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Cost of Living Indexes and Exact Index Numbers

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  • Diewert, Erwin

Abstract

The paper reviews and extends the theory of exact and superlative index numbers. Exact index numbers are empirical index number formula that are equal to an underlying theoretical index, provided that the consumer has preferences that can be represented by certain functional forms. These exact indexes can be used to measure changes in a consumer’s cost of living or welfare. Two cases are considered: the case of homothetic preferences and the case of nonhomothetic preferences. In the homothetic case, exact index numbers are obtained for square root quadratic preferences, quadratic mean of order r preferences and normalized quadratic preferences. In the nonhomothetic case, exact indexes are obtained for various translog preferences.

Suggested Citation

  • Diewert, Erwin, 2009. "Cost of Living Indexes and Exact Index Numbers," Economics working papers erwin_diewert-2009-6, Vancouver School of Economics, revised 13 Feb 2009.
  • Handle: RePEc:ubc:bricol:erwin_diewert-2009-6
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    File URL: http://www.econ.ubc.ca/diewert/dp0906.pdf
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    References listed on IDEAS

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    6. Diewert, W. E. & Wales, T. J., 1988. "A normalized quadratic semiflexible functional form," Journal of Econometrics, Elsevier, vol. 37(3), pages 327-342, March.
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    9. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
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    Cited by:

    1. Brynjolfsson, Erik & Collis, Avinash & Diewert, Erwin & Eggers, Felix & FOX, Kevin J., 2019. "GDP-B: Accounting for the Value of New and Free Goods in the Digital Economy," Microeconomics.ca working papers erwin_diewert-2019-6, Vancouver School of Economics, revised 27 Mar 2019.
    2. Balk Bert M., 2010. "Lowe and Cobb-Douglas Consumer Price Indices and their Substitution Bias," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 230(6), pages 726-740, December.
    3. W. Diewert & Kevin Fox, 2010. "Malmquist and Törnqvist productivity indexes: returns to scale and technical progress with imperfect competition," Journal of Economics, Springer, vol. 101(1), pages 73-95, September.

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    More about this item

    Keywords

    Exact index numbers; superlative index numbers; flexible functional forms; Fisher ideal index; normalized quadratic preferences; mean of order r index;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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