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Weight Restrictions in DEA:Misplaced Emphasis?

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  • R. Førsund, Finn

    ()
    (Dept. of Economics, University of Oslo)

Abstract

Measuring productive efficiency is an important research strand within fields of economics, management science and operations research. One definition of efficiency is the proportional scaling needed for observations of an inefficient unit to be projected onto an efficient production function and another definition is a ratio index of weighted outputs on weighted inputs. When linear programming is used to estimate efficiency the two definitions give identical results due to the fundamental duality of linear programming. Empirical applications of DEA using linear programming showed a prevalence of zero weights leading to questioning the consequence for the efficiency score estimate based on the ratio definition. Early literature on weight restrictions is exclusively based on the ratio efficiency. It was stated that variables with zero weights had no influence on the efficiency score, in spite of the alleged importance of the variables. This has been one motivation for introducing restrictions on weights. Another empirical result was that often there were too many efficient units. This problem could also be overcome by introducing weight restrictions. Weight restrictions were said to introduce values for inputs and outputs. The paper makes a critical examinations of these claims based on defining efficiency relative to a frontier production function.

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Bibliographic Info

Paper provided by Oslo University, Department of Economics in its series Memorandum with number 05/2011.

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Length: 28 pages
Date of creation: 17 Feb 2011
Date of revision:
Publication status: Published as R. Førsund, Finn, 'Weight Restrictions in DEA:Misplaced Emphasis?' in journal of productivity analysis, 2013, pages 271-283.
Handle: RePEc:hhs:osloec:2011_005

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Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
Phone: 22 85 51 27
Fax: 22 85 50 35
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Web page: http://www.oekonomi.uio.no/indexe.html
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Keywords: Weight restrictions; DEA; efficiency; frontier production function; primal and dual linear programming problems;

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  1. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
  2. 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.
  3. Forsund, Finn R. & Sarafoglou, Nikias, 2005. "The tale of two research communities: The diffusion of research on productive efficiency," International Journal of Production Economics, Elsevier, vol. 98(1), pages 17-40, October.
  4. Forsund,F.R. & Sarafoglou,N., 2000. "On the origins of data envelopment analysis," Memorandum 24/2000, Oslo University, Department of Economics.
  5. Charnes, A. & Cooper, W. W. & Huang, Z. M. & Sun, D. B., 1990. "Polyhedral Cone-Ratio DEA Models with an illustrative application to large commercial banks," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 73-91.
  6. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
  7. O. B. Olesen & N. C. Petersen, 1996. "Indicators of Ill-Conditioned Data Sets and Model Misspecification in Data Envelopment Analysis: An Extended Facet Approach," Management Science, INFORMS, vol. 42(2), pages 205-219, February.
  8. Podinovski, V. V., 1999. "Side effects of absolute weight bounds in DEA models," European Journal of Operational Research, Elsevier, vol. 115(3), pages 583-595, June.
  9. Thompson, Russell G. & Langemeier, Larry N. & Lee, Chih-Tah & Lee, Euntaik & Thrall, Robert M., 1990. "The role of multiplier bounds in efficiency analysis with application to Kansas farming," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 93-108.
  10. Allen, R. & Thanassoulis, E., 2004. "Improving envelopment in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 154(2), pages 363-379, April.
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