IDEAS home Printed from https://ideas.repec.org/p/ssb/dispap/944.html

An exact additive decomposition of the weighted arithmetic mean

Author

Listed:
  • Thomas von Brasch

  • Håkon Grini

  • Magnus Berglund Johnsen

  • Trond Christian Vigtel

    (Statistics Norway)

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.

Suggested Citation

  • Thomas von Brasch & Håkon Grini & Magnus Berglund Johnsen & Trond Christian Vigtel, 2021. "An exact additive decomposition of the weighted arithmetic mean," Discussion Papers 944, Statistics Norway, Research Department.
    • Handle: RePEc:ssb:dispap:944
    as

    Download full text from publisher

    File URL: https://www.ssb.no/en/forskning/discussion-papers/_attachment/438047?_ts=175daeaee98
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mick Silver, 2010. "The Wrongs And Rights Of Unit Value Indices," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(s1), pages 206-223, June.
    2. Mick Silver, 2009. "An Index Number Formula Problem: The Aggregation of Broadly Comparable items," IMF Working Papers 2009/019, International Monetary Fund.
    3. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    4. Diewert W.Erwin & Lippe Peter von der, 2010. "Notes on Unit Value Index Bias," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 230(6), pages 690-708, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Thomas von Brasch & Ådne Cappelen & Diana-Cristina Iancu, 2015. "Understanding the productivity slowdown. The importance of entry and exit of workers," Discussion Papers 818, Statistics Norway, Research Department.
    2. Diewert W.Erwin & Lippe Peter von der, 2010. "Notes on Unit Value Index Bias," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 230(6), pages 690-708, December.
    3. Thomas von Brasch, 2013. "The cost-of-living index with trade barriers," Discussion Papers 751, Statistics Norway, Research Department.
    4. Mick Silver, 2010. "The Wrongs And Rights Of Unit Value Indices," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(s1), pages 206-223, June.
    5. Andreas Benedictow & Pål Boug, 2014. "Calculating the real return of the Norwegian Government Pension Fund Global by alternative measures of the deflator," Discussion Papers 775, Statistics Norway, Research Department.
    6. Abe, Naohito & Inakura, Noriko & Tonogi, Akiyuki, 2017. "Effects of the Entry and Exit of Products on Price Indexes," RCESR Discussion Paper Series DP17-2, Research Center for Economic and Social Risks, Institute of Economic Research, Hitotsubashi University.
    7. Diewert, Erwin, 2019. "Quality Adjustment and Hedonics: A Unified Approach," Microeconomics.ca working papers erwin_diewert-2019-2, Vancouver School of Economics, revised 14 Mar 2019.
    8. Abe, Naohito & Enda, Toshiki & Inakura, Noriko & Tonogi, Akiyuki, 2015. "Effects of New Goods and Product Turnover on Price Indexes," RCESR Discussion Paper Series DP15-2, Research Center for Economic and Social Risks, Institute of Economic Research, Hitotsubashi University.
    9. Robert J. Hill & Alice O. Nakamura, 2010. "Improving Inflation And Related Performance Measures For Nations: An Introduction," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(s1), pages 1-10, June.
    10. W. Erwin Diewert & Kevin J. Fox, 2020. "Measuring Real Consumption and CPI Bias under Lockdown Conditions," NBER Working Papers 27144, National Bureau of Economic Research, Inc.
    11. Lorraine Ivancic & Kevin J. Fox, 2013. "Understanding Price Variation Across Stores and Supermarket Chains: Some Implications for CPI Aggregation Methods," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 59(4), pages 629-647, December.
    12. Andreas Benedictow & Pål Boug, 2022. "Exact and inexact decompositions of trade price indices," Empirical Economics, Springer, vol. 62(4), pages 1981-1994, April.
    13. W. Erwin Diewert & Kevin J. Fox & Jan de Haan, 2015. "Weekly versus Monthly Unit Value Price Indexes," Discussion Papers 2015-15, School of Economics, The University of New South Wales.
    14. Ludwig von Auer & Jochen Wengenroth, 2021. "Consistent aggregation with superlative and other price indices," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(2), pages 589-615, April.
    15. Ryadh M. Alkhareif & William A. Barnett, 2012. "Divisia Monetary Aggregates for the GCC Countries," International Symposia in Economic Theory and Econometrics, in: Recent Developments in Alternative Finance: Empirical Assessments and Economic Implications, pages 1-37, Emerald Group Publishing Limited.
    16. Volpe Martincus, Christian & Estevadeordal, Antoni, 2009. "Trade Policy and Specialization," IDB Publications (Working Papers) 2489, Inter-American Development Bank.
    17. Santos, João & Domingos, Tiago & Sousa, Tânia & St. Aubyn, Miguel, 2016. "Does a small cost share reflect a negligible role for energy in economic production? Testing for aggregate production functions including capital, labor, and useful exergy through a cointegration-based method," MPRA Paper 70850, University Library of Munich, Germany.
    18. Lescaroux, François, 2008. "Decomposition of US manufacturing energy intensity and elasticities of components with respect to energy prices," Energy Economics, Elsevier, vol. 30(3), pages 1068-1080, May.
    19. Muhammad Ali Chaudhary & Eatzaz Ahmad & Abid A. Burki & Mushtaq A. Khan, 1999. "Industrial Sector Input Demand Responsiveness and Policy Interventions," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 38(4), pages 1083-1100.
    20. Michael Peneder & Fabian Unterlass, 2024. "Die Produktivitätsentwicklung österreichischer Unternehmen in den Jahren 2013 bis 2020. Eine Auswertung von Mikrodaten," WIFO Monatsberichte (monthly reports), WIFO, vol. 97(1), pages 43-56, February.

    More about this item

    Keywords

    ;
    ;
    ;

    JEL classification:

    • J21 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Labor Force and Employment, Size, and Structure
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ssb:dispap:944. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: L Maasø (email available below). General contact details of provider: https://edirc.repec.org/data/ssbgvno.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.