On the Commensurability of Directional Distance Functions
Shephard’s distance functions are widely used instruments for characterizing technology and for estimating efficiency in contemporary economic theory and practice. Recently, they have been generalized by the Luenberger shortage function, or Chambers-Chung-Färe directional distance function. In this study, we explore a very important property of an economic measure known as commensurability or independence of units of measurement up to scalar transformation. Our study discovers both negative and positive results for this property in the context of the directional distance function, which in turn helps us narrow down the most critical issue for this function in practice—the choice of direction of measurement.
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- Bol, Georg, 1986. "On technical efficiency measures: A remark," Journal of Economic Theory, Elsevier, vol. 38(2), pages 380-385, April.
- Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
- Robert Russell, R., 1990. "Continuity of measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 51(2), pages 255-267, August.
- Luenberger David G., 1994. "Optimality and the Theory of Value," Journal of Economic Theory, Elsevier, vol. 63(2), pages 147-169, August.
- Fare, Rolf & Knox Lovell, C. A., 1978. "Measuring the technical efficiency of production," Journal of Economic Theory, Elsevier, vol. 19(1), pages 150-162, October.
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