IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpem/0111002.html
   My bibliography  Save this paper

The Differential Approach to Superlative Index Number Theory

Author

Listed:
  • William A. Barnett

    (Washington University in St. Louis)

  • Ke- Hong Choi

    (National Pension Research Center in Seoul, Korea)

  • Tara M. Sinclair

    (Washington University in St. Louis)

Abstract

Diewert's "superlative" index numbers, defined to be exact for second order aggregator functions, unify index number theory with aggregation theory, but have been difficult to identify. We present a new approach to finding elements of this class. This new approach, related to that advocated by Henri Theil (1973), transforms candidate index numbers into growth rate form and explores convergence rates to the Divisia index. Since the Divisia index in continuous time is exact for any aggregator function, any discrete time index number that converges to the Divisia index and that has a third order remainder term is superlative.

Suggested Citation

  • William A. Barnett & Ke- Hong Choi & Tara M. Sinclair, 2001. "The Differential Approach to Superlative Index Number Theory," Econometrics 0111002, University Library of Munich, Germany, revised 28 Dec 2001.
    • Handle: RePEc:wpa:wuwpem:0111002
    Note: Type of Document - Word; prepared on IBM PC; to print on HP;
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0111/0111002.ps.gz
    Download Restriction: no
    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0111/0111002.pdf
    Download Restriction: no
    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0111/0111002.doc.gz
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Allen, Robert C & Diewert, W Erwin, 1981. "Direct versus Implicit Superlative Index Number Formulae," The Review of Economics and Statistics, MIT Press, vol. 63(3), pages 430-435, August.
    2. Barnett, William A & Lee, Yul W, 1985. "The Global Properties of the Miniflex Laurent, Generalized Leontief, and Translog Flexible Functional Forms," Econometrica, Econometric Society, vol. 53(6), pages 1421-1437, November.
    3. Barnett, William A. & Lee, Yul W. & Wolfe, Michael D., 1985. "The three-dimensional global properties of the minflex laurent, generalized leontief, and translog flexible functional forms," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 3-31.
    4. Sato, Kazuo, 1976. "The Ideal Log-Change Index Number," The Review of Economics and Statistics, MIT Press, vol. 58(2), pages 223-228, May.
    5. William Barnett, 2005. "Monetary Aggregation," Macroeconomics 0503017, University Library of Munich, Germany.
    6. Jean Ville & P. K. Newman, 1951. "The Existence-Conditions of a Total Utility Function," Review of Economic Studies, Oxford University Press, vol. 19(2), pages 123-128.
    7. 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.
    8. Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-1025, November.
    9. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Barnett, William A. & Choi, Ki-Hong, 2008. "Operational identification of the complete class of superlative index numbers: An application of Galois theory," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 603-612, July.

    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. Barnett, William A. & Choi, Ki-Hong, 2008. "Operational identification of the complete class of superlative index numbers: An application of Galois theory," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 603-612, July.
    2. Jean-Christophe Bureau & Jean-Pierre Butault & Jean-Marc Rousselle, 1989. "Les indices de productivité. Aspects méthodologiques et application à l'agriculture," Économie rurale, Programme National Persée, vol. 192(1), pages 88-94.
    3. Serletis, Apostolos & Xu, Libo, 2020. "Functional monetary aggregates, monetary policy, and business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 121(C).
    4. William Barnett & Barry E. Jones & Milka Kirova & Travis D. Nesmith & Meenakshi Pasupathy1, 2004. "The Nonlinear Skeletons in the Closet," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200403, University of Kansas, Department of Economics, revised May 2004.
    5. Vartia, Yrjö O., . "Relative Changes and Index Numbers," ETLA A, The Research Institute of the Finnish Economy, number 4.
    6. 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.
    7. James J. Heckman & Apostolos Serletis, "undated". "Introduction to Internally Consistent Modeling, Aggregation, Inference, and Policy," Working Papers 2014-73, Department of Economics, University of Calgary, revised 29 Sep 2014.
    8. Douglas Fisher & Adrian R. Fleissig & Apostolos Serletis, 2006. "An Empirical Comparison of Flexible Demand System Functional Forms," World Scientific Book Chapters, in: Money And The Economy, chapter 13, pages 247-277, World Scientific Publishing Co. Pte. Ltd..
    9. 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.
    10. 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.
    11. William A Barnett & Unja Chae & John W Keating, 2012. "Forecast Design In Monetary Capital Stock Measurement," Global Journal of Economics (GJE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-53.
    12. Lipovetsky, Stan & Conklin, W. Michael, 2006. "Data aggregation and Simpson's paradox gauged by index numbers," European Journal of Operational Research, Elsevier, vol. 172(1), pages 334-351, July.
    13. Wang, Ce & Liao, Hua & Pan, Su-Yan & Zhao, Lu-Tao & Wei, Yi-Ming, 2014. "The fluctuations of China’s energy intensity: Biased technical change," Applied Energy, Elsevier, vol. 135(C), pages 407-414.
    14. Binner, Jane & Elger, Thomas, 2002. "The UK Personal Sector Demand for Risky Money," Working Papers 2002:9, Lund University, Department of Economics.
    15. Bellaïche, Joël, 2010. "On the path-dependence of economic growth," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 163-178, March.
    16. Diewert, Erwin, 2019. "Quality Adjustment and Hedonics: A Unified Approach," Microeconomics.ca working papers erwin_diewert-2019-2, Vancouver School of Economics, revised 14 Mar 2019.
    17. Gregory Kurtzon, 2022. "How much does formula versus chaining matter for a cost‐of‐living index? The CPI‐U versus the C‐CPI‐U," Economic Inquiry, Western Economic Association International, vol. 60(2), pages 645-667, April.
    18. William A. Barnett & Milka Kirova & Meenakshi Pasupathy, 1996. "Technology Modeling: Curvature is not Sufficient for Regularity," Econometrics 9602002, University Library of Munich, Germany, revised 24 Jun 1999.
    19. Chambers, Robert & Färe, Rolf & Grosskopf, Shawna & Vardanyan, Michael, 2013. "Generalized quadratic revenue functions," Journal of Econometrics, Elsevier, vol. 173(1), pages 11-21.
    20. Georganta, Zoe, 1997. "The effect of a free market price mechanism on total factor productivity: The case of the agricultural crop industry in Greece," International Journal of Production Economics, Elsevier, vol. 52(1-2), pages 55-71, October.

    More about this item

    Keywords

    Theil Diewert superlative index numbers Divisia differential approach;

    JEL classification:

    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

    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:wpa:wuwpem:0111002. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.