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Inner and outer approximations of technology: A shadow profit approach

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  • Leleu, Hervé

Abstract

In this paper we extend the taxonomy on inner and outer approximations to a technology by assuming that price data are not available. Mimicking Varian [Varian H., Econometrica 1984;52(3):579], we introduce a Weak Axiom of Shadow Profit Maximization (WASPM) to test if observed production plans are compatible with technically efficient behavior. If the test fails for an observed sample, we then characterize the maximal subset of observed production plans that meets WASPM and we derive lower and upper bounds on technical efficiency for production plans that are observed but not in this subset. We also derive linear programs to implement these bounds.

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Bibliographic Info

Article provided by Elsevier in its journal Omega.

Volume (Year): 41 (2013)
Issue (Month): 5 ()
Pages: 868-871

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Handle: RePEc:eee:jomega:v:41:y:2013:i:5:p:868-871

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Related research

Keywords: Technical efficiency; Shadow prices; Inefficiency bounds;

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References

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  1. Fare, Rolf & Li, Sung Ko, 1998. "Inner and outer approximations of technology: a data envelopment analysis approach," European Journal of Operational Research, Elsevier, vol. 105(3), pages 622-625, March.
  2. Per Andersen & Niels Christian Petersen, 1993. "A Procedure for Ranking Efficient Units in Data Envelopment Analysis," Management Science, INFORMS, vol. 39(10), pages 1261-1264, October.
  3. Subhash Ray, 2007. "Shadow profit maximization and a measure of overall inefficiency," Journal of Productivity Analysis, Springer, vol. 27(3), pages 231-236, June.
  4. 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 568-98, October.
  5. Laurens Cherchye & Tom Van Puyenbroeck, 2002. "Profit Efficiency Analysis Under Limited Information. With an Application to German Farm Types," Public Economics Working Paper Series ces0202, Katholieke Universiteit Leuven, Centrum voor Economische Studiën, Working Group Public Economics.
  6. Banker, Rajiv D & Maindiratta, Ajay, 1988. "Nonparametric Analysis of Technical and Allocative Efficiencies in Production," Econometrica, Econometric Society, vol. 56(6), pages 1315-32, November.
  7. Tsionas, Efthymios G. & Papadakis, Emmanuel N., 2010. "A Bayesian approach to statistical inference in stochastic DEA," Omega, Elsevier, vol. 38(5), pages 309-314, October.
  8. 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 256-75, March-Apr.
  9. Chen, Yao & Du, Juan & Huo, Jiazhen, 2013. "Super-efficiency based on a modified directional distance function," Omega, Elsevier, vol. 41(3), pages 621-625.
  10. Varian, Hal R., 1985. "Non-parametric analysis of optimizing behavior with measurement error," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 445-458.
  11. Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-97, May.
  12. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
  13. Robert Russell, R., 1985. "Measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 35(1), pages 109-126, February.
  14. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
  15. Fang, Hsin-Hsiung & Lee, Hsuan-Shih & Hwang, Shiuh-Nan & Chung, Cheng-Chi, 2013. "A slacks-based measure of super-efficiency in data envelopment analysis: An alternative approach," Omega, Elsevier, vol. 41(4), pages 731-734.
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Cited by:
  1. Portela, Maria Conceição A. Silva & Thanassoulis, Emmanuel, 2014. "Economic efficiency when prices are not fixed: disentangling quantity and price efficiency," Omega, Elsevier, vol. 47(C), pages 36-44.

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