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Axiomatic foundations of efficiency measurement on data-generated technologies

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  • R. Russell

    ()

  • William Schworm

    ()

Abstract

Dmitruk and Koshevoy [1991 JET] provided a complete characterization of the class of technologies for which there exists an efficiency index satisfying the Fare-Lovell [1978 JET] axioms. The technologies implicit in the standard mathematical-programming methods of measuring efficiency, data envelopment analysis (DEA) and free-disposal-hull (FDH) analysis, belong to this class. We assess the ability of three well-known indexes, the Debreu-Farrell index, the Fare-Lovell index, and the Zieschang index, to satisfy not only the Fare-Lovell axioms but also continuity axioms (for technologies as well as input quantities), on this restricted class of technologies. Our principal conclusions are that (a) restriction to these data-based technologies adds continuity in input quantities to the properties satisfied by the Fare-Lovell and the Zieschang indexes (thus eliminating a salient advantage of the Debreu-Farrell index), but (b) none of the indexes satisfies all Fare-Lovell axioms (nor all continuity axioms) on either DEA or FDH technologies, and hence (c) trade-offs among the indexes remain. These findings provide motivation for the search for an index that does satisfy these axioms on DEA and FDH technologies.

(This abstract was borrowed from another version of this item.)

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File URL: http://hdl.handle.net/10.1007/s11123-008-0119-1
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Bibliographic Info

Article provided by Springer in its journal Journal of Productivity Analysis.

Volume (Year): 31 (2009)
Issue (Month): 2 (April)
Pages: 77-86

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Handle: RePEc:kap:jproda:v:31:y:2009:i:2:p:77-86

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Web page: http://www.springerlink.com/link.asp?id=100296

Related research

Keywords: Technical efficiency indexes; Technical efficiency axioms; C43; C61; D24;

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  1. Allen N. Berger & David B. Humphrey, 1997. "Efficiency of financial institutions: international survey and directions for future research," Finance and Economics Discussion Series 1997-11, Board of Governors of the Federal Reserve System (U.S.).
  2. Robert Russell, R., 1985. "Measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 35(1), pages 109-126, February.
  3. Daniel J. Henderson & R. Robert Russell, 2005. "Human Capital And Convergence: A Production-Frontier Approach ," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(4), pages 1167-1205, November.
  4. Subodh Kumar & R. Robert Russell, 2002. "Technological Change, Technological Catch-up, and Capital Deepening: Relative Contributions to Growth and Convergence," American Economic Review, American Economic Association, vol. 92(3), pages 527-548, June.
  5. Fare, Rolf & Knox Lovell, C. A., 1978. "Measuring the technical efficiency of production," Journal of Economic Theory, Elsevier, vol. 19(1), pages 150-162, October.
  6. Fare, Rolf & Grosskopf, Shawna & Noh, Dong-Woon & Weber, William, 2005. "Characteristics of a polluting technology: theory and practice," Journal of Econometrics, Elsevier, vol. 126(2), pages 469-492, June.
  7. Dmitruk, Andrei V. & Koshevoy, Gleb A., 1991. "On the existence of a technical efficiency criterion," Journal of Economic Theory, Elsevier, vol. 55(1), pages 121-144, October.
  8. Pollitt, M.G., 1995. "Ownership and Efficiency in Nuclear Power Production," Cambridge Working Papers in Economics 9518, Faculty of Economics, University of Cambridge.
  9. DEPRINS, Dominique & SIMAR, Léopold & TULKENS, Henry, . "Measuring labor-efficiency in post offices," CORE Discussion Papers RP -571, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Robert Russell, R., 1990. "Continuity of measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 51(2), pages 255-267, August.
  11. R. Robert Russell & William Schworm, 2009. "Axiomatic Foundations of Inefficiency Measurement on Space," Discussion Papers 2009-07, School of Economics, The University of New South Wales.
  12. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
  13. Zieschang, Kimberly D., 1984. "An extended farrell technical efficiency measure," Journal of Economic Theory, Elsevier, vol. 33(2), pages 387-396, August.
  14. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
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Citations

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Cited by:
  1. Diewert, W. Erwin & Fox, Kevin J., 2014. "Reference technology sets, Free Disposal Hulls and productivity decompositions," Economics Letters, Elsevier, vol. 122(2), pages 238-242.
  2. Roberto Gómez-Calvet & David Conesa & Ana Rosa Gómez-Calvet & Emili Tortosa-Ausina, 2013. "Energy efficiency in the European Union: What can be learned from the joint application of directional distance functions and slacks-based measures?," Working Papers 2013/17, Economics Department, Universitat Jaume I, Castellón (Spain).
  3. Fukuyama, Hirofumi & Maeda, Yasunobu & Sekitani, Kazuyuki & Shi, Jianming, 2014. "Input–output substitutability and strongly monotonic p-norm least distance DEA measures," European Journal of Operational Research, Elsevier, vol. 237(3), pages 997-1007.
  4. Chambers, Christopher P. & Miller, Alan D., . "Inefficiency," Working Papers WP2011/14, University of Haifa, Department of Economics, revised 30 Nov 2011.
  5. Peyrache, Antonio, 2013. "Industry structural inefficiency and potential gains from mergers and break-ups: A comprehensive approach," European Journal of Operational Research, Elsevier, vol. 230(2), pages 422-430.
  6. Christopher P. Chambers & Alan D. Miller, 2014. "Inefficiency Measurement," American Economic Journal: Microeconomics, American Economic Association, vol. 6(2), pages 79-92, May.
  7. R. Russell & William Schworm, 2011. "Properties of inefficiency indexes on 〈input, output〉 space," Journal of Productivity Analysis, Springer, vol. 36(2), pages 143-156, October.
  8. Kerstens, Kristiaan & Mounir, Amine & Van de Woestyne, Ignace, 2010. "Benchmarking Mean-Variance Portfolios. Using a Shortage Function: The Choice of Direction Vector," Working Papers 2010/01, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
  9. Briec, Walter & Cavaignac, Laurent & Kerstens, Kristiaan, 2011. "Directional measurement of technical efficiency of production: An axiomatic approach," Economic Modelling, Elsevier, vol. 28(3), pages 775-781, May.
  10. Hirofumi Fukuyama & Kazuyuki Sekitani, 2012. "An efficiency measure satisfying the Dmitruk–Koshevoy criteria on DEA technologies," Journal of Productivity Analysis, Springer, vol. 38(2), pages 131-143, October.

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