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Weight restrictions in DEA: misplaced emphasis?

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  • Finn Førsund

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 inefficient units 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. Copyright Springer Science+Business Media, LLC 2013

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  • Finn Førsund, 2013. "Weight restrictions in DEA: misplaced emphasis?," Journal of Productivity Analysis, Springer, vol. 40(3), pages 271-283, December.
    • Handle: RePEc:kap:jproda:v:40:y:2013:i:3:p:271-283
    DOI: 10.1007/s11123-012-0296-9
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    1. V E Krivonozhko & O B Utkin & M M Safin & A V Lychev, 2009. "On some generalization of the DEA models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1518-1527, November.
    2. 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.
    3. Finn Førsund & Nikias Sarafoglou, 2002. "On the Origins of Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 17(1), pages 23-40, January.
    4. 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.
    5. 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.
    6. Peter Smith, 1997. "Model misspecification in Data Envelopment Analysis," Annals of Operations Research, Springer, vol. 73(0), pages 233-252, October.
    7. V V Podinovski, 2005. "The explicit role of weight bounds in models of data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(12), pages 1408-1418, December.
    8. Allen, R. & Thanassoulis, E., 2004. "Improving envelopment in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 154(2), pages 363-379, April.
    9. 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.
    10. 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.
    11. T Joro & E-J Viitala, 2004. "Weight-restricted DEA in action: from expert opinions to mathematical models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(8), pages 814-821, August.
    12. A. Bessent & W. Bessent & J. Elam & T. Clark, 1988. "Efficiency Frontier Determination by Constrained Facet Analysis," Operations Research, INFORMS, vol. 36(5), pages 785-796, October.
    13. R. Allen & A. Athanassopoulos & R.G. Dyson & E. Thanassoulis, 1997. "Weights restrictions and value judgements in Data Envelopment Analysis: Evolution, development and future directions," Annals of Operations Research, Springer, vol. 73(0), pages 13-34, October.
    14. M. Stone, 2002. "How not to measure the efficiency of public services (and how one might)," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(3), pages 405-434, October.
    15. 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.
    16. 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.
    17. V V Podinovski, 2007. "Improving data envelopment analysis by the use of production trade-offs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(10), pages 1261-1270, October.
    18. 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.
    19. Francisco Pedraja-Chaparro & Javier Salinas-Jimenez & Peter Smith, 1997. "On the Role of Weight Restrictions in Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 8(2), pages 215-230, May.
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    2. Afsharian, Mohsen & Bogetoft, Peter, 2023. "Limiting flexibility in nonparametric efficiency evaluations: An ex post k-centroid clustering approach," European Journal of Operational Research, Elsevier, vol. 311(2), pages 633-647.
    3. Aldanondo, Ana M. & Casasnovas, Valero L., 2015. "More is better than one: the impact of different numbers of input aggregators in technical efficiency estimation," MPRA Paper 64120, University Library of Munich, Germany.
    4. Zuoren Sun & Rundong Luo & Dequn Zhou, 2015. "Optimal Path for Controlling Sectoral CO 2 Emissions Among China’s Regions: A Centralized DEA Approach," Sustainability, MDPI, vol. 8(1), pages 1-20, December.
    5. Førsund, Finn R., 2018. "Economic interpretations of DEA," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 9-15.
    6. Martin Bod’a & Martin Dlouhý & Emília Zimková, 2018. "Unobservable or omitted production variables in data envelopment analysis through unit-specific production trade-offs," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(4), pages 813-846, December.
    7. Subhash C. Ray, 2014. "Data Envelopment Analysis: An Overview," Working papers 2014-33, University of Connecticut, Department of Economics.
    8. Ray, Subhash C, 2019. "The transformation function, technical efficiency, and the CCR ratio," European Journal of Operational Research, Elsevier, vol. 278(2), pages 422-429.
    9. Vladimir E. Krivonozhko & Finn R. Førsund & Andrey V. Lychev, 2017. "On comparison of different sets of units used for improving the frontier in DEA models," Annals of Operations Research, Springer, vol. 250(1), pages 5-20, March.
    10. González, Eduardo & Cárcaba, Ana & Ventura, Juan, 2015. "How car dealers adjust prices to reach the product efficiency frontier in the Spanish automobile market," Omega, Elsevier, vol. 51(C), pages 38-48.
    11. Costa, Marcelo Azevedo & Lopes-Ahn, Ana Lúcia & Kilger, Alexander de Carvalho & Micas, Artur Fontenelle, 2023. "Limitations of weight restrictions in data envelopment analysis for benchmarking Brazilian electricity distribution system operators," Utilities Policy, Elsevier, vol. 82(C).
    12. Sen Subir, 2020. "Analysis of Cost Efficiency of Indian Life Insurers: A comparison of Quantity vs Value based DEA Approach," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 14(1), pages 1-25, January.
    13. Aldanondo, Ana M. & Casasnovas, Valero L., 2016. "A note on the impact of multiple input aggregators in technical efficiency estimation," MPRA Paper 75290, University Library of Munich, Germany.
    14. da Silva, Aline Veronese & Costa, Marcelo Azevedo & Ahn, Heinz & Lopes, Ana Lúcia Miranda, 2019. "Performance benchmarking models for electricity transmission regulation: Caveats concerning the Brazilian case," Utilities Policy, Elsevier, vol. 60(C), pages 1-1.

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    More about this item

    Keywords

    Weight restrictions; DEA; Efficiency; Frontier production function; Primal and dual linear programming problems; C61; D20;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D20 - Microeconomics - - Production and Organizations - - - General

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