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Technological inefficiency indexes: a binary taxonomy and a generic theorem

Author

Listed:
  • R. Robert Russell

    () (University of California)

  • William Schworm

    () (University of New South Wales)

Abstract

Over the years following Debreu’s (1951) seminal formulation of a “coefficient of resource utilization”, a large number of indexes of technological inefficiency have been specified and a spate of papers has examined the properties satisfied by these indexes. This paper approaches the subject more synthetically, presenting generic results on classes of indexes and their properties. In particular, we consider a broad class of indexes containing almost all known indexes and a partition of this class into two subsets, slacks-based indexes and path-based indexes. Slacks-based indexes are expressed in terms of additive or multiplicative slacks for all inputs and outputs, and particular indexes are generated by specifying the form of aggregation over the coordinate-wise slacks. Path-based indexes are expressed in terms of a common contraction/expansion factor, and particular indexes are generated by specifying the form of the path to the frontier of the technology. Owing to an impossibility result in one of our earlier papers, we know that the set of all inefficiency indexes can be partitioned into three subsets: those that satisfy continuity (in quantities and technologies) and violate indication (equal to some specified value if and only if the quantity vector is efficient), those that satisfy indication and violate continuity, and those that satisfy neither. We prove two generic theorems establishing the equivalence of these two partitions: all slacks-based indexes satisfy indication and hence violate continuity, and all path-based indexes satisfy continuity and hence violate indication. We also discuss the few indexes that do not belong to either of these two sets. Our hope is that these results will help guide decisions about specification of the form of efficiency indexes used in empirical analysis.

Suggested Citation

  • R. Robert Russell & William Schworm, 2018. "Technological inefficiency indexes: a binary taxonomy and a generic theorem," Journal of Productivity Analysis, Springer, vol. 49(1), pages 17-23, February.
  • Handle: RePEc:kap:jproda:v:49:y:2018:i:1:d:10.1007_s11123-017-0518-2
    DOI: 10.1007/s11123-017-0518-2
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    References listed on IDEAS

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    1. R. Russell & William Schworm, 2009. "Axiomatic foundations of efficiency measurement on data-generated technologies," Journal of Productivity Analysis, Springer, vol. 31(2), pages 77-86, April.
    2. Briec, W., 2000. "An extended Fare-Lovell technical efficiency measure," International Journal of Production Economics, Elsevier, vol. 65(2), pages 191-199, April.
    3. R. Robert Russell & William Schworm, 2009. "Axiomatic Foundations of Inefficiency Measurement on Space," Discussion Papers 2009-07, School of Economics, The University of New South Wales.
    4. R. Banker & W. Cooper & E. Grifell-Tajté & Jesús Pastor & Paul Wilson & Eduardo Ley & C. Lovell, 1994. "Validation and generalization of DEA and its uses," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(2), pages 249-314, December.
    5. Fare, Rolf & Knox Lovell, C. A., 1978. "Measuring the technical efficiency of production," Journal of Economic Theory, Elsevier, vol. 19(1), pages 150-162, October.
    6. Pastor, J. T. & Ruiz, J. L. & Sirvent, I., 1999. "An enhanced DEA Russell graph efficiency measure," European Journal of Operational Research, Elsevier, vol. 115(3), pages 596-607, June.
    7. Robert Russell, R., 1990. "Continuity of measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 51(2), pages 255-267, August.
    8. William Cooper & Kyung Park & Jesus Pastor, 1999. "RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models, and Relations to Other Models and Measures in DEA," Journal of Productivity Analysis, Springer, vol. 11(1), pages 5-42, February.
    9. R. Russell & William Schworm, 2011. "Properties of inefficiency indexes on 〈input, output〉 space," Journal of Productivity Analysis, Springer, vol. 36(2), pages 143-156, October.
    10. Zieschang, Kimberly D., 1984. "An extended farrell technical efficiency measure," Journal of Economic Theory, Elsevier, vol. 33(2), pages 387-396, August.
    11. Steven Levkoff & R. Russell & William Schworm, 2012. "Boundary problems with the “Russell” graph measure of technical efficiency: a refinement," Journal of Productivity Analysis, Springer, vol. 37(3), pages 239-248, June.
    12. Fukuyama, Hirofumi & Weber, William L., 2009. "A directional slacks-based measure of technical inefficiency," Socio-Economic Planning Sciences, Elsevier, vol. 43(4), pages 274-287, December.
    13. Charnes, A. & Cooper, W. W. & Golany, B. & Seiford, L. & Stutz, J., 1985. "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 91-107.
    14. Tone, Kaoru, 2001. "A slacks-based measure of efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 130(3), pages 498-509, May.
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    Cited by:

    1. Walter Briec & Laurent Cavaignac & Kristiaan Kerstens, 2020. "Input Efficiency Measures: A Generalized, Encompassing Formulation," Operations Research, INFORMS, vol. 68(6), pages 1836-1849, November.
    2. Balk, B.M. & Zofío, J.L., 2018. "The Many Decompositions of Total Factor Productivity Change," ERIM Report Series Research in Management ERS-2018-003-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Halická, Margaréta & Trnovská, Mária, 2021. "A unified approach to non-radial graph models in data envelopment analysis: common features, geometry, and duality," European Journal of Operational Research, Elsevier, vol. 289(2), pages 611-627.
    4. Lin, Ruiyue & Li, Zongxin, 2020. "Directional distance based diversification super-efficiency DEA models for mutual funds," Omega, Elsevier, vol. 97(C).

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    More about this item

    Keywords

    Efficiency indexes; Inefficiency indexes; Specification;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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