On technical inefficiency indicators at the industry level

Abstract

In this note, we show how alternative measures of technical inefficiency at the industry level–evaluated along different direction vectors–are related to one another. We exploit the homogeneity property of the directional distance function with respect to the direction vector, to verify that aggregate (industry) efficiency evaluated relative to the industry aggregate input-output vector is equal to the average of the individual efficiency scores in the industry evaluated relative to the average input-output vector.