مقاله سال ۲۰۱۶

 مجله امگا – Omega

The measurement of input technical efficiency relative to the efficient subset of an input set goes back to Färe (1975) who proposed minimizing inputs one at a time, i.e., nonradially. Later, Färe and Lovell (1978) proposed what they called the Russell measure (also referred to by others as the Färe-Lovell measure) which was also nonradial but summed over the individual input inefficiency components. These measures eliminated all technical inefficiencies including those due to ‘slacks’ as opposed to the radial Farrell (1957) measure of input technical efficiency which uses the isoquant rather than the efficient subset as the reference for technical efficiency. Thus, when the efficient subset differs from the isoquant, radial measures of technical efficiency such as the Farrell measure and nonradial measures may differ. Furthermore this may affect not only technical efficiency but allocative efficiency as well, resulting in different decompositions of the overall (e.g., cost or revenue) efficiency. This discrepancy is the motivation for considering nonradial measures as part of a decomposition of the overall Farrell measure of cost or revenue efficiency. The first such result was obtained by Färe, Grosskopf and Zelenyuk (2007). Their decomposition comes from introducing a multiplicative version of the Russell measure; and here we expand on their result. In this paper we will focus on the cost efficiency or input orientation, but similar decompositions can be developed for revenue efficiency as well.

The introduction of the directional distance functions1 , by Chambers, Chung and Färe (1998), is another alternative nonradial (additive) way of estimating technical (in)efficiency. In fact, the directional input distance function may be turned into a slack-based additive efficiency measure2 . We can identify two classes of nonradial slack-based technical efficiency measures, a multiplicative and an additive measure, both with an indication property such that the multiplicative (additive) measure equals one (zero) if and only if the input vector belongs to the efficient subset. The efficient subset is particularly important in efficiency measurement because input vectors in the efficient subset cannot be reduced without decreasing at least one input and/or increasing at least one output. On the other hand, if the input vector is in the isoquant but not in the efficient subset, then it is possible to reduce at least one input given a fixed level of outputs. Whereas the Farrell measure and the directional input distance function are constructed relative to an isoquant, the slack-based measures are constructed relative to the efficient subset. Consequently, it is of great interest to develop efficiency analysis based on a slack-based efficiency measurement framework.