Empirical tools to assess the sensitivity of directional distance functions to direction selection

Directional Distance Functions (DDFs) are becoming a popular way of measuring efficiency as they encompass the Shephard output and input distance functions as special cases. However, the most critical and still unsolved issue related to DDF remains the selection of the direction along which to measure the distance from the efficient frontier. In this article, we propose some empirical tools which allow to quantify the sensitivity of the efficiency measurement to the selection of the direction. The proposed tools are applied on a dataset on the Italian agricultural sector.