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An Index Number Formula Problem: The Aggregation of Broadly Comparable items

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  • Mick Silver

Abstract

Index number theory informs us that if data on matched prices and quantities are available, a superlative index number formula is best to aggregate heterogeneous items, and a unit value index to aggregate homogeneous ones. The formulas can give very different results. Neglected is the practical case of broadly comparable items. This paper provides a formal analysis as to why such formulas differ and proposes a solution to this index number problem.

Suggested Citation

  • Mick Silver, 2009. "An Index Number Formula Problem: The Aggregation of Broadly Comparable items," IMF Working Papers 2009/019, International Monetary Fund.
    • Handle: RePEc:imf:imfwpa:2009/019
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    References listed on IDEAS

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    1. Hong, Pilky & McAfee, R. Preston & Nayyar, Ashish, 2002. "Equilibrium Price Dispersion with Consumer Inventories," Journal of Economic Theory, Elsevier, vol. 105(2), pages 503-517, August.
    2. Silver, Mick & Heravi, Saeed, 2007. "Why elementary price index number formulas differ: Evidence on price dispersion," Journal of Econometrics, Elsevier, vol. 140(2), pages 874-883, October.
    3. Jerry Hausman & Ephraim Leibtag, 2009. "CPI Bias from Supercenters: Does the BLS Know that Wal-Mart Exists?," NBER Chapters, in: Price Index Concepts and Measurement, pages 203-231, National Bureau of Economic Research, Inc.
    4. Silver, Mick & Heravi, Saeed, 2005. "A Failure in the Measurement of Inflation: Results From a Hedonic and Matched Experiment Using Scanner Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 269-281, July.
    5. Mick Silver & Saeed Heravi, 2006. "Why Elementary Price Index Number Formulas Differ: Price Dispersion and Product Heterogeneity," IMF Working Papers 2006/174, International Monetary Fund.
    6. Mick Silver, 2007. "Do Unit Value Export, Import, and Terms of Trade Indices Represent or Misrepresent Price Indices?," IMF Working Papers 2007/121, International Monetary Fund.
    7. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    8. Alan T. Sorensen, 2000. "Equilibrium Price Dispersion in Retail Markets for Prescription Drugs," Journal of Political Economy, University of Chicago Press, vol. 108(4), pages 833-862, August.
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    Cited by:

    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.
    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. Daniel Ripperger-Suhler, 2024. "Consumer Learning and Price Index Bias: How Diffusion of Product Quality Knowledge Impacts Measures of Price Change," BEA Papers 0131, Bureau of Economic Analysis.
    4. 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.
    5. de Haan, Jan & Diewert, W. Erwin & Fox, Kevin J., 2015. "Weekly versus Monthly Unit Value Price Indexes," Economics working papers erwin_diewert-2015-15, Vancouver School of Economics, revised 20 Jul 2015.
    6. 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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