Finding Common Ground: Eciency Indices

Introduction The last two decades have witnessed a revival in interest in the measurement of productive efficiency pioneered by Farrell (1957) and Debreu (1957). 1978 was a watershed year in this revival with the christening of DEA by Charnes, Cooper and Rhodes (1978) and the critique of Farrell technical efficiency in terms of axiomatic production and index number theory in Fare and Lovell (1978). These papers have inspired many others to apply these methods and to add to the debate on how best to define technical efficiency. In this paper we try to pull together some of the variants that have arisen over these decades and show when they are equivalent. The specific cases we take up include: 1) the original Debreu-Farrell measure versus the Russell measure—the latter introduced by Fare and Lovell, and 2) the directional distance function and the additive measure. The former was introduced by Luenberger (1992) and the latter by Charnes, Cooper, Golany and Seiford (1985). We also provide a discussion of the associated cost interpretations. Basic Production Theory Details In this section we introduce the basic production theory that we employ in this paper. We will be focusing on the input based efficiency measures here, but the analysis could readily be extended to the output oriented case as well. To begin, technology may be represented by its input requirement sets L( , (1) y) ={x: x can produce y}, y∈ℜ