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Consistent Aggregation With Superlative and Other Price Indices

Author

Listed:
  • Ludwig von Auer
  • Jochen Wengenroth

Abstract

Various fields of economic analysis (e.g., growth and productivity) and economic policy (e.g., monetary and social policy) rely on accurate measures of price change. Unfortunately, the price index formulae that most price statisticians consider as particularly accurate – the superlative indices of Fisher, Törnqvist, and Walsh – are believed to violate the property of consistency in aggregation. This property, however, is indispensable for economic studies that attempt to disaggregate the overall result into the contributions of individual entities such as sectors of the economy or groups of products. The present paper introduces a thoroughly motivated formal definition of consistency in aggregation and proves that, contrary to general perception, the three superlative price indices can be considered as consistent in aggregation. Furthermore, many other price indices are shown to be consistent in aggregation. The theoretical findings are applied to the Swedish consumer price index.

Suggested Citation

  • Ludwig von Auer & Jochen Wengenroth, 2019. "Consistent Aggregation With Superlative and Other Price Indices," Research Papers in Economics 2019-13, University of Trier, Department of Economics.
    • Handle: RePEc:trr:wpaper:201913
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    References listed on IDEAS

    as
    1. Balk,Bert M., 2012. "Price and Quantity Index Numbers," Cambridge Books, Cambridge University Press, number 9781107404960.
    2. Ludwig Auer, 2014. "The Generalized Unit Value Index Family," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 60(4), pages 843-861, December.
    3. Bert M. Balk, 1996. "Consistency‐In‐Aggregation And Stuvel Indices," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 42(3), pages 353-363, September.
    4. Hill, Robert J., 2006. "Superlative index numbers: not all of them are super," Journal of Econometrics, Elsevier, vol. 130(1), pages 25-43, January.
    5. G. Stuvel, 1989. "The Index-Number Problem and Its Solution," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-349-10816-9.
    6. Theodore M. Crone & N. Neil K. Khettry & Loretta J. Mester & Jason A. Novak, 2013. "Core Measures of Inflation as Predictors of Total Inflation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(2‐3), pages 505-519, March.
    7. Blackorby, Charles & Primont, Daniel, 1980. "Index numbers and consistency in aggregation," Journal of Economic Theory, Elsevier, vol. 22(1), pages 87-98, February.
    8. Balk, Bert M, 1996. "Consistency-in-Aggregation and Stuvel Indices," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 42(3), pages 353-363, September.
    9. Diewert, W Erwin, 1978. "Superlative Index Numbers and Consistency in Aggregation," Econometrica, Econometric Society, vol. 46(4), pages 883-900, July.
    10. repec:mcb:jmoncb:v:45:y:2013:i::p:505-519 is not listed on IDEAS
    11. Vartia, Yrjö O., . "Relative Changes and Index Numbers," ETLA A, The Research Institute of the Finnish Economy, number 4.
    12. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Consistent aggregation; index theory; superlative price index; decomposition; CPI;
    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

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