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Notes on Unit Value Index Bias

Author

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  • Diewert W.Erwin

    (Department of Economics, University of British Columbia, Vancouver, B.C., Canada, V6T 1Z)

  • Lippe Peter von der

    (Universität Duisburg-Essen Campus Duisburg, Mercator School of Business, Lotharstrasse 65, LB 146, 47057 Duisburg, Germany)

Abstract

It is often the case that the value of a number of somewhat similar units (e. g., automobiles of a certain general type) is divided by the number of units in order to form a unit value price and these unit value prices are compared over two periods in order to form a unit value price index. This unit value price index or Drobisch price index can then be compared with other standard index number formulae and the bias in the index can be determined. The present paper presents most of the known results on this bias (and derives some new ones) in a coherent framework using a simple identity from the statistics literature. A related question first considered by Párniczky (1974) is also considered: does disaggregation of a unit value into more homogeneous subgroups reduce the unit value bias? The answer seems to be: probably yes.

Suggested Citation

  • 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.
    • Handle: RePEc:jns:jbstat:v:230:y:2010:i:6:p:690-708
    DOI: 10.1515/jbnst-2010-0606
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    References listed on IDEAS

    as
    1. Mick Silver, 2009. "An Index Number Formula Problem: The Aggregation of Broadly Comparable items," IMF Working Papers 2009/019, International Monetary Fund.
    2. W. Erwin Diewert, 1995. "Axiomatic and Economic Approaches to Elementary Price Indexes," NBER Working Papers 5104, National Bureau of Economic Research, Inc.
    3. Timmer, Marcel P., 1996. "On the Reliability of Unit Value Ratios in International Comparisons," GGDC Research Memorandum 199631, Groningen Growth and Development Centre, University of Groningen.
    4. repec:dgr:rugggd:199631 is not listed on IDEAS
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.

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    More about this item

    Keywords

    Price indexes; unit value indexes; unit values; bias; Bortkiewicz; Drobisch; Paasche; Laspeyres; Fisher; Párniczky; Balk; von der Lippe;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • E01 - Macroeconomics and Monetary Economics - - General - - - Measurement and Data on National Income and Product Accounts and Wealth; Environmental Accounts
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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