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Index Numbers

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  • Diewert, Erwin

Abstract

Index numbers are used to aggregate detailed information on prices and quantities into scalar measures of price and quantity levels or their growth. The paper reviews four main approaches to bilateral index number theory where two price and quantity vectors are to be aggregated: fixed basket and average of fixed baskets, stochastic, test or axiomatic and economic approaches. The paper also considers multilateral index number theory where it is necessary to construct price and quantity aggregates for more than two value aggregates. A final section notes some of the recent literature on related aspects of index number theory the construction of indexes when there is seasonality in the underlying data, sources of bias in consumer price indexes, the use of index numbers in measuring productivity, the problem of quality change and index number theory that is based on taking differences rather than ratios.

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File URL: http://microeconomics.ca/erwin_diewert/dp0702.pdf
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Paper provided by Vancouver School of Economics in its series Economics working papers with number diewert-07-01-03-08-17-23.

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Length: 47 pages
Date of creation: 03 Jan 2007
Date of revision: 31 Jan 2007
Handle: RePEc:ubc:bricol:diewert-07-01-03-08-17-23
Contact details of provider: Web page: http://www.economics.ubc.ca/

Keywords: Index numbers; stochastic; test and economic approaches to index number theory; hedonic regressions; bilateral index number theory; multilateral index;

Find related papers by JEL classification:

  • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
  • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
  • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
  • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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  1. Hill, Robert J., 2003. "Constructing price indexes across space and time: the case of the European Union," Research Report 03C20, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
  2. David E. Lebow & Jeremy B. Rudd, 2003. "Measurement Error in the Consumer Price Index: Where Do We Stand?," Journal of Economic Literature, American Economic Association, vol. 41(1), pages 159-201, March.
  3. Kholi, U. & Fox, K., 1996. "GDP Growth, Terms-of-Trade Effects and Total Factor Productivity," Papers 96/28, New South Wales - School of Economics.
  4. Alan Heston & Robert E. Lipsey, 1999. "International and Interarea Comparisons of Income, Output, and Prices," NBER Books, National Bureau of Economic Research, Inc, number hest99-1, November.
  5. Diewart, W Erwin & Morrison, Catherine J, 1986. "Adjusting Output and Productivity Indexes for Changes in the Terms of Trade," Economic Journal, Royal Economic Society, vol. 96(383), pages 659-79, September.
  6. Silver, Mick & Heravi, Saeed, 2002. "A failure in the measurement of inflation: results from a hedonic and matched experiment using scanner data," Working Paper Series 0144, European Central Bank.
  7. W. Diewert & Alice Nakamura, 2003. "Index Number Concepts, Measures and Decompositions of Productivity Growth," Journal of Productivity Analysis, Springer, vol. 19(2), pages 127-159, April.
  8. W. Erwin Diewert, 1998. "Index Number Issues in the Consumer Price Index," Journal of Economic Perspectives, American Economic Association, vol. 12(1), pages 47-58, Winter.
  9. Kevin J. Fox & W. Erwin Diewert, 2004. "On the Estimation of Returns to Scale, Technical Progress and Monopolistic Markups," Econometric Society 2004 Australasian Meetings 310, Econometric Society.
  10. 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.
  11. Robert J. Hill, 1999. "Comparing Price Levels across Countries Using Minimum-Spanning Trees," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 135-142, February.
  12. Hill, Robert J, 2001. "Measuring Inflation and Growth Using Spanning Trees," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(1), pages 167-85, February.
  13. W. Erwin Diewert, 1995. "Axiomatic and Economic Approaches to Elementary Price Indexes," NBER Working Papers 5104, National Bureau of Economic Research, Inc.
  14. Bert Balk, 2003. "The Residual: On Monitoring and Benchmarking Firms, Industries, and Economies with Respect to Productivity," Journal of Productivity Analysis, Springer, vol. 20(1), pages 5-47, July.
  15. Kohli, Ulrich, 2004. "Real GDP, real domestic income, and terms-of-trade changes," Journal of International Economics, Elsevier, vol. 62(1), pages 83-106, January.
  16. Sidney N. Afriat, 1972. "The Theory of International Comparisons of Real Income and Prices," NBER Chapters, in: International Comparisons of Prices and Output, pages 11-84 National Bureau of Economic Research, Inc.
  17. Pollak, Robert A., 1981. "The social cost of living index," Journal of Public Economics, Elsevier, vol. 15(3), pages 311-336, June.
  18. Pollak, Robert A, 1980. "Group Cost-of-Living Indexes," American Economic Review, American Economic Association, vol. 70(2), pages 273-78, May.
  19. Kravis, Irving B, 1984. "Comparative Studies of National Incomes and Prices," Journal of Economic Literature, American Economic Association, vol. 22(1), pages 1-39, March.
  20. Hill, Robert J, 1997. "A Taxonomy of Multilateral Methods for Making International Comparisons of Prices and Quantities," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 43(1), pages 49-69, March.
  21. Marshall Reinsdorf, 1993. "The Effect of Outlet Price Differentials on the U.S. Consumer Price Index," NBER Chapters, in: Price Measurements and Their Uses, pages 227-258 National Bureau of Economic Research, Inc.
  22. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
  23. Kohli, Ulrich, 2003. "Growth accounting in the open economy: international comparisons," International Review of Economics & Finance, Elsevier, vol. 12(4), pages 417-435.
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