Theory and Application of Directional Distance Functions
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In 1957 Farrell demonstrated how cost inefficiency could be decomposed into two mutually exclusive and exhaustive components: technical and allocative inefficiency. This result is consequence of the fact that—as shown by Shephard—the cost function and the input distance function (the reciprocal of Farrell's technical efficiency measure) are ‘dual’ to each other. Similarly, the revenue function and the output distance function are dual providing the basis for the decomposition of revenue inefficiency into technical and allocative components (see for example, Färe, Grosskopf and Lovell (1994)). Here we extend those results to include the directional distance function and its dual, the profit function. This provides the basis for defining and decomposing profit efficiency. As we show, the output and input distance functions (reciprocals of Farrell efficiency measures) are special cases of the directional distance function. We also show how to use the directional distance function as a tool for measuring capacity utilization using DEA type techniques.
KeywordsCost Function Distance Function Technical Efficiency Efficiency Measure Capacity Utilization
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- Ball, E., R. Färe,S. Grosskopf, and R. Nehring. “Productivity of the U.S. Agricultural Sector: The Case of Undesirable Outputs.” Paper presented at the 1998 Conference on Research in Income and Wealth, New Developments in Productivity Analysis.Google Scholar
- Chambers, R. G., Y. Chung, and R. Färe.(1996). “Benefit and Distance Functions.” Journal of Economic Theory 70, 407-419.Google Scholar
- Chambers, R. G.,Y. Chung, and R. Färe.(1998). “Profit, Directional Distance Functions and Nerlovian Efficiency.” Journal of Optimization Theory and Application.Google Scholar
- Chung, Y., R. Färe, and S. Grosskopf.(1997). “Productivity and Undesirable Outputs: A Directional Distance Function Approach.” Journal of Environmental Management, 229-240.Google Scholar
- Färe, R., and S. Grosskopf.(1997). “Profit Efficiency, Farrell Decompositions and the Mahler Inequality.” Economics Letters, 283-287.Google Scholar
- Färe, R., and S. Grosskopf. (forthcoming). “Separability of the Profit Function.” Journal of Optimization Theory and Application.Google Scholar
- Färe, R., S. Grosskopf, and C. A. K. Lovell.(1994). Production Frontiers.Cambridge: Cambridge University Press.Google Scholar
- Färe, R., S. Grosskopf, and W. Weber.(1999). “The Effect of Risk Based Capital Requirements on Profit Efficiency in Banking.” Oregon State University working paper.Google Scholar
- Färe, R., and T. Mitchell.(1993). “Multiple Outputs and Homotheticity.” Southern Economic Journal, 287-296.Google Scholar
- Färe, R., and D. Primont.(1995). Multi-Output Production and Duality: Theory and Applications.Boston: Kluwer Academic Publishers.Google Scholar
- Farrell, M. (1957). “The Measurement of Productive Efficiency.” Journal of the Royal Statistical Society, Series A, General, 120, Part 3, 253-281.Google Scholar