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An overall measure of technical inefficiency at the firm and at the industry level: The ‘lost profit on outlay’

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  • Aparicio, Juan
  • Pastor, Jesus T.
  • Ray, Subhash C.

Abstract

As a measure of overall technical inefficiency, the Directional Distance Function (DDF) introduced by Chambers, Chung, and Färe ties the potential output expansion and input contraction together through a single parameter. By duality, the DDF is related to a measure of profit inefficiency, which is calculated as the normalized deviation between optimal and actual profit at market prices. As we show, in the most usual case, the associated normalization represents the sum of the actual revenue and the actual cost of the assessed firm. Consequently, the corresponding profit inefficiency measure associated with the DDF has no obvious economic interpretation. In contrast, in this paper we allow outputs to expand and inputs to contract by different proportions. This results in a modified DDF that retains most of the properties of the original DDF. The corresponding dual problem has a much simpler interpretation as the lost profit on (average) outlay that can be decomposed into a technical and an allocative inefficiency component. In addition, an overall measure of technical inefficiency at the industry level is introduced resorting to the direction corresponding to the average input–output bundle.

Suggested Citation

  • Aparicio, Juan & Pastor, Jesus T. & Ray, Subhash C., 2013. "An overall measure of technical inefficiency at the firm and at the industry level: The ‘lost profit on outlay’," European Journal of Operational Research, Elsevier, vol. 226(1), pages 154-162.
    • Handle: RePEc:eee:ejores:v:226:y:2013:i:1:p:154-162
    DOI: 10.1016/j.ejor.2012.10.028
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    References listed on IDEAS

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    10. William Cooper & Jesús Pastor & Fernando Borras & Juan Aparicio & Diego Pastor, 2011. "BAM: a bounded adjusted measure of efficiency for use with bounded additive models," Journal of Productivity Analysis, Springer, vol. 35(2), pages 85-94, April.
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    Cited by:

    1. Pastor, Jesus T. & Zofio, Jose L., 2017. "Can Farrell's allocative efficiency be generalized by the directional distance function approach?Author-Name: Aparicio, Juan," European Journal of Operational Research, Elsevier, vol. 257(1), pages 345-351.
    2. Hien Thu Pham & Antonio Peyrache, 2015. "Industry Inefficiency Measures: A Unifying Approximation Proposition," CEPA Working Papers Series WP102015, School of Economics, University of Queensland, Australia.
    3. Hidemichi Fujii & Jing Cao & Shunsuke Managi, 2015. "Decomposition of Productivity Considering Multi-environmental Pollutants in Chinese Industrial Sector," Review of Development Economics, Wiley Blackwell, vol. 19(1), pages 75-84, February.
    4. Aparicio, Juan & Ortiz, Lidia & Pastor, Jesus T., 2017. "Measuring and decomposing profit inefficiency through the Slacks-Based Measure," European Journal of Operational Research, Elsevier, vol. 260(2), pages 650-654.
    5. Peyrache, Antonio, 2015. "Cost constrained industry inefficiency," European Journal of Operational Research, Elsevier, vol. 247(3), pages 996-1002.
    6. 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.
    7. Subhash C. Ray & Kankana Mukherjee, 2017. "A Reverse Directional Distance Function to Reconcile Between Competing Efficiency Goals: An Application to Indian Manufacturing," Working papers 2017-08, University of Connecticut, Department of Economics.
    8. Kenneth Løvold Rødseth, 2017. "Environmental regulations and allocative efficiency: application to coal-to-gas substitution in the U.S. electricity sector," Journal of Productivity Analysis, Springer, vol. 47(2), pages 129-142, April.
    9. Peyrache, Antonio & Zago, Angelo, 2016. "Large courts, small justice!," Omega, Elsevier, vol. 64(C), pages 42-56.

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