Predicting efficiency in Islamic banks: An integrated multicriteria decision making (MCDM) approach Peter Wanke a , Md. Abul Kalam Azad b , Carlos Pestana Barros c , M. Kabir Hassan d,⇑ a COPPEAD Graduate Business School, Federal University of Rio de Janeiro, Rua Paschoal Lemme, 355, 21949-900 Rio de Janeiro, Brazil b University of Malaya, Department of Applied Statistics, Faculty of Economics and Administration, 50603 Kuala Lumpur, Malaysia c Instituto Superior de Economia e Gestão, University of Lisbon, Rua Miguel Lupi, 20, 1249-078 Lisbon, Portugal d Department of Economics and Finance, University of New Orleans, New Orleans, LA 70148, United States article info Article history: Received 2 February 2016 Accepted 5 July 2016 Available online 14 July 2016 Keywords: Islamic banks TOPSIS Two-stage Neural networks Efficiency abstract This paper presents an efficiency assessment of the 114 Islamic banks from 24 countries using the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS). TOPSIS is a multicriteria decision making technique similar to Data Envelopment Analysis (DEA), which ranks a finite set of units based on the minimization of distance from an ideal point and the maximization of distance from an anti-ideal point. In this research, TOPSIS is used first in a two-stage approach to assess the relative efficiency of Islamic banks using the most frequent indicators adopted by the literature. Then, in the second stage, neural networks are combined with TOPSIS results as part of an attempt to produce a model for banking performance with effective predictive ability. The results reveal that variables related to both country origin and cost structure have a prominent impact on effi- ciency. Findings also indicate that the Islamic banking market would benefit from higher level of competition between institutions. Ó 2016 Elsevier B.V. All rights reserved. 1. Introduction One of the major research streams in banking is to measure the relative importance of banks using popular multicriteria decision making such as DEA (Berger and Humphrey, 1997; Chen, 2002). Taking a different approach than the majority of previous studies in banking, this paper examines the efficiency of major Islamic banks using TOPSIS. Thus far, applications of TOPSIS to measure bank efficiency have been few. In fact, efficiency in Islamic banking has been only recently addressed by a few studies focused on specific countries (Sufian and Kamarudin, 2015; Wanke et al., 2016, 2015). A deeper analysis of worldwide Islamic banks has not yet been undertaken in terms of the assessment of its efficiency drivers, which justifies this research. More precisely, the need for examining the efficiency of wide-reaching Islamic banks has become inevitable with the rapid increase of awareness of Islamic financial products by both Muslims and non-Muslims worldwide (Kumru and Sarntisart, 2016). Some countries with a majority of Muslim citizens (i.e. Malaysia, Bahrain, UAE and others) have shown enormous growth in their Islamic banking system (Johnes et al., 2014). To this end, this paper firstly fills the literature gap by examining the efficiency of major Islamic banks worldwide. Secondly, this paper differs from previous studies in http://dx.doi.org/10.1016/j.intfin.2016.07.004 1042-4431/Ó 2016 Elsevier B.V. All rights reserved. ⇑ Corresponding author. E-mail addresses: [email protected](P. Wanke), [email protected](Md. A.K. Azad), [email protected](C.P. Barros), [email protected](M.K. Hassan). J. Int. Financ. Markets Inst. Money 45 (2016) 126–141 Contents lists available at ScienceDirect Journal of International Financial Markets, Institutions & Money journal homepage: www.elsevier.com/locate/intfin
Transcript
J. Int. Financ. Markets Inst. Money 45 (2016) 126–141
Contents lists available at ScienceDirect
Journal of International FinancialMarkets, Institutions & Money
Peter Wanke a, Md. Abul Kalam Azad b, Carlos Pestana Barros c, M. Kabir Hassan d,⇑aCOPPEAD Graduate Business School, Federal University of Rio de Janeiro, Rua Paschoal Lemme, 355, 21949-900 Rio de Janeiro, BrazilbUniversity of Malaya, Department of Applied Statistics, Faculty of Economics and Administration, 50603 Kuala Lumpur, Malaysiac Instituto Superior de Economia e Gestão, University of Lisbon, Rua Miguel Lupi, 20, 1249-078 Lisbon, PortugaldDepartment of Economics and Finance, University of New Orleans, New Orleans, LA 70148, United States
a r t i c l e i n f o a b s t r a c t
Article history:Received 2 February 2016Accepted 5 July 2016Available online 14 July 2016
This paper presents an efficiency assessment of the 114 Islamic banks from 24 countriesusing the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS).TOPSIS is a multicriteria decision making technique similar to Data EnvelopmentAnalysis (DEA), which ranks a finite set of units based on the minimization of distance froman ideal point and the maximization of distance from an anti-ideal point. In this research,TOPSIS is used first in a two-stage approach to assess the relative efficiency of Islamicbanks using the most frequent indicators adopted by the literature. Then, in the secondstage, neural networks are combined with TOPSIS results as part of an attempt to producea model for banking performance with effective predictive ability. The results reveal thatvariables related to both country origin and cost structure have a prominent impact on effi-ciency. Findings also indicate that the Islamic banking market would benefit from higherlevel of competition between institutions.
� 2016 Elsevier B.V. All rights reserved.
1. Introduction
One of the major research streams in banking is to measure the relative importance of banks using popular multicriteriadecision making such as DEA (Berger and Humphrey, 1997; Chen, 2002). Taking a different approach than the majority ofprevious studies in banking, this paper examines the efficiency of major Islamic banks using TOPSIS. Thus far, applicationsof TOPSIS to measure bank efficiency have been few. In fact, efficiency in Islamic banking has been only recently addressedby a few studies focused on specific countries (Sufian and Kamarudin, 2015; Wanke et al., 2016, 2015). A deeper analysis ofworldwide Islamic banks has not yet been undertaken in terms of the assessment of its efficiency drivers, which justifies thisresearch.
More precisely, the need for examining the efficiency of wide-reaching Islamic banks has become inevitable with therapid increase of awareness of Islamic financial products by both Muslims and non-Muslims worldwide (Kumru andSarntisart, 2016). Some countries with a majority of Muslim citizens (i.e. Malaysia, Bahrain, UAE and others) have shownenormous growth in their Islamic banking system (Johnes et al., 2014). To this end, this paper firstly fills the literaturegap by examining the efficiency of major Islamic banks worldwide. Secondly, this paper differs from previous studies in
P. Wanke et al. / J. Int. Financ. Markets Inst. Money 45 (2016) 126–141 127
which two broad areas were examined: (i) efficiency of Islamic banks with comparison to conventional banks and (ii) effi-ciency analysis of Islamic banks for a specific country or region (Iqbal and Molyneux, 2005; Johnes et al., 2014; Sufian andNoor, 2009; Wanke et al., 2016, 2015). Thus far, to the best of our knowledge, this is the first time Islamic banking efficiencyhas been studied on a worldwide basis without relating to any specific issue.
This paper innovates in this context first by focusing on 114 Islamic banks from 24 countries and second by adopting TOP-SIS combined with neural networks in a two-stage approach. The motivations for the present research are as follows: First,we evaluate the relative efficiency among Islamic banks. Efficiency is the relative position of the units analyzed in the fron-tier of best practices, which is defined by the target group of banks. In this research, a TOPSIS analysis of Islamic banks isundertaken for the first time. Second, this paper expands the existing literature by virtue of its use of neural networks topredict and interpret the role of major contextual variables in achieving higher levels of efficiency in Islamic banks. Typically,contextual variables such as financial ratios related to cost structure or other business characteristics are used in fuzzy AHPtechniques for determining the criteria weights (Secme et al., 2009). In this research, however, these contextual variables areused in neural networks in order to build an efficiency model with predictive ability. Third, our analysis covers the periodfrom 2010 to 2014. Finally, our analysis is based on a representative sample of 114 Islamic banks worldwide. The purposeof this study is to propose a predictive model for banking efficiency on the financial and operational criteria commonly foundin the literature. Therefore, in this context, efficiency refers to the relative competitive environment in which they belong to.
In order to achieve this objective, neural networks are presented in a two-stage approach. TOPSIS analysis is then carriedout because it aims to render prediction of performance more flexible and informative than traditional statistical methods.The remainder of the paper is organized as follows: Section 2 presents the contextual setting. Section 3 then covers the lit-erature review. Section 4 presents the data and the model. The empirical results are presented and discussed in terms of pol-icy implications in Section 5. Conclusions follow in Section 6.
2. Contextual setting
The role of banks are imperative for any economy (whether secular or Islamic) due to the following four reasons (Iqbaland Molyneux, 2005): (i) intermediation services, (ii) creation of a wide range of assets and liabilities, (iii) offering financialservices, and (iv) creation of incentives. The most cited rationale for offering an alternative banking system (Islamic banks) isthe involvement of interest as a means of performing the above mentioned roles by traditional banks. According to Islamicregulations (Shariah), the prohibition of interest is justified for two reasons (Iqbal and Molyneux, 2005). First, any contractbased on interest does not share risk among parties. Rather than accumulate risk from all involved parties, the burdenunfairly accrues to a single party. This unjust practice has an adverse effect on incumbent parties. Second, the applicationof interest in an economy has proven to be inefficient in resource allocation. Since banks prefer to lend money only tothe most profitable projects to ensure returns on their investments, investors with low credit worthiness remain underval-ued. This creates a deviation between high income and low income groups in that society.
The theoretical development of Islamic banking took place in the 1950s. The establishment of the first Islamic bankoccurred in 1963, with a small village in Egypt as the test case (Iqbal and Molyneux, 2005). The growth of Islamic bankingwas patronized by the establishment of the Islamic Development Bank in 1975. Today Islamic banking, either in a completeformat or as a wing of traditional banking, is commonly practiced by every international bank. A functional difference in themajor operating indicators is shown in Table 1.
The distribution of assets, equity and net income among Islamic banks worldwide is presented on a regional basis inTable 2.
3. Literature review
Banks play a very important role in society, occupying a pivotal position in the process of fostering economic growth. As aresult, the evaluation of bank performance has received much attention over the past several years, both for theoretical and
Table 1Islamic banking at global level in comparison with competing commercial banking.
Indicators Islamic commercial banksat global level (%)
Other commercial banks in countrieswith dual system (%)
Total assets 81.3 59.7Equity 54.9 45Net income 81.3 42.4Customers’ deposits 93.6 61.5Income from financing or interest income 111.6 46.4Personal expenses 6.8 48.4Cost of deposits 185.1 32.1
Note: (%) Growth in fundamental values during Last 3-year period.Source: DCIBF Annual Report (2014).
Table 2Regional distribution of assets, equity and net income among Islamic banks.
Total assets billion $ Total equity billion $ Net income billion $
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practical purposes. These studies are often grouped into two main approaches, i.e., parametric and nonparametric (Bergerand Humphrey, 1997). The most popular parametric method is known as the stochastic frontier approach (SFA). The mostpopular nonparametric method is DEA (Chen, 2002).
Although applying these methods might be sufficient to determine efficiency levels, they do not afford details of deter-minants related to inefficiency. To remedy this, several studies proposed a combination approach of measuring and explain-ing bank efficiency scores using DEA or SFA in the first stage to determine efficiency scores and a regression model in thesecond stage to explain the respective drivers. TOPSIS application to assess efficiency in the financial sector still remainsscarce (Berger and Humphrey, 1997).
More recently, some researchers have started using predictive modeling techniques (Wanke et al., 2016, 2015) in the sec-ond stage to assess efficiency drivers in financial institutions. Predictive modeling is the process by which a technique is cre-ated or chosen to try to best predict the probability of an outcome. Specifically, Wanke et al. (2016) used Artificial NeuralNetworks. Artificial Neural Networks are powerful nonlinear regression techniques inspired by theories about how the brainworks. They are formed by a set of computing units (neurons) linked to each other. Each neuron executes two consecutivecalculations: a linear combination of its inputs followed by a nonlinear computation of the result to obtain an output valuethat is then fed to other neurons in the network.
Note, however, that the current literature on financial institutions still lacks a more systematic and integrated approach inthe second stage that might put these predictive modeling techniques into perspective (Wanke et al., 2016). This paper aimsto contribute to the current state of the art of the literature by combining Artificial Neural Networks and TOPSIS in a two-stage procedure to predict banking performance in Islamic banks.
4. Methodology
This section presents the major methodological steps adopted in this research. After presenting the data collected interms of ranking of criteria and contextual variables, the two-stage approach is explained in detail. Section 4.2 is devotedto a discussion of the application of the TOPSIS method to this research, in light of the major differences with DEA models.Section 4.3 depicts the neural network analysis adopted here and explains how the results were validated and interpreted bymeans of sensitivity analysis.
4.1. The data
The data on 114 Islamic banks from 24 countries was obtained from the BankScope database from 2010 to 2014. As pre-viously mentioned, the TOPSIS alternatives consisted of each of the 570 samples formed by the combination of 114 banks forfive years. We followed the positive negative criteria used in literature to select input and output variables for our research.Positive criteria, which reflect higher efficiency levels, included assets (USD), deposits (USD), operational results (USD/year),and banking product (USD/year). Negative criteria, which reflect lower efficiency levels, included equity (USD), provisions(USD), personal expenses (USD/year), and number of employees. Their descriptive statistics are presented in Table 3.
Table 3Descriptive statistics for the TOPSIS criteria and the contextual variables.
Contextual and business-related characteristics Years of operations 5 72 23.49123 14.53935Trend 1 5 3 1.415456Cost of capital �2.83 3.72 0.289895 0.403936Cost of labor �12 100 3.09379 13.32523Cost of cash reserves �4.061 31.381 0.26596 1.347863Cost of operations �42.16 433.759 7.52416 21.68641Geographical area Percentage
AFRICA 11.404%ASIA 14.035%EUROPE 6.140%MIDDLE EAST 12.281%PERSIAN GULF 13.158%SOUTH ASIA 7.018%SOUTH EAST ASIA 17.544%WEST ASIA 13.158%WESTERN ASIA 5.263%
Table 4Expected impact of contextual variables over bank efficiency.
Contextual variables Impact onefficiency
Remark
Years of operations + These given contextual variables were found to be significant when calculating efficiencies amongdifferent studies including Sufian and Noor (2009), Wanke et al. (2015), Hassan (2006), Abdul Majid andHassan (2012) and Wanke et al., 2016
Trend +/�Cost of capital +Cost of labor �Cost of cash reserves �Cost of operations �
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In addition, six contextual and business-related variables were collected to explain differences in the efficiency levels.These variables are also presented in Table 3 and are related to major elements of the banking cost structure They are: (i)cost of capital (measured as the amortizations/assets ratio); (ii) cost of labor (measured as the salaries/number of employeesratio); (iii) cost of cash reserves (measured as the provisions/deposits ratio); (iv) cost of operations (measured as the oper-ational costs/banking product ratio); (v) year of operations (year); and (vi) a time variable to measure the trend effect whichreflects the dynamics of Islamic banking. Their expected impacts on efficiency scores are shown in Table 4.
4.2. TOPSIS
The TOPSIS method, which was first developed by Hwang and Yoon, is a widely accepted MCDM technique (Behzadianet al., 2012), which is based on the concept that the positive ideal alternative has the best level for all considered attributes,while the negative ideal is the one with the worst attributed values. More precisely, the ideal solution is the one thatmaximizes benefits and also minimizes total costs. On the contrary, the negative-ideal solution is the one which minimizesbenefits while maximizing costs.
Despite its general resemblance to DEA objectives – where outputs may be maximized and (or) inputs minimized in non-radial (radial) models – the determination of the weights of the relative importance of each criteria (namely benefits andcosts, or simply outputs and inputs, respectively) is a milestone step in TOPSIS methodology, whereas in the case of DEAthese weights are calculated within the ambit of the model (Behzadian et al., 2012). Moreover, DEA may suffer from a lackof discriminatory power due to the fact that many entities are located on the frontier of efficiency, which differs from TOPSISand other MCDMmodels where discriminatory power is high. However, unlike SFA, both DEA and TOPSIS do not impose anyfunctional form on the data, neither do they make any distributional assumption for the calculated scores. This issue is ofutmost importance when conducting the robustness analysis on the global separability of criteria and contextual variables(cf. Section 4.4), in the sense that conditional distributions on efficiency scores are assessed empirically rather than imposinga functional form between them as done in SFA models. Therefore, DEA stands as a sound basis of comparison to TOPSISresults rather than using SFA scores, which is further corroborated in Fig. 5 that indicates that the discriminatory powerof SFA scores are low when compared to DEA and TOPSIS, that is their efficiency scores is more upwards biased towards one.
The basic TOPSIS principle assumes that the chosen alternative should simultaneously have the shortest distance from thepositive-ideal solution and the farthest distance from the negative-ideal solution. Another difference from DEA models is thefact that, while DEA optimizes the distance from each firm to the convex-efficient production frontier by finding a proper setof weights for inputs and outputs (Chen, 2002), TOPSIS purely employs analytical methods based on applying Euclidean dis-tance functions on normalized vectors of positive (outputs) and negative (inputs) criteria, given that the weights havealready been defined previously by the decision-maker. Since TOPSIS is comparatively simpler when compared to DEA mod-els, there are virtually no computational constraints with respect to the number of companies and criteria that can beassessed. In sum, the major advantages of TOPSIS methods over DEA models relate to the fact that: (i) weights are subjectto the discretion of decision-makers, and (ii) no assumption that requires convexity of data is required. The major TOPSISanalytic steps are depicted below.
Fig. 1 shows the analytical framework for the TOPSIS method. In this illustration, X⁄ and X0 are the positive ideal and neg-ative ideal solutions, respectively, while f 1 and f 2 represent the benefit attributes. It is easy to evaluate the alternatives ofx1; x2; x3 and x6 based on their distances from X⁄. While x4 and x5 are equally distant from X�, another determinant – the dis-tance between the alternative and the negative ideal solution X0 – is selected to arrive at the decision. This way, x4 has arelatively efficient score relative to x5 because of this relative longer distance with respect to X0. Based on this algorithm,
Fig. 1. Analytical framework for the TOPSIS method.
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the problem of the inconsistency of the units posed by different criteria can also be evaluated. Due to its advantages in rank-ing and selecting a number of externally determined alternatives through a distance measure, this method has been widelyapplied in efficiency analysis and risk management.
In our research, the TOPSIS technique for efficiency analysis of the Islamic banks is carried out as follows:Step 1: An evaluation matrix consisting of m alternatives and n criteria is developed, with the intersection of each alter-
native and criteria given as xij, yielding a matrix ðxijÞmxn. In this study, the criteria represent the inputs or outputs that theauthors choose for efficiency analysis while the alternatives are the number of samples.
Step 2: The matrix xij�mxn
�is then normalized to form a Regulatedmatrix R� ¼ rij
��. In this study, the authors use the vector
normalization method, as demonstrated in Eq. (1).
rij ¼ xij
ffiffiffiffiffiffiffiffiffiffiffiffiXmi¼1
x2ij
vuut ; i ¼ 1;2; . . .m ^ j ¼ 1;2; . . . ; n
,ð1Þ
Step 3: Calculate the Weighted normalized decision matrix for efficiency assessment by Eq. (2)
W ¼ ðwijÞmxn ¼ ðwjrijÞmxn ð2Þ
where wj is the weight given to the criteria j andPn
j¼1wj ¼ 1.With respect to the definition of the weights of the different criteria, several different methods can be found in the liter-
ature, thus there is no single methodological procedure to be followed. Secme et al. (2009) used fuzzy AHP for determiningthe weights of main and sub-criteria. In our study, nine attributes have been given the same weight since the literaturereview provides no clear indication as to which criteria are preferable for ranking banks in the Islamic context. Readersshould recall, however, that the contextual variables customarily used in fuzzy AHP procedures for determining the criteriaweights will now be used as performance predictors in the neural network analysis in order to predict performance levels.
Step 4: Determine the worst alternative (the negative ideal assessment unit) Aa and the best alternative (the positive idealassessment unit) Ab by using Eqs. (3) and (4):
where dia and dib are the Euclidean distance from the target alternative i to the worst and best conditions, respectively.Step 6: Calculate the similarity of alternative i to the worst condition (the inefficient best conditions), respectively:
Si ¼ diajðdia þ dibÞ ð7Þ
where 0 6 Si 6 1, i = 1,2, . . ., m.Si ¼ 0, if and only if the alternative solution has the worst condition.Si ¼ 1, if and only if the alternative solution has the best condition.
Step 7: Rank the alternatives according to Si, where a higher value of Si indicates a better solution with respect to higherefficiency levels within the ambit of the 114 Islamic banks, thereby allowing the subsequent assessment of the impact ofcontextual variables.
For the sake of illustrative purposes the spider graph presented in Fig. 2. illustrates how the positive ideal and thenegative ideal solutions are spread out through the different TOPSIS criteria. It is worth mentioning that the ideal points(positive ideal solution) are the ones where all the positive criteria are maximal and the negative criteria are minimal.The anti-ideal points (negative ideal solution) are the ones where all the positive criteria are minimal and the negativecriteria are maximal.
-2000000
0
2000000
4000000
6000000
8000000
10000000Asset
Deposits
Opera�onal Result
Banking Product
Equity
Provisions
Personal Expenses
Number of Employees
Ideal pointsAn�-ideal points
Fig. 2. TOPSIS positive ideal and negative ideal solutions.
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4.3. Neural networks for predicting efficiency
In this research, the choice of the predictive modeling technique observes the fact that new developments in statisticalsoftware technologies can be used to support systematic theory testing and development (James et al., 2013). Predictivemodeling is the process by which a technique is created or chosen to try to best predict the probability of an outcome. Morespecifically, established management science techniques such as TOPSIS can be used in combination with several predictivemodeling techniques to more effectively explore research questions on efficiency measurement.
It is worth noting that these new developments in statistical software technologies have resulted in a new reality thatconfronts predictive modeling techniques: the trade-off between prediction and interpretation (James et al., 2013). Whilethe primary interest of predictive modeling is to generate accurate predictions, a secondary interest may be to interpretthe model and understand why it works. However, when striving for higher accuracy, models tend to become more complexand interpretability more difficult. Thus, if a model is created to make some prediction, it should not be constrained by therequirement of interpretability and/or significance of statistical results; moreover, as long as the model can be appropriatelyvalidated, it should not matter whether it is a black box or a simple, interpretable model.
Importantly, with respect to the context of Islamic banks, most of the studies previously presented aimed to explain thefactors affecting efficiency (using bootstrapped truncated and Tobit regressions, for example), yet no predictive analysis hasbeen done, in the sense of pushing up the predictive limits of the model. However, the prediction of bank performance isextremely important; poor performance may lead to bankruptcy. Thus, conceiving a predictive model for bank performancewould be useful in avoiding or at least limiting such undesirable consequences to customers. Therefore, this study also pro-poses the use of contextual variables to predict banking performance. More specifically, neural networks are trained toassess how contextual variables could be used as predictors of efficiency levels in Islamic banks. Emerging literature existswhich combines MCDM results (TOPSIS included) from the first stage with variations on the neural network architecturefrom the second stage for predictive modeling in several areas of knowledge.
Artificial neural networks are one of the frequently used learning models for prediction. An artificial neural network isinspired by the structure of biological neural networks where neurons are interconnected and learn from experience. Neuralnetworks are composed of nodes (neurons) arranged in layers that are fully connected with the preceding layer via a systemof weights (Simons, 1996). Numerous different neural network architectures have been studied. These are networks in whichthere is an input layer, one or more hidden layers, and an output layer. The next step is to apply a transfer function to thissum; the most popular transfer function is the logistic function. Finally, the output layer obtains input values from the hid-den layer and the same transfer function is applied to create the output.
The neural networks have important parameters that cannot be directly estimated from the data. These parameters areusually referred to as tuning parameters because there is no analytical formula available to calculate an appropriate value forthem (Kuhn and Johnson, 2013). Cross-validation may be used to control the choice of the tuning parameters, thereby avoid-ing what is called over-fitting. Over-fitting refers to a situation in which the model learns the structure of the data set so wellthat when the model is applied to the original data it correctly predicts every sample.
Hence, cross-validation allows the assessment of the accuracy profile for a given model across the candidate values of thetuning parameter. In such cases it is very common to find that accuracy rapidly increases with the tuning parameter andthen, after the peak, decreases at a slower rate as over-fitting begins to manifest. The best model is then chosen based onthe numerically optimal value of the tuning parameter, that is, the one that yields the highest accuracy. The number of hid-den layers and the decay rate (weights) are tuning parameters frequently used in neural networks.
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4.4. On global separability and the adequacy of the two-stage approach
Simar and Wilson (2011) examined the widespread practice where efficiency estimates are regressed on some environ-mental variables in what is commonly known as a two-stage analysis. In a broader sense, the authors argue that this is donewithout specifying a statistical model in which such structures would follow from the first stage where the initial DEA esti-mates are obtained. As such, these two-stage approaches are not structural, but rather ad hoc. The most important under-lying assumption regarding two-stage analysis is the one on global separability. The next paragraphs detail this assumption.
In general lines, the vector of environmental factors or contextual variables, Z, may affect the range of attainable values ofthe inputs and the outputs (X,Y), including the shape of the production set, or it may only affect the distribution of ineffi-ciencies inside a set with boundaries not depending on Z (meaning that only the probability of being less or more far fromthe efficient frontier may depend on Z), or both. Under separability, the environmental factors have no influence whatsoeveron the support of XY and the only potential remaining impact of the environmental factors on the production process may beon the distribution of the efficiencies.
To understand the importance of the ‘‘separability” condition, let X 2 Rp+ denote a vector of p input quantities, and letY 2 Rq+ denote a vector of q output quantities. In addition, let Z 2 Z # Rr denote a vector of r environmental variables withdomain Z. Let Sn = (Xi,Yi,Zi) ni = 1 denote a set of observations. The separability assumption in Simar and Wilson (2011)implies that the sample observations (Xi,Yi,Zi) in Sn are realizations of identically independently distributed random vari-ables (X,Y,Z) with probability density function f(x,y,z) which has support over a compact set P � Rp + q+ � Rr with level setsP(z) defined by P(z) = (X,Y) | Z = z, X can produce Y. Now let F = U P(z) � Rp + q, z 2 Z. Under the ‘‘separability” condition, P(z)= F " z 2 Z and hence P = F � Z. If this condition is violated, then P(z) is different from F for some z 2 Z. Whether this is the caseor not is ultimately an empirical question to be assessed within the ambit of each study.
Daraio et al. (2010) provided a method for testing H0: P(z) = F " z 2 Z versus H1: P(z) is different from F for some z 2 Z. Inorder to test the null hypothesis consider the test statistics sFrontier;nðSnÞ ¼ n�1Pn
i¼1DFrontier;i^ D
Frontier;i^ P 0 where
DFrontier;i
^ ¼ ðYikFrontier;iðX^i;Yi=SnÞ � YikFrontier;iðX
^i;Yi=ZiSnÞÞand its complementary Frontier; i
^is (q � 1) vectors. The test statistics
give estimates of the mean integrated square difference between P and F � Z. If the separability assumption holds, we shouldexpect these statistics to be ‘‘close” to zero; otherwise, we should expect them to lie ‘‘far” from zero.
In this study, an R code was structured upon the packages np (Hayfield and Racine, 2008) and FNN (Beygelzimer et al.,2015) to compute the test statistics. In situations where the ‘‘separability” condition is satisfied, it would be straightforwardto perform the second stage analysis. For instance, one might estimate the regression model by the maximum-likelihoodmethod using standard software. Readers should pay attention to the fact that under standard assumptions where propertiesof traditional DEA estimators have been derived, the mass of estimates equal to one may negatively affect this test statistic,leading to values far from zero.
5. Results and discussion
The efficiency levels are calculated for 114 selected Islamic banks from 2010 to 2014 using the TOPSIS approach andconsidering different grouping criteria given in Fig. 3. Importantly, although median efficiency levels are quite stable over
Fig. 3. Islamic banking efficiency levels grouped by year.
Fig. 4. Efficiency levels grouped by country.
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the period (cf. Fig. 3) analyzed, there are substantial differences when efficiency levels are grouped by country (cf. Fig. 4). Forinstance, efficiency scores for Islamic banks tends to be significantly smaller in Syria, United Kingdom, Yemen, Pakistan,Singapore, Sudan, Lebanon, Malaysia, Brunei Darussalam, Egypt, and Indonesia, when compared to that of Turkey, Pakistan,Saudi Arabia, Kuwait, and Oman. Some mixed results are also found in efficiency scores for Islamic banks in United ArabEmirates, Jordan, and Bahrain. This suggests the eventual impact of contextual variables that may be embedded within con-textual variables of individual countries.
A robustness analysis was performed in order to compare the TOPSIS scores with those computed from the traditionalBCC and CCR (Charnes et al., 1978) models (cf. Fig. 5). The major idea is not only to assess whether the TOPSIS methodincreases the discriminatory power of the analysis against the efficient frontier but also whether their scores are less sym-metrical around the mean when compared to the traditional models, in order to increase contrasts for the subsequent neuralnetwork analysis.
The mean overall efficiency scores in the TOPSIS method is 0.33, whereas the traditional BCC and CCR models presentedmean values of 0.39 and 0.26, respectively. These results suggest that the discriminatory power of the TOPSIS method ishigher than those observed in BCC model, because the score is lower. An opposite relation is observed between TOPSISand CCR model. However, the impact of TOPSIS efficiency modeling can be also found in other statistical properties derivedfrom the frequency distribution of efficiency estimates in both models. Skewness is farther than zero (0.949 against 0.667[BCC] and 0.667 [CCR]), suggesting that, in the TOPSIS method, efficiency scores are not symmetrical around the mean,favoring the neural network analysis. Nevertheless, Spearman rank correlations between efficiency scores derived fromtraditional DEA models and the TOPSIS method were found to be extremely high and significant at 0.01 (0.63 and 0.60 inthe CCR and BCC cases, respectively), thus suggesting isotonic results for both models. It is worth noting that SFA modelswere also taken into consideration, but as expected, their discriminatory power was the lowest among the three models.
Scale: 0.03073Gaussian distributionNumber of Newton–Raphson iterations: 5Log-likelihood: 1176 on 30 DfWald-statistic: 1287 on 28 Df, p-value: 2.22e�16Adjusted R-squared: 0.8998671
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Since there are four outputs and four inputs, four SFA set of results, considering one output at a time, are presented in Fig. 5below.
Now, with regards to the contextual variables and test of global separability (Daraio et al., 2010), the empirical value ofthe test statistic for the TOPSIS scores was not only found to be close to zero (0.0639) but also to be inferior than the test
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values on the BCC (0.131) and the CCR frontiers (0.085). As expected, this test value goes far from zero in cases where esti-mates are biased towards one (cf. Fig. 5). Global separability, therefore, appears to be consistent with the use of TOPSIS onthe sample data to the detriment of DEA models. This suggests that the contextual variables considered here affect only thedistribution of efficiencies and not the attainable input/output combinations (or the shape of the underlying production set).
Moreover, a robustness analysis was also performed before running the neural network analysis. More precisely, TOPSISscores were regressed against the set of contextual variables presented in Table 5 using a Tobit regression. The results, pre-sented in Table 5, indicate that country origin (e.g. Indonesia, Iran, Pakistan, Sudan, Syria, Tunisia, and Yemen) has a negativeimpact on efficiency levels. On the contrary, contextual settings of countries like Jordan, Oman, Qatar, Saudi Arabia, Turkey,and United Arab Emirates have a positive impact on bank efficiencies. It appears that banks of Persian Gulf and Middle Eastorigin are slightly more efficient than banks with South Asian, East Asian, and African origins.
Among the contextual variables, cost of capital and cost of operations have a negative impact on bank efficiency levels.Alternatively, the cost of labor is seen to have a positive impact on efficiency levels. Since employee motivation is alwaysensured through monetary incentives and salary (Masum et al., 2015), this result is in line with previous research. The costof operations and cost of capital, however, seem to overshadow the origin effect. Although weak in terms of significance, costof labor merits attention due to its positive impact.
Next, a neural network analysis is performed on the TOPSIS efficiency scores, using the contextual variables presented inTable 5 as their predictors. All steps taken follow those presented in Faraway (2005). When different cross-validation mea-sures are applied and different numbers of hidden layers are considered, a clear picture emerges with respect to the responsebias or the over-fitting within each predictive technique. Fig. 6 illustrates the apparent Root Mean Squared Error (RMSE),which tends to decrease with a higher number of hidden layers of the neural network. These results clearly suggest a positiveresponse bias towards a larger number of hidden layers.
Additionally, Fig. 7 illustrates that a common pattern within the cross-validation methods is seen where RMSE is higherfor lower hidden layer values and smaller at higher values in the context of this particular neural network. The most accurateneural network obtained (RMSE = 0.020) used the repeated 10-fold cross-validation technique, for 15 hidden layers and adecay rate of 0.0178. This signifies a mean error rate of less than 2.00 percentage points if we consider the efficiency scaleranging from 0% to 100%. Moreover, the pseudo R squared for the 10-fold cross-validation with 15 layers it is 0.8563457,comparable in magnitude to the pseudo R squared found in the Tobit regression.
The relative importance of each contextual variable (both country origin and cost structure) is given in Fig. 8. As regardsTOPSIS efficiency scores, the top two predictors for the neural networks of Islamic banks are regional cluster (Europe andPersian Gulf region) while the seven next best predictors are country origin (Qatar, Kuwait, Sudan, Turkey, Indonesia, Iraq,and Bahrain). The variables cost of cash reserved and cost of labor, which are related to the cost structure of Islamic banks,are found in the 17th and 20th positions respectively and were found to have a moderate level of predictability. Note thatcountry origin is revealed to be responsible for a substantial part of the efficiency indicators in Islamic banks, while coststructure tends to present a limited impact on efficiency levels when compared to regional origin. This indicates thatcorporate governance (Berger et al., 2005) matters more driving the banking efficiency scores. A detailed analysis of Islamic
Fig. 6. Apparent RMSE.
Fig. 7. Cross-validated performance profiles over different values of the tuning parameter.
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banking around the world is presented in the DCIBF Annual Report. The remaining cost structure variables, cost of capital andcost of operations, presented a negligible impact on efficiency, as did the variable for capturing the time trend.
Fig. 9 presents the sensitivity analysis on the TOPSIS efficiency estimates for the best neural network model. Theysupplement results presented in Fig. 8. in the sense that they provide the direction of the relationship between the efficiencyscores (vertical axis) and the variations in the respective contextual variables (horizontal axis). A positive (negative) associ-ation is found when the sensitive analysis curve systematically increases (decreases). Since most contextual variables aredummy ones related to the country or region of origin of the bank, readers should notice that only two dots are plotted withrespect to 0 and 1 values, but the interpretation of the impact on efficiency levels is similar. Contextual variables were stan-dardized before performing this marginal analysis, as suggested in Faraway (2005). The numbers on the vertical axis repre-sent the sensitivity analysis for the predicted relationship between the outcome (efficiency) and the standardized predictors(contextual variables), using the artificial neural network model (while maintaining all other standardized predictors at theirmean value, that is, zero). Both the magnitude of the scales on the vertical axis and their variation intervals are related to themaximum and minimum TOPSIS scores. The similitude of the vertical axis for different predictors or contextual variables isrelated to their standardization. However, their marginal variation with respect to the unit (holding all other predictors at
Relative Importance (%)
TrendYears of Operations
Cost of OperationsBrunei Darussalam
YemenSingaporeSouth Asia
TunisiaWestern AsiaSaudi Arabia
JordanUAE
OmanSyria
Cost of CapitalEgypt
LebanonBangladesh
UKCost of Labor
PakistanAsia
Cost of Cash ReservesAfrica
South East AsiaMalaysia
IranMiddle EastPalestinianWest Asia
BahrainIraq
IndonesiaTurkeySudanKuwaitQatar
Persian GulfEurope
0 1 2 3 4 5 6 7
Fig. 8. Relative importance of contextual variables.
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their mean value) should be interpreted in terms of the magnitude of the values of the horizontal axis, which tends to varysubstantially, depending upon the predictor.
The results confirm the signs found in the Tobit regression results, despite their significance levels and relative impor-tance, as measured by the regression coefficients. A negative impact of cost structure – capital and operations – is discernibleon efficiency levels, although the cost of cash reserves and cost of labor, when considered in an isolated fashion, present apositive impact due to greater parsimony and smaller risk assumed in loans. As regards country origin, it is interesting tonote that there is significant deviation among the impacts of country origin on Islamic bank efficiency levels. It is also pos-sible that these lower efficiency levels may be derived from the absence of a learning curve for banking operations, as thetrend impact was found to be marginal. This fact is evident from a simple visual inspection of the scale of the vertical axisof the first graph in the first row of Fig. 9. In fact, in this case, scores presented variation in the fourth decimal place.
6. Conclusion
This paper presents an analysis of the efficiency of Islamic banks using TOPSIS and neural networks. TOPSIS enables aranking of the efficiency of the banks analyzed and, based on such ranking, a high variation in bank efficiency can be dis-cerned. Bank Asya, a Turkish bank, is ranked first with a score in 2014 of 0.621, which, relative to the frontier of best practices– a value equal to 1 signifies 100% efficiency – presents an inefficiency level of 1 � 0.621 = 0.379. The least efficient bank isElaf Islamic Bank, a bank from Iraq that in 2011 scored 0.353. Thus, the efficiency of the Islamic banking system in countriesrecently subjected to war is low when compared to normal economies. Causes for this result may stem from the operationalprocedures of the banks analyzed, the model adopted, or, most suitably, unstable economic conditions in recent wars. There-fore, no single definitive conclusion may be derived and further research is necessary to confirm these results. Assuming theresults are exclusively due to bank procedures, banks should review them and benchmark their practices against theEuropean and Persian Gulf banks in order to increase efficiency.
Based on the neural network results, it is possible to explain several correlates of inefficiency. The major factor relates tothe cost structure and the country origin of the bank. Therefore, high costs explain the low efficiency of Islamic banks,although the cost of cash reserves and cost of labor, when considered in an isolated fashion, presented a positive impact. Thismay be explained by the smaller risk assumed in loans. Additionally, bank origin also correlates with efficiency, signifyingthat cultural traditions are positively related to efficiency. The neural networks also predict a negligible impact of trend on
Fig. 9. Neural network sensitivity analysis for the efficiency scores.
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Fig. 9 (continued)
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efficiency levels, suggesting that Islamic banks do not learn from their operational procedures, that is, their learning curvesare somewhat limited due to low competition.
Decision-makers can benefit from these results by establishing an action plan over time to help Islamic banks increaseefficiency based on their distinct characteristics. For example, while banks with European and Persian Gulf origins couldimplement continuous improvement programs on their operations to benefit from a learning curve over time, regulatorsof public banks could consider different governance mechanisms with private stakeholders to allow these banks to closetheir efficiency gaps vis-à-vis private banks. Opportunities for rightsizing operations should also be explored so that the neg-ative impact of the cost of labor and operations on efficiency levels can be kept under control.
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Expert Syst. http://dx.doi.org/10.1111/exsy.12144 (Article first published online: 18 DEC 2015).
