A directional semi-oriented radial DEA measure: an application on financial stability and the efficiency of banks

Data envelopment analysis (DEA) is a widely used non-parametric technique for measuring the relative efficiencies of decision-making units with multiple inputs and multiple outputs. The main caveat of traditional DEA models is that they are applicable to positive inputs and outputs, while negative data are commonly present in most real applications. To accommodate variables that can take both negative and positive values, Emrouznejad et al. (Eur J Oper Res 200(1):297–304, 2010a) introduced the Semi-Oriented Radial Measure (SORM) model, which was later modified by Kazemi Matin et al. (Measurement 54:152–158, 2014). The present study proposes a new version of the modified SORM model, using directional distance function and choosing a relevant direction to efficiently deal with variables with both positive and negative values. Our Directional SORM (DSORM) model is superior to its predecessors from both computational and target settings perspectives while it allows for the dual formulation of linear programming. To illustrate our proposed model, we employ two widely used selections of inputs and outputs to estimate the efficiency scores for a sample of banks operating in Persian Gulf Council Countries (GCC) over the period of 2002–2011. The estimated efficiency scores are then used to study the impact of financial system stability on technical efficiency of individual banks.