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Defining a new graph inefficiency measure for the Proportional Directional Distance Function and introducing a new Malmquist productivity index

Jesus T. Pastor (), C. Lovell and Juan Aparicio ()
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Jesus T. Pastor: Center of Operations Research (CIO) at University Miguel Hernandez of Elche, Spain

No WP052018, CEPA Working Papers Series from University of Queensland, School of Economics

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.

Keywords: Proportional Directional Distance Function; Efficiency Measure; Malmquist productivity index; Data Envelopment Analysis. (search for similar items in EconPapers)
JEL-codes: C43 C61 O33 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-eff
Date: 2018-09
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