IDEAS home Printed from https://ideas.repec.org/a/ebl/ecbull/eb-20-00026.html
   My bibliography  Save this article

A Choice of an Index under Inefficiency: Tornqvist or Fisher Index? Evidence from Simulation

Author

Listed:
  • Yongseung Han

    (University of North Georgia)

  • Myeong Hwan Kim

    (Purdue University Fort Wayne)

Abstract

This study addresses a choice of quantity index when inefficiency exists. Performing simulations, we show that 1) the finding from the previous literature that the Fisher index and the Tornqvist index approximate each other is only a special case when inefficiency is negligible, 2) the Tornqvist index begins to deviate as inefficiency increases because the Tornqvist index uses the average cost shares as a weight in the calculation, and 3) the Tornqvist index eventually suffers from the Simpson's paradox, in which the average of two higher numbers are lower than the average of two lower numbers, when the factor substitutability is large. From these results, we conclude that the Fisher index is preferred to the Tornqvist index when any inefficient use of factors is suspected.

Suggested Citation

  • Yongseung Han & Myeong Hwan Kim, 2021. "A Choice of an Index under Inefficiency: Tornqvist or Fisher Index? Evidence from Simulation," Economics Bulletin, AccessEcon, vol. 41(1), pages 41-47.
    • Handle: RePEc:ebl:ecbull:eb-20-00026
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/Pubs/EB/2021/Volume0/EB-21-V41-I1-P4.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
    2. Balk,Bert M., 2008. "Price and Quantity Index Numbers," Cambridge Books, Cambridge University Press, number 9780521889070.
    3. Fried, Harold O. & Lovell, C. A. Knox & Schmidt, Shelton S. (ed.), 2008. "The Measurement of Productive Efficiency and Productivity Growth," OUP Catalogue, Oxford University Press, number 9780195183528.
    4. Diewert, W Erwin, 1978. "Superlative Index Numbers and Consistency in Aggregation," Econometrica, Econometric Society, vol. 46(4), pages 883-900, July.
    5. Dumagan, Jesus C., 2002. "Comparing the superlative Tornqvist and Fisher ideal indexes," Economics Letters, Elsevier, vol. 76(2), pages 251-258, July.
    6. Balk,Bert M., 2012. "Price and Quantity Index Numbers," Cambridge Books, Cambridge University Press, number 9781107404960.
    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. Robin C. Sickles & Jiaqi Hao & Chenjun Shang, 2014. "Panel data and productivity measurement: an analysis of Asian productivity trends," Journal of Chinese Economic and Business Studies, Taylor & Francis Journals, vol. 12(3), pages 211-231, August.
    2. Valentin Zelenyuk, 2019. "Data Envelopment Analysis and Business Analytics: The Big Data Challenges and Some Solutions," CEPA Working Papers Series WP072019, School of Economics, University of Queensland, Australia.
    3. Sickles, Robin C. & Hao, Jiaqi & Shang, Chenjun, 2015. "Panel Data and Productivity Measurement," Working Papers 15-018, Rice University, Department of Economics.
    4. Jesus C. Dumagan, 2010. "Computing Additive Chained Volume Measures of GDP Subaggregates," Macroeconomics Working Papers 23094, East Asian Bureau of Economic Research.
    5. Zelenyuk, Valentin, 2020. "Aggregation of inputs and outputs prior to Data Envelopment Analysis under big data," European Journal of Operational Research, Elsevier, vol. 282(1), pages 172-187.
    6. Inanoglu, Hulusi & Jacobs, Michael, Jr. & Liu, Junrong & Sickles, Robin, 2015. "Analyzing Bank Efficiency: Are "Too-Big-to-Fail" Banks Efficient?," Working Papers 15-016, Rice University, Department of Economics.
    7. Walden, John & Fissel, Ben & Squires, Dale & Vestergaard, Niels, 2015. "Productivity change in commercial fisheries: An introduction to the special issue," Marine Policy, Elsevier, vol. 62(C), pages 289-293.
    8. Pastor, Jesus T. & Lovell, C.A. Knox & Aparicio, Juan, 2020. "Defining a new graph inefficiency measure for the proportional directional distance function and introducing a new Malmquist productivity index," European Journal of Operational Research, Elsevier, vol. 281(1), pages 222-230.
    9. Bert M. Balk, 2010. "An Assumption‐Free Framework For Measuring Productivity Change," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(s1), pages 224-256, June.
    10. Diewert, Erwin, 2009. "Cost of Living Indexes and Exact Index Numbers," Economics working papers erwin_diewert-2009-6, Vancouver School of Economics, revised 13 Feb 2009.
    11. Su, Bin & Ang, B.W., 2014. "Attribution of changes in the generalized Fisher index with application to embodied emission studies," Energy, Elsevier, vol. 69(C), pages 778-786.
    12. Consuelo Nava & Maria Grazia Zoia, 2019. "An econometric analysis of the Italian cultural supply," Papers 1910.00073, arXiv.org, revised May 2020.
    13. 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.
    14. Boussemart, Jean-Philippe & Leleu, Hervé & Parvulescu, Raluca, 2022. "Value-based performance and its decomposition into direct price and quantity effects," European Journal of Operational Research, Elsevier, vol. 303(1), pages 298-311.
    15. Ludwig von Auer & Jochen Wengenroth, 2019. "Consistent Aggregation With Superlative and Other Price Indices," Research Papers in Economics 2019-13, University of Trier, Department of Economics.
    16. Rolf Färe & Valentin Zelenyuk, 2020. "POn Fisher Aggregation of Multi-factor Productivity Indexes," CEPA Working Papers Series WP082020, School of Economics, University of Queensland, Australia.
    17. Sutirtha Bandyopadhyay & Bharat Ramaswami, 2022. "The representative agent bias in cost of living indices," Bulletin of Economic Research, Wiley Blackwell, vol. 74(1), pages 155-178, January.
    18. Bert M. Balk, 2016. "Various Approaches to the Aggregation of Economic Productivity Indices," Pacific Economic Review, Wiley Blackwell, vol. 21(4), pages 445-463, October.
    19. Feng, Guohua & Serletis, Apostolos, 2010. "A primal Divisia technical change index based on the output distance function," Journal of Econometrics, Elsevier, vol. 159(2), pages 320-330, December.
    20. Diogo Cunha Ferreira & Rui Cunha Marques, 2016. "Malmquist and Hicks–Moorsteen Productivity Indexes for Clusters Performance Evaluation," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1015-1053, September.

    More about this item

    Keywords

    Index Numbers; Fisher Index; Tornqvist Index; Allocative Inefficiency;
    All these keywords.

    JEL classification:

    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • D2 - Microeconomics - - Production and Organizations

    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:ebl:ecbull:eb-20-00026. 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: John P. Conley (email available below). General contact details of provider: .

    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.