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

Author

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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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    Cited by:

    1. Chen, Xiang & Chen, Yong & Huang, Wenli & Zhang, Xuping, 2023. "A new Malmquist-type green total factor productivity measure: An application to China," Energy Economics, Elsevier, vol. 117(C).
    2. Yu, Ming-Miin & Nguyen, Minh-Anh Thi, 2023. "Productivity changes of Asia-Pacific airlines: A Malmquist productivity index approach for a two-stage dynamic system," Omega, Elsevier, vol. 115(C).
    3. Chen, Xiaodong & Miao, Zhuang & Wu, Ge & Zhu, Pengyu, 2024. "City-level green growth accounting: Evidence from China's thirteen urban agglomerations," Renewable and Sustainable Energy Reviews, Elsevier, vol. 203(C).
    4. Daraio, Cinzia & Di Leo, Simone & Simar, Léopold, 2025. "Conical Free Disposal Hull estimators of directional distances and Luenberger productivity indices for general technologies," European Journal of Operational Research, Elsevier, vol. 323(3), pages 907-917.
    5. Tavana, Madjid & Izadikhah, Mohammad & Toloo, Mehdi & Roostaee, Razieh, 2021. "A new non-radial directional distance model for data envelopment analysis problems with negative and flexible measures," Omega, Elsevier, vol. 102(C).
    6. Arabmaldar, Aliasghar & Sahoo, Biresh K. & Ghiyasi, Mojtaba, 2023. "A generalized robust data envelopment analysis model based on directional distance function," European Journal of Operational Research, Elsevier, vol. 311(2), pages 617-632.
    7. Miao, Zhuang & Chen, Xiaodong, 2022. "Combining parametric and non-parametric approach, variable & source -specific productivity changes and rebound effect of energy & environment," Technological Forecasting and Social Change, Elsevier, vol. 175(C).
    8. Wei, Fangqing & Yuan, Chenxi & Song, Jiayun & Peng, Fei & Han, Longyan, 2025. "Carbon productivity: Reexamining the quality of economic growth in China with fixed-sum CO2 emission constraint," Energy Economics, Elsevier, vol. 144(C).
    9. Zhou, Yi & Zhou, Wenji & Wei, Chu, 2023. "Environmental performance of the Chinese cement enterprise: An empirical analysis using a text-based directional vector," Energy Economics, Elsevier, vol. 125(C).
    10. Briec, Walter & Dumas, Audrey & Kerstens, Kristiaan & Stenger, Agathe, 2022. "Generalised commensurability properties of efficiency measures: Implications for productivity indicators," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1481-1492.
    11. Chen, Chien-Ming & Wang, Hui, 2024. "Comparing eco-efficiency with productive efficiency: Addressing the dimensionality issue," European Journal of Operational Research, Elsevier, vol. 313(3), pages 1170-1179.
    12. Mergoni, Anna & Emrouznejad, Ali & De Witte, Kristof, 2025. "Fifty years of Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 326(3), pages 389-412.
    13. Khoshroo, Alireza & Izadikhah, Mohammad & Emrouznejad, Ali, 2022. "Total factor energy productivity considering undesirable pollutant outputs: A new double frontier based malmquist productivity index," Energy, Elsevier, vol. 258(C).
    14. Deng, Zhongqi & Song, Shunfeng & Jiang, Nan & Pang, Ruizhi, 2023. "Sustainable development in China? A nonparametric decomposition of economic growth," China Economic Review, Elsevier, vol. 81(C).

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    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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