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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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    5. Hill, Robert J., 2006. "Superlative index numbers: not all of them are super," Journal of Econometrics, Elsevier, vol. 130(1), pages 25-43, January.
    6. Samuelson, Paul A, 1974. "Complementarity-An Essay on the 40th Anniversary of the Hicks-Allen Revolution in Demand Theory," Journal of Economic Literature, American Economic Association, vol. 12(4), pages 1255-1289, December.
    7. Diewert, W E & Wales, T J, 1988. "Normalized Quadratic Systems of Consumer Demand Functions," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 303-312, July.
    8. Diewert, W E & Wales, T J, 1992. "Quadratic Spline Models for Producer's Supply and Demand Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 705-722, August.
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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. Nicholas Oulton, 2012. "How To Measure Living Standards And Productivity," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 58(3), pages 424-456, September.
    3. Cardullo, Gabriele & Sechi, Agnese, 2023. "Local Labor Markets with Non-homothetic Preferences," IZA Discussion Papers 16533, Institute of Labor Economics (IZA).
    4. Michael C. Nwogugu, 2020. "Decision-Making, Sub-Additive Recursive "Matching" Noise And Biases In Risk-Weighted Stock/Bond Index Calculation Methods In Incomplete Markets With Partially Observable Multi-Attribute Pref," Papers 2005.01708, arXiv.org.
    5. 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.
    6. 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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