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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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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 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 Malmquist index has not been considered a TFP index. Additionally, a new decomposition of the 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.

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  • Jesus T. Pastor & Knox Lovell & Juan Aparicio, 2018. "Defining a new graph inefficiency measure for the Proportional Directional Distance Function and introducing a new Malmquist productivity index," CEPA Working Papers Series WP052018, School of Economics, University of Queensland, Australia.
  • Handle: RePEc:qld:uqcepa:126
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    File URL: https://economics.uq.edu.au/files/8395/WP052018.pdf
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    Keywords

    Proportional Directional Distance Function; Efficiency Measure; Malmquist productivity index; Data Envelopment Analysis.;

    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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