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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.

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File URL: http://www.econ.ubc.ca/diewert/dp0906.pdf
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Bibliographic Info

Paper provided by Vancouver School of Economics in its series Economics working papers with number erwin_diewert-2009-6.

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Length: 34 pages
Date of creation: 21 Jan 2009
Date of revision: 13 Feb 2009
Handle: RePEc:ubc:bricol:erwin_diewert-2009-6

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Web page: http://www.economics.ubc.ca/

Related research

Keywords: Exact index numbers; superlative index numbers; flexible functional forms; Fisher ideal index; normalized quadratic preferences; mean of order r index;

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References

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  1. Blackorby, Charles & Diewert, W E, 1979. "Expenditure Functions, Local Duality, and Second Order Approximations," Econometrica, Econometric Society, vol. 47(3), pages 579-601, May.
  2. Samuelson, Paul A & Swamy, S, 1974. "Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis," American Economic Review, American Economic Association, vol. 64(4), pages 566-93, September.
  3. Hill, Robert J., 2006. "Superlative index numbers: not all of them are super," Journal of Econometrics, Elsevier, vol. 130(1), pages 25-43, January.
  4. Balk,Bert M., 2008. "Price and Quantity Index Numbers," Cambridge Books, Cambridge University Press, number 9780521889070, October.
  5. 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 1255-89, December.
  6. 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 303-12, July.
  7. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
  8. W. Erwin Diewert & T.J. Wales, 1989. "Flexible Functional Forms and Global Curvature Conditions," NBER Technical Working Papers 0040, National Bureau of Economic Research, Inc.
  9. M. Denny, 1974. "The Relationship Between Functional Forms for the Production System," Canadian Journal of Economics, Canadian Economics Association, vol. 7(1), pages 21-31, February.
  10. Diewert, W. E. & Wales, T. J., 1988. "A normalized quadratic semiflexible functional form," Journal of Econometrics, Elsevier, vol. 37(3), pages 327-342, March.
  11. 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 705-22, August.
  12. W. E. Diewert & T. J. Wales, 1993. "Linear and Quadratic Spline Models for Consumer Demand Functions," Canadian Journal of Economics, Canadian Economics Association, vol. 26(1), pages 77-106, February.
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Cited by:
  1. 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.
  2. Bert M. Balk, 2010. "Lowe and Cobb-Douglas Consumer Price Indices and their Substitution Bias," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), Justus-Liebig University Giessen, Department of Statistics and Economics, vol. 230(6), pages 726-740, December.

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