On Farrell Measures of Technical Efficiency

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Abstract
In this paper we consider the problem of evaluating the performance of production units in terms of their technical efficiency. Several attempts have been made to solve this problem and a number of different measures appear in the economic literature : the technical efficiency, here used, is defined to be the ability of a productive organization to operate close to, or on the boundary of its production set; the problem will be analyzed only in terms of physical input and output quantities, without any references to prices or costs structures. This concept of technical efficiency is inspired from the work by Koopmans (1951); it received a first empirical application in Farrel (1957). An interesting survey on this topic may be formed in Førsund, Lovell and Schmidt (1980). Measuring efficiency of this kind for any data set requires first to determine what the boundary of the unknown production set can be; and then, to measure the distance between any observed point and this boundary. In this paper, we concentrate on the Farrel method of estimating technical efficiencies. There the production set is typically a convex polyhedron generated from the observed data with small modifications in view of the assumptions on disposabilities of input and/or on disposibilities of outputs. The distances from the efficient frontier are then measured in a radial sense, i.e. with fixed technology.

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