are of opposite signs.
Subjects: 
Weighted Arithmetic Mean
decomposition
index theory
JEL: 
C43
J21
Document Type: 
Working Paper

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