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Local Circularity of Six Classic Price Indexes

In: Advances in Efficiency and Productivity II

Author

Listed:
  • Jesús T. Pastor

    (Centro de Investigación Operativa, Universidad Miguel Hernández)

  • C. A. Knox Lovell

    (Centre for Efficiency and Productivity Analysis, School of Economics, University of Queensland)

Abstract

In this paper, we characterize local circularity for the Laspeyres, Paasche, and Fisher price indexes. In the first two cases, we begin by deriving a sufficient condition for achieving circularity that establishes that at least one of two proposed equalities must hold. We end up showing that the sufficient condition is also necessary. We continue with the Fisher price index that is the geometric mean of the two, and we find a sufficient circularity condition that is a direct consequence of the corresponding sufficient conditions for its two component indexes. However, we also show that, unlike its Laspeyres and Paasche components, this sufficient circularity condition for the Fisher price index is not necessary. We reach different conclusions when we extend our investigation to the circularity properties of the geometric Laspeyres, geometric Paasche, and Törnqvist price indexes, for which none of the proposed sufficient conditions is necessary. Throughout, we distinguish local circularity, which all six price indexes satisfy, from global circularity, which none of the price indexes satisfies.

Suggested Citation

  • Jesús T. Pastor & C. A. Knox Lovell, 2020. "Local Circularity of Six Classic Price Indexes," International Series in Operations Research & Management Science, in: Juan Aparicio & C. A. Knox Lovell & Jesus T. Pastor & Joe Zhu (ed.), Advances in Efficiency and Productivity II, pages 107-123, Springer.
    • Handle: RePEc:spr:isochp:978-3-030-41618-8_7
    DOI: 10.1007/978-3-030-41618-8_7
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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, January.
    2. Juan Aparicio & C. A. Knox Lovell & Jesus T. Pastor (ed.), 2016. "Advances in Efficiency and Productivity," International Series in Operations Research and Management Science, Springer, number 978-3-319-48461-7, January.
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    More about this item

    Keywords

    Price index; Local circularity;

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation

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