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The Directional Distance Function and Measurement of Super-Efficiency: An Application to Airlines Data

  • Subhash C. Ray

    (University of Connecticut)

Lovell and Rouse (LR) have recently proposed a modification of the standard DEA model that overcomes the infeasibility problem often encountered in computing super-efficiency. In the LR procedure one appropriately scales up the observed input vector (scale down the output vector) of the relevant super-efficient firm thereby usually creating its inefficient surrogate. An alternative procedure proposed in this paper uses the directional distance function introduced by Chambers, Chung, and Fare and the resulting Nerlove-Luenberger (NL) measure of super-efficiency. The fact that the directional distance function combines features of both an input-oriented and an output-oriented model, generally leads to a more complete ranking of the observations than either of the oriented models. An added advantage of this approach is that the NL super-efficiency measure is unique and does not depend on any arbitrary choice of a scaling parameter. A data set on international airlines from Coelli, Perelman, and Griffel-Tatje (2002) is utilized in an illustrative empirical application.

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Paper provided by University of Connecticut, Department of Economics in its series Working papers with number 2004-16.

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Length: 15 pages
Date of creation: May 2004
Date of revision:
Handle: RePEc:uct:uconnp:2004-16
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Web page: http://www.econ.uconn.edu/

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  1. Coelli, Tim & Grifell-Tatje, Emili & Perelman, Sergio, 2002. "Capacity utilisation and profitability: A decomposition of short-run profit efficiency," International Journal of Production Economics, Elsevier, vol. 79(3), pages 261-278, October.
  2. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
  3. Jean-Paul Chavas & Thomas L. Cox, 1999. "A Generalized Distance Function and the Analysis of Production Efficiency," Wisconsin-Madison Agricultural and Applied Economics Staff Papers 422, Wisconsin-Madison Agricultural and Applied Economics Department.
  4. 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.
  5. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
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