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Defining a new graph inefficiency measure for the proportional directional distance function and introducing a new Malmquist productivity index

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  • Pastor, Jesus T.
  • Lovell, C.A. Knox
  • Aparicio, Juan

Abstract

A natural multiplicative efficiency measure for the Constant Returns to Scale proportional directional distance function (pDDF) is derived, relating its associated linear program to that of the well-known output-oriented radial efficiency measurement model. Based on this relationship, a traditional CCD (Caves, Christensen and Diewert) Malmquist index is introduced to show that, when it is based on the new efficiency measure associated with the pDDF, rather than on a radial efficiency measure associated with an oriented distance function, it becomes a Total Factor Productivity (TFP) index. This constitutes a new result, because heretofore the traditional CCD Malmquist index has not been considered a TFP index. Additionally, a new decomposition of the CCD Malmquist index is proposed that expresses productivity change as the ratio of two components, productivity change due to output change in the numerator and productivity change due to input change in the denominator. In an Appendix the efficiency measure is extended to include any returns to scale pDDF.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:281:y:2020:i:1:p:222-230
    DOI: 10.1016/j.ejor.2019.08.021
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    More about this item

    Keywords

    Data envelopment analysis; Proportional directional distance function; Efficiency measure; Malmquist productivity index;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes

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