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A Quasi-Malmquist Productivity Index

Profile image of Emili Grifell-tatjéEmili Grifell-tatjé

1998, Journal of Productivity Analysis

https://doi.org/10.1023/A:1018329930629
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Abstract

The Malmquist productivity index is based on distance functions, which are reciprocals of radial Debreu-Farrell efficiency measures, and which have a number of desirable properties. Linear programming techniques are frequently employed to calculate the efficiency measures. However these techniques can leave slacks, which constitute a non-radial form of inefficiency which is not incorporated into the analysis. Thus a radial efficiency

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References (39)

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  24. Pastor, J. T. (1994), "New Additive DEA Models for Handling Zero and Negative Data," Working Paper, Departamento de Estadistica e Investigacion Operativa, Universidad de Alicante, 03071
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  28. Russell, R. R. (1988), "On the Axiomatic Approach to the Measurement of Technical Efficiency," in W. Eichhorn, ed., Measurement in Economics. Heidelberg: Physica-Verlag.
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  30. Torgersen, A. M., F. R. Førsund and S. A. C. Kittelsen (1996), "Slack Adjusted Efficiency Measures: The Case of Norwegian Labour Employment Offices," Journal of Productivity Analysis 7:4 (October), 379-98.
  31. Törnqvist, L. (1936), "The Bank of Finland's Consumption Price Index," Bank of Finland Monthly Bulletin 10, 1-8.
  32. Zieschang, K. D. (1984), "An Extended Farrell Technical Efficiency Measure," Journal of Economic Theory 33:2 (August), 387-96.
  33. Grifell-Tatjé, E., C.A.k. Lovell and J.T. Pastor (1998), "The Quasi-Malmquist Index," Journal of Productivity Analysis vol 10, issue1, July, pages 7-20.
  34. U3 as (1; 40, 24, 20) and U4 as (1; 30, 24, 10). Here U4 is less efficient than U3. If we perform a DEA analysis resorting to the BCC output-oriented model we get that U1 and U2 are efficient units and that the value of the efficiency score associated with U3 is 1.10, while the value associated with U4 is 1.25. Surprisingly enough, if we consider the total (radial plus nonradial) slacks associated with U3 and with U4, which are given by (0; 30, 5.5, 2) and (0; 7.5, 6, 2.5) respectively, we get Ωo t (U3) = 1.340 and Ωo t (U4) = 1.25, which constitutes again a contradiction.
  35. It is possible to incorporate weighted input slacks into equation (10). In this event our new efficiency measure would satisfy strict inclusion (of output slacks and input slacks). However in this output-oriented productivity measurement context we choose not to do so.
  36. Although we assume that y t ≥ 0, (10) requires that y t > 0. In our empirical illustration, y t > 0.
  37. Our nonradial technical efficiency measure is similar to the oriented nonradial technical efficiency measure proposed by Zieschang (1984), and to the "slack-adjusted" measures proposed by Torgersen et al. (1996). However Torgersen et al. did not weight slacks by observed values, as we do, and so they are unable to obtain a single efficiency measure. Their output-oriented efficiency measures are output-specific, and cannot be aggregated across noncommensurate outputs. Other nonradial efficiency measures have recently been proposed by Aida et al. (1996), Briec (1996), Frei and Harker (1996), González and Alvarez (1996), and Pastor (1995), and a nonradial Malmquist productivity index has been proposed by Thompson et al. (1996). A review of nonradial DEA-based efficiency measures can be found in Cooper and Pastor (1996).
  38. Like the Malmquist productivity index, the quasi-Malmquist productivity index decomposes into indexes of technical change and efficiency change, and this two-way decomposition can be extended if desired. However because quasi-distance functions do not satisfy a homogeneity property, the interpretation of the components of the quasi-Malmquist productivity index is complicated.
  39. Grifell-Tatjé, E., C.A.k. Lovell and J.T. Pastor (1998), "The Quasi-Malmquist Index," Journal of Productivity Analysis vol 10, issue1, July, pages 7-20.

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Related topics

  • Mathematics
  • Econometrics
  • Data Envelopment Analysis
  • Applied Economics
  • Productivity Analysis
  • LINEAR PROGRAM
  • Malmquist productivity index
  • Distance Functions
  • Efficiency Measurement

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