Arbeitspapier
An exact additive decomposition of the weighted arithmetic mean
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.
- Language
-
Englisch
- Bibliographic citation
-
Series: Discussion Papers ; No. 944
- Classification
-
Wirtschaft
Index Numbers and Aggregation; Leading indicators
Labor Force and Employment, Size, and Structure
- Subject
-
Weighted Arithmetic Mean
decomposition
index theory
- Event
-
Geistige Schöpfung
- (who)
-
Thomas von Brasch
Grini, Håkon
Johnsen, Magnus Berglund
Vigtel, Trond C.
- Event
-
Veröffentlichung
- (who)
-
Statistics Norway, Research Department
- (where)
-
Oslo
- (when)
-
2021
- Handle
- Last update
-
10.03.2025, 11:44 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Arbeitspapier
Associated
- Thomas von Brasch
- Grini, Håkon
- Johnsen, Magnus Berglund
- Vigtel, Trond C.
- Statistics Norway, Research Department
Time of origin
- 2021
Other Objects (12)
An exact algorithm for weighted-mean trimmed regions in any dimension
Weighted Mean Impact Analysis
Exact computation of max weighted score estimators
Exact computation of max weighted score estimators
Weighted power mean copulas: Theory and application
Cylindrical algebraic decomposition for nonlinear arithmetic problems
On axiomizing and extending the quasi-arithmetic mean
12. Reciprocity; Gauss' Theorem of the Arithmetic Mean.
The blocking technique : weighted mean operators and Hardy's inequality
The proximal map of the weighted mean absolute error
A decomposition of functions with vanishing mean oscillation
Exact optimal designs for weighted least squares analysis with correlated errors
An exact algorithm for weighted-mean trimmed regions in any dimension
Weighted Mean Impact Analysis
Exact computation of max weighted score estimators
Exact computation of max weighted score estimators
Weighted power mean copulas: Theory and application
Cylindrical algebraic decomposition for nonlinear arithmetic problems
On axiomizing and extending the quasi-arithmetic mean
12. Reciprocity; Gauss' Theorem of the Arithmetic Mean.
The blocking technique : weighted mean operators and Hardy's inequality
The proximal map of the weighted mean absolute error
A decomposition of functions with vanishing mean oscillation
Exact optimal designs for weighted least squares analysis with correlated errors
An exact algorithm for weighted-mean trimmed regions in any dimension
Weighted Mean Impact Analysis
Exact computation of max weighted score estimators
Exact computation of max weighted score estimators
Weighted power mean copulas: Theory and application
Cylindrical algebraic decomposition for nonlinear arithmetic problems
On axiomizing and extending the quasi-arithmetic mean
12. Reciprocity; Gauss' Theorem of the Arithmetic Mean.
The blocking technique : weighted mean operators and Hardy's inequality
The proximal map of the weighted mean absolute error
A decomposition of functions with vanishing mean oscillation