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Inner and Outer Approximations of Technology: A Shadow Profit Approach

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  • Hervé Leleu

    ()
    (CNRS-LEM (UMR 8179) and IESEG School of Management)

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 [Econometrica, 52(3) (1984) 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

Paper provided by IESEG School of Management in its series Working Papers with number 2012-ECO-06.

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Length: 10 pages
Date of creation: Apr 2012
Date of revision:
Handle: RePEc:ies:wpaper:e201206

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Keywords: Technical efficiency; Shadow prices; Bounds on inefficiency;

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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. Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-97, May.
  3. 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.
  4. 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.
  5. Subhash Ray, 2007. "Shadow profit maximization and a measure of overall inefficiency," Journal of Productivity Analysis, Springer, vol. 27(3), pages 231-236, June.
  6. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
  7. 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.
  8. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
  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. 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.
  11. 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.
  12. Varian, Hal R., 1985. "Non-parametric analysis of optimizing behavior with measurement error," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 445-458.
  13. Robert Russell, R., 1985. "Measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 35(1), pages 109-126, February.
  14. 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.
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