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Integrating group frontier and metafrontier directional distance functions to evaluate the efficiency of production units

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  • Yu, Ming-Miin
  • See, Kok Fong
  • Hsiao, Bo

Abstract

Over the last decade, many studies have adopted the data envelopment analysis (DEA)-type metafrontier framework to relax the constraint of technological heterogeneity. In conventional metafrontier analyzes, either radial or nonradial DEA models are used in two separate DEA efficiency analyzes. The results of a metafrontier analysis may be biased if this approach is adopted in a nonradial DEA model. One possible problem is that the value of the technology gap ratio is greater than one because the technology gaps to be estimated for decision-making units (DMUs) under different technology groups relative to the metatechnology have no connection between group frontiers and metafrontiers. Furthermore, the direction of projection of each DMU onto the metafrontier is totally independent of the direction to the efficiency frontier of the respective group frontier. Our proposed integration of group technology and metatechnology constraints into a union model offers a possible solution to the existing metafrontier problem and provides more robust metafrontier results regardless of whether radial or nonradial DEA models are used. Four numerical examples and one empirical application are demonstrated, and the results appear to support the use of our proposed model.

Suggested Citation

  • Yu, Ming-Miin & See, Kok Fong & Hsiao, Bo, 2022. "Integrating group frontier and metafrontier directional distance functions to evaluate the efficiency of production units," European Journal of Operational Research, Elsevier, vol. 301(1), pages 254-276.
    • Handle: RePEc:eee:ejores:v:301:y:2022:i:1:p:254-276
    DOI: 10.1016/j.ejor.2021.10.054
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    as
    1. Simar, Léopold & Vanhems, Anne, 2012. "Probabilistic characterization of directional distances and their robust versions," Journal of Econometrics, Elsevier, vol. 166(2), pages 342-354.
    2. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    3. Chambers, Robert G. & Fare, Rolf & Grosskopf, Shawna, 1996. "Productivity Growth in APEC Countries," Working Papers 197843, University of Maryland, Department of Agricultural and Resource Economics.
    4. Habtamu Alem & Gudbrand Lien & J. Brian Hardaker & Atle Guttormsen, 2019. "Regional differences in technical efficiency and technological gap of Norwegian dairy farms: a stochastic meta-frontier model," Applied Economics, Taylor & Francis Journals, vol. 51(4), pages 409-421, January.
    5. Kerstens, Kristiaan & O’Donnell, Christopher & Van de Woestyne, Ignace, 2019. "Metatechnology frontier and convexity: A restatement," European Journal of Operational Research, Elsevier, vol. 275(2), pages 780-792.
    6. Zhang, Ning & Zhou, P. & Choi, Yongrok, 2013. "Energy efficiency, CO2 emission performance and technology gaps in fossil fuel electricity generation in Korea: A meta-frontier non-radial directional distance functionanalysis," Energy Policy, Elsevier, vol. 56(C), pages 653-662.
    7. Ya Chen & Wei Xu & Qian Zhou & Zhixiang Zhou, 2020. "Total Factor Energy Efficiency, Carbon Emission Efficiency, and Technology Gap: Evidence from Sub-Industries of Anhui Province in China," Sustainability, MDPI, vol. 12(4), pages 1-21, February.
    8. Wang, Qunwei & Chiu, Yung-Ho & Chiu, Ching-Ren, 2017. "Non-radial metafrontier approach to identify carbon emission performance and intensity," Renewable and Sustainable Energy Reviews, Elsevier, vol. 69(C), pages 664-672.
    9. Chambers, Robert G., 1996. "A New Look at Exact Input, Output, Productivity, and Technical Change Measurement," Working Papers 197840, University of Maryland, Department of Agricultural and Resource Economics.
    10. Chen, Ying-Hsiu & Lai, Po-Lin & Piboonrungroj, Pairach, 2017. "The relationship between airport performance and privatisation policy: A nonparametric metafrontier approach," Journal of Transport Geography, Elsevier, vol. 62(C), pages 229-235.
    11. Gang Tian & Jian Shi & Licheng Sun & Xingle Long & Benhai Guo, 2017. "Dynamic changes in the energy–carbon performance of Chinese transportation sector: a meta-frontier non-radial directional distance function approach," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 89(2), pages 585-607, November.
    12. Cliff Huang & Tai-Hsin Huang & Nan-Hung Liu, 2014. "A new approach to estimating the metafrontier production function based on a stochastic frontier framework," Journal of Productivity Analysis, Springer, vol. 42(3), pages 241-254, December.
    13. Torben Tiedemann & Tammo Francksen & Uwe Latacz-Lohmann, 2011. "Assessing the performance of German Bundesliga football players: a non-parametric metafrontier approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(4), pages 571-587, December.
    14. Chuang-Min Chao & Ming-Miin Yu & Nan-Hsing Hsiung & Li-Hsueh Chen, 2018. "Profitability efficiency, marketability efficiency and technology gaps in Taiwan’s banking industry: meta-frontier network data envelopment analysis," Applied Economics, Taylor & Francis Journals, vol. 50(3), pages 233-250, January.
    15. Yao, Xin & Zhou, Hongchen & Zhang, Aizhen & Li, Aijun, 2015. "Regional energy efficiency, carbon emission performance and technology gaps in China: A meta-frontier non-radial directional distance function analysis," Energy Policy, Elsevier, vol. 84(C), pages 142-154.
    16. Kuan-Chen Chen & Hong-Ming Chen & Li-Nien Chien & Ming-Miin Yu, 2019. "Productivity growth and quality changes of hospitals in Taiwan: does ownership matter?," Health Care Management Science, Springer, vol. 22(3), pages 451-461, September.
    17. Kao, Chiang & Hwang, Shiuh-Nan, 2008. "Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan," European Journal of Operational Research, Elsevier, vol. 185(1), pages 418-429, February.
    18. Hayami, Yujiro & Ruttan, Vernon W, 1970. "Agricultural Productivity Differences Among Countries," American Economic Review, American Economic Association, vol. 60(5), pages 895-911, December.
    19. Víctor Giménez & Jorge R. Keith & Diego Prior, 2019. "Do healthcare financing systems influence hospital efficiency? A metafrontier approach for the case of Mexico," Health Care Management Science, Springer, vol. 22(3), pages 549-559, September.
    20. Qunwei Wang & Ye Hang & Jin‐Li Hu & Ching‐Ren Chiu, 2018. "An alternative metafrontier framework for measuring the heterogeneity of technology," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(5), pages 427-445, August.
    21. Christopher O’Donnell & D. Rao & George Battese, 2008. "Metafrontier frameworks for the study of firm-level efficiencies and technology ratios," Empirical Economics, Springer, vol. 34(2), pages 231-255, March.
    22. Wang, Qunwei & Su, Bin & Zhou, Peng & Chiu, Ching-Ren, 2016. "Measuring total-factor CO2 emission performance and technology gaps using a non-radial directional distance function: A modified approach," Energy Economics, Elsevier, vol. 56(C), pages 475-482.
    23. Afsharian, Mohsen & Podinovski, Victor V., 2018. "A linear programming approach to efficiency evaluation in nonconvex metatechnologies," European Journal of Operational Research, Elsevier, vol. 268(1), pages 268-280.
    24. Wang, Nannan & Chen, Ji & Yao, Shengnan & Chang, Yen-Chiang, 2018. "A meta-frontier DEA approach to efficiency comparison of carbon reduction technologies on project level," Renewable and Sustainable Energy Reviews, Elsevier, vol. 82(P3), pages 2606-2612.
    25. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
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