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Notes on Unit Value Index Bias


  • Diewert, Erwin


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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Diewert, Erwin, 2010. "Notes on Unit Value Index Bias," Economics working papers erwin_diewert-2010-26, Vancouver School of Economics, revised 23 Sep 2010.
  • Handle: RePEc:ubc:bricol:erwin_diewert-2010-26

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    References listed on IDEAS

    1. W. Erwin Diewert, 1995. "Axiomatic and Economic Approaches to Elementary Price Indexes," NBER Working Papers 5104, National Bureau of Economic Research, Inc.
    2. 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.
    3. Mick Silver, 2009. "An Index Number Formula Problem; The Aggregation of Broadly Comparable items," IMF Working Papers 09/19, International Monetary Fund.
    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.
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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. 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.
    3. 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.
    4. 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.
    5. 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.

    More about this item


    Price indexes; unit value indexes; unit values; bias; Bortkiewicz; Drobisch; Paasche; Laspeyres; Fisher; Parniczky; Balk; von der Lippe;

    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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