MBA Managerial Economics: Analyzing the 2008 Crisis & UAE Banks

This case study examines the impact of the 2008 global financial crisis on the banking sector of the United Arab Emirates (UAE). It aims to provide an in-depth understanding and application of managerial economics concepts to analyze the economic challenges faced by the UAE during and after the crisis. The study explores the causes of the crisis, its specific impact on UAE banks (identifying affected institutions), the broader economic market effects, and the consequences for bank employees, including terminations. It employs a problem-solving approach, identifying alternative options, supporting data, and both quantitative and qualitative evaluations to assess the crisis's effects and potential recovery strategies. The analysis considers technical, pure technical, and scale efficiency to provide a comprehensive view of the banking sector's performance during this period, referencing various research and methodologies such as Data Envelopment Analysis (DEA) to evaluate bank efficiency.

Review of International Business and Strategy
Efficiency of Gulf Cooperation Council Banks: Empirical evidence using Data
Envelopment Analysis
Peter A Aghimien Fakarudin Kamarudin Mohamad Hamid Bany Noordin
Article information:
To cite this document:
Peter A Aghimien Fakarudin Kamarudin Mohamad Hamid Bany Noordin , (2016),"Efficiency of Gulf
Cooperation Council Banks", Review of International Business and Strategy, Vol. 26 Iss 1 pp. 118 -
136
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Efficiency of Gulf Cooperation
Council Banks
Empirical evidence using Data
Envelopment Analysis
Peter A. Aghimien
Department of Accounting, Indiana University South Bend, South Bend
Indiana, USA, and
Fakarudin Kamarudin, Mohamad Hamid and Bany Noordin
Universiti Putra Malaysia, Serdang, Malaysia
Abstract
Purpose – This paper aims to investigate the efficiency level of Gulf Cooperation Council (G
on technical efficiency (TE), pure technical efficiency (PTE) and scale efficiency (SE). Both PT
represent the potential factors that influence the efficiency of the GCC banks.In total,43 GCC banks
were observed in this study over the period from 2007 until 2011.
Design/methodology/approach – The Data EnvelopmentAnalysis,a non-parametric method
using variable returns to scale under Banker,Charnes and Cooper model,was used with assets and
deposit (as input) and loan and income (as output).
Findings – On average, the results show that many GCC banks are operating within an opti
of efficiency.Nevertheless,the results also show managerialinefficiency in the use ofresources.
Furthermore, the results indicate that, while the larger banks (the 22 largest) tend to operat
returns to scale (CRS) or decreasing returns to scale, the smaller banks (the 21 smallest) are
to operate at either CRS or increasing returns to scale.
Research limitations/implications – Because of the chosen research method, the results
generalisation.Therefore,researchers are encouraged to test the propositions further.An additional
implication of the results is that it was able to identify some banks that may become potent
outside acquisition.
Practical implications – The findings should be usefulto banks in the GCC in increasing their
efficiencies and recognizing those with a potential for outside acquisition.
Originality/value – The findings are valuable because they will facilitate the maintenance o
banks in the GCC.This is necessary to enable the countries to maintain a healthy and sustaina
economy.
Keywords GCC banks, Scale efficiency, Technical efficiency, Pure technical efficiency
Paper type Research paper
Glossary of terms
AE ⫽ allocative efficiency
AIE ⫽ allocative inefficiency
BCC ⫽ Banker, Charnes and Cooper
CRS ⫽ constant returns to scale
DEA ⫽ Data Envelopment Analysis
The current issue and full text archive of this journal is available on Emerald Insight at:
www.emeraldinsight.com/2059-6014.htm
RIBS
26,1
118
Received 2 November 2013
Revised 13 April 2014
Accepted 17 April 2014
Review of International Business
and Strategy
Vol. 26 No. 1, 2016
pp. 118-136
© Emerald Group Publishing Limited
2059-6014
DOI 10.1108/RIBS-11-2013-0111
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DFA ⫽ distribution-free approach
DMU ⫽ decision-making unit
DRS ⫽ decreasing returns to scale
FDH ⫽ free disposal hull
GCC ⫽ Gulf Cooperation Council
IRS ⫽ increasing returns to scale
MENA ⫽ Middle East and North Africa
PTE ⫽ pure technical efficiency
PTIE ⫽ pure technical inefficiency
SE ⫽ scale efficiency
SFA ⫽ stochastic frontier approach
SIE ⫽ scale inefficiency
TE ⫽ technical efficiency
TFA ⫽ thick frontier approach
TIE ⫽ technical inefficiency
UAE ⫽ United Arab Emirates
USD ⫽ US dollar
VRS ⫽ variable returns to scale
VRTS ⫽ variable returns to scale
WTO ⫽ World Trade Organisation
1. Introduction
The Gulf Cooperation Council (GCC) was established in an agreement completed on 25
May 1981 in Riyadh,Saudi Arabia.The GCC bloc comprises Bahrain,Kuwait,Oman,
Qatar, Saudi Arabia and the UAE. The six-member countries declared that the GCC is
established in view of the special relations, joint destiny, common objectives and also the
similarity of political systems based on Islamic beliefs between them.
The GCC has a well-financed economy through their oilmarkets since the 1970s
when the oil market boom began.To enhance and improve the economies of the GCC
countries,a well-functioning financial system is important for economic growth.The
links between financial intermediation and economic growth focus on the key functions
of financial systems in the saving-investment-growth nexus.Nissanke and Stein (2003)
assert that these include effective channelling of funds from surplus to deficit units and
ensuring an efficient transformation of funds into real productive capital. According to
Levine (1998),the efficiency of financialintermediation affects a country’s economic
growth and,at the same time,the bank (financialintermediation)could resultin
systemic crises which have negative consequences for the economy as a whole.The
financial intermediation also changes the maturity of the portfolios of investors while
providing sufficientliquidity to the system as the need arises.In addition,the
diversification and techniques ofrisk sharing may affectthe reduction ofrisks.
The banking sector in the GCC countries is one of the most important mechanisms of
their financial system. It is important to maintain a stable banking system for healthy
profitability and a sustainable economy to exist.
Nevertheless, there are many challenges that may significantly impact their ability to
grow and operate within a more competitive environment.First,the sector is heavily
dependent on oil sector activities. Oil still represents a very large portion of their export
earnings and budgetrevenues.As a resultof the over-dependence on oiland the
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dominance of the public sector, growth in the region remains vulnerable to the
of world oil prices.Investorshave uncoveredlimited profitableinvestment
opportunities in a few sectors such as real estate and stock market activities. T
banks have restricted their focus to lending mainly in consumer loans,realestate,
construction and trade finance.Second,GCC has reduced competitive pressure on
domestic banks through over-protection from foreign competition. However, GC
are expected to face massive competitive pressure from foreign banks,as they have
committed to liberalise many financialservices including banking through their
membership in theWorld TradeOrganisation (WTO).Finally,GCC banksare
experiencing a pressure to fulfil higher demanding international standards in te
risk management, capital adequacy and accounting practise.
The capability ofGCC banks to face allthese challenges willdepend on how
efficiently they are performing. However, there are very few researches on the
of the GCC banking sector. This study will investigate the technical efficiency (T
technicalefficiency (PTE)and scale efficiency (SE)of the GCC banks.Furthermore,
the technicalinefficiency (TIE)of the GCC banks could be discovered through pure
technical inefficiency (PTIE) or scale inefficiency (SIE). The PTE represents man
efficiency,while the SE refers to the scale or size ofoperation efficiency.The TE
measures the proportional reduction in input usage that can be attained if the
operates on the efficient frontier, or the effectiveness of the limited set of inpu
produce maximum outputs. TE is related to managerial factors (Isik and Hassan, 2002).
Meanwhile,PTE is the measurement of TE devoid of the SE (Sufian,2004 and Coelli
et al., 1998).
All theseinformation arevaluableand usefulto the investor,managerand
consumers.This study will also use the non-parametric Data Envelopment Analys
(DEA) method.Rickards (2003) discovered that, although widely used to evaluate
efficiency in the West,the DEA is less well known within the banking sector in the
developing countries including the GCC countries. This study attempts to fill th
via several investigations of the efficiency of GCC banks, using recent data (20
because there are very few studies that look into this issue. Additionally, this p
contributes in the methodology segment by using the DEA methods.
The paper is set out as follows:the next section provides the related literature in
regard to efficiency of banks all over the world and the use of DEA method in e
banks efficiency. Section 3 outlines the approach to the measurement of bank
and SE and data used to construct the efficiency frontiers. Section 4 discusses
and, finally, the paper concludes in Section 5.
2. Literature review
2.1 Technical, pure technical and scale efficiency
Ramanathan (2007) examined the performance of banks operating in the six c
the GCC. His study used the DEA method and used data, from year 2000-2004.
of the 55 banks are rated as efficient under constant returns to scale (CRS) or T
number of efficient banks nearly doubled to 27 under variable returns to scale
PTE and an additional 12 banks could not register unit CRS efficiencies due to t
limitation (also known as scale inefficiency).His analysis showed that the selected
banks in all the six countries have registered same efficiencies for 2000-2004.
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a significant increase in the TE of the selected banks in the GCC countries for the period
2000-2004.
Sufian et al.(2008) performed an analysis on the efficiency of Islamic banks using
empirical evidence from the Middle East and North Africa and Asian Countries. Using
the non-parametric DEA,they estimate three different types of efficiency measures,
namely,TE, PT and SE.The result shows that PTIE outweighs SIE in most Islamic
banks. Although Islamic banks have been operating at a relatively optimal scale, they
were managerially inefficient to exploit their resources to the fullest.
On the other hand,Hassan and Hussein (2003) studied the efficiency of the Sudanese
banking system during the period of 1992-2000.They applied a variety of parametric
and non-parametric DEA techniques to a panel of 17 Sudanese banks. They discovered
that the Sudanese banking system exhibited 37 per cent allocative efficiency (AE) and 60
per cent TE, suggesting that the overall inefficiency of the Sudanese Islamic banks was
mainly due to the TE (managerially related) rather than the AE (regulatory).
Yudistira (2004) provides an analysis of the efficiency levels of Islamic Banking in an
empirical analysis of 18 Islamic banks during the period of 1997-2000 which were made
available by the London-based International Bank Credit Analysis Ltd.’s BankScope
database. The sample are grouped by total assets in which banks with more than $600
million of assets are categorised as large size and banks below this level are categorised
as small-to-medium size. Concentrating on SE, it is clear that the largest degrees of SIE
come from large-size Islamic banks (i.e. DRS). It is interesting to note that all but one of
the large-size Islamic banks in 1997-1998 exhibited DRS,whilst in 1999-2000,most
large-size banks show CRS. The level of TIE in 1998 is more attributable to PTIE rather
than SIE.
Saaid (2003) investigates the X-efficiency (TE and AE) of 12 Sudanese banks using
Stochastic Frontier Approach (SFA).He asserts that the overall inefficiency could be
attributed moreon TIE rather than on allocativeinefficiency (AIE).Thus, the
inefficiency in the Sudanese Islamic banks could be associated more with input wasting
(TIE) rather than choosing the incorrect input combinations (AIE).
Drake (2001) finds that the big four UK banks suffer from DRS over the period of
1984-1995. However, X-efficiencies are exhibited by these banks and are similar to US
banking studies, which suggest that very large banks are likely to minimise their costs
better than their smaller counterparts. Evidently, the result shows that these banks have
higher TE and SE.
Size (SE) and technology are also important considerations. Research by Ferrier and
Lovell (1990), on a sample of 575 US commercial banks, found that 88 per cent exhibited
IRS (a resultwhich supports our choice ofthe VRTS variantof the DEA model).
Somewhatsurprisingly,the mostefficientbanks in the sample belonged to the
smallest-size class.This was attributed to the successfulapplication of technology,
which allowed smaller banks to overcome capitalcost disadvantages and distribute
products more effectively.The results prove thatthe banks were higher in PTE
compared to SE.
Furukawa (1996) finds that the major factor contributing to TIE is PTIE,not SIE.
This would suggest that size is not an important factor for Japanese banks to perform
efficiently. On the contrary, the recent study of Japanese banks by Drake and Hall (2003)
reveals powerful size-efficiency relationships between PTE and SE, explaining the logic
of the large-scale merger in the Japanese banking system.
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In conclusion, based on the literatures above, most of the International Islam
face similar problems where their PTIE outweighs SIE.In other words,although the
Islamic banks have been operating at a relatively optimal scale of operations, t
managerially inefficient to exploit their resources. On the other hand, the oppo
for the internationalconventionalbanks.Most of thesestudieshavepresented
inefficiency from the scale side (wrong scale of operations).
2.2 Data Envelopment Analysis applied
The earliest attempt to use DEA for banking was reported by Sherman and Gol
in the context of evaluating branches of bank. Subsequently, there are some st
applying the DEA method in measuring the banking sectors’ efficiency.
With experiences garnered from the USA,the use of DEA has become a popular
method in evaluating financial institutions’efficiency among banking researchers in
other nations. The DEA method has been used widely to evaluate banking insti
during the late 1980s and particularly in 1990s. Berger and Humphrey (1997) d
130 studies on the efficiency of the banking sector in 21 countries;116 of them were
published between 1992 and 1997.
In Asia, Fukuyama (1993 and 1995) is among the early researchers who ado
method to examine the efficiency of the banking sector in Japan. He found that
average to be around 0.86 and SE around 0.98, implying that the major source
PTIE (managerial inefficiency).
The DEA was also used by Alirezaee et al. (1998) to examine the bank branc
Canada using 1,282 data of banks.They suggest that the average branch efficiency
score varied inversely with the number of branches in the sample and directly
total number of inputs and outputs.
What is more, there are many studies that applied the DEA method to identi
efficiency of banks; for example, Golany and Storbeck (1999), Vassiloglou and
(1990),Sherman and Ladino (1995)and Kantor and Maital(1999)in the context of
evaluating branches of a bank.Meanwhile,other studies compare the performance of
the different banks in many countries using the DEA such as Darrat et al.(2002) in
Kuwait, Wheelock and Wilson (1999) in the USA, Saha and Ravisankar (2000) in
Stanton (2002) in Canada, Brown (2001) in Australia and Mercana et al. (2003)
3. Methodology
3.1 Sources of data
The present study gathers data from a list of the top 43 commercial GCC banks
2007-2011 (Table I).The primary source forfinancialdata is obtained from the
BankScope database produced by the Bureau van Dijk which provides the bank
balance sheets and income statements.BankScope database contains specific data on
25,800banks worldwide,includingcommercialbanks in the GCC countries.
Furthermore, BankScope database presents the original currencies’ data of the
countries and provides the option to convert the data to any other currencies.
are updated monthly. To maintain homogeneity, US Dollar (US$) is used in this
the study involves six countries in the GCC bloc.
3.2 Inputs, outputs, approaches and the choice of variables
The definition and measurement of bank’s inputs and outputs in the banking fu
remains arguable among researchers (Sufian,2007).To determine what constitutes
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Table I.
Top commercial
banks operating in
the GCC countries in
2007-2011
No. Bank Country
1 Arab Banking Corp Bahrain
2 Arcapita Bahrain
3 Gulf International Bank Bahrain
4 Investcorp Bahrain
5 Kuwait Finance House Bahrain
6 National Bank of Bahrain Bahrain
7 United Gulf Bank Bahrain
8 Ahli United Bank KSC Kuwait
9 Al-Ahli Bank of Kuwait Kuwait
10 Bank of Kuwait & Middle East Kuwait
11 Burgan Bank Kuwait
12 Commercial Bank of Kuwait Kuwait
13 Gulf Bank Kuwait
14 National Bank of Kuwait Kuwait
15 Bank Muscat Oman
16 National Bank of Oman Oman
17 Commercial Bank of Qatar Qatar
18 Doha Bank Qatar
19 Qatar Islamic Bank Qatar
20 Qatar National Bank Qatar
21 Al-Rajhi Banking & Invest Corp Saudi Arabia
22 Arab National Bank Saudi Arabia
23 Bank Al Jazira Saudi Arabia
24 Banque Saudi Fransi Saudi Arabia
25 National Commercial Bank Saudi Arabia
26 Riyad Bank Saudi Arabia
27 SAMBA Saudi Arabia
28 Saudi British Bank Saudi Arabia
29 Saudi Hollandi Bank Saudi Arabia
30 Saudi Invest Bank Saudi Arabia
31 Abu Dhabi Commercial Bank UAEUAE
32 Abu Dhabi Islamic Bank UAE
33 Bank of Sharjah UAE
34 Commercial Bank of Dubai UAE
35 Dubai Islamic Bank UAE
36 Emirates Bank International PJSC UAE
37 First Gulf Bank UAE
38 Union National Bank UAE
39 United Arab Bank UAE
40 Investbank UAE
41 Mashreqbank UAE
42 National Bank of Abu Dhabi UAE
43 National Bank of Dubai UAE
Source:Ramanathan (2007), Mostafa (2007) and BankScope database
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inputs and outputs of banks, one should first decide on the nature of banking t
(banks’ approaches). There are two main approaches that are widely used in th
theory literature,namely,production and intermediation approaches (Sealey and
Lindley,1977).The first approach is the production approach which assumes that
financial institutions serve as producers of services for account holders;that is,they
should perform transactions on deposit accounts and process documents such
Previous studies that adopted this approach are Ferrier and Lovell (1990),Fried et al.
(1993) and DeYoung (1997). The second approach is the intermediation approa
is a preferred approach among many researchers to apply in the first stage of t
analysis.This approach is ofthe opinion thatbanks basically actas financial
intermediaries whose primary role is to obtain funds from savers in exchange f
liabilities, and the banks, in turn, will provide loans to others for profit-making (
Lim,1998).The present study views the banks as intermediaries and it willapply
intermediation approach as well.
The intermediation approach is also known as an assetapproach,whereby the
financial firms are assumed to act as an intermediary between the savers and
Banks are seen as purchasing labour, materials and deposit funds that produce
of loans and investments.The inputs include interest expense,non-interest expense,
deposits, other purchased capital, number of staff (full time equivalent), physic
(fixed assets and equipment), demographics and competition. The potential ou
measured as the dollar value of the bank’s earning assets, where the costs incl
the interest and operating expenses (Berger et al., 1987). Under this approach
outputs are found on the asset side of the balance sheet and deposits are seen
Avkiran (1999)suggestedthat potentialoutputsincludenet interestincome,
non-interest income, consumer loans, housing loans, commercial loans and inv
Previous banking-efficiency studies that had adopted this approach include,among
others, Charnes et al. (1990), Bhattacharyya et al. (1997), Sathye (2001) and S
Habibullah (2009). They also applied different accounting standards. Thus, the
of the efficiency scores will be affected and may vary depending on the selectio
variables for each of the banks efficiency. The DEA method requires bank input
outputs whose choice is always an arbitrary issue (Ariff and Can, 2008 and Ber
Humphrey, 1997).
Because the issue of selecting approaches is still arbitrary, this study has de
use an intermediation approach because we assume a bank is more suitable to
classified as an intermediary entity. The GCC banks are modelled as multi-prod
producing two inputs and two outputs (Table II).Outputs consists of total loans (y1),
which includes short-term loan and long-term loan and income (y2),which includes
income derived from investment of depositors’funds and other income from banking
operations.There are two inputs,namely,totalassets (x1),which include cash and
short-term funds and other assets,and deposits (x2),which include deposits from
customers and from other banks. All variables are measured in US Dollars (Tab
Table II.
Output and input
variables
Output Input
y1: Total loans x1: Total assets
y2: Income x2: Deposit
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3.3 Method of measurement
There are two different frontier analysis methods which focus on measuring a bank’s
efficiency, namely, the non-parametric and parametric methods (Berger and Humphrey,
1997).The most commonly used non-parametric approaches are the DEA and Free
DisposalHull (FDH),while for the parametric approaches are SFA,Thick Frontier
Approach (TFA)and Distribution-FreeApproach (DFA).According to Murillo-
Zamorano (2004), the choice of estimation approach has attracted debate, as no method
is strictly preferable over the other.Nevertheless,due to its several advantages,this
study will apply the DEA method.
There are six reasons why this study adopts the DEA method (Sufian,2007 and
2004). First, each decision-making unit (DMU) is assigned a single efficiency score that
allows ranking amongst the DMUs in the sample. Second, the DEA highlights the areas
of improvement for each single DMU such as either the input has been excessively used
or output has been under produced by the DMU (so they could improve on efficiency).
Third, there is a possibility of making inferences on the DMU’s general profile. The DEA
allows the comparison between the production performances of each DMU to a set of
efficient DMUs (called reference set). Thus, the owner of the DMUs may be interested to
know which DMU frequently appears in this set. A DMU that appears more than others
in this set is called the global leader.Apparently,a DMU owner may obtain a huge
benefit from this information, especially in positioning its entity in the market. Fourth,
severalstudies suggest that the DEA does not require a preconceived structure or
specific functional form to be imposed on the data in identifying and determining the
efficient frontier,error and inefficiency structures of the DMUs (Bauer etal.,1998;
Evanoff and Israelvich,1991;Grifell-Tatje and Lovell,1997).Fifth,the DEA does not
Table III.
Summary statistics
of the variables input
and output in the
DEA model (in
million USD)
Year
Descriptive
statistics Loan (y1) Income (y2) Asset (x1) Deposit (x2)
2011 Min 30.700 5.950 322.507 125.913
Max 54,017.420 2,954.368 82,954.757 69,172.564
Mean 15,846.848 939.826 25,779.872 20,073.932
SD 13,424.152 783.064 21,559.059 17,405.487
2010 Min 34.212 1.426 231.290 86.244
Max 38,256.637 2,739.780 75,299.204 64,931.177
Mean 14,573.653 920.431 23,783.797 18,420.388
SD 11,497.315 750.079 18,876.693 15,181.320
2009 Min 50.907 4.533 300.558 127.615
Max 36,736.773 2,779.680 68,653.924 58,175.310
Mean 13,941.828 966.232 22,489.905 17,521.954
SD 10,753.566 735.521 17,363.273 14,074.479
2008 Min 7.800 9.784 344.628 131.183
Max 37,265.786 3,178.320 59,147.203 49,215.469
Mean 13,770.485 1,073.880 21,959.831 17,381.946
SD 10,368.568 801.027 15,975.606 12,880.195
2007 Min 50.916 8.059 413.553 158.608
Max 27,716.514 2,817.517 55,732.230 45,744.299
Mean 10,673.287 980.716 18,857.663 14,800.455
SD 7,926.643 733.803 13,723.864 11,192.612
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need standardisation,and this allows the researcher to choose any kind of input an
output of managerial interest (arbitrary), regardless of the different measurem
(Ariff and Can, 2008; Avkiran, 1999; Berger and Humphrey, 1997). Finally, the
suitable with a small sample.
3.4 Data Envelopment Analysis
The non-parametricDEA method wasused with theVRS model,to measure
input-oriented TE of the GCC banks.The VRS model was proposed by Banker et al.
(1984). The BCC model (VRS) extended the model proposed by Charnes et al. (
The CCR model presupposes that there is no significant relationship between
scale of operations and efficiency by assuming CRS and it delivers the OE or TE
CRS assumption is only justifiable when all DMUs are operating at an optimal s
However,firms or DMUs,in practice,might face either economies or diseconomies of
scale. Thus, if one makes the CRS assumption when not all DMUs are operating
optimal scale, the computed measures of TE will be contaminated with SIE.
Banker et al. (1984) extended the CCR model (CRS) by relaxing the CRS assu
The resulting BCC model was used to assess the efficiency of DMUs characteris
VRTS. The VRTS assumption provides the measurementof PTE, which is the
measurement of TE devoid of the SE effects. In fact, the TE measures the effici
the DMU’s management.The PTE measuresthe efficiency ofthe DMU’s pure
managerial without contamination by scale. Meanwhile, the SE measures the s
DMU. If there appears to be a difference between the TE and PTE scores of a pa
DMU, then it indicates the existence of SIE (Coelli, 1996 and Sufian, 2004).
The score of the TE will take a value between zero and one. If the score show
than one,it is indicating that the DMU is relatively technically inefficient and not
operating at the efficiency frontier. On the other hand, the DMU will be conside
fully technically efficient if the TE’s score shows the value of one (i.e. operating
efficiency frontier).
3.5 The constant returns to scale model under the CCR model
Assume there are data on K inputs and M outputs on each of N firms or DMUs.
i-th firm or DMU,these are represented by the column vectors xi and yi , respectively.
The K ⫻ N input matrix, X and the M ⫻ N output matrix and Y represent the dat
all N firms or DMUs. For each firm, we measure all outputs over all inputs in the
ratios as u=
yi/v=
xi, where u is an M ⫻ 1 vector of output weights and v is a K ⫻ 1 ve
of input weights. As such, the following mathematical programming is used to
optimal weight (Coelli et al., 1998):
maxu, v (u=yi/v=xi ),
subject to u=yj/v=xj ⱕ 1, j ⫽ 1, 2, …, N
u, v ⱖ 0.
(1)
One problem with this particular ratio formulation is that it has infinite number
solutions, as the original mathematical formulation is not linear. To avoid this,
impose the constraint v=xi, which provides:
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max␮,v (␮=yi ), t v=xi ⫽ 1,
subject to ␮=yj ⫺ v=xj ⱕ 0, j ⫽ 1, 2, …, N,
␮, v ⱖ 0,
(2)
Where the change of notation from u and v to␮ and v is used to stress that this is a
different linear programming problem. Using the dual form of the above problem, one
can derive an equivalent envelopment form as:
min␮, ␮ ␮,
subject to ⫺yi ⫹ Y ␮ ⱖ 0,␮xi ⫺ X ␮ ⱖ 0,␮ ⱖ 0,
(3)
Where:␮is a scalar; and␮is a N⫻1 vector of constant.
This envelopmentform involves fewer constraints than the multiplier form (K ⫹
M ⬍ N ⫹ 1), and hence, is generally the preferred form to solve (Coelli et al., 1998).
3.6 The variable returns to scale model and scale efficiency under the BCC model
3.6.1 The variable returns to scale model. The CRS linear programming problem could
be simply modified to account for VRS by adding the convexity constraint: N1=␮⫽ 1 to
equation (3) to provide (Coelli et al., 1998):
min␮, ␮ ␮,
subject to ⫺yi ⫹ Y ␮ ⱖ 0,␮xi ⫺ X ␮ ⱖ 0,
N1=␮ ⫽ 1␮ ⱖ 0,
(4)
Where: N1 is an N⫻1 vector of ones.
This approach forms a convex hull of intersecting planes which envelope the data
points more tightly than the CRS conical hull and thus provides TE scores which are
greater than or equal to those obtained using the CRS model.
3.6.2 Calculation of scale efficiencies.TE scores obtained from a CRS DEA can be
divided into two components,one due to SIE and one due to the PTIE.This may be
completed by conducting both a CRS and a VRS DEA upon the same data. If there is a
difference in two TE scores of DMU, it indicates that the DMU has SIE and the SIE could
be measured from the difference between the VRS TE (PTE) score and CRS TE (TE)
score (Coelli et al., 1998). Although the SE measure will provide information concerning
the degree of inefficiency resulting from the failure to operate with CRS,it cannot
provide the information as to whether a DMU is operating in an area of increasing
returns to scale (IRS) or decreasing returns to scale (DRS). This may be determined by
running an additionalDEA problem with non-increasing returns to scale (NIRS)
imposed. This can be done by altering the DEA model in equation (4) by substituting the
N1=␮⫽ 1 restriction with N1=␮ⱕ 1, to provide:
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Cooperation
Council Banks
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min␮, ␮ ␮,
subject to ⫺yi ⫹ Y ␮ ⱖ 0,␮xi ⫺ X ␮ ⱖ 0,
N1=␮ ⱕ 1␮ ⱖ 0,
(5)
Therefore,the nature of the scale inefficiencies,due to either IRS or DRS,could be
determined by the difference between the NIRS TE and VRS TE score: if the VR
PTE ⫽ NIRS TE, then the DMU is operating at IRS (point B) and if the VRS TE @
PTE ⫽ NIRS TE, then the DMU is operating at DRS (point D) in Figure 1.
4. Result and discussion
This section will discuss the TE change of the GCC banks that is measured by t
method and its decomposition into PTE and SE components.In the eventof the
existence of SIE, this study could provide evidence on the nature of the returns
of each bank.
According to DeYoung and Hasan (1998),Bauer et al.(1998) and Isik and Hassan
(2002),constructing an annual frontier specific to each year is more flexible and
suitable than estimating a single multiyear frontier for the banks in the sample
on the earlier studies, for the purpose of this study, separate annual efficiency
for each yearis morepreferable.Therefore,therewerefive separatefrontiers
constructed for the study. According to Isik and Hassan (2002), the principal ad
of having panel data is the ability to observe each bank more than once over a
time. The issue is also critical in a continuously changing business environmen
the technology of a bank that is most efficient in one period may not be the mo
Figure 1.
Calculation of scale
economies in DEA
RIBS
26,1
128
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