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) slacks-based 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 RD model, but only a limited sensitivity to the choice of risk control variable under the SORM SBM model. With respect to group rankings, most model combinations find the ‘state-owned’ group to be the most efficient, with average overall efficiency levels ranging between 64% and 97%; while all model combinations find the ‘regional government-owned’ group to be the least efficient, with average overall efficiency levels ranging between 41% and 64%. As for the impact of bank ‘status’ on the efficiency scores, both the Islamic banks and the listed banks perform better than the industry average in the majority of model combinations. Finally, the results for the impact of scale on the efficiency scores are ambiguous. Under the RD model, and irrespective of the choice of risk control variable, size is very important in determining intermediation-based efficiency. Under the SORM SBM model, however, large banks’ performance is not significantly different from that of the medium-sized banks when equity capital is used as the risk control variable, although the medium-sized banks do out-perform small banks. Moreover, when loan loss provisions are used as the risk control variable, medium-sized banks are shown to significantly out-perform both large and small banks, with the large banks being the least efficient.