[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/p/kan/wpaper/200604.html
   My bibliography  Save this paper

Operational identification of the complete class of superlative index numbers: an application of Galois theory

Author

Listed:
  • William Barnett

    (Department of Economics, The University of Kansas)

  • Ki-Hong Choi

    (National Pension Research Institute)

Abstract
We provide an operational identification of the complete class of superlative index numbers to track the exact aggregator functions of economic aggregation theory. If an index number is linearly homogeneous and a second order approximation in a formal manner that we define, we prove the index to be in the superlative index number class of nonparametric functions. Our definition is mathematically equivalent to Diewert°Øs most general definition. But when operationalized in practice, our definition permits use of the full class, while Diewert°Øs definition, in practice, spans only a strict subset of the general class. The relationship between the general class and that strict subset is a consequence of Galois theory. Only a very small number of elements of the general class have been found by Diewert°Øs method, despite the fact that the general class contains an infinite number of functions. We illustrate our operational, general approach by proving for the first time that a particular family of nonparametric functions, including the Sato-Vartia index, is within the superlative index number class.

Suggested Citation

  • William Barnett & Ki-Hong Choi, 2006. "Operational identification of the complete class of superlative index numbers: an application of Galois theory," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200604, University of Kansas, Department of Economics.
    • Handle: RePEc:kan:wpaper:200604
    as

    Download full text from publisher

    File URL: http://www.ku.edu/~bgju/2006Papers/200604.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Blackorby, Charles & Davidson, Russell & Schworm, William, 1991. "Implicit separability: Characterisation and implications for consumer demands," Journal of Economic Theory, Elsevier, vol. 55(2), pages 364-399, December.
    2. Lau, Lawrence J, 1979. "On Exact Index Numbers," The Review of Economics and Statistics, MIT Press, vol. 61(1), pages 73-82, February.
    3. Diewert, W E, 1992. "Exact and Superlative Welfare Change Indicators," Economic Inquiry, Western Economic Association International, vol. 30(4), pages 562-582, October.
    4. Theil, Henri, 1973. "A New Index Number Formula," The Review of Economics and Statistics, MIT Press, vol. 55(4), pages 498-502, November.
    5. Diewert, W Erwin, 1978. "Superlative Index Numbers and Consistency in Aggregation," Econometrica, Econometric Society, vol. 46(4), pages 883-900, July.
    6. Barnett, William A. & Choi, Ki-Hong & Sinclair, Tara M., 2003. "The Differential Approach to Superlative Index Number Theory," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 35(Supplemen), pages 1-6.
    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. Sato, Kazuo, 1974. "Ideal Index Numbers that Almost Satisfy the Factor Reversal Text," The Review of Economics and Statistics, MIT Press, vol. 56(4), pages 549-552, November.
    10. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    11. Sato, Kazuo, 1976. "The Ideal Log-Change Index Number," The Review of Economics and Statistics, MIT Press, vol. 58(2), pages 223-228, 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. Hideyuki Mizobuchi & Valentin Zelenyuk, 2021. "Quadratic-mean-of-order-r indexes of output, input and productivity," Journal of Productivity Analysis, Springer, vol. 56(2), pages 133-138, December.
    2. Gabriel Ehrlich & John Haltiwanger & Ron Jarmin & David Johnson & Ed Olivares & Luke Pardue & Matthew D. Shapiro & Laura Yi Zhao, 2023. "Quality Adjustment at Scale: Hedonic vs. Exact Demand-Based Price Indices," Working Papers 23-26, Center for Economic Studies, U.S. Census Bureau.
    3. Thomas von Brasch & Arvid Raknerud & Diana-Cristina Iancu, 2018. "Productivity growth, firm turnover and new varieties," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2018-11, Economic Statistics Centre of Excellence (ESCoE).
    4. Wankeun Oh & Seung Won Kang, 2022. "Attribution of Changes in Vietnam’s Labor Productivity," Sustainability, MDPI, vol. 14(11), pages 1-19, May.
    5. 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.
    6. Thomas von Brasch & Ådne Cappelen & Diana‐Cristina Iancu, 2018. "Measuring Labour Services: Quality‐Adjusting the Entry and Exit of Workers," Scandinavian Journal of Economics, Wiley Blackwell, vol. 120(2), pages 597-623, April.
    7. Hennessy, David A. & Lapan, Harvey E., 2009. "Harmonic symmetries of imperfect competition on circular city," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 124-146, January.
    8. Hjertstrand, Per & Swofford, James L. & Whitney, Gerald A., 2019. "Index Numbers and Revealed Preference Rankings," Working Paper Series 1308, Research Institute of Industrial Economics.
    9. Thomas von Brasch & Diana-Cristina Iancu & Arvid Raknerud, 2018. "Productivity growth, firm turnover and new varieties," Discussion Papers 872, Statistics Norway, Research Department.

    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. Vartia, Yrjö O., . "Relative Changes and Index Numbers," ETLA A, The Research Institute of the Finnish Economy, number 4, June.
    2. Claude Hillinger, 2002. "A General Theory of Price and Quantity Aggregation and Welfare Measurement," CESifo Working Paper Series 818, CESifo.
    3. 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.
    4. 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.
    5. Barnett, William A. & Choi, Ki-Hong & Sinclair, Tara M., 2003. "The Differential Approach to Superlative Index Number Theory," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 35(Supplemen), pages 1-6.
    6. 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.
    7. 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.
    8. Hillinger, Claude, 2008. "Measuring Real Value and Inflation," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 2, pages 1-26.
    9. Craig, Barbara J. & Pardey, Philip G., 1990. "Multidimensional Output Indices," Staff Papers 13828, University of Minnesota, Department of Applied Economics.
    10. DECANCQ, Koen & FLEURBAEY, Marc & SCHOKKAERT, Erik, 2014. "Inequality, income, and well-being," LIDAM Discussion Papers CORE 2014018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Andreas Benedictow & Pål Boug, 2014. "Calculating the real return of the Norwegian Government Pension Fund Global by alternative measures of the deflator," Discussion Papers 775, Statistics Norway, Research Department.
    12. 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.
    13. Liao, Hua & Fan, Ying & Wei, Yi-Ming, 2007. "What induced China's energy intensity to fluctuate: 1997-2006?," Energy Policy, Elsevier, vol. 35(9), pages 4640-4649, September.
    14. W. Erwin Diewert, 1980. "Aggregation Problems in the Measurement of Capital," NBER Chapters, in: The Measurement of Capital, pages 433-538, National Bureau of Economic Research, Inc.
    15. Adam Gorajek, 2018. "Econometric Perspectives on Economic Measurement," RBA Research Discussion Papers rdp2018-08, Reserve Bank of Australia.
    16. 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.
    17. Binner, Jane & Elger, Thomas, 2002. "The UK Personal Sector Demand for Risky Money," Working Papers 2002:9, Lund University, Department of Economics.
    18. Bellaïche, Joël, 2010. "On the path-dependence of economic growth," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 163-178, March.
    19. 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.
    20. Daniel Melser, 2019. "Valuing the quantity and quality of product variety to consumers," Empirical Economics, Springer, vol. 57(6), pages 2107-2128, December.

    More about this item

    Keywords

    Exact index numbers; superlative index number class; Divisia line integrals; aggregator function space; Galois theory.;
    All these keywords.

    JEL classification:

    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
    • E01 - Macroeconomics and Monetary Economics - - General - - - Measurement and Data on National Income and Product Accounts and Wealth; Environmental Accounts
    • D - Microeconomics

    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:kan:wpaper:200604. 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: Professor Zongwu Cai (email available below). General contact details of provider: https://edirc.repec.org/data/deuksus.html .

    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.