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Data Variations

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  1. The main problem in treating economies of scope revolves around access to data in which some firms (or plants) produce all the products of interest while other produce only subsets. See pp.263–269 in R. Färe, S. Grosskopf and C.A.K. Lovell (1994), Production Frontiers, (Cambridge, Cambridge University Press) and the references cited therein.

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  2. P.L. Brockett, W.W. Cooper, H.C. Shin and Y. Wang (1994) “Congestion and Inefficiency in Chinese Production Before and After the 1978 Economic Reforms,” Socio-Economic Planning Sciences 32, pp. 1–20.

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  3. W.W. Cooper, L.M. Seiford and J. Zhu (1999) “A Unified Additive Model Approach for Evaluating Inefficiency and Congestion with Associated Measures in DEA,” Socio-Economic Planning Sciences (to appear). See also the responses by R. Fare and S. Grosskopf in this same journal.

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  4. A.Y. Lewin and L.M. Seiford From Efficiency Calculations to a New Approach for Organizing and Analyzing Data: DEA Fifteen Years Later, Baltzer, The Netherlands, (1997)

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  5. W.W. Cooper, B. Gu and S. Li (1999) “Comparisons and Evaluations of Alternative Approaches to Evaluating Congestion in DEA” European Journal of Operational Research (submitted).

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  6. W.W. Cooper and K. Tone (1997) “Measures of Inefficiency in Data Envelopment Analysis and Stochastic Frontier Estimation,” European Journal of Operational Research 99, pp.72–88.

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  7. P.W. Wilson (1995) “Detecting Influential Observations in Data Envelopment Analysis,” Journal of Productivity Analysis 6, pp.27–46.

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  8. See, for instance, R.M. Thrall (1989) “Classification of Transitions under Expansion of Inputs and Outputs,” Managerial and Decision Economics 10, pp.159–162.

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  9. R.D. Banker, H. Chang and W.W. Cooper (1996) “Simulation Studies of Efficiency, Returns to Scale and Misspecification with Nonlinear Functions in DEA,” Annals of Operations Research 66, pp.233–253.

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  10. A. Charnes, W.W. Cooper, A.Y. Lewin, R.C. Morey and J.J. Rousseau (1985) “Sensitivity and Stability Analysis in DEA,” Annals of Operations Research 2, pp.139–156.

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  11. A. Charnes and W.W. Cooper (1968) “Structural Sensitivity Analysis in Linear Programming and an Exact Product Form Left Inverse,” Naval Research Logistics Quarterly 15, pp.517–522.

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  12. For a summary discussion see A. Charnes and L. Neralic (1992) “Sensitivity Analysis of the Proportionate Change of Inputs (or Outputs) in Data Envelopment Analysis,” Glasnik Matematicki 27, pp.393–405. A subsequent extension is L. Neralic (1997) “Sensitivity in Data Envelopment Analysis for Arbitrary Perturbations of Data,” Glasnik Matematicki 32, pp.315–335.

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  13. A. Charnes, S. Haag, P. Jaska and J. Semple (1992) “Sensitivity of Efficiency Calculations in the Additive Model of Data Envelopment Analysis,” International Journal of System Sciences 23, pp.789–798. Extensions to other classes of models may be found in A. Charnes, J.J. Rousseau and J.H. Semple (1996) “Sensitivity and Stability of Efficiency Classifications in DEA,” Journal of Productivity Analysis 7, pp.5–18.

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  14. The shape of this “ball” will depend on the norm that is used. For a discussion of these and other metric concepts and their associated geometric portrayals see A. Charnes and W.W. Cooper (1961), Management Models and Industrial Applications of Linear Programming (New York: John Wiley & Sons.)

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  15. This omission of DMU0 is also used in P. Andersen and N.C. Petersen (1993) “A Procedure for Ranking Efficient Units in DEA,” Management Science 39, pp.1261–1264. Their use is more closely associated with stability when a DMU is omitted, however, so we do not cover it here. See also R.M. Thrall (1996) “Duality Classification and Slacks in DEA,” Annals of Operations Research 66, pp.104–138.

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  16. A. Charnes, J.J. Rousseau and J.H. Semple (1996) “Sensitivity and Stability of Efficiency Classification in Data Envelopment Analysis,” Journal of Productivity Analysis 7, pp.5–18.

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  17. In fact, Seiford and Zhu propose an iterative approach to assemble an exact stability region in L. Seiford and J. Zhu, “Stability Regions for Maintaining Efficiency in Data Envelopment Analysis,” European Journal of Operational Research 108, 1998, pp.127–139.

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  18. R.G. Thompson, P.S. Dharmapala and R.M. Thrall (1994) “Sensitivity Analysis of Efficiency Measures with Applications to Kansas Farming and Illinois Coal Mining,” in A. Charnes, W.W. Cooper, A.Y. Lewin and L.M. Seiford, eds., Data Envelopment Analysis: Theory, Methodology and Applications (Norwell, Mass., Kluwer Academic Publishers) pp.393–422.

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  19. R.G. Thompson, P.S. Dharmapala, J. Diaz, M.D. Gonzales-Lina and R.M. Thrall (1996) “DEA Multiplier Analytic Center Sensitivity Analysis with an Illustrative Application to Independent Oil Cos.,” Annals of Operations Research 66, pp.163–180.

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  20. A. Charnes, W.W. Cooper and R.M. Thrall (1991) “A Structure for Classifying and Characterizing Efficiency in Data Envelopment Analysis,” Journal of Productivity Analysis 2, pp.197–237.

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  21. An alternate approach to simultaneous variations in all data has recently become available which is effected by the envelopment model. See L.M. Seiford and J. Zhu (1998) “Sensitivity Analysis of DEA Models for Simultaneous Changes in All Data,” Journal of the Operational Research Society 49, pp.1060–1071.

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  22. This status is easily recognized because θ * 1 =θ * 2 =θ * 3 =1 are all associated with uniquely obtained solutions with zero slacks. See A. Charnes, W.W. Cooper and R.M. Thrall (1991) “A Structure for Classifying and Characterizing Efficiency in Data Envelopment Analysis,” Journal of Productivity Analysis 2, pp.197–237.

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  23. R.D. Banker (1993) “Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation,” Management Science 39, pp.1265–1273.

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  24. Quoted from p.139 in R.D Banker (1996) “Hypothesis Tests Using Data Envelopment Analysis,” Journal of Productivity Analysis, pp.139–159.

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  26. See the discussion in L. Simar (1996) “Aspects of Statistical Analysis in DEA-Type Frontier Models,” Journal of Productivity Analysis 7, pp.177–186.

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  27. L. Simar and P.W. Wilson (1998) “Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models,” Management Science 44, pp.49–61.

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  30. D.J. Aigner, C.A.K. Lovell and P. Schmidt (1977) “Formulation and Estimation of Stochastic Frontier Production Models,” Journal of Econometrics 6, pp.21–37. See also W. Meeusen and J. van den Broeck (1977) “Efficiency Estimation from Cobb-Douglas Functions with Composed Error,” International Economic Review 18, pp.435–444.

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  31. J. Jondrow, C.A.K. Lovell, I.S. Materov and P. Schmidt (1982) “On the Estimation of Technical Inefficiency in the Stochastic Frontier Production Model,” Journal of Econometrics 51, pp.259–284.

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  32. B.H. Gong and R.C. Sickles (1990) “Finite Sample Evidence on the Performance of Stochastic Frontiers and Data Envelopment Analysis using Panel Data,” Journal of Econometrics 51, pp.259–284.

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  33. P. Schmidt (1985–1986) “Frontier Production Functions,” Econometric reviews 4, pp.289–328. See also P.W. Bauer (1990) “Recent Development in Econometric Estimation of Frontiers,” Journal of Econometrics 46, pp.39–56.

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  34. G.D. Ferrier and C.A.K. Lovell (1990) “Measuring Cost Efficiency in Banking — Econometric and Linear Programming Evidence,” Journal of Econometrics 6, pp.229–245.

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  35. A. Charnes, W.W. Cooper and T. Sueyoshi (1988) “A Goal Programming/Constrained Regression Review of the Bell System Breakup,” Management Science 34, pp.1–26.

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  36. See R.S. Barr, L.M. Seiford and T.F. Siems (1994) “Forcasting Bank Failure: A Non-Parametric Frontier Estimation Approach,” Recherches Economiques de Louvain 60, pp. 417–429. for an example of a different two-stage DEA regression approach in which the DEA scores from the first stage served as an independent variable in the second stage regression model.

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  37. V. Arnold, I.R. Bardhan, W.W. Cooper and S.C. Kumbhakar (1994) “New Uses of DEA and Statistical Regressions for Efficiency Evaluation and Estimation — With an Illustrative Application to Public Secondary Schools in Texas,” Annals of Operations Research 66, pp.255–278.

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  38. I.R. Bardhan, W.W. Cooper and S.C. Kumbhakar (1998) “A Simulation Study of Joint Uses of Data Envelopment Analysis and Stochastic Regressions for Production Function Estimation and Efficiency Evaluation,” Journal of Productivity Analysis 9, pp.249–278

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  39. S. Thore (1987) “Chance-Constrained Activity Analysis,” European Journal of Operational Research 30, pp.267–269.

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  40. See the following three papers by K.C. Land, C.A.K. Lovell and S. Thore: “Productive Efficiency under Capitalism and State Socialism: the Chance Constrained Programming Approach” in Pierre Pestieau, ed. in Public Finance in a World of Transition (1992) supplement to Public Finance 47, pp.109–121

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  41. See the following three papers by K.C. Land, C.A.K. Lovell and S. Thore: “Chance-Constrained Data Envelopment Analysis,” Managerial and Decision Economics 14, 1993, pp.541–554

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  42. See the following three papers by K.C. Land, C.A.K. Lovell and S. Thore: “Productive Efficiency under Capitalism and State Socialism: An Empirical Inquiry Using Chance-Constrained Data Envelopment Analysis,” Technological Forecasting and Social Change 46, 1994, pp. 139–152. In “Four Papers on Capitalism and State Socialism” (Austin Texas: The University of Texas, IC 2 Institute) S. Thore notes that publication of (2) was delayed because it was to be presented at a 1991 conference in Leningrad which was cancelled because of the Soviet Crisis.

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  43. W.W. Cooper, Z. Huang and S. Li (1996) “Satisficing DEA Models under Chance Constraints,” Annals of Operations Research 66, pp.279–295.

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  44. See Chapter 15 in H.A. Simon (1957) Models of Man (New York: John Wiley & Sons, Inc.)

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  45. A. Charnes and W.W. Cooper (1963) “Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints,” Operations Research 11, pp.18–39.

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  46. See W.F. Sharpe (1970) Portfolio Theory and Capital Markets (New York: McGraw Hill, Inc.)

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  51. R. Färe and S. Grosskopf (1996) Intertemporal Production Frontiers with Dynamic DEA (Boston: Kluwer Academic Publishers).

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  52. This work was subsequently incorporated in his Ph. D. thesis: G. Klopp (1985) “The Analysis of the Efficiency of Production System with Multiple Inputs and Outputs” (Chicago: University of Illinois at Chicago, Industrial and Systems Engineering College). Also available from University Microfilms, Inc., 300 North Zeeb Road, Ann Arbor, Mich. 48106. See also A. Charnes, T. Clark, W.W. Cooper and B. Golany (1985) “A Developmental Study of Data Envelopment Analysis in Measuring the Efficiency of Maintenance Units in the U.S. Air Force,” Annals of Operations Research 2, pp.95–112. See also W.F. Bowlin (1984) “A Data Envelopment Analysis Approach to Performance Evaluation in Not-for Profit Entities with an Illustrative Application to the U.S. Air Force,” Ph. D. Thesis (Austin, Texas: The University of Texas, Graduate School of Business). Also available from University Microfilms, Inc.

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  54. D.B. Sun (1988) “Evaluation of Managerial Performance in Large Commercial Banks by Data Envelopment Analysis,” Ph.D. Thesis (Austin, Texas: The University of Texas, Graduate School of Business). Also available from University Microfilms, Inc. See Footnote 51.

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(2002). Data Variations. In: Data Envelopment Analysis. Springer, Boston, MA. https://doi.org/10.1007/0-306-47541-3_9

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  • DOI: https://doi.org/10.1007/0-306-47541-3_9

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