Skip to main content

The Modified Directional Distance Function (MDDF): Economic Inefficiency Decompositions

  • 91 Accesses

Part of the International Series in Operations Research & Management Science book series (ISOR,volume 315)

Abstract

As we showed in Chap. 8, by duality, the directional distance function (DDF) is related to a measure of profit inefficiency that is calculated as the normalized deviation between optimal and actual profit at market prices. However, in the most usual case where the selected directional vector corresponds to the observed values in inputs and outputs of the evaluated firm, the associated normalization coincides with the sum of its actual revenue and the actual cost (see expression (8.10)). Although some authors have interpreted this normalization quantity as an indication of the “size” of the firm (see Leleu & Briec, 2009), it is clear that it has no obvious economic meaning from a managerial point of view since this quantity is not present in day-to-day manager’s control panel for decision-making.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-030-84397-7_11
  • Chapter length: 17 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   119.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-84397-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book
USD   159.99
Price excludes VAT (USA)
Fig. 11.1

Notes

  1. 1.

    We refer the reader to Sect. 2.6.1 in Chap. 2 for the installation of the “Benchmarking Economic Efficiency” Julia package. All Jupyter notebooks implementing the different economic models in this book can be downloaded from the reference site: http://www.benchmarkingeconomicefficiency.com

Bibliography

  • Aparicio, J., Pastor, J. T., & Ray, S. C. (2013a). An overall measure of technical inefficiency at the firm and at the industry level: The ‘lost profit on outlay’. European Journal of Operational Research, 226(1), 154–162.

    CrossRef  Google Scholar 

  • Aparicio, J., Borras, F., Pastor, J. T., & Vidal, F. (2013b). Accounting for slacks to measure and decompose revenue efficiency in the Spanish designation of origin wines with DEA. European Journal of Operational Research, 231(2), 443–451.

    CrossRef  Google Scholar 

  • Aparicio, J., Pastor, J. T., & Zofio, J. L. (2017b). Can Farrell’s allocative efficiency be generalized by the directional distance function approach? European Journal of Operational Research, 257(1), 345–351.

    CrossRef  Google Scholar 

  • Chambers, R. G., Chung, Y., & Färe, R. (1998, August). Profit, directional distance functions, and Nerlovian efficiency. Journal of Optimization Theory and Applications, 98(2), 351–364.

    CrossRef  Google Scholar 

  • Farrell, M. J. (1957). The measurement of productive efficiency. Journal of Royal Statistical Society, Series A, 120(III), 253–290.

    Google Scholar 

  • Juo, J.-C., Fu, T.-T., Yu, M.-M., & Lin, Y.-H. (2015). Profit-oriented productivity change. Omega, 57, 76–87.

    Google Scholar 

  • Leleu, H., & Briec, W. (2009). A DEA estimation of a lower bound for firms’ allocative efficiency without information on Price data. International Journal of Production Economics, 121, 203–211.

    CrossRef  Google Scholar 

  • Nerlove, M. (1965). Estimation and identification of Cobb-Douglas production functions. Rand McNally.

    Google Scholar 

  • Petersen, N. C. (2018). Directional distance functions in DEA with optimal endogenous directions. Operations Research, 66(4), 1068–1085.

    Google Scholar 

  • Ray, S. C. (2004). Data envelopment analysis. Theory and techniques for economics and operations research. Cambridge University Press.

    CrossRef  Google Scholar 

  • Zofio, J. L., Pastor, J. T., & Aparicio, J. (2013). The directional profit efficiency measure: On why profit inefficiency is either technical or allocative. Journal of Productivity Analysis, 40(3), 257–266.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this chapter

Verify currency and authenticity via CrossMark

Cite this chapter

Pastor, J.T., Aparicio, J., Zofío, J.L. (2022). The Modified Directional Distance Function (MDDF): Economic Inefficiency Decompositions. In: Benchmarking Economic Efficiency. International Series in Operations Research & Management Science, vol 315. Springer, Cham. https://doi.org/10.1007/978-3-030-84397-7_11

Download citation