IDEAS home Printed from https://ideas.repec.org/p/ubc/bricol/diewert-07-01-03-08-17-23.html
   My bibliography  Save this paper

Index Numbers

Author

Listed:
  • 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.

Suggested Citation

  • Diewert, Erwin, 2007. "Index Numbers," Economics working papers diewert-07-01-03-08-17-23, Vancouver School of Economics, revised 31 Jan 2007.
    • Handle: RePEc:ubc:bricol:diewert-07-01-03-08-17-23
    as

    Download full text from publisher

    File URL: http://microeconomics.ca/erwin_diewert/dp0702.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Marshall Reinsdorf, 1993. "The Effect of Outlet Price Differentials on the US Consumer Price Index," NBER Chapters, in: Price Measurements and Their Uses, pages 227-258, National Bureau of Economic Research, Inc.
    2. Diewert, W. Erwin & Fox, Kevin J., 2008. "On the estimation of returns to scale, technical progress and monopolistic markups," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 174-193, July.
    3. D. W. Jorgenson & Z. Griliches, 1967. "The Explanation of Productivity Change," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(3), pages 249-283.
    4. Robert J. Hill, 2004. "Constructing Price Indexes across Space and Time: The Case of the European Union," American Economic Review, American Economic Association, vol. 94(5), pages 1379-1410, December.
    5. 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.
    6. Jack E. Triplett & Richard J. McDonald, 1977. "Assessing The Quality Error In Output Measures: The Case Of Refrigerators," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 23(2), pages 137-156, June.
    7. 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.
    8. repec:bla:revinw:v:23:y:1977:i:2:p:137-56 is not listed on IDEAS
    9. Chen, Yi Vivian & Heston, Alan & Lipsey, Robert, 2000. "International and interarea comparisons of income, output and prices," Journal of Asian Economics, Elsevier, vol. 11(3), pages 363-364, December.
    10. 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.
    11. W. Erwin Diewert, 1995. "Axiomatic and Economic Approaches to Elementary Price Indexes," NBER Working Papers 5104, National Bureau of Economic Research, Inc.
    12. 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.
    13. Paul Schreyer, 2001. "The OECD Productivity Manual: A Guide to the Measurement of Industry-Level and Aggregate Productivity," International Productivity Monitor, Centre for the Study of Living Standards, vol. 2, pages 37-51, Spring.
    14. Sidney N. Afriat, 1972. "The Theory of International Comparisons of Real Income and Prices," NBER Chapters, in: International Comparisons of Prices and Output, pages 13-84, National Bureau of Economic Research, Inc.
    15. 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 566-593, September.
    16. Robert J. Hill, 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.
    17. Vartia, Yrjö O., . "Relative Changes and Index Numbers," ETLA A, The Research Institute of the Finnish Economy, number 4, June.
    18. Silver, Mick & Heravi, Saeed, 2005. "A Failure in the Measurement of Inflation: Results From a Hedonic and Matched Experiment Using Scanner Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 269-281, July.
    19. 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 659-679, September.
    20. Kohli, Ulrich, 2003. "Growth accounting in the open economy: international comparisons," International Review of Economics & Finance, Elsevier, vol. 12(4), pages 417-435.
    21. 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.
    22. Pollak, Robert A., 1981. "The social cost of living index," Journal of Public Economics, Elsevier, vol. 15(3), pages 311-336, June.
    23. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    24. Kevin Fox & Ulrich Kohli, 1998. "GDP growth, terms-of-trade effects, and total factor productivity," The Journal of International Trade & Economic Development, Taylor & Francis Journals, vol. 7(1), pages 87-110.
    25. Pollak, Robert A, 1980. "Group Cost-of-Living Indexes," American Economic Review, American Economic Association, vol. 70(2), pages 273-278, May.
    26. Jack Triplett, 2004. "Handbook on Hedonic Indexes and Quality Adjustments in Price Indexes: Special Application to Information Technology Products," OECD Science, Technology and Industry Working Papers 2004/9, OECD Publishing.
    27. 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.
    28. 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.
    29. 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 167-185, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Diewert, W. Erwin & Fox, Kevin J., 2016. "Kevin J. Fox Interview of W. Erwin Diewert," Microeconomics.ca working papers erwin_diewert-2016-6, Vancouver School of Economics, revised 02 Jun 2016.
    2. Barnett, William A. & Erwin Diewert, W. & Zellner, Arnold, 2011. "Introduction to measurement with theory," Journal of Econometrics, Elsevier, vol. 161(1), pages 1-5, March.
    3. Diewert, W. Erwin, 2017. "Productivity Measurement in the Public Sector: Theory and Practice," Microeconomics.ca working papers erwin_diewert-2017-1, Vancouver School of Economics, revised 02 Feb 2017.
    4. W. Diewert, 2011. "Measuring productivity in the public sector: some conceptual problems," Journal of Productivity Analysis, Springer, vol. 36(2), pages 177-191, October.
    5. W. Erwin Diewert & Kevin J. Fox, 2017. "Decomposing Value Added Growth into Explanatory Factors," Discussion Papers 2017-02, School of Economics, The University of New South Wales.
    6. W. Erwin Diewert, 2022. "Scanner Data, Elementary Price Indexes and the Chain Drift Problem," Springer Books, in: Duangkamon Chotikapanich & Alicia N. Rambaldi & Nicholas Rohde (ed.), Advances in Economic Measurement, chapter 0, pages 445-606, Springer.
    7. Diewert, Erwin & Marandola, Tina, 2018. "Scanner Data, Elementary Price Indexes and the Chain Drift Problem," Microeconomics.ca working papers tina_marandola-2018-9, Vancouver School of Economics, revised 10 Oct 2018.
    8. Diewert, W. Erwin, 2014. "Decompositions of profitability change using cost functions," Journal of Econometrics, Elsevier, vol. 183(1), pages 58-66.
    9. Chihiro Shimizu & Erwin Diewert, 2023. "Scanner Data, Product Churn and Quality Adjustment," Working Papers e185, Tokyo Center for Economic Research.
    10. Robert J. Hill & Alice O. Nakamura, 2010. "Improving Inflation And Related Performance Measures For Nations: An Introduction," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(s1), pages 1-10, June.
    11. Diewert, Erwin & Fox, Kevin J., 2019. "Productivity Indexes and National Statistics: Theory, Methods and Challenges," Microeconomics.ca working papers erwin_diewert-2019-8, Vancouver School of Economics, revised 25 Apr 2019.
    12. W. Diewert, 2012. "The measurement of productivity in the nonmarket sector," Journal of Productivity Analysis, Springer, vol. 37(3), pages 217-229, June.
    13. Diewert, Erwin & Mizobuchi, Hideyuki, 2009. "An Economic Approach to the Measurement of Productivity Growth Using Differences Instead of Ratios," Economics working papers erwin_diewert-2009-2, Vancouver School of Economics, revised 09 Jan 2009.
    14. W. Diewert, 2014. "US TFP growth and the contribution of changes in export and import prices to real income growth," Journal of Productivity Analysis, Springer, vol. 41(1), pages 19-39, February.
    15. W. Erwin Diewert, 1995. "Price and Volume Measures in the System of National Accounts," NBER Working Papers 5103, National Bureau of Economic Research, Inc.
    16. Diewert, W. Erwin & Fox, Kevin J., 2017. "Substitution Bias in Multilateral Methods for CPI Construction using Scanner Data," Microeconomics.ca working papers erwin_diewert-2017-3, Vancouver School of Economics, revised 23 Mar 2017.
    17. 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.
    18. Marshall Reinsdorf & Jack E. Triplett, 2009. "A Review of Reviews: Ninety Years of Professional Thinking About the Consumer Price Index," NBER Chapters, in: Price Index Concepts and Measurement, pages 17-83, National Bureau of Economic Research, Inc.
    19. W. Erwin Diewert & Kevin J. Fox, 2020. "Measuring Real Consumption and CPI Bias under Lockdown Conditions," NBER Working Papers 27144, National Bureau of Economic Research, Inc.
    20. Diewert, Erwin, 2008. "Changes in the Terms of Trade and Canada's Productivity Performance," Economics working papers diewert-08-03-11-11-03-49, Vancouver School of Economics, revised 18 Jul 2008.

    More about this item

    Keywords

    Index numbers; stochastic; test and economic approaches to index number theory; hedonic regressions; bilateral index number theory; multilateral index;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ubc:bricol:diewert-07-01-03-08-17-23. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Maureen Chin (email available below). General contact details of provider: http://www.economics.ubc.ca/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.