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Abstract
Fre and Lovell (Journal of Economic Theory; 19(1978), 150-162) have introduced a criterion which an index should satisfy in order to serve as an efficiency index. The radial measure of efficiency proposed by Farrell (Journal of the Royal Statistical Society 120(3) (1957), 253-290) and which is commonly used to gauge and compare the technical efficiency across production units fails to satisfy most of the conditions outlined in this criterion. As an alternate non-radial efficiency measures have been suggested. Studies have shown that these non-radial measures of technical efficiency have weaknesses of their own. This study proposes a new non-radial measure of technical efficiency and shows that this new measure may satisfy the required criteria to a greater extent as compared to the existing technical efficiency measures. The new measure which we call the Non-radial Farrell measure of technical efficiency is constructed as a ratio of the Euclidean norm of the efficient data point to the Euclidean norm of the observed data point in a transformed data space for both input and output orientations. We provide a comparison of this newly proposed measure of technical efficiency with some of the existing technical efficiency measures and are able to show that this new measure is a generalization of the existing measures. The discussion is extended to the concepts of cost efficiency, Revenue Efficiency and the decomposition of cost and revenue efficiencies into technical efficiency and allocative efficiency. In order to support our inferences we provide numerical examples based on hypothetical data sets.