Slack-based directional distance function in the presence of bad outputs: theory and application to Vietnamese banking

In this paper we extend the slack-based directional distance function introduced by Färe and Grosskopf (Eur J Oper Res 200(1):320–322, 2010) to measure efficiency in the presence of bad outputs and illustrate it through an application on data of Vietnamese commercial banks. We also compare results from the slack-based directional distance function relative to the directional distance function, the enhanced hyperbolic efficiency measure (Färe et al. in Rev Econ Stat 71(1):90–98, 1989) and the Farrell-type technical efficiency and confirm that it has greater discriminative power.