Summary of Chapter 8
This chapter has covered the approaches which have been studied in DEA evaluations of efficiencies such as “allocative” and “overall” efficiencies. These standard approaches were also extended in models that permit substitutions so that worsening of some inputs or outputs may be made in order to improve other inputs or outputs.
Such inefficiencies are price-cost related. This can cause problems in the use of these concepts since many companies are unwilling to disclose their unit costs. Unit prices may also be a problem when these values are subject to large fluctuations. One may, of course, use averages or other summaries of such prices and also deduce or infer which unit costs are applicable. However even this may not be a satisfactory treatment in many cases like those encountered in attempts to evaluate public programs such as education, health, welfare, military or police activities and so on.
Earlier in this book a variety of approaches were suggested. This includes the case of assurance regions and like concepts, as treated in Chapter 6, which can replace the required exact knowledge of prices and costs with corresponding bounds on their values. When this is done, however, the precise relations between allocative, overall and technical efficiencies may become blurred.
These are topics which have been (and are being)researched but we do not treat them here in this book.
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Notes
R. Färe, S. Grosskopf and C.A. Knox Lovell, Measurement of Efficiency of Production (Boston: Kluwer-Nijhoff Publishing Co., Inc., 1985). A more general treatment of “profit efficiency” was subsequently developed by Färe and Grosskopf and will be published in “Theory and Applications of Directional Distance Functions,” Journal of Productivity Analysis (submitted, 1999).
W.W. Cooper, K.S. Park and J.T. Pastor (1999) “RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models and Relations to Other Models and Measures in DEA,” Journal of Productivity Analysis 11, pp.5–42.
M.J. Farrell (1957) “The Measurement of Productive Efficiency,” Journal of the Royal Statistical Society, Series A, 120, III, pp.253–281. G. Debreu (1951) “The Coefficient of Resource Utilization,” Econometrica 19, pp.273–292.
Relaxation of nonnegativity for some variables is also undertaken in a target setting context in E. Thanassoulis and R. Dyson (1992) “Estimating Preferred Target Input-Output Levels Using Data Envelopment Analysis,” European Journal of Operational Research. 56, pp.80–97. See also A. Athanassopoulos (1998) “Decision Support for Target-Based Resource Allocation of Public Services,” Management Science 44, pp.173–187. In neither of these studies, however, is a worsening of some inputs or outputs allowed in order to improve other inputs or outputs.
S. Thore, G. Kozmetsky and F. Phillips (1994) “DEA of Financial Statements Data: The U.S. Computer Industry,” Journal of Productivity Analysis 5, pp.229–248.
R. Färe, S. Grosskopf and C.A.K. Lovell (1985), The Measurement of Efficiency of Production (Boston: Kluwer-Nijhoff Publishing Co.). R. Färe, S. Grosskopf and C.A.K. Lovell (1994), Production Frontiers (Cambridge: Cambridge University Press).
See Note 4. See also M.J. Farrell and M. Fieldhouse (1962) “Estimating Efficient Production Functions Under Increasing Returns to Scale,” Journal of the Royal Statistical Society, Series A, 125, Part 2, pp.252–267.
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(2002). Allocation Models. In: Data Envelopment Analysis. Springer, Boston, MA. https://doi.org/10.1007/0-306-47541-3_8
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