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Is the directional distance function a complete generalization of the Farrell approach?

Juan Aparicio (), Jesus Pastor and José Zofío

No 2014/05, Working Papers in Economic Theory from Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History)

Abstract: Cost or revenue efficiency measurement based on the approach initiated by Farrell has received great attention from academics and practitioners since the fifties. Farrell’s approach decomposes cost efficiency into two different sources, viz. technical efficiency and allocative efficiency. Technical efficiency is estimated by the implementation of the Shephard’s input or output distance functions, while allocative efficiency is derived as a residual between cost or revenue efficiency and its corresponding technical efficiency component. The directional distance function (DDF) was introduced later in the literature to complete duality theory with respect to the profit function and as a generalization of the Shephard input and output distance functions. Considering the case of cost efficiency we show that, although the DDF correctly encompasses the technical efficiency component of the Farrell approach, this is not true for the allocative component. Additionally, we show that allocative inefficiency is underestimated when the DDF-additive approach is used for decomposing cost inefficiency unless technical efficiency is assumed.

Keywords: Technical efficiency; Allocative efficiency; Directional Distance Functions (search for similar items in EconPapers)
JEL-codes: C61 D21 D24 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-eff
Date: 2014-09
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