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

Abstract

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.

Acknowledgements

The authors thank ISMEA that allows for the use of the database based on ‘Indagine Conoscitiva sulle caratteristiche Socio-Economiche delle Aziende Agricole’.

Notes

¹ See for instance Chung et al. (1997), Chambers et al. (1998), Fare and Grosskopf (2000), Cherchye et al. (2001), Nin et al. (2003), Jeon and Sickles (2004) and Zago and Dongili (2005).

² These relations may be derived as follow:

³ Cherchye et al. (2001) apply a computational algorithm that allows to estimate Free Disposable Hull (FDH) production frontier where such a restriction on the direction does not hold. They emphasize that with undesirable outputs (such as pollution) we have to allow for directions outside the dominance set. Here, we exclude these cases by referring only to directions towards the interior of the dominance set because in the illustrative example, we do not have bad outputs.