IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/38566.html
   My bibliography  Save this paper

Covariances and relationships between price indices: Notes on a theorem of Ladislaus von Bortkiewicz on linear index functions

Author

Listed:
  • von der Lippe, Peter

Abstract

The note examines a generalization of a theorem of Bortkiewicz which relates the difference between a Paasche and a Laspeyres price index to a covariance between price and quantity relatives. The generalized theorem is used to demonstrate a number of interesting special applications. It turns out that some known relationships between two index functions can be expressed more elegantly. In other cases where not much is known yet about how the two functions are related to one another, we could establish an interesting equation on the basis of this theorem. This demonstrates the remarkable flexibility and usefulness of the generalized Bortkiewicz - theorem.

Suggested Citation

  • von der Lippe, Peter, 2012. "Covariances and relationships between price indices: Notes on a theorem of Ladislaus von Bortkiewicz on linear index functions," MPRA Paper 38566, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:38566
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/38566/1/MPRA_paper_38566.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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. 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.
    2. Thomas von Brasch & Ådne Cappelen & Diana‐Cristina Iancu, 2018. "Measuring Labour Services: Quality‐Adjusting the Entry and Exit of Workers," Scandinavian Journal of Economics, Wiley Blackwell, vol. 120(2), pages 597-623, April.
    3. 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.
    4. Fast Don & Fleck Susan E. & Smith Dominic A., 2022. "Unit Value Indexes for Exports – New Developments Using Administrative Trade Data," Journal of Official Statistics, Sciendo, vol. 38(1), pages 83-106, March.
    5. 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.
    6. Thomas von Brasch, 2015. "On measuring the contribution from firm turnover to aggregate productivity growth. Selection on profitability and not productivity," Discussion Papers 819, Statistics Norway, Research Department.
    7. 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.

    More about this item

    Keywords

    price indices of Laspeyres; Paasche; Drobisch; Carli; Dutot; covariance; Bortkiewicz; unit value index;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pra:mprapa:38566. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.