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Malmquist Productivity Indexes and DEA

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Handbook on Data Envelopment Analysis

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 164))

Abstract

In this chapter, we provide an overview of our recent work on data envelopment analysis (DEA) and Malmquist productivity indexes. First, we review the construction of static and dynamic DEA technologies. Based on these technologies we show how DEA can be used to estimate the Malmquist productivity index introduced by Caves et al. (Econometrica 50(6):1393–14, 1982) in the static case as well as its extension into the dynamic case.

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Notes

  1. 1.

    See also Färe et al. (1998).

  2. 2.

    This figure is adapted from Färe and Grosskopf (1996).

  3. 3.

    This model is also adapted from Färe and Grosskopf (1996). For an empirical application of this model, see Bogetoft et al. (2009).

  4. 4.

    This idea was developed by Färe et al. (2009).

  5. 5.

    Note that each component is equipped with a unit of measurement.

  6. 6.

    This allows us to cost minimize with nonnegative prices.

  7. 7.

    The proof is similar to that of Färe and Lovell (1978) on the Russell measure.

  8. 8.

    See Färe and Lovell (1978).

  9. 9.

    See Färe et al. (1998).

  10. 10.

    See Färe and Grosskopf (1992).

  11. 11.

    This figure is adapted from Färe and Grosskopf (1996).

  12. 12.

    We discuss alternative decompositions and interpretations presently.

  13. 13.

    There are a number of software packages to estimate the Malmquist index and DEA problems in general, see R. Barr (2004) for a discussion.

  14. 14.

    See Chambers and Färe (1994) for various notions of neutral technical change.

  15. 15.

    Nonradial Malmquist productivity indexes are discussed by Tone (2004) and have been applied to data by, e.g., Chen (2003) and Fukuyama and Weber (2001).

  16. 16.

    See Färe and Grosskopf (2004) for its uses.

  17. 17.

    This section is based on Färe and Grosskopf (2010).

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Authors and Affiliations

  1. Department of Economics, Oregon State University, Corvallis, OR, 97331, USA

    Rolf Färe & Shawna Grosskopf

  2. Department of Accounting & Finance, University of Auckland Business School, Auckland, New Zealand

    Dimitris Margaritis

Authors
  1. Rolf Färe
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  2. Shawna Grosskopf
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  3. Dimitris Margaritis
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Correspondence to Dimitris Margaritis .

Editor information

Editors and Affiliations

  1. McCombs School of Business, Dept. Management Science &, University of Texas, Austin, University Station 1, Austin, 78712-0212, Texas, USA

    William W. Cooper

  2. Dept. Industrial and, Operations Engineering, University of Michigan, Beal Avenue 1205, Ann Arbor, 48109-2117, Michigan, USA

    Lawrence M. Seiford

  3. Dept. Management, Worcester Polytechnic Institute, Institute Road 100, Worcester, 01609, Massachusetts, USA

    Joe Zhu

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Färe, R., Grosskopf, S., Margaritis, D. (2011). Malmquist Productivity Indexes and DEA. In: Cooper, W., Seiford, L., Zhu, J. (eds) Handbook on Data Envelopment Analysis. International Series in Operations Research & Management Science, vol 164. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6151-8_5

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