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Productivity Interpretations of the Farrell Efficiency Measures and the Malmquist Index and its Decomposition

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  • Førsund, Finn. R.

    (Dept. of Economics, University of Oslo)

Abstract

The ratio definition of efficiency has the form of a productivity measure. But the weights are endogenous variables and they do not function as weights in a productivity index proper. It is shown that extended Farrell measures of efficiency can all be given an interpretation as productivity measures as observed productivity relative to productivity at the various projection points on the frontier. The Malmquist productivity index is the efficiency score for a unit in a period relative to the efficiency score in a previous period, thus based on a maximal common expansion factor for outputs or common contraction factor for inputs not involving any individual weighting of outputs or inputs, as is the case if a Törnqvist or ideal Fisher index is used. The multiplicative decomposition of the Malmquist productivity index into an efficiency part and a frontier shift part should not be taken to imply causality.

Suggested Citation

  • Førsund, Finn. R., 2015. "Productivity Interpretations of the Farrell Efficiency Measures and the Malmquist Index and its Decomposition," Memorandum 14/2015, Oslo University, Department of Economics.
    • Handle: RePEc:hhs:osloec:2015_014
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    File URL: http://www.sv.uio.no/econ/english/research/unpublished-works/working-papers/pdf-files/2015/memo-14-2015.pdf
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    References listed on IDEAS

    as
    1. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    2. Hanoch, Giora, 1970. "Homotheticity in joint production," Journal of Economic Theory, Elsevier, vol. 2(4), pages 423-426, December.
    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. Constantin Belu, 2015. "Are distance measures effective at measuring efficiency? DEA meets the vintage model," Journal of Productivity Analysis, Springer, vol. 43(3), pages 237-248, June.
    5. repec:bla:scandj:v:94:y:1992:i:0:p:s211-28 is not listed on IDEAS
    6. Finn Førsund & Lennart Hjalmarsson & Vladimir Krivonozhko & Oleg Utkin, 2007. "Calculation of scale elasticities in DEA models: direct and indirect approaches," Journal of Productivity Analysis, Springer, vol. 28(1), pages 45-56, October.
    7. Nishimizu, Mieko & Page, John M, Jr, 1982. "Total Factor Productivity Growth, Technological Progress and Technical Efficiency Change: Dimensions of Productivity Change in Yugoslavia, 1965-78," Economic Journal, Royal Economic Society, vol. 92(368), pages 920-936, December.
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    Cited by:

    1. Dag Fjeld Edvardsen & Finn R. Førsund & Sverre A. C. Kittelsen, 2017. "Productivity development of Norwegian institutions of higher education 2004–2013," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(4), pages 399-415, April.
    2. Norliyana Kamarudin & Bany-Ariffin, A. N & Hussin Yusof & Yusnita Tugiran & Asrizam Esam & Yushaida Yusof, 2018. "Analysing the Importance of Demographic Factor as Determinant ofResearch Efficiency through Data Envelopment Analysis," International Journal of Business and Economic Affairs (IJBEA), Sana N. Maswadeh, vol. 3(3), pages 114-129.

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    More about this item

    Keywords

    Farrell efficiency measures; Technically optimal scale; Malmquist productivity index; Decomposition of the Malmquist productivity index;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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