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Axiomatic modeling of fixed proportion technologies

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  • Xun Zhou
  • Timo Kuosmanen

Abstract

Understanding input substitution and output transformation possibilities is critical for efficient resource allocation and firm strategy. There are important examples of fixed proportion technologies where certain inputs are non-substitutable and/or certain outputs are non-transformable. However, there is widespread confusion about the appropriate modeling of fixed proportion technologies in data envelopment analysis. We point out and rectify several misconceptions in the existing literature, and show how fixed proportion technologies can be correctly incorporated into the axiomatic framework. A Monte Carlo study is performed to demonstrate the proposed solution.

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  • Xun Zhou & Timo Kuosmanen, 2024. "Axiomatic modeling of fixed proportion technologies," Papers 2404.12462, arXiv.org.
  • Handle: RePEc:arx:papers:2404.12462
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    References listed on IDEAS

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    1. Darold Barnum & John Gleason, 2011. "Measuring efficiency under fixed proportion technologies," Journal of Productivity Analysis, Springer, vol. 35(3), pages 243-262, June.
    2. Güner, Samet & İbrahim Cebeci, Halil, 2021. "Multi-period efficiency analysis of major European and Asian airports under fixed proportion technologies," Transport Policy, Elsevier, vol. 107(C), pages 24-42.
    3. Afriat, Sidney N, 1972. "Efficiency Estimation of Production Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(3), pages 568-598, October.
    4. Darold Barnum & Jason Coupet & John Gleason & Abagail McWilliams & Annaleena Parhankangas, 2017. "Impact of input substitution and output transformation on data envelopment analysis decisions," Applied Economics, Taylor & Francis Journals, vol. 49(15), pages 1543-1556, March.
    5. Henry Tulkens, 2006. "On FDH Efficiency Analysis: Some Methodological Issues and Applications to Retail Banking, Courts and Urban Transit," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 311-342, Springer.
    6. 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.
    7. SIMAR , Léopold, 1995. "Aspects of Statistical Analysis in DEA-Type Frontier Models," LIDAM Discussion Papers CORE 1995061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. 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.
    9. R. Allen & A. Athanassopoulos & R.G. Dyson & E. Thanassoulis, 1997. "Weights restrictions and value judgements in Data Envelopment Analysis: Evolution, development and future directions," Annals of Operations Research, Springer, vol. 73(0), pages 13-34, October.
    10. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
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