A new approach to dealing with negative numbers in efficiency analysis: An application to the Indonesian banking sector

In one of the first stand-alone studies covering the whole of the Indonesian banking industry, and utilising a unique dataset provided by the Indonesian central bank, this paper analyses the levels of intermediation-based efficiency obtaining during the period 2003-2007. Using a new approach (i.e., semi-oriented radial measure Data Envelopment Analysis, or ‘SORM DEA’) to handling negative numbers (Emrouznejad et al., 2010) and combining it with Tone’s (2001) slacksbased model (SBM) to form an input-oriented, non-parametric SORM SBM model, we firstly estimate the relative average efficiencies of Indonesian banks, both overall, by group, as determined by their ownership structure, and by status (‘listed’/’Islamic’). For robustness, a range-directional (RD) model suggested by Silva Portela et al. (2004) was also employed to handle the negative numbers. In the second part of the analysis, we adopt Simar and Wilson’s (2007) bootstrapping methodology to formally test for the impact of size, ownership structure and status on Indonesian bank efficiency. In addition, we formally test the two models most widely suggested in the literature for controlling for bank risk – namely, those involving the inclusion of provisions for loan losses and equity capital respectively as inputs – to check the robustness of the results to the choice of risk variable. The results demonstrate a high degree of sensitivity of the average bank efficiency scores to the choice of methodology for handling negative numbers – with the RD model consistently delivering efficiency scores some 14% on average above those from the SORM SBM model – and to the choice of risk control variable under ∗ The opinions expressed in this paper do not necessarily reflect those of Bank Indonesia or its staff. . Corresponding Author. [email protected] (R. Simper): Tel: +44 (0) 1509 222701; Fax: +44 (0) 1509 223910.