Evaluating the Relative Efficiency of Commercial Banks in Turkey : An Integrated AHP / DEA Approach

This study measures the relative efficiency of 13 commercial banks in Turkey for the year of 2011 with an integrated approach includes Analytic Hierarchy Process and Data Envelopment Analysis. It uses two inputs (personnel expenditures and number of branch) and four outputs (deposits-national currency, deposits-foreign currency and precious metal, cash loans, and non-cash loans) in terms of production approach. According to empirical result, state-owned commercial banks are efficient in both CCR (Charnes-Cooper-Rhodes) and BCC (Banker-Charnes-Cooper) model. However, foreign-owned commercial banks have the lower efficiency scores than both state-owned and private-owned commercial banks. The results also suggest that inefficient banks should especially improve their non-cash loans and should focus on their annual personnel expenditure. Moreover, more than half of the commercial banks are scale inefficiency. The results of the study may be useful for the bank managers in assessing their performance.


Introduction
Banking sector in transition and developing economies has experienced major transformations since the 1990s.Over the last few decades, the banking sectors around the world have experienced financial globalization, technological changes, and competition.Banks are also faced with increasing competition and rising costs as a result of regulatory requirements, financial and technological innovation, and challenges of the recent financial crisis.Moreover, banking sector has changed with the advanced applications in computer and communications technology and introduction of new financial instruments.Such changes have significantly modified bank production.In this regard, a frequently asked question is about the effect of these changes on the efficiency of banks (Grigorian & Manole, 2002).So, efficiency analysis of banks has received increasing attention from researchers in recent years.It has also become important to assess the relative role of different institutional and policy settings in explaining the difference between banks (Grigorian & Manole, 2002).
Due to the increased competition in developed countries, financial institutions look for expanding their market shares in developing countries as Turkey.The banking system in Turkey is the most common instrument in exercising economic and monetary policy.Thus, efficiency analysis of the banks is the key issue in the Turkish managers' agenda.Also, efficiency measurement of the banks has an important role in the efficiency of Turkish financial system.It is not surprising that the banking sector and its efficiency is one of the most popular issues in Turkey.
Turkey has a notably (8.5%) economic growth while average economic growth rate of the world is 3.9% in 2011 (The Banks Association of Turkey, 2012).Therefore, Turkish banking sector has been taken attention all over the world.According to data from The Banks Association of Turkey (2012), Figure 1 presents proportion of size Turkish banking sector to Gross Domestic Product (GDP) by years.As shown the Figure 1, proportion of total assets, loans and deposits to GDP invariably in last seven years exception for decrease deposit rate in 2011.Especially it can be said that increase of asset/GDP with 90% is most remarkable growing.Consequently, Turkish banking sector has grown as far as GDP upward.DEA was also used to measure the bank efficiency for various countries by many researchers (Berg et al., 1993;Altunbas & Molyneux, 1996;Allen & Rai, 1996;Pastor et al., 1997;Kuosmanen & Post, 2001;Grigorian & Manole, 2002;Maudos et al., 2002;Maea, 2010).They aimed to present the effects of country's regulatory environments on bank efficiency.
This study focuses on the efficiency measurement of commercial banks in Turkey.So, its literature review was restricted with studies using DEA models for efficiency measurement of commercial banks.As a conclusion, much information about selected studies is given in Table 1.There are a number of studies about commercial banks in Turkey.Denizer et al. (2000) employed the DEA to estimate the relative efficiency of 49 commercial banks in Turkey for each year from 1970 to 1994.Jackson and Fethi (2000) investigate the performance of Turkish commercial banking sector.Isik and Hassan (2002) investigated input and output efficiency in the Turkish banking industry to understand the impact of various measures.They also estimated the efficiency of Turkish banks over the 1988-1996 periods.Yunten and Caner (2004) investigated the relative efficiencies of 19 Turkish commercial banks that have been operated between 1999 and 2002.Ozkan-Gunay and Tektas ( 2006) determined the relative technical efficiency of non-public commercial banks in Turkey between 1990 and 2001 by DEA model.Percin and Ayan (2006) evaluated the efficiency of 31 commercial banks in Turkey using DEA and Malmquist Productivity Index methodologies for the year 2003and 2004. Ayranci (2011) ) analyzed the private Turkish commercial banking sector (48 banks) with DEA.
AHP is a tool at the hands of decision makers as one of the most widely used multiple criteria decision making tools.Many studies have been done based on AHP including applications of AHP in different fields such as planning, selecting a best alternative, resource allocations, resolving conflict, optimization, etc. (Vaidya & Kumar, 2006).Many studies have indicated that AHP can be applied form an AHP/DEA ranking model for improving DEA usability by deriving comparative weight from inputs/outputs via AHP pair wise comparison (Tseng & Lee, 2009).
Efficiency analysis via a combined method with AHP and DEA can be performed by two approaches.In the first approach, DEA is run for each pair of units separately and then the pair wise evaluation matrix generated DEA stage is utilized to rank scale the units via AHP approach.This approach was used in many fields such as 3PL vendor selection (Zhang et al., 2006) and hotel ranking (Rouyendegh & Erkan, 2010).
In the second approach, AHP was used to determine the weight of any qualitative criteria (input or outputs) verified and then, the DEA model was used for solving the multi-objective model to identify the best alternatives.AHP is used for the weight determination or restriction in this approach.It was used in warehouse operators selection (Korpela et al., 2007), bridge risks assessment (Wang et al., 2008),relative efficiency of greenhouse gas technologies (Lee et al., 2008), supplier performance (Yuan et al., 2008), the efficiency of R&D management activities in universities (Feng et al., 2004) and also hydrogen R&D programs (Lee et al., 2010), smartphone comparisons (Peaw & Mustafa, 2006), evaluating the flexible manufacturing systems (Rezaie at al., 2010), measuring the agility of manufacturing systems (Saleeshya & Babu, 2012).
As shown in literature review, there is no study focus on relative efficiency of commercial banks by integrated with AHP and DEA approach.Furthermore, such a study that analyzes the relative efficiency of commercial banks in Turkey can be considered an important contribution to the literature.

Data Envelopment Analysis
Data Envelopment Analysis (DEA) is a non-parametric approach to efficiency measurement of similar organizational units called Decision Making Units (DMUs).Its basic foundation was generated from Farrell's (1957) original work that was later popularized by Charnes et al. (1978).DEA provides a single measure and easily deals with multiple inputs and multiple outputs (Agha et al., 2011).
DEA has two models as CCR and BCC.CCR (Charnes-Cooper-Rhodes) model is the basic DEA model which assumes constant returns to scale (CRS) was proposed by Charnes et al. (1978).This model assumes that all DMUs are operating at an optimal scale.However, Banker et al. (1984) suggested BCC (Banker-Charnes-Cooper) model as an extension of the CRS model to account for variable returns to scale (VRS) situation.
DEA models typically measure technical efficiency in one of two ways.Input oriented models measure how much each DMU can reduce its inputs while producing the original level of output.However, output oriented models measure how much each DMU can expand its output while holding inputs unchanged.
Assuming n DMUs with m inputs and s outputs, the primal output CCR and BCC model related to DMU k are as shown in Equations 1 and 2. Efficiency score is less than or equal to 1.When the efficiency score is 1, DMU is regarded as an efficient frontier.

Output Oriented CCR Model
Output Oriented BCC Model According to Bobe (2009), DEA is a powerful tool in that because (i) it evaluates the efficiency performance of a DMU relative to other DMUs either for a period or over number of periods (benchmarking); (ii) it provides monitoring information for a specific DMU over a period of time; (iii) it suggests the benchmark DMUs (reference set) that can be used to estimate the efficient amount of resources required to achieve the same level of outputs; and (iv) it estimates the potential reductions in inputs needed to achieve the same level of outputs and/or the potential increase in outputs using the same level of inputs.There are, however, some limitations of DEA.First, the efficiency score obtained by a DMU is sensitive to the number of inputs and outputs used in the analysis.Second, classical DEA does not provide statistical inferences.Third, DEA results may be misleading.An efficiency score of 1 does not necessarily mean that the performance of a DMU is the best.It only indicates, relative to the other DMUs in the group, that the DMU is considered to be efficient.Fourth, specification of inputs and outputs may appear to be more subjective.

Analytic Hierarchy Process
The Analytic Hierarchy Process (AHP) enables decision makers to structure a complex problem in the form of a simple hierarchy and to evaluate a large number of quantitative and qualitative factors in a systematic manner under multiple conflicting criteria (Lee et al., 2008).
According to Saaty (2008), to make a decision in an organized way to generate priorities we need to decompose the decision into the following steps: (i) Define the problem and determine the kind of knowledge sought.(ii) Structure the decision hierarchy from the top with the goal of the decision, then the objectives from a broad perspective, through the intermediate levels (criteria) to the lowest level (alternatives).(iii) Construct a set of pairwise comparison matrices.Each element in an upper level is used to compare the elements in the level immediately below with respect to it.(iv) Use the priorities obtained from the comparisons to weight the priorities in the level immediately below.Then for each element in the level below add its weighted values and obtain its global priority.
To make comparing, AHP uses the scale for pairwise comparisons.The numbers 1, 3, 5, 7, and 9 are used as scaling ratios, and correspond to the strength of preference for one element over another.For example, the number 9 indicates a case of extreme importance over another element.After pairwise comparisons are conducted, the weights of the criteria are calculated and checked for consistency.Then, a review of the consistency ratio (CR) is conducted in order to ensure that it falls between 0 and 0.10.CR is determined to be the ratio of Consistency Index (CI) to Random Index (RI).The fact that CR is determined to be greater than 0 but less than 0.10 implies a satisfactory degree of consistency in the pairwise comparisons matrix.We then aggregate the weights.

Integrated with AHP and DEA
Efficiency that refers to the relationship between output and input does not employ multiple inputs to produce multiple outputs because it is limited only to a single output and a single input.Hence, it is extended into weighted sum of outputs and weighted sum of inputs.So, it can be said that the key issue is how to assign weights to each input and output in the efficiency analysis.Thus, the weights, u j and v j , are determined by solving the DEA model.These weights developed by DEA may not represent the same relative subjective weights that management might apply as to the relative importance of the variables (especially the output variables) used in the DEA models (Al-Delaimi & Al-Ani, 2006).This is a significant point to management when evaluating the performance of a DMU.Thus, weights have an important effect on the efficiency of the DMU.
Literature proposes to several approaches to determine weights.Majority of them can be classified into subjective approaches and objective approaches (Ma et al., 1999).Subjective approaches determine the weights according to the preferential judgments of decision maker.Eigenvector method, weighted least square method, and Delphi method can be example for these approaches (Ma et al., 1999).On the other hand, objective approaches determine the weights by making use of mathematical models, but they neglect subjective judgment (Liu, 2003).They include principal element analysis, entropy method, and multiple objective programming model (Ma et al., 1999;Ginevicius & Podvezko, 2004).
This paper proposes AHP as a subjective method to determine weights.The AHP approach was employed to ascertain the relative weights of the criteria.It makes use of pairwise comparison matrices, hierarchical structures, and ratio scaling to apply weights to attributes (Lee et al., 2008).The advantage of this method is that experts can reasonably identify the weight index that corresponds to the real problems (Liu, 2003).Thus, despite the different placement of weights on the index, the method can still determine the order of priority and avoid conflicts between the reality and the index weights (Liu, 2003).Furthermore,AHP which is technically valid and practically useful does not need to large sample (Lam & Zhao, 1998).It also can be used in combination with other methods.DEA is proposed in this study to generate local weights of criteria from pairwise comparison judgment matrices used in the AHP.

Input and Output Variables
Using DEA model in measuring bank efficiency requires selection of appropriate input and output variables.However, there is no consensus in the banking literature regarding the proper selection of inputs and outputs (Rao & Lakew, 2012).Furthermore, commercial banking is a very difficult service industry in which to measure output, technical change, or productivity growth (Berger & Humphrey, 1992).
The choice of output and input variables is the first difficult question that must be addressed by any study on banking.Such a choice will be influenced by the selected concept of banking firm, by the particular question under consideration and, also, by the availability of data (Pastor et al., 1997).Two different approaches appear in the literature regarding the measurement of banks inputs and outputs, popularly known as production approach and intermediation approach (Berger & Humphrey, 1997).The production approach views banks as using purchased inputs to produce deposits and various categories of bank assets.It considers to banks as institutions that use capital and labor to produce loans and deposit account services.In this approach, labor, capital and operating costs are treated as inputs and loans, deposits, and transactions are considered the outputs.
The intermediation approach, on the other hand, views banks as financial intermediaries whose primary business is to borrow funds from depositors and lend those funds to others for profit (Yue, 1992).It generally uses loans as output and various costs such as interest expense, labor, capital and operating as outputs.It views the banks as using deposits together with purchased inputs to produce various categories of bank assets.However, there is still no current consensus on which of the two methodologies outlined above should be utilized in bank efficiency analysis.We have used production approach with restricted choice of variables.
To obtain input and output variables in this study, a preliminary list was composed using all input and output variables used in the literature.This list was shown to three branch managers of different banks who were asked to give their feedback whether the list is reasonable.Further, they were asked to add, delete or combine variables.Based on these responses, a refined list was compiled and shown again to bank administration until a consensus was reached on what variables should be used to better represent the efficiency of the department.Thus, a final list of variables was obtained.These variables are shown in Table 2.It also gives more details about the measures.

Sample Selection
Turkish banking system consists of three functional bank types such as commercial banks, development and investment banks, and participation banks (noninterest banking).The goal of the sample selection was to find comparable banks.Thereby, we decided to include only commercial banks and to neglect other types of banks.
Commercial banks produce 92% of the Turkish banking sector's total assets (Banking Regulation and Supervision Agency, 2011).Thus, commercial banks have an important role in Turkish banking system.Bank sample was also restricted to large banks which are more than one percent market share.As the market share, it has been taken account of total assets.As a result, the thirteen of 31 commercial banks operated in Turkey were chosen as the sample.Thus, this study applies DEA to compare operational performance of 13 commercial banks in Turkey.Much information about these banks according to 2011 statistics can be seen in Table 3.To ensure meaningful efficiency scores, the number of DMUs must be large enough relative to the number of input and output variables.A rule of thumb is given by Boussofiane et al. (1991) and Ramanathan (2003) as [N ≥ 2*(s+m)], where s is the number of output variables, m is the number of input variables, and N is the number of DMUs.In this research, the number of DMUs ( 13) is more than twice the sum of the number of input and output variables.However, small sample size in this study can be compared with some of the other small sample sizes in the DEA literature (Oral & Yolalan, 1990;Haag & Jaska, 1995;Li, 2006;Cronje, 2007;Chen-guo et al., 2007;Akhtar et al., 2011;Rao & Lakew, 2012).

Data
We use annual data compiled mainly from balance sheet and income statements of banks in database of The Banks Association of Turkey ( 2011) and The Banking Regulation and Supervision Agency (2012).We cover only thirteen out of 31 commercial banks operating in Turkey which can be seen in Table 4.It also includes data of each bank and descriptive statistics of each variable.Due to the fact that operational performance was measured by outputs in banks, this study employs the output-oriented model.Efficiency Measurement System (EMS) software version 1.3 (Scheel, 2000) is used in this research to measure the technical efficiency of the departments based on both CCR and BCC models.

Weight Restrictions
Pairwise comparison matrix should be done before the generate weight restriction.Thus, constrained weighting vectors were obtained from the AHP pairwise matrix.Then, in order to take the decision maker's preferences into the evaluation, extra constraints were added to model.
Pairwise comparison matrix were constituted based on data from three experts from three commercial banks.They work as a department manager in their banks.Data collection phase are combined using the geometric mean approach to obtain the corresponding consensus pairwise comparison judgment matrices.Finally, AHP pairwise matrix can be seen in Table 5.All the consistency rates are less than 0.10.

Efficiency Scores
Table 6 shows the efficiency scores and the reference set(s) for each DMU.According to CCR efficiency scores in the second column, four (Garanti, Halkbank, Vakıfbank, and Ziraat) of the thirteen banks under evaluation are best performers.These banks require neither input reduction nor output augmentation.However, Denizbank turned out to be the bank with the lowest performance (0.438).Moreover, average CCR score of thirteen banks is 0.674.It means that an average bank should produce 48.4% ( . .more output with the same input level if it wishes to do business more efficiently.The third column includes the corresponding reference units for the inefficient DMUs and the λ values which are the raw weights assigned to peer units when solving the DEA optimization problem.The higher the contribution, the closer in performance is the peer to the unit under consideration (Marschall & Flessa, 2008).For example, Akbank can virtually become efficient by combining the Halkbank and Vakıfbank as peers, with weights of 0.63 and 0.65 respectively.Vakıfbank is the peer unit with the highest value in the reference set and thus the most comparable unit according to CCR results.
According to BCC results, six banks (Garanti, Halkbank, İşbankası, Şekerbank, Vakıfbank, and Ziraat) operate with technical efficiency.Moreover, average BCC score of thirteen banks is 0.834.It means that an average bank should produce 19.9% more output with the same input level if it wishes to do business more efficiently.
In terms of the reference set, Vakıfbank and Şekerbank are the most comparable units with their reference number in BCC efficient banks.Denizbank, which has the lowest BCC efficiency score, can virtually become efficient by combining the Halkbank, Vakıfbank, and Şekerbank as peers, with weights of 0.11, 0.63, and 0.25 respectively.
Scale efficiency shows how close or far the size of the DMU is from its optimal size (Sporcic et al., 2009).So, scale efficiency scores allow for some interesting remarks.It can be said that the average efficient score is 0.852 based on the scale efficiency results.It means that an average bank should increase their relative efficiency on average by 17.4% if it adapted their size or volume of activities to the optimal value.The size and volume of activities of four banks (Garanti, Halkbank, Vakıfbank, and Ziraat) are well balanced because they have the efficiency of 100%.However, other banks, which have the efficiency values lower than 100%, partly under influence of size or volume of activities.
The issue of scale inefficiencies is explored with greater detail by considering returns to scale indicators.Among 13 banks, 6 banks operate under increasing returns to scale (IRS), 4 banks operate under constant returns to scale (CRS), and the remaining 3 banks operate under decreasing returns to scale (DRS).Both CCR efficiency and scale efficiency are equal to 1 are considered as operating at the most productive scale size.
Relatively scale efficient banks are also efficient according to CCR model.However, two banks (İşbankası & Şekerbank) are efficient only according to the BCC model.They do not show the same efficiency level in terms of scale efficiency.According to it, it can be said that their inadequate size or volume of activities expressed by the main parameters of their performance (Sporcic et al., 2009).In other words, the banks of İşbankası and Şekerbank which are efficient on BCC model but inefficient on CCR model have been efficiently operated except the effect of scale.The major causes of inefficiency are from scale inefficiency.In other words, they operate locally efficiently whereas its overall technical inefficiency is caused by its failure to achieve scale efficiency.These banks should enhance their own efficiency by increasing their input level as these have IRS characteristics.
Akbank, Şekerbank, and Yapıkredi showing DRS characteristics should decrease of their inputs or the increase of their outputs because they have been operated by the inputs over optimal scale.In the cases of the banks of which both BCC efficiency and scale efficiency is less than 1, both can be the causes of inefficiency (So et al., 2007).

Potential Improvements
One of the attractiveness of DEA is that it provides reference set so that inefficient DMUs have benchmark DMU to learn from their experiences (Bobe, 2009).So, in addition to providing efficiency measures, DEA also provides other information relevant for the inefficient DMUs.Because efficient DMUs do not have any slack, this information is only of interest for inefficient DMUs (Tongzon, 2011).
Table 7 shows the banks' target input/output data and projection obtained from the DEA calculations.A DMU is BCC efficient if it has no input excesses and no output shortfalls.Thus, the difference between original data and projection is 0.00%.So, it can be seen the potential improvements for the seven inefficient banks under BCC model (Marschall and Flessa, 2008).The projections suggest that particularly the analyzed banks are too big to be efficient.The results demonstrate that the efficiency of Denizbank which is the most inefficient can be improved when the personnel expenditure (PE) is reduced by 53.6%.Similarly, its efficiency can be attained if all of the output values are increased by 115.4%.When the number of branches (NB) is analyzed, it is seen that any DMU doesn't have to decrease it.So, it can be said that banks are working with optimal number of branches.
For inefficient banks to benefit from the study, the amounts by which these DMUs should increase their outputs to become efficient are calculated using the BCC model.In this study, the targeted value of a variable represents the amount to which a given DMU can increase its production of that specific variable.In the following figures (Figure 2-3-4-5), the light columns indicates the actual value of outputs while dark column indicates potential improvements to enhance required output amount.One limitation is that this study has not implications from a customer's perspective.Technical efficiency can vary widely across commercial banks.So, in future studies, the model should be expanded to customer perspective with including related outputs such as customer satisfaction, transactions time.
A last limitation is about some special problems of DEA.Since it is a deterministic procedure, it does not provide fit statistics such as r-square or p-value that can be used for statistical inferences.Moreover, there is no role for statistical error in the calculations and a number of questions need to be answered about the validity of the DEA score.
Managerial relevance of our research is quite important.It is widely accepted that to succeed a company must perform well.Moreover, the simplicity of the results, and the fact that they arise directly from observed input/output data that allow for better acceptance of the results by the bank managers.Bank management should pay more attention to personnel expenditure among the input variables and non-cash loans among the output variables.Furthermore, managers can use DEA to compare their business units.
efficiency score of k th DMU v ik : weight given to i th input by k th DMU x ik : amount of i th input utilized by k th DMU u rk : weight given to r th output by k th DMU y rk : amount of r th output produced by k th DMU x ij : i th input of the j th DMU y rj : r th output of the j th DMU ε: sufficiently small positive number (e.g.0,00001) the branch efficiency.They focused on branches of the only one bank.

Table 1 .
Selected studies focus on the efficiency measurement of commercial banks

Table 2 .
Variables and descriptions

Table 3 .
Much information about the sample Notes: *Ordered by general market share.**According to total assets.

Table 4 .
Data and descriptive statistics

Table 5 .
Pairwise comparison matrix for inputs and outputs

Table 6 .
Efficiency scores, reference set and scale efficiency

Table 7 .
Target values (%) for inefficient banks according to BCC model Therefore, future researchers may focus on developing a framework for input/output variable selection.