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Stochastic metafrontiers

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  • Christine Amsler
  • Christopher J. O’Donnell
  • Peter Schmidt

Abstract

We consider the case of production units arranged into a number of groups. All units within a group choose output–input combinations from the same production possibilities set that is represented by a stochastic frontier model. The metafrontier is the envelope of the group-specific frontiers. We are interested in the metafrontier distance, which is the amount by which the group-specific frontier lies below the metafrontier.Previous work has measured the metafrontier distance using the deterministic portion of the frontier. In a stochastic frontier model, this is not appropriate. We show how to evaluate the metafrontier distance, and we demonstrate the empirical relevance of this issue.

Suggested Citation

  • Christine Amsler & Christopher J. O’Donnell & Peter Schmidt, 2017. "Stochastic metafrontiers," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 1007-1020, October.
    • Handle: RePEc:taf:emetrv:v:36:y:2017:i:6-9:p:1007-1020
    DOI: 10.1080/07474938.2017.1308345
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    References listed on IDEAS

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    1. Tim J. Coelli & D. S. Prasada Rao, 2005. "Total factor productivity growth in agriculture: a Malmquist index analysis of 93 countries, 1980–2000," Agricultural Economics, International Association of Agricultural Economists, vol. 32(s1), pages 115-134, January.
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    5. Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 233-238, August.
    6. George Battese & D. Rao & Christopher O'Donnell, 2004. "A Metafrontier Production Function for Estimation of Technical Efficiencies and Technology Gaps for Firms Operating Under Different Technologies," Journal of Productivity Analysis, Springer, vol. 21(1), pages 91-103, January.
    7. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
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    Cited by:

    1. Walheer, Barnabé, 2018. "Aggregation of metafrontier technology gap ratios: the case of European sectors in 1995–2015," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1013-1026.
    2. Owusu, Eric S. & Bravo-Ureta, Boris E., 2022. "Reap when you sow? The productivity impacts of early sowing in Malawi," Agricultural Systems, Elsevier, vol. 199(C).
    3. Neubauer, Florian & Songsermsawas, Tisorn & Kámiche-Zegarra, Joanna & Bravo-Ureta, Boris E., 2022. "Technical efficiency and technological gaps correcting for selectivity bias: Insights from a value chain project in Nepal," Food Policy, Elsevier, vol. 112(C).
    4. Núñez, F. & Arcos-Vargas, A. & Villa, G., 2020. "Efficiency benchmarking and remuneration of Spanish electricity distribution companies," Utilities Policy, Elsevier, vol. 67(C).
    5. Walheer, Barnabé & He, Ming, 2020. "Technical efficiency and technology gap of the manufacturing industry in China: Does firm ownership matter?," World Development, Elsevier, vol. 127(C).
    6. 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.
    7. Lajos Baráth & Imre Fertő & Jakub Staniszewski, 2024. "Are technological or efficiency differences more pronounced between Hungarian and Polish poultry farms? A stochastic metafrontier analysis," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 70(8), pages 406-413.
    8. Tsionas, Mike G., 2023. "Clustering and meta-envelopment in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 304(2), pages 763-778.
    9. Walheer, Barnabé, 2023. "Meta-frontier and technology switchers: A nonparametric approach," European Journal of Operational Research, Elsevier, vol. 305(1), pages 463-474.
    10. Tsionas, Mike G., 2020. "On a model of environmental performance and technology gaps," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1141-1152.
    11. Bu, Lin-Lan & Kopsakangas-Savolainen, Maria & Xie, Bai-Chen & Li, Hong-Zhou & Liu, Yi-Meng & Yin, Shao-Peng, 2024. "Has benchmarking improved the performance of the Australian electricity distribution utilities? A meta-frontier model," Utilities Policy, Elsevier, vol. 88(C).

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