Predicting Efficiency in Angolan Banks: A TwoStage TOPSIS ... · central bank, BPC (Banco de...

PREDICTING EFFICIENCY IN ANGOLAN BANKS:

A TWO-STAGE TOPSIS AND NEURAL

NETWORKS APPROACH

PETER WANKE*, CARLOS BARROS‡

AND NKANGA PEDRO JOÃO MACANDA†

AbstractThis paper presents an efficiency assessment of the Angolan banks using Technique for OrderPreference by Similarity to the Ideal Solution (TOPSIS). TOPSIS is a multi-criteria decision-making technique similar to data envelopment analysis, which ranks a finite set of units based on theminimisation of distance from an ideal point and the maximisation of distance from an anti-idealpoint. In this research, TOPSIS is used first in a two-stage approach to assess the relative efficiencyof Angolan banks 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 produce a modelfor banking performance with effective predictive ability. The results reveal that variables related tocost structure have a prominent negative impact on efficiency. Findings also indicate that theAngolan banking market would benefit from higher level of competition between institutions.JEL Classification: D24, D2, G21, G2Keywords: Banks, Angola, TOPSIS, two-stage, neural networks, efficiency ranks

1. INTRODUCTION

One of the major research streams in banking is to measure the relative importance ofbanks using popular multi-criteria decision making (MCDM), such as the dataenvelopment analysis (DEA) and the Technique for Order Preference by Similarity to theIdeal Solution (TOPSIS) (Hemmati et al., 2013). This paper analyses the efficiency ofAngolan banks with TOPSIS. Thus far, applications of TOPSIS to measure bankefficiency have been scarce (Seçme et al., 2009; Shaverdi et al., 2011; Hemmati et al.,2013; Bilbao-Terol et al., 2014), although efficiency per se has been the focus of muchrecent research (Briec and Lemaire, 1999; Camanho and Dyson, 2005; Boussemart et al.,2009; Briec and Liang, 2011), especially in relation to banking (Berger and Humphrey,1992, 1997; De Borger et al., 1998; DeYoung, 1998; Camanho and Dyson, 1999; Ariffand Can, 2009; Drake et al., 2009; Sahoo and Tone, 2009; Fukuyama and Weber 2009a,2009b, 2010; Ray and Das, 2010; Tone and Tsutsui, 2010; Epure et al., 2011; Wu et al.,2014). However, efficiency in African banking has been addressed in few studies (see, e.g.,O’Donnell and Van der Westhuizen, 2002; Ikhide, 2008; Barros, et al., 2014), and a deep

* Corresponding author: Associate professor, COPPEAD Graduate Business School, Center forStudies in Logistics, Infrastructure and Management, Rua Paschoal Lemme 355, Rio de Janeiro,Brazil 20520120. E-mail: [email protected].† Faculdade de Economia, Universidade Agostinho Neto, Luanda, Angola.‡ University of Lisbon, Lisbon, Portugal.Please acknowledge this Research made with support of Calouste Gulbenkian Foundation.

bs_bs_banner South African Journal of Economics

South African Journal of Economics Vol. ••:•• •• 2015

© 2015 Economic Society of South Africa. doi: 10.1111/saje.121031

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analysis of Angolan banks has not yet been undertaken in terms of the assessment of itsefficiency drivers, which justifies this research.

Therefore, this paper innovates in this context first by focusing on Angolan banks andsecond by adopting TOPSIS combined with neural networks in a two-stage approach. Themotivations for the present research are the following. First is to evaluate the relativeefficiency among Angolan banks. Efficiency is the relative position of the units analysed inthe frontier of best practices, which is defined by the target group of banks. In this research,a TOPSIS analysis of Angolan banks is undertaken for the first time. Second, the paperexpands the existing literature by virtue of its use of neural networks to predict and interpretthe role of major contextual variables in achieving higher levels of efficiency in Angolanbanks. Typically, contextual variables, such as financial ratios related to cost structure orother business characteristics, are used in fuzzy analytical hierarchy process (AHP)techniques for determining the criteria weights (Seçme et al., 2009; Shaverdi et al., 2011).In this research, however, these contextual variables are used in neural networks in order tobuild an efficiency model with predictive ability. Third, our analysis covers the period from2006 to 2012. Finally, our analysis is based on a representative sample of Angolan banks.

The purpose of this study is to propose a predictive model for banking efficiency inAngola based on the financial and operational criteria commonly found in the literature.Angola attracts banks every year, and there is almost evidence that the market is saturatedbecause profits have started decreasing and mergers have already started (Russian bankVTB África and Angola Banco Privado Atlântico merged in 2014). Therefore, in thiscontext, efficiency calls the attention of the banks for the relative competition in whichthey have been engaged.

In order to achieve this objective, neural networks are presented in a two-stageapproach; TOPSIS analysis is then carried out because it aims to render prediction ofperformance more flexible and informative than traditional statistical methods (Brockettet al., 1997). The remainder of the paper is organised as follows: Section 2 presents thecontextual setting, then Section 3 covers the literature review. Section 4 presents the dataand the model. The empirical results are presented and discussed in terms of policyimplications in Section 5. Conclusions follow in Section 6.

2. CONTEXTUAL SETTING

Banking activity in Angola started in 1865 when the National Ultramarine colonial bankwas established to fund colonial activities. Until 1926 this bank served as Angola’s centralbank, but due to the uncontrolled growth of money, the Bank of Angola (BA) wasestablished. In 1957, other banks established themselves in Angola: Banco Comercial deAngola, Banco de Crédito Comercial e Industrial, Banco Totta Standard de Angola,Banco Pinto e Sotto Mayor and Banco Inter-Unido. After gaining independence from thecolonial power, Portugal, in 1975, the Angolan government nationalised the BA andBanco Comercial de Angola. The government also established Banco Nacional de Angola(BNA), which today serves as the central bank, as well as Banco Popular de Angola (BPA).In 1978, the banking system was reduced to two public banks: BNA and BPA. However,in 1987, with the abandonment of the socialist organisation, the Angolan governmentallowed new banks to enter the country and forced BNA to end its commercial activity,allocating it to a new bank, Caixa de Credito Agro-Pecuário, which was shut down in2000. In 2005, Angola’s banking system included three public banks (BNA, which is the


© 2015 Economic Society of South Africa.

central bank, BPC (Banco de Poupança e Crédito), and BCI (Banco de Comércio eIndústria)), seven private national banks (e.g. BAI (Banco Angolano de Investimentos),BCA (Banco Comercial Angolano), Banco Sol and Banco Keve) and four foreign banks(e.g. BTA (Banco Totta e Açores); BFA (Banco de Fomento de Angola)). After 2005, otherforeign banks entered Angola’s banking market. Currently, the banks operating in thecountry can be broken down (see Table 1).

This paper uses panel data on Angola’s banks from 2006 to 2012 that include all banksexisting from 2006 onwards. These include the two public commercial banks (Banco dePoupança e Crédito (BPC) and Banco de Comércio e Indústria (BCI)) and foreign bankssuch as Banco Espírito Santo Angola (BESA) (51.9% of the capital is held by thePortuguese bank BES (Banco Espírito Santo). The rest are held by Angolan nationals incompliance with the foreign investment act, which requires each foreign investment to havea local partner with around 50% of the total capital. BES was recently embroiled inaccusations of theft in Portugal, and also had around 4 million euros of bad credit.Therefore, BNA nominated an administration to decide on the future of BES. Theremainder banks consists of Millennium (68.5% of capital is held by the Portuguese bankMillennium) and BFA (50% of the capital is owned by the Portuguese bank BPI (BancoPortuguês de Investimento)), while the Banco Caixa Geral Totta de Angola jointly belongsto the oil company Sonangol (49%) and the public Portuguese bank Caixa Geral deDepósitos (51%). All foreign banks that enter the Angolan market must have a localpartner, and the proportion of control varies. This means that Portugal, the formercoloniser, maintains a strong presence in the banking activity of its former colony. Otherforeign-owned banks include Banco Comercial Portugues (BCP), which belongs to SouthAfrican Bank and Barclays (50%), and to Angola’s private sector. The remaining banks areunder Angolan sole ownership. Banco de Indústria e Comércio (BIC) belongs to the peopleof Angola (25%), in partnership with a Portuguese entrepreneur (Américo Amorim), whoalso owns 25%. The other 50% of the capital is spread among various Angolanbusinessmen. BIC is the only Angolan bank also established in Portugal, and recentlybought a bankrupt Portuguese bank, BPN (Banco Português de Negócios). Keve is a smallAngolan bank with multiple owners; the maximum share is 6.95% of capital. Banco Sol isa bank owned by private Angolan capital. BPC is a public bank and BAI belongs toSonangol. The Sonangol Oil Company accounts for 52% of national gross domesticproduct, as such the contextual setting is one where foreign capital is merged with nationalcapital.

Table 2 shows that the largest banks in terms of the number of employees includeBPC, BCA, BFA, BAI and BIC (Banco BIC). However, in terms of the ratio of loans tothe number of employees, BESA ranks first, followed by Millennium; thus, efficiencyvaries across banks (Barros et al., 2014). With mergers waiting to continue, Angola banksare facing conjuncture changes associated with the fall of the oil price in 2014, but alsostructural changes associated with increasing costs and market congestion. Within this

Table 1. Banks in Angola during the period

Banks 2005 2006 2007 2010 2011

Public 2 3 2 3 3Mixed 0 0 0 0 1Private national 7 9 10 12 12Foreign banks 4 5 6 7 7Total 13 17 19 23 23

3South African Journal of Economics Vol. ••:•• •• 2015


context, efficiency analysis is of paramount importance since it highlights the relativecompetition and resources-based competition that is behind the efficiency analysisundertaken in the present research.

3. LITERATURE REVIEW

Banks play a very important role in the society, presenting a pivotal position in the processof promoting economic growth. As a result, the evaluation of bank performance hasreceived much attention over the past several years, both for theoretical and practicalpurposes. These studies are often grouped into two main approaches, i.e. parametric andnon-parametric (Berger and Humphrey, 1997; De Borger et al., 1998; Brandouy et al.,2010; Brissimis et al., 2010; Briec and Liang, 2011; Kerstens et al., 2011; Lampe andHilgers, 2014). The most popular parametric method is known as the stochastic frontierapproach (SFA), whereas the most popular non-parametric method is DEA (Chen, 2002;Yang, 2009).

Although applying these methods might be sufficient to determine efficiency levels,they do not afford details of the determinants related to inefficiency. In this sense, severalstudies proposed a combination approach of measuring and explaining bank efficiencyscores (Fethi and Pasiouras, 2010) using DEA or SFA in the first stage to determineefficiency scores and a regression model in the second stage to explain the respectivedrivers. Casu and Molyneux (2003), Ariff and Can (2008), and San et al. (2011)employed Tobit regression to explain bank performance. TOPSIS applications to assessefficiency in the financial sector still remain scarce (Bilbao-Terol et al., 2014).

More recently, some researchers have started using predictive modelling techniques(Wanke and Barros, 2014) in the second stage to assess efficiency drivers in financialinstitutions. Predictive modelling is the process by which a technique is created or chosento try to best predict the probability of an outcome (Geisser, 1993). Specifically, Anouze(2010), Emrouznejad and Anouze (2010), and Seol et al. (2007) used regression trees; incontrast, Azadeh et al. (2011) used artificial neural networks. Artificial neural networks arepowerful non-linear regression techniques inspired by theories about how the brain works

Table 2. Characteristics of Angola’s banks, 2012

Nobs Banks Number ofemployees

Loans (Angolankwanza, millions)1

Deposits (Angolankwanza, millions)1

1 Banco Angolano de Investimentos 1,631 367,463 714,2362 Banco BAI Microfinanças 1,294 5,035 14,4973 Banco Comercial Angolano 1,075 17,513 28,2544 Banco Caixa Geral Totta de Angola 1,172 25,096 42,3385 Banco de Comércio e Indústria 4,538 233,642 131,5526 Banco Espírito Santo Angola 2,582 170,118 254,0857 Banco de Fomento Angola 1,468 180,091 196,3688 Banco BIC 584 43,124 31,3659 Banco Millennium Angola 1,165 264,041 292,050

10 Banco de Poupança e Crédito 18,658 23,860 47,00611 Banco Sol 3,168 19,730 17,45212 Banco Regional do Keve 2,712 21,655 34,93813 Banco de Negócios Internacional 569 77,933 125,10214 Banco Privado Atlântico 518 145,745 204,76315 Banco de Desenvolvimento de Angola 79 3,388,306 22,067

Source: KPMG report on Angola banking.1 The exchange rate between the national currency (kwanza) and the US dollar in December 2006was 100 USD = 1.04 AOA.



(Ripley, 1995; Bishop, 2006; Titterington, 2010). They are formed by a set of computingunits (neurons) linked to each other. Each neuron executes two consecutive calculations: alinear combination of its inputs, followed by a non-linear computation of the result toobtain an output value that is then fed to other neurons in the network (Torgo, 2011).

Note, however, that the current literature on financial institutions still lacks a moresystematic and integrated approach in the second stage that might put these predictivemodelling techniques into perspective (Yeh et al., 2012; Hajek and Michalak, 2013; Sunet al., 2014). This paper aims to contribute to the current state of the art of the literatureby combining artificial neural networks and TOPSIS in a two-stage procedure to predictbanking performance in Angola.

4. METHODOLOGY

This section presents the major methodological steps adopted in this research. Afterpresenting the data collected in terms of ranking of criteria and contextual variables, thetwo-stage approach is explained in detailed. Section 4.2 is devoted to discuss theapplication of the TOPSIS method to this research, in light of the major differences withrespect to DEA models. Section 4.3 depicts the neural network analysis adopted here andexplains how the results were validated and interpreted by means of sensitivity analysis.

4.1 The DataThe data on 15 Angolan banks were obtained from financial statements obtained yearlyby KPMG from 2006 to 2012. As previously mentioned, the TOPSIS alternativesconsisted of each one of the 105 samples formed by the combination of 15 banks forseven years. The criteria observed the inputs and the outputs commonly found in theliterature review and the availability of data. Criteria included number of employees,labour cost (USD/year), equity (USD), provisions (USD) and amortisations (USD), witha negative impact on efficiency levels; and banking product (USD/year), operationalresults (USD/year), deposits (USD) and assets (USD), with a positive impact onefficiency levels. Their descriptive statistics are presented in Table 3.

In addition, 10 contextual and business-related variables were collected to explaindifferences in the efficiency levels. These variables are also presented in Table 3 and arerelated to major elements of the banking cost structure: (i) cost of capital (measured as theamortisations/assets ratio); (ii) cost of labour (measured as the salaries/number ofemployees ratio); (iii) cost of cash reserves (measured as the provisions/deposits ratio); (iv)cost of operations (measured as the operational costs/banking product ratio); (v)ownership/origin of the bank (whether Portuguese, South African, public orinternational); and (vi) a time variable to measure the trend effect. These contextualvariables describe the ownership status of the banks (public vs. private), the nationalityorigin of the banks that identify the foreign investment in Angola banking and the timeeffect which reflects the time dynamic of Angola banking.

4.2 TOPSISThere is a tradition in MCDM methods, namely the AHP (Saaty, 1980; Ramanathan,2013); Promethee (Brans and Vincke, 1985; Corrente et al., 2013); Electre(Hatami-Marbini and Tavana, 2011; Corrente et al., 2013); Dematel (Tsay et al., 2009),Vikor (Opricovic, 1998; Opricovic and Tzeng, 2007); TOPSIS (Lai et al., 1994); and Uta



(Siskos et al., 2014). TOPSIS has been used in energy (Wang et al, 2014) and in theassessment of government bond funds (Bilbao-Terol et al., 2014).

The TOPSIS method, which was first developed by Hwang and Yoon (1981), is awidely accepted MCDM technique, which is based on the concept that the positiveideal alternative has the best level for all considered attributes, while the negative idealis the one with the worst attributed values. More precisely, the ideal solution is the onethat maximises benefit and also minimises total costs. On the contrary, the negativeideal solution is the one that minimises benefit and also maximises cost (Seçme et al.,2009).

Wang and Luo (2006) made a significant contribution to the literature by showing thatthe TOPSIS idea can be used in the same way as DEA to create a comprehensive rankingof Decision Making Units (DMUs) (Wu, 2006). Despite its general resemblance withDEA objectives (Wang et al., 2014) – where outputs may be maximised and (or) inputsminimised in non-radial (radial) models – the determination of the weightings of therelative importance of each criteria (namely benefits and costs, or simply outputs andinputs, respectively) is a milestone step in TOPSIS methodology, while in the case ofDEA these weightings are calculated within the ambit of the model (Bouyssou, 1999).Besides, DEA may suffer from a lack of discriminatory power, due to the fact that manyentities are located on the frontier of efficiency, which is different from TOPSIS and otherMCDC models, where discriminatory power is high (Wu, 2006). However, differentfrom the case of SFA, both DEA and TOPSIS do not impose any functional form on thedata, neither do they make any distributional assumption for the calculated scores (Wanget al., 2014).

The basic TOPSIS principle assumes that the chosen alternative should simultaneouslyhave the shortest distance from the positive ideal solution, and also the farthest distancefrom the negative ideal solution (Ertugrul and Karakasoglu, 2009). Another differencefrom DEA models is the fact that while DEA optimises the distance from each firm to theconvex-efficient production frontier by finding a proper set of weightings for inputs and

Table 3. Descriptive statistics for the TOPSIS criteria and the contextual variables

Variables Min Max Mean SD

TOPSIS criteria

Number of employees 58.21 19,113.00 2,379.49 3,093.22Labour cost (USD/year) $18.53 $7,257.96 $811.55 $1,109.75Equity (USD) $8,218.35 $941,076.02 $87,519.29 $113,935.33Provisions (USD) − $9,538.00 $1,568.94 $1,817.73Amortisations (USD) $1,712.00 $1,722,516.00 $182,859.44 $310,494.18Banking product (USD/year) $242.00 $843,970.75 $80,433.49 $202,557.20Operational results (USD/year) $97.00 $549,859.55 $39,801.95 $101,991.17Deposits (USD) $594.00 $714,236.46 $109,312.28 $146,765.70Assets (USD) $21,520.54 $3,198,759.55 $408,153.96 $548,690.47

Contextual andbusiness-relatedcharacteristics

Trend 1.00 7.00 4.00 2.01Trend 2 1.00 49.00 20.00 16.45Cost of capital

(amortisations/assets)– 18.31 1.14 2.61

Cost of labour (salaries/number ofemployees)

0.21 0.45 0.33 0.04

Cost of cash reserves(provisions/deposits)

– 0.06 0.02 0.01

Cost of operations (operationalcosts/banking product)

– 0.21 0.03 0.04

Portuguese bank – 1.00 0.27 0.44South African bank – 1.00 0.07 0.25Public bank – 1.00 0.20 0.40International bank – 1.00 0.14 0.35



outputs (Charnes et al., 1978; Banker et al., 1984), TOPSIS purely employs analyticalmethods based on applying Euclidean distance functions on normalised vectors of positive(outputs) and negative (inputs) criteria, given that the weightings have already been definedpreviously by the decision maker (Shaverdi et al., 2011). In synthesis, the major advantagesofTOPSIS methods over DEA models relate to the fact that (i) weightings are subject to thediscretion of decision makers, and (ii) no assumption that requires convexity of data isrequired. The major TOPSIS analytic steps are next depicted below.

Fig. 1 shows the analytical framework for the TOPSIS method. In this illustration, X*and X0 are the positive ideal and negative ideal solutions, respectively, while f1 and f2

represent the benefit attributes. It is easy to evaluate the alternatives of x1, x2, x3 and x6

based on their distances with X*. While x4 and x5 are equally distant from X*, anotherdeterminant – the distance between the alternative and the negative ideal solution X0 – isselected to arrive at the decision. This way, x4 has a relatively efficient score relative to x5

because of this relative longer distance with respect to X0. Based on this algorithm, theproblem of the inconsistency of the units posed by different criteria can also be evaluated.Due to its advantages in ranking and selecting a number of externally determinedalternatives through a distance measure, this method has been widely applied in efficiencyanalysis and risk management.

In our research, the TOPSIS technique for efficiency analysis of the Angolan banks iscarried out as follows:

Step 1: An evaluation matrix consisting of m alternatives and n criteria is developed,with the intersection of each alternative and criteria given as xij; therefore, one obtains amatrix (xij)mxn. In this study, the criteria represent the inputs or outputs that the authorschoose for efficiency analysis, while the alternatives are the number of samples.

Step 2: The matrix (xij)mxn is then normalised to form a regulated matrix R* = (rij). Inthis study, the authors use the vector normalisation method, as demonstrated in equation(1).

r x x i m and j nij ij ijim= = ==∑ 2

1 1 2 1 2, , , , , ,… … (1)

Step 3: Calculate the weighted normalised decision matrix for efficiency assessment byequation (2):

Figure 1. Analytical framework for the TOPSIS method



W w w rij mxn j ij mxn= ( ) = ( ) (2)

where wj is the weight given to the criteria j and ∑ ==jn

jw1 1.With respect to the definition of weight of the different criteria, several different

methods can be found in literature; thus, there is not a single methodological procedureto be followed. Hemmati et al. (2013), for instance, used the entropy technique. Seçmeet al. (2009) and Shaverdi et al. (2011), in contrast, used fuzzy AHP for determining theweights of the main and subcriteria. In our study, nine attributes have been given the sameweight since the literature review provides no clear indication on which criteria arepreferable to the detriment of the others for ranking banks in the Angolan context (Barroset al., 2014). Readers should recall, however, that the contextual variables customarilyused in fuzzy AHP procedures for determining the criteria weights will now be used asperformance predictors in the neural network analysis in order to predict performancelevels.

Step 4: Determine the worst alternative (the negative ideal assessment unit) Aa and thebest alternative (the positive ideal assessment unit) Ab by using equations (3) and (4):

A w i m j J w i m j Jj

a ij ij

aj

= =( ) ∈ =( ) ∈{ }= =

+ −min , , , , max , , ,,

1 2 1 21

… …α 22, ,… n{ } (3)

A max w i m j J w i m j Jj

b ij ij

bj

= = ∈( =( ) ∈{ }= =

+ −, , , , min , , ,, ,

1 2 1 21 2

… …α ……n{ } (4)

where J+ = {j|j ∈ positive} and J− = {j|j ∈ negative}, which are a set of positive (benefit) andnegative (cost) attributes, respectively.

Step 5: Calculate the distance dia between the target alternative i and the worstcondition Aa by equation (5):

d w i mia ij ajjn= −( ) ==∑ α 2

1 1 2, , , ,… (5)

and the distance dib between the alternative i and the best condition Ab by equation (6).

d w i mib ij bjjn= −( ) ==∑ α 2

1 1 2, , , ,… (6)

where dia and dib are the Euclidean distance from the target alternative i to the worst andbest conditions, respectively.

Step 6: Calculate the similarity of alternative i to the worst condition (the inefficientbest conditions, respectively):

S d d di ia ia ib= +( ) (7)

where 0 ≤ Si ≤ 1, i = 1, 2, . . . , m.Si = 0, if and only if the alternative solution has the worst condition.Si = 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 abetter solution with respect to higher efficiency levels within the ambit of the 15 Angolanbanks, thereby allowing the subsequent assessment of the impact of contextual variables.

4.3 Predicting Efficiency Levels Using Neural NetworksIn this research, the choice of the predictive modelling technique observes the fact thatnew developments in statistical software technologies can be used to support systematictheory testing and development (Tsui et al., 2000; Chen and Cheng, 2013; Osei-Brysonand Ngwenyama, 2014). Predictive modelling is the process by which a technique iscreated or chosen to try to best predict the probability of an outcome (Geisser, 1993).More specifically, established management science techniques such as TOPSIS can beused in combination with several predictive modelling techniques to more effectivelyexplore research questions on efficiency measurement (Chen, 2007).

It is worth noting that these new developments in statistical software technologies haveresulted in a new reality that confronts predictive modelling techniques: the trade-offbetween prediction and interpretation (James et al., 2013; Kahraman et al., 2013; Kuhnand Johnson, 2013). While the primary interest of predictive modelling is to generateaccurate predictions, a secondary interest may be to interpret the model and understandwhy it works. However, when striving for higher accuracy, models tend to become morecomplex and interpretability more difficult. In this paper, the ideas of Kuhn and Johnson(2013) on managing this trade-off are followed. Thus, if a model is created to make someprediction, it should not be constrained by the requirement of interpretability and/orsignificance 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 Angolan banks, most of the studiespreviously presented aimed to explain the factors affecting efficiency (using bootstrappedtruncated and Tobit regressions, for example), yet no predictive analysis has been done, inthe sense of pushing up the predictive limits of the model. Whereas the prediction of bankperformance is extremely important, poor performance may lead to bankruptcy. Thus,conceiving a predictive model for bank performance would be useful in avoiding or atleast limiting such undesirable consequences to customers. Therefore, this study alsoproposes the use of contextual variables to predict banking performance. Morespecifically, neural networks are trained to assess how contextual variables could be usedas predictors of efficiency levels in Angolan banks. Emerging literature exists thatcombines MCDM results (TOPSIS included) from the first stage, with variations on theneural network architecture from the second stage, for predictive modelling in severalareas of knowledge (Azadeh et al., 2014). For example, Sheu (2008) combined TOPSIS,among other MCDM techniques, and neural networks, based on fuzzy logic, for selectingthe most adequate global logistics management system. Yan et al. (2012) first usedTOPSIS to determine the synthetic scores of different companies’ business informationsystems, and then applied neural networks to predict them from 18 different partialindicators. Recently, Koyee et al. (2014) used TOPSIS to overcome the conflict betweenthe need to minimise production cost and to maximise the production rate inmanufacturing, and then neural network-based models were developed to study themajor variables that affected this trade-off.

Artificial neural networks are one of the frequently used learning models for prediction(Jagric and Strasek, 2005; Ledolter, 2013). An artificial neural network is inspired by the



structure of biological neural networks where neurons are interconnected and learnedfrom experience. Neural networks are composed of nodes (neurons) arranged in layersthat are fully connected with the preceding layer via a system of weights (Simons, 1996;Gurney, 1997). Numerous different neural network architectures have been studied.However, the most successful applications of neural networks have been multilayerfeed-forward networks (Fausett, 1994). These are networks in which there is an inputlayer, one or more hidden layers and an output layer. The next step is to apply a transferfunction to this sum; the most popular transfer function is the logistic function. Finally,the output layer obtains input values from the hidden layer, and the same transferfunction is applied to create the output. Readers should refer to Shmueli et al. (2010) formore details.

The neural networks have important parameters that cannot be directly estimatedfrom the data. These parameters are usually referred to as tuning parameters because thereis no analytical formula available to calculate an appropriate value for them (Kuhn andJohnson, 2013). Cross-validation may be used to control the choice of the tuningparameters, thereby avoiding what is called over-fitting. Over-fitting refers to a situationin which the model learns the structure of the data set so well that when the model isapplied to the original data it correctly predicts every sample (Kuhn and Johnson, 2013).This type of model is said to be over-fit and will usually have poor accuracy whenpredicting a new sample (James et al., 2013).

Hence, cross-validation allows the assessment of the accuracy profile for a given modelacross the candidate values of the tuning parameter (Kuhn and Johnson, 2013). In suchcases, it is very common to find that accuracy rapidly increases with the tuning parameter,and then after the peak decreases at a slower rate as over-fitting begins to manifest. Thebest model is then chosen based on the numerically optimal value of the tuningparameter, i.e. the one that yields the highest accuracy. The number of hidden layers andthe decay rate (weights) are tuning parameters frequently used in neural networks (Torgo,2011).

4.4 On Global Separability and the Adequacy of the Two-Stage ApproachSimar and Wilson (2011) examined the widespread practice where efficiency estimates areregressed on some environmental variables in what is commonly known as a two-stageanalysis. In a broader sense, the authors argue that this is done without specifying astatistical model in which such structures would follow from the first stage where theinitial DEA estimates are obtained. As such, these two-stage approaches are not structural,but rather ad hoc. The most important underlying assumption regarding two-stageanalysis is the one on global separability (Kourtesi et al., 2012). The next paragraphsdetail this assumption.

In general lines, the vector of environmental factors or contextual variables, Z, mayeither affect the range of attainable values of the inputs and the outputs (X ,Y),including the shape of the production set, or it may only affect the distribution ofinefficiencies inside a set with boundaries not depending on Z (meaning that only theprobability of being less or more far from the efficient frontier may depend on Z) orboth (Badin et al., 2012). Under separability, the environmental factors have noinfluence whatsoever on the support of XY, and the only potential remaining impact ofthe environmental factors on the production process may be on the distribution of theefficiencies.



To understand the importance of the “separability” condition, let X ∈ Rp + denote avector of p input quantities, and let Y ∈ Rq + denote a vector of q output quantities. Inaddition, let Z ∈ Z ⊆ Rr denote a vector of r environmental variables with domain Z. LetSn = {(Xi, Y i,Zi)}ni = 1 denote a set of observations. The separability assumption inSimar and Wilson (2011) implies that the sample observations (Xi, Y i,Zi) in Sn arerealisations of identically, independently distributed random variables (X, Y ,Z) withprobability density function f(x, y, z), which has support over a compact setP ⊂ Rp+q+ × Rr with level sets P(z) defined by P(z) = {(X, Y) | Z = z, X can produce Y}.Now let F = U P(z) ⊂ Rp+q, z ∈ Z. Under the “separability” condition,P(z) = F ∀ z ∈ Z, and hence P = F × Z. If this condition is violated, then P(z) is differentthan F for some z ∈ Z. Whether this is the case or not is ultimately an empirical questionto be assessed within the ambit of each research.

Daraio et al. (2010) provided a method for testing H0: P(z) = F ∀ z ∈ Z vs.H1: P(z) is different than F for some z ∈ Z. In order to test these null hypothesis,consider the test statistics τ Frontier n n Frontier i Frontier ii

nS n D D, , ,( ) = ≥−=∑11 0��′ , where

D Y X Y S Y X Y Z SFrontier i i Frontier i i n i Frontier i i i n, , , ,� � �= ( ) − (λ λ ))( ) and its complementary

D Frontier i′ ,� are (q × 1) vectors. This statistics give estimates of the mean integrated squaredifference between P and F × Z. If separability assumption holds, we should expect thesestatistics to be “close” to zero; otherwise, we should expect them to lie “far” from zero.

In this research, an R code was structured upon the packages np (Hayfield and Racine,2008) and FNN (Beygelzimer et al., 2015) to compute this test statistics. In situationswhere the “separability” condition is satisfied, it would be straightforward to perform thesecond stage analysis. For instance, one might estimate the model regression model by themaximum-likelihood method using standard software (Simar and Wilson, 2011).Besides, readers should pay attention to the fact that under standard assumptions, whereproperties of traditional DEA estimators have been derived, the mass of estimates equalto one may negatively affect this test statistic, leading to values far from zero.

5. RESULTS AND DISCUSSION

The efficiency levels calculated for 15 selected Angolan banks from 2006 to 2012 usingthe TOPSIS approach and considering different grouping criteria are given in Figs. 2and 3; additionally, the complete efficiency ranking is presented in the Appendix.Importantly, although median efficiency levels are quite stable over the period analysed,there are substantial differences when efficiency levels are grouped by bank. Forinstance, efficiency tends to be significantly smaller in BPC, a savings bank, whencompared with Banco de Desenvolvimento de Angola, an investment bank. Thissuggests the eventual impact of contextual variables that may be embedded withindifferent types of banks.

A robustness analysis was performed in order to compare the TOPSIS scores with thosecomputed from the traditional BCC (Banker et al., 1984) and CCR (Charnes et al., 1978)models (cf. Fig. 4). The major idea is not only to assess whether the TOPSIS methodincreases the discriminatory power of the analysis against the efficient frontier but alsowhether their scores are less symmetrical around the mean when compared with thetraditional models, in order to increase contrasts for the subsequent neural networkanalysis.



The mean overall efficiency scores in the TOPSIS method is 0.56, whereas thetraditional BCC and CCR models presented mean values of 0.95 and 0.91, respectively.This result suggests that the discriminatory power of the TOPSIS method is higher thanthose observed in traditional models because their scores are lower. The impact ofTOPSIS efficiency modelling can be also found in other statistical properties derivedfrom the frequency distribution of efficiency estimates in both models. Skewness is fartherthan zero (0.829 against −0.569 (BCC) and −0.298 (CCR)), suggesting that in theTOPSIS method, efficiency scores are not symmetrical around the mean, favouring theneural network analysis. Nevertheless, Spearman rank correlations between efficiencyscores derived from traditional DEA models and the TOPSIS method were found to beextremely high and significant at 0.01 (0.63 and 0.60 in the CCR and BCC cases,respectively), thus suggesting isotonic results for both models.

Now, as regards the contextual variables and test of global separability (Daraio et al.,2010), the empirical value of the test statistic for the TOPSIS scores was not only foundto be close to zero (0.0639) but also to be inferior than the test values on the BCC (0.131)and the CCR frontiers (0.085). As expected, this test value goes far from zero in caseswhere estimates are biased towards one (cf. Fig. 4). Global separability, therefore, appearsto be consistent with the use of TOPSIS on the sample data to the detriment of DEAmodels. This suggests that the contextual variables considered here affect only thedistribution of efficiencies and not the attainable input/output combinations (or theshape of the underlying production set).

Besides, a robustness analysis was also performed before running the neural networkanalysis. More precisely, TOPSIS scores were regressed against the set of contextualvariables presented in Table 3 using Tobit regression (see Moyo, 2012, for instance, forfurther details on Tobit regression). The results, presented in Table 4, indicate thatcost of operations and bank origin (whether Portuguese or South African) present anegative impact on efficiency levels. It appears that banks with a Portuguese originare slightly more inefficient than banks with a South African origin. The cost ofoperations, however, seems to overshadow the origin effect. Although weak in terms ofsignificance, international banks and cost of capital also merit attention due to theirpositive impact.

Figure 2. Angolan banking efficiency levels grouped by year



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Next, a neural network analysis was performed on the TOPSIS efficiency scores, usingthe contextual variables presented in Section 4 as their predictors. All steps taken followedthose presented in Faraway (2006) and in Kuhn and Johnson (2013). When differentcross-validation measures are applied and different numbers of hidden layers areconsidered, a clear picture emerges with respect to the response bias or the over-fittingwithin each predictive technique. Fig. 5 illustrates the apparent root mean squared error(RMSE), which tends to increase with the number of hidden layers of the neural network.This result clearly suggests a negative response bias towards a larger number of hiddenlayers.

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Additionally, Fig. 6 illustrates that a common pattern within the cross-validationmethods is seen where RMSE is smaller for lower hidden layer values and peaks at highervalues in the context of this particular neural network. The most accurate neural networkobtained (RMSE = 0.0344) used the 10-fold cross-validation technique, for one hiddenlayer and a decay rate of 0.0178. This signifies a mean error rate of 3.44% points if weconsider the efficiency scale ranging from 0% to 100%.

The relative importance of each contextual variable is given in Fig. 7. As regardsTOPSIS efficiency scores, the top five predictors for the neural networks of Angolan

Table 4. Tobit regression results

Coefficients Estimate Std. error z Value Pr(>|z|)

(Intercept) 0.6304194 0.0362061 17.412 <2e-16***Portuguese banks −0.0476679 0.0099756 −4.778 1.77e-06***Cost of operations −0.4492618 0.1281072 −3.507 0.000453***South African banks −0.0395065 0.0135360 −2.919 0.003516**International banks 0.0184820 0.0117456 1.574 0.115597Cost of capital 0.0034254 0.0021793 1.572 0.116005Cost of labour −0.1367835 0.0941480 −1.453 0.146264Public banks −0.0139993 0.0110678 −1.265 0.205918Trend 2 −0.0009323 0.0008908 −1.047 0.295312Cost of cash reserves 0.1719180 0.2947670 0.583 0.559736Trend 0.0041848 0.0073472 0.570 0.568965Log (scale) −3.4591114 0.0690066 −50.127 <2e-16***

Signifi. codes: 0 “***”, 0.001 “**”, 0.01 “*”, 0.05 “.”.Scale: 0.03146.Gaussian distribution.Number of Newton–Raphson iterations: 4.Log-likelihood: 214.2 on 12 df.Wald statistic: 61.24 on 10 df, p-value: 2.1132e-09.

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Figure 6. Cross-validated performance profiles over different values of the tuning parameter

Figure 7. Relative importance of contextual variables



banks are variables related to the banking cost structure (cost of operations, cost of labourand cost of cash reserves) and origin (whether Portuguese or South African). Note thatcost structure explains a substantial part of efficiency indicators in Angolan banks, whileownership tends to present a limited impact on efficiency levels when compared with thecultural origins. The remainder cost structure variable, cost of capital, presented anegligible impact on efficiency, as did the variable for capturing the time trend.

Fig. 8 presents the sensitivity analysis on the TOPSIS efficiency estimates for the bestneural network model. Contextual variables were standardised before performing thismarginal analysis, as suggested in Faraway (2006). The numbers on the vertical axesrepresent the sensitivity analysis for the predicted relationship between the outcome(efficiency) and the standardised predictors (contextual variables), using the artificialneural network model (while maintaining all other standardised predictors at their meanvalue, i.e. zero). Both the magnitude of the scales on the vertical axis and their variationintervals are related to the maximum and minimum TOPSIS scores. The similitude of thevertical axis for different predictors or contextual variables is related to theirstandardisation. However, their marginal variation with respect to the unit (holding allother predictors at their mean value) should be interpreted in terms of the magnitude ofthe values of the horizontal axis, which tends to vary substantially, depending upon thepredictor.

Results confirmed the signs found in Tobit regression results, despite their significancelevels and relative importance, as measured by the regression coefficients. A negativeimpact of cost structure – labour and operations – is discernible on efficiency levels,although the cost of cash reserves, when considered in an isolated fashion, presented apositive impact due to a greater parsimony and smaller risk assumed in loans. As regardsownership and cultural origin, it is interesting to note the negative impact of publicownership, in addition to Portuguese and South African origin, on efficiency levels, whileother international ownerships present a positive impact. This suggests that efficiencylevels in Angolan banks tend to be low compared with their North American andEuropean counterparts, possibly a result of low competition between the Portuguese andSouth African banks that dominate the market until very recently. It is also possible thatthese lower efficiency levels may be derived from the inexistence of a learning curve forbanking operations in Angola because the trend impact was found to be marginal. Thisfact is evident from a simple visual inspection of the scale of the vertical axis of the firstgraph in the first row of Fig. 8. As a matter of fact, in this case, scores presented variationin the sixth decimal place.

6. CONCLUSION

This paper presents an analysis of the efficiency of Angolan banks using TOPSIS andneural networks. TOPSIS enables a ranking of the efficiency of the banks analysed, andbased on such ranking a high variation in bank efficiency can be discerned. Banco deDesenvolvimento de Angola, a public bank that finances investments in “strategic longterms” is ranked first with a score in 2012 of 0.69, which, relative to the frontier of bestpractices – a value equal to 1 signifies 100% efficiency – presents an inefficiency level of1 − 0.69 = 0.31. The least efficient bank is BPC, a Sonangol bank that in 2012 scored0.40. Thus, the efficiency of the Angolan banking system is low when compared with USand European banks. Causes for this result may stem from the operational procedures of



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the banks analysed or the model adopted. Therefore, no single definitive conclusion maybe derived and further research is necessary to confirm these results. Assuming the resultsare exclusively due to bank procedures, banks should review them and benchmark theirpractices against US and European banks in order to increase efficiency.

Based on the neural network results, it is possible to explain several correlates ofinefficiency. The major factor relates to the cost structure and the origin of the bank.Therefore, high costs explain the low efficiency of Angola banks, although the cost of cashreserves, when considered in an isolated fashion, presented a positive impact. This may beexplained by the smaller risk assumed in loans. Additionally, bank origin also patternswith efficiency, signifying that cultural traditions are positively related to efficiency. Theneural networks also predict a negligible impact of trend on efficiency levels, suggestingthat Angolan banks do not learn from their operational procedures, i.e. their learningcurves are somewhat limited due to low competition.

Decision makers could benefit from these results by establishing an action plan overthe course of time so that Angolan banks could increase in efficiency, based on theirdistinct characteristics. For example, while banks with Portuguese or South Africanorigins could implement continuous improvement programmes on their operations sothat they would benefit from a learning curve over the course of time, regulators of publicbanks could consider difference governance mechanisms with private stakeholders so thatthese banks could close their efficiency gap with private ones. Opportunities forrightsizing the operations should also be explored so that the negative impact of the costof labour and operations on efficiency levels could be kept under control.

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APPENDIX

Efficiency RankingYear Name TOPSIS score Ranking

2012 Banco_de_Desenvolvimento_de_Angola 0.69 12011 Banco_de_Desenvolvimento_de_Angola 0.67 22010 Banco_de_Desenvolvimento_de_Angola 0.67 32009 Banco_de_Desenvolvimento_de_Angola 0.66 42008 Banco_de_Desenvolvimento_de_Angola 0.66 52007 Banco_de_Desenvolvimento_de_Angola 0.65 62006 Banco_de_Desenvolvimento_de_Angola 0.65 72008 Banco_Privado_Atlantico 0.64 82007 Banco_Privado_Atlantico 0.64 92006 Banco_Privado_Atlantico 0.64 102009 Banco_Espirito_Santo_Angola 0.60 112010 Banco_Espirito_Santo_Angola 0.60 122011 Banco_Sol 0.59 132009 Banco_Poupança_e_Crédito 0.58 142008 Banco_Espirito_Santo_Angola 0.58 152010 Banco_Poupança_e_Crédito 0.58 162012 Banco_Comercial_Angolano 0.57 172009 Banco_Angolano_de_Investimentos 0.57 182012 Banco_Millenium_Angola 0.57 192007 Banco_Poupança_e_Crédito 0.57 202010 Banco_Angolano_de_Investimentos 0.57 212007 Banco_de_Negócios_Internacional 0.57 222006 Banco_de_Negócios_Internacional 0.57 232008 Banco_de_Negócios_Internacional 0.57 242011 Banco_Espirito_Santo_Angola 0.57 252009 Banco_de_Negócios_Internacional 0.57 262008 Banco_BIC 0.57 272010 Banco_de_Negócios_Internacional 0.56 282008 Banco_Comercio_e_Industria 0.56 292006 Banco_Espirito_Santo_Angola 0.56 302011 Banco_Angolano_de_Investimentos 0.56 312009 Banco_Privado_Atlantico 0.56 322011 Banco_de_Negócios_Internacional 0.56 332012 Banco_BIC 0.56 342007 Banco_Espirito_Santo_Angola 0.56 352010 Banco_Sol 0.56 362010 Banco_Privado_Atlantico 0.56 372011 Banco_Millenium_Angola 0.56 382012 Banco_de_Negócios_Internacional 0.56 392010 Banco_Comercio_e_Industria 0.56 402010 Banco_BIC 0.56 41



Year Name TOPSIS score Ranking

2012 Banco_Caixa_Geral_Totta_de_Angola 0.56 422009 Banco_Comercio_e_Industria 0.56 432011 Banco_Privado_Atlantico 0.56 442007 Banco_Comercio_e_Industria 0.56 452009 Banco_BIC 0.56 462006 Banco_Millenium_Angola 0.56 472008 Banco_Regional_do_Keve 0.56 482012 Banco_Angolano_de_Investimentos 0.56 492006 Banco_Regional_do_Keve 0.56 502009 Banco_Sol 0.56 512012 Banco_Privado_Atlantico 0.56 522008 Banco_Millenium_Angola 0.56 532011 Banco_Comercial_Angolano 0.56 542006 Banco_Comercio_e_Industria 0.56 552006 Banco_Sol 0.55 562008 Banco_Comercial_Angolano 0.55 572008 Banco_Sol 0.55 582006 Banco_Angolano_de_Investimentos 0.55 592009 Banco_Caixa_Geral_Totta_de_Angola 0.55 602009 Banco_Comercial_Angolano 0.55 612010 Banco_Regional_do_Keve 0.55 622011 Banco_Regional_do_Keve 0.55 632009 Banco_Millenium_Angola 0.55 642007 Banco_Comercial_Angolano 0.55 652009 Banco_Regional_do_Keve 0.55 662006 Banco_Comercial_Angolano 0.55 672012 Banco_Regional_do_Keve 0.55 682006 Banco_BAI_Microfinanças 0.55 692010 Banco_Caixa_Geral_Totta_de_Angola 0.55 702006 Banco_Poupança_e_Crédito 0.55 712012 Banco_Sol 0.55 722007 Banco_Millenium_Angola 0.55 732007 Banco_Caixa_Geral_Totta_de_Angola 0.55 742007 Banco_Angolano_de_Investimentos 0.55 752008 Banco_de_Fomento_Angola 0.55 762007 Banco_BAI_Microfinanças 0.54 772006 Banco_Caixa_Geral_Totta_de_Angola 0.54 782011 Banco_Comercio_e_Industria 0.54 792011 Banco_BAI_Microfinanças 0.54 802012 Banco_de_Fomento_Angola 0.54 812012 Banco_BAI_Microfinanças 0.54 822008 Banco_BAI_Microfinanças 0.54 832012 Banco_Comercio_e_Industria 0.54 842010 Banco_Comercial_Angolano 0.54 852009 Banco_BAI_Microfinanças 0.54 862009 Banco_de_Fomento_Angola 0.54 872007 Banco_Sol 0.54 882008 Banco_Angolano_de_Investimentos 0.53 892007 Banco_Regional_do_Keve 0.53 902008 Banco_Poupança_e_Crédito 0.53 912010 Banco_BAI_Microfinanças 0.53 922011 Banco_Caixa_Geral_Totta_de_Angola 0.53 932010 Banco_Millenium_Angola 0.53 942006 Banco_BIC 0.53 952011 Banco_BIC 0.52 962010 Banco_de_Fomento_Angola 0.52 972006 Banco_de_Fomento_Angola 0.52 982007 Banco_de_Fomento_Angola 0.51 992011 Banco_Poupança_e_Crédito 0.51 1002007 Banco_BIC 0.50 1012012 Banco_Espirito_Santo_Angola 0.49 1022008 Banco_Caixa_Geral_Totta_de_Angola 0.49 1032011 Banco_de_Fomento_Angola 0.45 1042012 Banco_Poupança_e_Crédito 0.44 105



Predicting Efficiency in Angolan Banks: A TwoStage TOPSIS ... · central bank, BPC (Banco de...

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