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How to properly decompose economic efficiency using technical and allocative criteria with non-homothetic DEA technologies

Author

Listed:
  • Aparicio, Juan

    (Center of Operations Research, Universidad Miguel Hernández, Elche, Spain)

  • Pastor, Jesús

    (Center of Operations Research, Universidad Miguel Hernández, Elche, Spain)

  • Zofío, José Luis

    (Departamento de Análisis Económico (Teoría e Historia Económica). Universidad Autónoma de Madrid.)

Abstract
We discuss how to properly decompose economic efficiency when the underlying technology is non-homothetic using alternative allocative and technical efficiency criteria. We first show that only under the production of one output and assuming the particular case of constant returns to scale homotheticity, we may claim that the standard radial models correctly measure pure technical efficiency. Otherwise, when non-homotheticity is assumed, we then show that these traditional estimations would measure an undetermined mix of technical and allocative efficiency. To restore a consistent measure of technical efficiency in the non-homothetic case we introduce a new methodology that takes as reference for the economic efficiency decomposition the preservation of the allocative efficiency of firms producing in the interior of the technology. This builds upon the so-called reversed approach recently introduced by Bogetoft et al. (2006) that allows estimating allocative efficiency without presuming that technical efficiency has been already accomplished. We illustrate our methodology within the Data Envelopment Analysis framework adopting the most simple nonhomothetic BCC model and a numerical example. We show that there are significant differences in the allocative and technical efficiency scores depending on the approach.

Suggested Citation

  • Aparicio, Juan & Pastor, Jesús & Zofío, José Luis, 2013. "How to properly decompose economic efficiency using technical and allocative criteria with non-homothetic DEA technologies," Working Papers in Economic Theory 2013/11, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
  • Handle: RePEc:uam:wpaper:201311
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    References listed on IDEAS

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    1. Jose Zofio & Jesus Pastor & Juan Aparicio, 2013. "The directional profit efficiency measure: on why profit inefficiency is either technical or allocative," Journal of Productivity Analysis, Springer, vol. 40(3), pages 257-266, December.
    2. Sato, Ryuzo, 1977. "Homothetic and Non-Homothetic CES Production Functions," American Economic Review, American Economic Association, vol. 67(4), pages 559-569, September.
    3. Bogetoft, Peter & Fare, Rolf & Obel, Borge, 2006. "Allocative efficiency of technically inefficient production units," European Journal of Operational Research, Elsevier, vol. 168(2), pages 450-462, January.
    4. Simar, Léopold & Vanhems, Anne & Wilson, Paul W., 2012. "Statistical inference for DEA estimators of directional distances," European Journal of Operational Research, Elsevier, vol. 220(3), pages 853-864.
    5. Manthos Delis & Maria Iosifidi & Efthymios G. Tsionas, 2014. "On the Estimation of Marginal Cost," Operations Research, INFORMS, vol. 62(3), pages 543-556, June.
    6. R. Färe & S. Grosskopf & G. Whittaker, 2013. "Directional output distance functions: endogenous directions based on exogenous normalization constraints," Journal of Productivity Analysis, Springer, vol. 40(3), pages 267-269, December.
    7. Ray,Subhash C., 2012. "Data Envelopment Analysis," Cambridge Books, Cambridge University Press, number 9781107405264, September.
    8. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    9. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    10. Fare, Rolf & Knox Lovell, C. A., 1978. "Measuring the technical efficiency of production," Journal of Economic Theory, Elsevier, vol. 19(1), pages 150-162, October.
    11. W. Briec & J. B. Lesourd, 1999. "Metric Distance Function and Profit: Some Duality Results," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 15-33, April.
    12. Christensen, Laurits R & Greene, William H, 1976. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 655-676, August.
    13. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    14. Jacobsen, S E, 1970. "Production Correspondences," Econometrica, Econometric Society, vol. 38(5), pages 754-771, September.
    15. Lee, Chia-Yen, 2014. "Meta-data envelopment analysis: Finding a direction towards marginal profit maximization," European Journal of Operational Research, Elsevier, vol. 237(1), pages 207-216.
    16. Robert Chambers & Thomas Mitchell, 2001. "Homotheticity and Non-Radial Changes," Journal of Productivity Analysis, Springer, vol. 15(1), pages 31-39, January.
    17. Kopp, Raymond J. & Diewert, W. Erwin, 1982. "The decomposition of frontier cost function deviations into measures of technical and allocative efficiency," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 319-331, August.
    18. Walter Briec & Philippe Gardères, 2004. "Generalized benefit functions and measurement of utility," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(1), pages 101-123, September.
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    Cited by:

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    3. Monastyrenko, Evgenii, 2017. "Eco-efficiency outcomes of mergers and acquisitions in the European electricity industry," Energy Policy, Elsevier, vol. 107(C), pages 258-277.
    4. Juan Aparicio & José L. Zofío, 2017. "Revisiting the decomposition of cost efficiency for non-homothetic technologies: a directional distance function approach," Journal of Productivity Analysis, Springer, vol. 48(2), pages 133-146, December.
    5. Pastor, Jesus T. & Zofio, Jose L., 2017. "Can Farrell's allocative efficiency be generalized by the directional distance function approach?Author-Name: Aparicio, Juan," European Journal of Operational Research, Elsevier, vol. 257(1), pages 345-351.
    6. Álvarez, Inmaculada & Barbero, Javier & Zofío, Jose Luis, 2016. "A Data Envelopment Analysis Toolbox for MATLAB," Working Papers in Economic Theory 2016/03, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
    7. Aparicio, Juan & Zofío, José L., 2021. "Economic cross-efficiency," Omega, Elsevier, vol. 100(C).
      • Aparicio, J. & Zofío, J.L., 2019. "Economic Cross-Efficiency," ERIM Report Series Research in Management ERS-2019-001-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    8. Rolf Färe & Giannis Karagiannis, 2022. "Aggregation and decomposition of Farrell efficiencies," Operational Research, Springer, vol. 22(5), pages 5675-5683, November.
    9. Maria-Eugenia Sanin & Sylvain Sourisseau, 2019. "Pervasive EUAs free allocation: the case of the steel industry," Documents de recherche 19-06, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    10. Xin ZHAO & Yong PENG & Yuemei XUE & Shun YUAN, 2016. "Spatial Patterns of Ocean Economic Efficiency and their Influencing Factors in Chinese Coastal Regions," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 35-49, December.
    11. Zhang, Puwei & You, Jianxin & Jia, Guangshe & Chen, Jindao & Yu, Anyu, 2018. "Estimation of carbon efficiency decomposition in materials and potential material savings for China's construction industry," Resources Policy, Elsevier, vol. 59(C), pages 148-159.
    12. Gulati, Rachita, 2022. "Global and local banking crises and risk-adjusted efficiency of Indian banks: Are the impacts really perspective-dependent?," The Quarterly Review of Economics and Finance, Elsevier, vol. 84(C), pages 23-39.
    13. Partovi, Elmira & Matousek, Roman, 2019. "Bank efficiency and non-performing loans: Evidence from Turkey," Research in International Business and Finance, Elsevier, vol. 48(C), pages 287-309.
    14. Jianqing Zhang & Song Wang & Peilei Yang & Fei Fan & Xueli Wang, 2020. "Analysis of Scale Factors on China’s Sustainable Development Efficiency Based on Three-Stage DEA and a Double Threshold Test," Sustainability, MDPI, vol. 12(6), pages 1-26, March.
    15. Balk, B.M. & Zofío, J.L., 2018. "The Many Decompositions of Total Factor Productivity Change," ERIM Report Series Research in Management ERS-2018-003-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    16. Juan Aparicio & José L. Zofío, 2020. "New Definitions of Economic Cross-efficiency," International Series in Operations Research & Management Science, in: Juan Aparicio & C. A. Knox Lovell & Jesus T. Pastor & Joe Zhu (ed.), Advances in Efficiency and Productivity II, pages 11-32, Springer.
    17. Dao, Kieu Oanh & Nguyen, Thi Yen & Hussain, Sarfraz & Nguyen, V.C., 2020. "Factors affecting non-performing loans of commercial banks: The role of bank performance and credit growth," OSF Preprints 6ykd8, Center for Open Science.
    18. Zhikang Xie & Xinglin Liu & Hina Najam & Qinghua Fu & Jawad Abbas & Ubaldo Comite & Laura Mariana Cismas & Andra Miculescu, 2022. "Achieving Financial Sustainability through Revenue Diversification: A Green Pathway for Financial Institutions in Asia," Sustainability, MDPI, vol. 14(6), pages 1-16, March.
    19. 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.
    20. Louhichi, Awatef & Boujelbene, Younes, 2020. "Credit risk pricing and the rationality of lending decision-making within dual banking systems: A parametric approach," Economic Systems, Elsevier, vol. 44(1).

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    More about this item

    Keywords

    Data Envelopment Analysis; Overall efficiency; Technical efficiency; Allocative efficiency; Homotheticity.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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