IDEAS home Printed from https://ideas.repec.org/p/qld/uqcepa/194.html
   My bibliography  Save this paper

Homothetic Data Generated Production Metatechnologies

Author

Listed:
  • Antonio Peyrache

    (School of Economics and Centre for Efficiency and Productivity Analysis (CEPA) at The University of Queensland, Australia)

Abstract

This study tackles the problem of building nonparametric production technologies that satisfy homotheticity and (Hicks) neutrality. Since no current method is available, the paper proposes a method for constructing a homothetic metatechnology and proves that this metatechnology can be obtained as the union of homothetic group technologies that satisfy (Hicks) neutrality. It is shown that all these technologies are the minimal technologies that will satisfy the given set of axioms, therefore providing an axiomatic foundation for the method. There is a non-negligible computational aspect in the fact that all technologies are not only LP computable but are in fact computable as a linear function of the size of the dataset (in fact in the non-convex case enumeration algorithms can be used). An empirical illustration is provided to show the strength and range of applicability of the method.

Suggested Citation

  • Antonio Peyrache, 2024. "Homothetic Data Generated Production Metatechnologies," CEPA Working Papers Series WP022024, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uqcepa:194
    as

    Download full text from publisher

    File URL: https://economics.uq.edu.au/files/50237/WP022024.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ivaldi, Marc, et al, 1996. "Comparing Fourier and Translog Specifications of Multiproduct Technology: Evidence from an Incomplete Panel of French Farmers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 649-667, Nov.-Dec..
    2. Kerstens, Kristiaan & Vanden Eeckaut, Philippe, 1999. "Estimating returns to scale using non-parametric deterministic technologies: A new method based on goodness-of-fit," European Journal of Operational Research, Elsevier, vol. 113(1), pages 206-214, February.
    3. 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.
    4. Pastor, Jesus T. & Lovell, C.A. Knox, 2005. "A global Malmquist productivity index," Economics Letters, Elsevier, vol. 88(2), pages 266-271, August.
    5. Olesen, Ole B. & Ruggiero, John, 2014. "Maintaining the Regular Ultra Passum Law in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 235(3), pages 798-809.
    6. Hanoch, Giora & Rothschild, Michael, 1972. "Testing the Assumptions of Production Theory: A Nonparametric Approach," Journal of Political Economy, University of Chicago Press, vol. 80(2), pages 256-275, March-Apr.
    7. Walheer, Barnabé, 2023. "Meta-frontier and technology switchers: A nonparametric approach," European Journal of Operational Research, Elsevier, vol. 305(1), pages 463-474.
    8. Walter Briec & Kristiaan Kerstens, 2006. "Input, output and graph technical efficiency measures on non-convex FDH models with various scaling laws: An integrated approach based upon implicit enumeration algorithms," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 135-166, June.
    9. Podinovski, V. V., 2004. "On the linearisation of reference technologies for testing returns to scale in FDH models," European Journal of Operational Research, Elsevier, vol. 152(3), pages 800-802, February.
    10. Antonio Peyrache, 2013. "Multilateral productivity comparisons and homotheticity," Journal of Productivity Analysis, Springer, vol. 40(1), pages 57-65, August.
    11. Jin, Qianying & Basso, Antonella & Funari, Stefania & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2024. "Evaluating different groups of mutual funds using a metafrontier approach: Ethical vs. non-ethical funds," European Journal of Operational Research, Elsevier, vol. 312(3), pages 1134-1145.
    12. Jin, Qianying & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2020. "Metafrontier productivity indices: Questioning the common convexification strategy," European Journal of Operational Research, Elsevier, vol. 283(2), pages 737-747.
    13. Peyrache, Antonio, 2024. "A homothetic data generated technology," European Journal of Operational Research, Elsevier, vol. 316(1), pages 255-267.
    14. Olesen, Ole B., 2014. "A homothetic reference technology in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 233(3), pages 759-771.
    15. Blackorby, Charles & Lovell, C A Knox & Thursby, Marie C, 1976. "Extended Hicks Neutral Technical Change," Economic Journal, Royal Economic Society, vol. 86(344), pages 845-852, December.
    16. Primont, Daniel & Primont, Diane, 1994. "Homothetic non-parametric production models," Economics Letters, Elsevier, vol. 45(2), pages 191-195, June.
    17. Olesen, O.B. & Ruggiero, J., 2022. "The hinging hyperplanes: An alternative nonparametric representation of a production function," European Journal of Operational Research, Elsevier, vol. 296(1), pages 254-266.
    18. 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.
    19. J.H. Dulá & R.M. Thrall, 2001. "A Computational Framework for Accelerating DEA," Journal of Productivity Analysis, Springer, vol. 16(1), pages 63-78, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Antonio Peyrache, 2022. "A Homothetic Data Generated Technology," CEPA Working Papers Series WP042022, School of Economics, University of Queensland, Australia.
    2. Färe, Rolf & Mizobuchi, Hideyuki & Zelenyuk, Valentin, 2021. "Hicks neutrality and homotheticity in technologies with multiple inputs and multiple outputs," Omega, Elsevier, vol. 101(C).
    3. Mahmood Mehdiloo & Jafar Sadeghi & Kristiaan Kerstens, 2024. "Top Down Axiomatic Modeling of Metatechnologies and Evaluating Directional Economic Efficiency," Working Papers 2024-EQM-03, IESEG School of Management.
    4. Helu Xiao & Na Wang & Shanping Wang, 2023. "Dynamic sustainability assessment of poverty alleviation in China: evidence from both novel non-convex global two-stage DEA and Malmquist productivity index," Operational Research, Springer, vol. 23(2), pages 1-40, June.
    5. Kristiaan Kerstens & Ignace Van de Woestyne, 2018. "Enumeration algorithms for FDH directional distance functions under different returns to scale assumptions," Annals of Operations Research, Springer, vol. 271(2), pages 1067-1078, December.
    6. Kerstens, Kristiaan & Sadeghi, Jafar & Toloo, Mehdi & Van de Woestyne, Ignace, 2022. "Procedures for ranking technical and cost efficient units: With a focus on nonconvexity," European Journal of Operational Research, Elsevier, vol. 300(1), pages 269-281.
    7. Xiao, Helu & Zhou, Zhongbao & Ren, Teng & Liu, Wenbin, 2022. "Estimation of portfolio efficiency in nonconvex settings: A free disposal hull estimator with non-increasing returns to scale," Omega, Elsevier, vol. 111(C).
    8. Ching-Ren Chiu & Ming-Chung Chang & Jin-Li Hu, 2022. "Energy intensity improvement and energy productivity changes: an analysis of BRICS and G7 countries," Journal of Productivity Analysis, Springer, vol. 57(3), pages 297-311, June.
    9. Núñez, F. & Arcos-Vargas, A. & Villa, G., 2020. "Efficiency benchmarking and remuneration of Spanish electricity distribution companies," Utilities Policy, Elsevier, vol. 67(C).
    10. Tavakoli, Ibrahim M. & Mostafaee, Amin, 2019. "Free disposal hull efficiency scores of units with network structures," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1027-1036.
    11. Soleimani-damaneh, Majid & Mostafaee, Amin, 2015. "Identification of the anchor points in FDH models," European Journal of Operational Research, Elsevier, vol. 246(3), pages 936-943.
    12. Nguyen, Minh-Anh Thi & Yu, Ming-Miin & Lirn, Taih-Cherng, 2022. "Revenue efficiency across airline business models: A bootstrap non-convex meta-frontier approach," Transport Policy, Elsevier, vol. 117(C), pages 108-117.
    13. Fang, Lei, 2022. "Measuring and decomposing group performance under centralized management," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1006-1013.
    14. Antonio Peyrache, 2024. "A Homothetic and Additively Separable Production Frontier," CEPA Working Papers Series WP012024, School of Economics, University of Queensland, Australia.
    15. Afsharian, Mohsen & Ahn, Heinz & Harms, Sören Guntram, 2019. "Performance comparison of management groups under centralised management," European Journal of Operational Research, Elsevier, vol. 278(3), pages 845-854.
    16. Lewbel, Arthur & Linton, Oliver, 2003. "Nonparametric estimation of homothetic and homothetically separable functions," LSE Research Online Documents on Economics 2066, London School of Economics and Political Science, LSE Library.
    17. Cesaroni, Giovanni & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2017. "Global and local scale characteristics in convex and nonconvex nonparametric technologies: A first empirical exploration," European Journal of Operational Research, Elsevier, vol. 259(2), pages 576-586.
    18. Barnabé Walheer, 2019. "Disaggregation for efficiency analysis," Journal of Productivity Analysis, Springer, vol. 51(2), pages 137-151, June.
    19. 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.
    20. Haiyan Deng & Ge Bai & Kristiaan Kerstens & Zhiyang Shen, 2023. "Comparing green productivity under convex and nonconvex technologies: Which is a robust approach consistent with energy structure?," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(8), pages 4377-4394, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:qld:uqcepa:194. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SOE IT (email available below). General contact details of provider: https://edirc.repec.org/data/decuqau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.