Abstract
Shephard (1953, 1970,1974)introduced radial distance functions as representations of a firm’s technology and developed a number of dual representations that have been widely applied in empirical work. A systematic exposition of Shephard’s work can be found in Färe and Primont (1995). More recently, work by Luenberger (1992, 1995) has provided some new technology representations, the benefit and the shortage functions. Exploiting these results, Chambers, Chung, and Färe (1996, 1998a) introduced directional distance functions; these can be thought of as additive alternatives to the corresponding radial concepts. In this paper, the radial approach is further extended by introducing and characterizing indirect directional distance functions; these are directional versions of their radial counterparts. This, in turn, leads to a new set of duality results that will be of use in applied work.