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Families of Linear Efficiency Programs based on Debreu's Loss Function

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Gerard Debreu introduced a well known radial efficiency measure which he called a “coefficient of resource utilization.†He derived this scalar from a much less well known “dead loss†function that characterizes the monetary value sacrificed to inefficiency, and which is to be minimized subject to a normalization condition. We use Debreu’s loss function, together with a variety of normalization conditions, to generate several popular families of linear efficiency programs. Our methodology also can be employed to generate entirely new families of linear efficiency programs.

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  • Jesús T. Pastora & C.A. Knox Lovell & Juan Aparicioc, 2009. "Families of Linear Efficiency Programs based on Debreu's Loss Function," CEPA Working Papers Series WP042009, School of Economics, University of Queensland, Australia.
  • Handle: RePEc:qld:uqcepa:71
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    File URL: https://economics.uq.edu.au/files/5268/WP042009.pdf
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    1. William Cooper & Jesús Pastor & Fernando Borras & Juan Aparicio & Diego Pastor, 2011. "BAM: a bounded adjusted measure of efficiency for use with bounded additive models," Journal of Productivity Analysis, Springer, vol. 35(2), pages 85-94, April.
    2. Aparicio, Juan & Garcia-Nove, Eva M. & Kapelko, Magdalena & Pastor, Jesus T., 2017. "Graph productivity change measure using the least distance to the pareto-efficient frontier in data envelopment analysis," Omega, Elsevier, vol. 72(C), pages 1-14.
    3. Zhongqi Deng & Qianyu Zhao & Helen X. H. Bao, 2020. "The Impact of Urbanization on Farmland Productivity: Implications for China’s Requisition–Compensation Balance of Farmland Policy," Land, MDPI, vol. 9(9), pages 1-24, September.
    4. Aparicio, Juan & Kapelko, Magdalena & Ortiz, Lidia, 2023. "Enhancing the measurement of firm inefficiency accounting for corporate social responsibility: A dynamic data envelopment analysis fuzzy approach," European Journal of Operational Research, Elsevier, vol. 306(2), pages 986-997.
    5. Alcaraz, Javier & Anton-Sanchez, Laura & Aparicio, Juan & Monge, Juan F. & Ramón, Nuria, 2021. "Russell Graph efficiency measures in Data Envelopment Analysis: The multiplicative approach," European Journal of Operational Research, Elsevier, vol. 292(2), pages 663-674.
    6. Zhu, Qingyuan & Aparicio, Juan & Li, Feng & Wu, Jie & Kou, Gang, 2022. "Determining closest targets on the extended facet production possibility set in data envelopment analysis: Modeling and computational aspects," European Journal of Operational Research, Elsevier, vol. 296(3), pages 927-939.
    7. Juan Aparicio & José L. Zofío & Jesús T. Pastor, 2023. "Decomposing Economic Efficiency into Technical and Allocative Components: An Essential Property," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 98-129, April.
    8. Raul Moragues & Juan Aparicio & Miriam Esteve, 2023. "Measuring technical efficiency for multi-input multi-output production processes through OneClass Support Vector Machines: a finite-sample study," Operational Research, Springer, vol. 23(3), pages 1-33, September.
    9. Halická, Margaréta & Trnovská, Mária, 2021. "A unified approach to non-radial graph models in data envelopment analysis: common features, geometry, and duality," European Journal of Operational Research, Elsevier, vol. 289(2), pages 611-627.
    10. Halická, Margaréta & Trnovská, Mária, 2019. "Duality and profit efficiency for the hyperbolic measure model," European Journal of Operational Research, Elsevier, vol. 278(2), pages 410-421.
    11. Aparicio, Juan & Ortiz, Lidia & Pastor, Jesus T., 2017. "Measuring and decomposing profit inefficiency through the Slacks-Based Measure," European Journal of Operational Research, Elsevier, vol. 260(2), pages 650-654.
    12. Raphaël Fèvre & Thomas Michael Mueller, 2023. "Toward a “Prodigious Revival of French Economics”? Allais, Debreu, and the Dead Loss Controversy (1943–51)," Post-Print hal-04119618, HAL.
    13. Halická, Margaréta & Trnovská, Mária, 2018. "The Russell measure model: Computational aspects, duality, and profit efficiency," European Journal of Operational Research, Elsevier, vol. 268(1), pages 386-397.
    14. Rafael Benítez & Vicente Coll-Serrano & Vicente J. Bolós, 2021. "deaR-Shiny: An Interactive Web App for Data Envelopment Analysis," Sustainability, MDPI, vol. 13(12), pages 1-19, June.
    15. Aparicio, Juan & Monge, Juan F., 2022. "The generalized range adjusted measure in data envelopment analysis: Properties, computational aspects and duality," European Journal of Operational Research, Elsevier, vol. 302(2), pages 621-632.
    16. 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:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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