Discussion Papers no. 944
An exact additive decomposition of the weighted arithmetic mean
Several multiplicative decompositions of the unit value index are described in literature.
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.
About the publication
- Title
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An exact additive decomposition of the weighted arithmetic mean
- Author
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Thomas von Brasch, Håkon Grini, Magnus Berglund Johnsen and Trond Christian Vigtel
- Series and number
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Discussion Papers no. 944
- Publisher
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Statistisk sentralbyrå
- Topic
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Discussion Papers
- ISSN
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1892-753X
- About Discussion Papers
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Discussion papers comprise research papers intended for international journals and books. A preprint of a Discussion Paper may be longer and more elaborate than a standard journal article as it may include intermediate calculations, background material etc.
Contact
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Statistics Norway's Information Centre