Radial and directional measures of the rate of technical change

In this paper we develop radial and directional measures of the rate of technical change for the class of directional distance functions. For both types, we distinguish between primal and dual measures while the former are further divided into oriented (input- and output-based) and non-oriented. We highlight the pivotal role of translation elasticity in examining the interrelationships among the alternative directional measures and that of scale elasticity in the case of radial measures. We also show that the radial and directional measures are related one another through the normalized (with the value of the direction vector) dual functions.