Taller I

As explained earlier, we can observe from two angles Technical efficiency (TE), derived from DEA (Coelli, 1996b). Firstly, under the input-orientation approach, TE examines the feasibility of reducing inputs to generate a specified amount of outputs (Kumar and Gulati, 2008). Secondly, under the output orientation, TE views the

potential growth in outputs for a particular set of inputs (Kumar and Gulati, 2008). We can measure a DMU’s TE by dividing the actual amount of outputs with the maximum potential outputs on the assumption of the output-orientation. Alternatively, under the input-orientation, we can determine TE by calculating the ratio of minimum potential inputs to the actual inputs. In order to determine an estimate of TE, we have to find the variance between actual production and potential production on the possible production set (Kumar and Gulati, 2008). This set represents the entire potential production technology of converting an entity’s available inputs into outputs. An entity or a DMU is considered to be technically efficient if its production exists inside this particular technology set. A DMU is technically inefficient if production occurs within the interior of this production set (Kumar and Gulati, 2008). As mentioned previously, we can measure the Scale Efficiency (SE) by comparing the OTE and the PTE results from CRS and VRS approaches respectively. The OTE, derived from DEA-CRS approach, computes inefficiency related to the input and output configuration and the scale of operations (Kumar and Gulati, 2008). However, the PTE, derived from DEA-VRS approach, determines inefficiency related merely to managerial underperformance (Avkiran, 1999). SE is calculated by dividing OTE by PTE.

In DEA, TE can have a value which ranges between zero and one inclusive. A value, which is close to zero, signifies that a DMU is more inefficient whereas a value of one means that DMU is entirely efficient. For instance, a value of 0.8 indicates that a bank is 80% efficient relative to its best-performing peers and that the same amount of outputs could be produced by employing a 20% smaller amount of inputs.

Under the input-oriented assumption, the DEA-VRS approach can be written in the linear programming equation below (see for example, Murillo-Zamorano, 2004):

Min φ, λ, φ (Eq. 1)

subject to − φ_??+ Yλ, ≥0

??– Xλ ≥ 0

And λ ≥ 0 where,

λis anN× 1 density vector of constants andφis a scalar (1≥φ≤ ∞).N1 is anN× 1 vector of ones (see for example, Coelli, 1996). ForNnumber of banks, yirepresents theM×Noutput vectors and_?? represents the K×N input vectors. Y consists of the data for all the N banks. Given a fixed level of inputs for the ith firm, the corresponding growth in outputs to be attained by the bank is represented byφ −1. Eq. (1), representing VRS approach, turns into a DEA-CRS model if the convexity constraint N1′ λ= 1 is not counted (Coelli, 1996). This restraint, imposed on DEA, suggests that there is an assessment of an inefficient bank against other banks of similar size. As a result, the predicted point for that bank on the DEA frontier is a convex combination of the examined banks (Sufian, 2006). It is considred that a bank operates at CRS if TE scores are the same with or without the convexity constraint imposed on DEA. On the other hand, a bank operates at VRS if these TE scores are dissimilar (Sufian, 2006). The operating mode, at which a DMU should follow to become efficient, needs to be defined. Therefore, one should determine whether the bank operates at IRS or DRS (Sufian, 2006).This is done by presuming a Non-Increasing Returns to Scale (NIRS) model is applied in Eq.(1) and the convexity constraintN1′λ= 1 is replaced byN1′λ≤1. This is shown in the following equation (Sufian, 2006): Min φ, λ, φ (Eq. 2) Subject to −_??−Yλ, ≥0, φ_??– Xλ ≥ 0, N1'λ ≤ 1 λ ≥ 0.

The outcome of Eq. (2) discloses the mode of the SE (IRS or DRS). If the TE scores, derived from the NIRS model, are different from the PTE resulting from the VRS model then the particular bank is operating with IRS. On the other hand, it is

considered that the given bank operates with DRS if the NIRS-efficiency scores and PTE are equal (Sufian, 2006; Rosman, et al., 2014).

As discussed earlier, OTE is used to determine inefficiency resulting from pure technical inefficiency due to managerial deficiency and scale inefficiency as a result of the incorrect choice of scale size (Kumar and Gulati, 2008). On the other hand, unlike OTE, the PTE, obtained from the BCC model, is not influenced by the DMU scale/size. Consequently, the PTE shows that entire inefficiency is only due to inappropriate management practices and misplaced selection of input combination (Kumar and Gulati, 2008).

A non-parametric DEA is employed by applying both CCR and BCC models in order to derive OTE and PTE scores under CRS and VRS assumptions respectively. These models are used to determine the input-oriented efficiency (OTE, PTE and SE) of the Islamic banks when compared to their conventional counterparts at the global level. In line with the studies conducted by Charnes et al. (1990); Bhattacharyya, Lovell and Sahay (1997) and Sathye (2001); Hassan and Hussein (2003); Hassan (2005); Sufian (2006); Sufian et al. (2008); Mokhtar et al. (2008); Casu and Girardone, (2009); Johnes et al. (2014); and Rosman et al. (2014), the intermediation approach was applied to the selection of inputs and outputs used in the DEA first-stage of this research study. An additional reason for adopting the intermediation approach rather than the production approach is that the latter is more appropriate to study the efficiency of branches which are involved mainly in handling customer documents and bank funding (Berger and Humphrey, 1997).