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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

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    References listed on IDEAS

    as
    1. 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.
    2. Balk,Bert M., 2012. "Price and Quantity Index Numbers," Cambridge Books, Cambridge University Press, number 9781107404960, November.
    3. 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.
    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.
    Full references (including those not matched with items on IDEAS)

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    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

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