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Efficiency In Banking Sector Hong Kong Commercial Banks Finance Essay

This paper investigates a panel of commercial day-of-the-week effect in Chinese stock market by different market orientations. Empirical result reveals that there is a significant Tuesday effect in the Chinese stock market in each examined sub-periods. However, this Tuesday effect show contrary pattern in non-bear market period and bear market period. Positive Tuesday returns are observed in bear market period while negative Tuesday returns are found in non-bear market period. In the test of the full periods from 1995 to 2009, a significant negative Thursday effect instead of a Tuesday effect is observed. Similar Thursday effect is also found in the period over 2005 to 2009. Additionally, the week-of-the-month effect and the spillover effect as two potential explanations for the day-of-the-week effect are tested. Parameter estimates present a lower level of day-of-the-week effect. However, the day-of-the-week effect in Chinese stock market is found to be robust even after controlling for the week-of-the-month effect and the spillover effect.

Chapter 1. Introduction

Hong Kong has one of the largest representations of international banks in the world: about three-quarters of the world's 100 largest banks have a presence there. Hong Kong is a top-ten international banking centre in terms of the volume of external transactions, and the second largest in Asia after Japan. The banking sector plays a vital role in establishing Hong Kong as a major loan syndication centre in the region. The Hong Kong banking system has emerged from the financial crisis in much better shape than many of its counterparts in the US and Europe. According to the Hong Kong Monetary Authority, the aggregate capital adequacy ratio of the banking sector at the end of 2009 stood at 16.9% and the liquidity ratio at 47.8%. The classified loan ratio, despite an increase from 2008, remained low at 1.35% and other asset-quality indicators continued to be favourable. At the end of June, 2010, there were 146 licensed banks, 24 restricted licence banks and 27 deposit-taking companies in business. These 200 authorised institutions operate a comprehensive network of 1,600 local branches. In addition, there are 70 local representative offices of overseas banks in Hong Kong. Total Employment in the sector is around 80,000. Banking assets amount to more than HKD10 trillion.

The term of “efficiency” is used to describe the performance of the commercial banks. Efficiency refers to the utilization of resources in such a way as to maximize the production. A bank is classified as efficient when it cannot enhance its output without increasing inputs or cannot produce the same quantity of output by using less quantity of inputs. The efficiency of the bank can be measured in different years or in the same year. Normally, the efficiency of a commercial bank is usually measured in terms of minimization of inputs in order to produce a specific level of output or maximization of output given a certain level of inputs.

This paper aims to investigate the banking efficiency in Hong Kong using Data Envelopment Analysis (DEA). For measuring banking efficiency I use two indicators: (put those variables in your function here). Applying a panel data model, I will test whether (vector i.e. bank cost?) is a significant variable in the explanation of bank efficiency. Sample period of the data used in this paper is from 2005 to 2009. Original data set is obtained from DataStream and Banksgroup.

The paper continues as follows. In the next chapter I present some features of the banking system in Hong Kong. In chapter 3, I will explain the methodology and the data used in this paper. The empirical result is shown in chapter 4 and followed by conclusion shown in chapter 5.

Chapter 2. Background

2.1 Review of Banking Sector in Hong Kong

The banking sector plays an important role in the service-based economy of Hong Kong. Its value-added has been growing steadily over the past decade, from about 5½ percent of GDP in 1990 to 8½ percent in 2001. At the same time, its share in total employment has declined from 2.6 percent in 1995 to 2.3 percent in 2002, reflecting strong productivity gains achieved through bank consolidation, rationalisation of branch networks and greater utilisation of electronic banking services. The sector contributed 16 percent of total profits tax in 2001, accounting for about 3 percent of government revenue. The banking sector provides worldwide services that enhance the international financial centre status of Hong Kong. Of the world’s 500 largest banks, 168 had operations in Hong Kong in 2002, while 107 of the 133 licensed banks in Hong Kong were incorporated outside Hong Kong. Before the Asian Financial Crisis in 1997, loans to customers outside Hong Kong accounted for over 50 percent of total lending. This share has declined substantially since then to 12 percent in 2002, largely reflecting the contraction in Euro-yen Impact Loans and reduced foreign currency borrowing by other economies in the region. 1 Banks in Hong Kong have also been active in the Asian syndicated loans market, arranging on average about 15 percent of total lending over the past six years. There have been some important changes in the operating environment of the banking sector in Hong Kong in recent years, which have affected its profitability. These include the effects of the Asian Financial Crisis in 1997, declining global inflation and interest rates, the ongoing consolidation of global banks, and persistent weak domestic economic conditions. The banking sector in Hong Kong has experienced significant changes in its operating environment in recent years. Both external and domestic factors have affected its performance and structure. Notable external developments include the effects of the Asian Financial Crisis in 1997, declining global interest rates and an ongoing process of consolidation by the big international banks. The Asian Financial Crisis was characterised by large capital outflows over a short period of time from the region, sharp depreciation in the exchange rates of several regional economies, widespread corporate bankruptcies owing to currency and maturity mismatches, and a number of banking sector crises. In Hong Kong, the number of non-performing loans by the banking sector rose substantially, and reduced regional financing flows resulted in a sharp drop in credits extended to outside customers and Asian syndicated lending arranged by banks in Hong Kong.

2.2 The Three – tier Banking system in Hong Kong

The banking system in Hong Kong is characterized by its 3-tier system, which is formed by 3 types of banking institutions, namely licensed banks, restricted licensed banks and deposit-taking companies, which are authorised to take deposits from the general public. The 3rd tier of deposit-taking institutions operate under different restrictions. Only licensed banks and restricted licensed banks can be called banks.

Hong Kong maintains a three-tier system of deposit-taking institutions, namely, licensed banks, restricted licence banks, deposit-taking companies. They are collectively known as authorized institutions. Hong Kong has one of the highest concentration of banking institutions in the world. Seventy of the largest 100 banks in the world have an operation in Hong Kong. At the end of December 2009, there were 145 licensed banks, 26 restricted licence banks and 28 deposit-taking companies. These 199 authorized institutions operate a comprehensive network of 1,293 local branches. Of these 199 authorized institutions, 180 are beneficially owned by interests from 29 countries. In addition, there were 71 local representative offices of overseas banks in Hong Kong at the end of December 2009.

Chapter 3. Literature Review

Given the importance attached to banks in the development financial market, research on the performance measurement of banking system has been conducted widely in the past decades. And there is an enormous growth in the literature on efficiency of banking system. The following part aims at giving a summary on this literature.

In 1990s, regression analysis was broadly applied in the efficiency measurement. For example, by using regression analysis, some relationship between efficiency and product diversity, bank size, urbanization, location, market power, profitability were observed by Rangan et al (1988), Aly et al (1990), Favero and Papi (1995), and Miller and Noulas (1996). Then in 2000s, different approaches, such as the non-parametric frontier methodology and the censored regression technique, appeared and rapidly dominated in studies on determinants of banking efficiency. Jackson and Fethi (2000) applied a two-step methodology in investigating the efficiency of the Turkish (TR) commercial banks. In their study, the Data Envelopment Analysis (DEA), which is a non-parametric frontier methodology, is first conducted to measure the technical efficiency of the 48 TR banks in 1998. Under the DEA model, the maximum of a ratio of outputs to weighted inputs is calculated to evaluate the efficiency of a bank. The DEA model Jackson and Fethi (2000) used in their study is as follows,

Model 1:

Subject to:

where c represents the evaluated bank, … n, s and m are the number of banks, outputs and inputs respectively. It is set as a constrain that any other banks in the sample could not have a larger than unit efficiency by applying the same weights. Then in order to converted model (1) to linear regression, another constrain that the denominator of model (1) equals to unity. So the linear version appears to be:

Model 2

Subject to:

r=1,…,s; i=1,…,m and j=1,…n

Here the maximum output measurement turns out to be an input-based efficiency evaluation. So Jackson and Fethi (2000) formulate a dual companion by using to represent the input weights of bank c and to represent the input and output weights of any other banks in the sample. So the maximize problem is formulated as follows,

Model 3

Subject to:

j = 1, …, n

Where bank c is regarded to be efficient when the input weights of bank c is one and the slacks equal to zero. DEA model could be applied with either constant returns to scale (CRS) assumption or variable returns to scale (VRS) assumption. In Jakson and Fethi’s study, the latter one is made. And this DEA efficiency scores are applied to evaluate the technical efficiency of a bank. However, the DEA scores fall between 0 to 1 that results in a limited dependent variable. So in the second step, Jackson and Fethi (2000) conducted the Tobit model, which is known as censored regression model, to catch out the features of the distribution of efficiency measures and explain the different efficiency scores. Following Tobit model that used by Luoma et al (1996), Chilingerian (1995) and Kirjavainen and Loikkanen (1998) in different areas, Jackson and Fethi (2000) constructed the model as follows:

Model 4

Where , and β are vectors of explanatory variables and unknown parameters, respectively. The is a latent variable and is the DEA score.

Since outputs and inputs are the major variables to determine efficiency in DEA model, the selection of proper indicators for outputs and inputs determines the accuracy of the model. There are three main approaches in previous literature, which named as production approach, intermediation approach (Berger and Humphrey, 1997) and profit-oriented approach (Drake et al., 2006). The production approach, which is used under the assumption that banks produce loans and deposit, treats number and type of accounts as outputs, and labour and capital as inputs. The intermediation approach assumes that as financial intermediates, banks “collect purchased funds and use labour and capital to transform these funds into loans and other assets” (Pasiouras, 2008). The profit-oriented approach is actually in the context of stochastic frontier approach, which is found to be better in handling competitive and environmental situations.

Based on the characteristics of TR banks, Jackson and Fethi (2000) choose the production approach. So loans, demand deposits and time deposits are selected to be outputs indicators and the number of employees, the sum of non-labour operating expense, direct expenditure on buildings and amortization expenses are treated as inputs indicators. And the DEA model is carried out for one sample that includes all the TR commercial banks and the other one that excludes the very large state-owned banks. Efficiency measurements are obtained and empirical results show little variation in different groups. By conducting the Tobit model, the effects of bank size, profitability, ownership and capital adequacy ratio on technical efficiency are tested. The results reveal that bank size and profitability have positive effect on technical efficiency while ownership and capital adequacy ratio show negative sign in TR commercial banks.

3.1

According to a journal named as “Banking efficiency in China: Application of DEA to pre- and post – deregulation eras: 1993 - 2000” abstracted in China Economic Review 16 (2005) 229 – 245. This paper uses three different efficiencies (cost, technical and allocative efficiency) of 43 Chinese banks over the period 1993 to 2000. The main purpose of this analysis is to identify the change in Chinese bank’s efficiency following the program of deregulation which introduced by the Chinese government in 1995. The result indicated that the medium sized Chinese banks are less efficient than the large – state – owned and smaller banks. During the research of the paper, technical efficiency consistently dominates the allocative efficiency of Chinese banks. It was found to improve the cost efficiency levels both technical and allocative efficiency in the financial deregulation of 1995. Starting from 1978, Chinese government put her overall effort to transform from a centralized economy into a market – based economy by initiating the bank reforms. This study has a closer examination of the efficiency of Chinese banks for number of reasons. First of all, bond and equity markets are not well developed in China. Thus it enhances the importance of the banking sector. Secondly, the deregulation of foreign entry under WTO increases the competition of the Chinese banks. Thirdly, China was the only economy in East Asia that not only avoided the 1997 / 1998 Asian financial crises but also continued to exhibit strong economic growth. At last, these findings of this paper may help the policy makers and the managers of Chinese banks to evaluate their competitive viability. Moreover, this paper also investigates whether size plays an important role in efficiency levels and whether deregulation has had its intended impact. The results show that the deregulation in 1995 had a positive impact on Chinese bank efficiency. Based on the results on bank size, the Chinese financial market is characterized by its diversity. On the other hand, four state – owned – commercial banks absorb more than 80% of total deposits whilst many small newly formed joint – equity banks and investment corporations now actively compete with the state – owned banks. After calculating the mean efficiency score, smaller banks show a relatively high efficiency level. While joint – equity banks have had less administrative pressure from the Chinese Government, thus the placed to lean quickly about advanced technology. So they expected to have a relatively high efficiency level. However, these banks are relatively new to the Chinese financial market. So they would require a relatively high initial setting up costs when compared with the more established existing banks. Therefore, they may take some time to gain the full benefit from their investment especially in the technology advancement. Consequently the largest Chinese banks appear to be the most efficient ones, follow by the small banks. Medium sized banks would seem to need more improvement in terms of both their technical and allocative efficiencies. To conclude this paper, by using the technical efficiency scores was estimated using the non – parametric DEA approach. Finally, when dividing the sample banks into national joint – equity banks, state – owned commercial banks, regional joint – equity banks and investment banks; state – owned commercial banks has the highest mean efficiency score. This is consistent with Zhao (2000) who found similarly that state banks showed a high efficiency level in 1999. This paper also concerned the bank size, the result shown that large and small banks are the most efficient. This is contradictory to the U.S. experience where the average cost curve has a flat U – Shape. Furthermore, the continuous domination of technical efficiency over allocative efficiency implies that Chinese banks need to improve their ability to choose cost minimization input combinations. Starting from 1990 to 1996, the overall efficiency of Chinese banks increased. However, due to the international and domestic factors, Chinese banking efficiency seems to drop gradually. These may influenced by the world wide economy slowdown, Asian financial crisis and a huge increase in non – performing loans to state – owned enterprises (SOEs).

3.2

According to a journal named as “Market structure and competitive conditions in the Arab GCC banking system” written in the Journal of Banking & Finance 30 (2006) 3487 – 3501, this paper used the most frequently applied measures of concentration k – bank concentration ratio (CRk) and Herfindahl – Hirschman Index (HHI) to investigate the market structure of Arab GCC banking industry during the years of 1993 – 2002. Using the “H – Statistic” by Panazar and Rosse, it measures the monopoly power of banks over the ten years period. This paper also aims to test the market structure of the GCC banking industry in the decade 2002 with the aim of evaluating the monopoly power of the bank over this period. Furthermore, the paper also investigates the relationship between the competitive conditions of the banks in these six Arabian economies using the most frequently applied measures of concentration; namely the k – bank concentration ratio (CRk) and Herfindahl – Hirschman Index (HHI) to measure concentration and the h – statistic of the Panzar – Rosse model to measure monopoly power. As a result of this research findings, this paper suggest that except in the case of Saudi Arabia and Kuwait, the banking market in the rest of the GCC has yet some way to go in developing a competitive structure if it is to face the forces of global banking competition.

The two stages methodology that applied by Jackson and Fethi (2000) is also adopted in the study of Greek commercial banks by Pasiouras (2008). While unlike Jakson and Fethi(2000), Pasiouras(2008) use both the intermediation approach and the profit-oriented approach in his five DEA models, and he derives both the technical efficiency scores and the scale efficiency scores. In his model 1, in line with the classic intermediation approach, fixed assets, customer deposits, short term funding and number of employees are selected as inputs indicators, and loans and other earning assets stand for outputs. Considering that banks are heavily participated in off-balance sheet activities, the model 2 involves off-balance sheet items in outputs indicators. Model 3 adds loan loss provisions as inputs indicators to present credit risk. Model 4 is a combination of all the indicators in model 1, 2 and 3. Model 5 followed the profit-oriented approach and employee expenses, no-interest expenses and loan loss provisions stand for inputs while net interest income, net commission income and other income present outputs. Empirical result over the period from 2000 to 2004 presents that off-balance sheet items do not show significant effect on the efficiency scores, while by including the loan loss provisions, the efficiency scores tend to be higher. It is also found in the study that the variation of efficiency scores derived from the two approaches is small. Pasiouras (2008) also examines the efficiency differences in banks with international presences and those only operate in domestic markets. Statistically, banks with international branches gain higher efficiency scores. However, this case is only significant in testing technical efficiency and by applying the intermediation approach. Then in the second step, Tobit analysis is applied as well to investigate the determinants of efficiency. Technical and scale efficiency scores which derived from the profit-oriented model and the full intermediation model are treated as dependent variables; while independent variables are examined by two groups. The first group is the bank financial items that contain equity to assets, return on average assets, loan to assets and market power; the other group is bank’s strategic items including the number of ATMs, the number of branches, and two dummy variables (whether the bank offer international service through subsidiaries or branches). In the analysis of bank financial items, capitalization, loan activity and market share are found to be significantly related to bank efficiency in all cases. While the significantly positive relationship between profitability and efficiency scores that gain from profit-oriented approach. Turning to the bank’s strategy items, empirical results reveal that the number of ATMs has no significant effect in any specifications, whereas the number of branches is distinguishable in all cases. And, the result of dummy variables analysis is mixed.

3.3

Based on the Journal named as “Efficiency comparison of operational and Profitability: A case of Hong Kong Commercial Banks” published in Journal of Social Sciences 4 (4): 280 – 287, 2008, the traditional DEA models mainly deal with measuring of relative efficiency of DMUs regarding multiple – inputs vs multiple outputs. One of the disadvantages of using these models is the neglect of intermediate products or linking activities. The main purpose of this research paper is to show how to use DEA by two stages; with outputs from the first stage becoming inputs in the second stage. (ii) the comparative analysis of efficiency of bank manageable in Hong Kong. By using the two stage Data Envelopment Analysis (DEA) from period 2004 – 2006, this research conducts a comparative analysis of efficiency of bank manageable in Hong Kong using two – stage model which evaluates their operational Efficiency (OE) and Profitability Efficiency (PE). The result of this study show that the two stage DEA method of analysis can help the bank to know deeply and clearly about their specific advantages and disadvantages at various stages. Besides, they can better indicate their own managerial efficiency. It is believed that these findings could provide practical help to banks by giving them the direction how to change their strategies to suit their particular circumstances. The result of this research: Smaller newer banks are generally less efficient than the larger older banks in the operational model. In contrast, smaller banks are classified as a zone of the stars such as Hang Seng and Public banks. This means that the smaller banks have relatively better competitive power than those large banks. At last, Hong Kong’s financial system will move forward business diversification and in the future, banks will continue to enhance their operational efficiency.

By adopting non-parametric approach DAE methodology, Tahir, Bakar and Haron investigate the differences of technical, pure technical and scale efficiencies of commercial banks in Malaysia during the period of 2000 and 2006. In their study, loans and investments represent output measures, and labour, deposits and capital are treated as inputs indicators, which is followed the intermediation approach. And they further divide the Malaysian commercial banks into foreign group and domestic group. Their test result suggests that domestic banks has slightly higher technical efficiency than foreign banks, while has lower degree in scale efficiency. Statistically, pure technical efficiency presents more important effect in determining the technical efficiency of Malaysian commercial banks.

3.4

Regarding to the journal named as “Scale Efficiency in Banking Sector of Pakistan” published in International Journal of Business and Management. This study uses data envelopment analysis to a series of commercial banks operating in Pakistan from a period of Year 2001 to Year 2008 as to measure the technical efficiency of banks. Technical efficiency is divided into two components; pure technical and scale components. In this paper, the banks are broken into three categories for analyzing; state owned banks, domestic private banks and foreign owned banks. This paper finds that the foreign owned banks are the most efficient, followed by state owned banks and domestic private banks which are classified as the least efficient one. Moreover, it is also found that pure technical efficiency contributes more towards technical efficiency. The banks faced with serious scale problems. During the research of this paper, the scale inefficiency is found to be the main source of overall technical inefficiency. They therefore observe a increasing trend in using the pure technical efficiency whereas an opposite trend is found in scale efficiency during the sample period.

Chapter 4. Methodology:

To measure the efficiency of banking sector, there are a few techniques that can be used. However, there is no agreement about which technique is the best to measure the bank efficiency. Later on, the concept of productive efficiency or economic efficiency was introduced by Farrel (1957). He divided the productive efficiency into two components: allocative efficiency and productive efficiency. For this paper, I am going to measure technical efficiency of commercial banks operating in Hong Kong. Technical efficiency is defined as the ability of a firm to produce maximum output with a given set of inputs or use minimum inputs to produce a given level of outputs.

Assuming a bank has two inputs X1 and X2 as to produce a single output Y under constant returns to scale and production function of fully efficient banks is known for given level of inputs. We can be more understood the measures of technical efficiency with FIGURE 1. Based on the figure 1 we can observe the banks us the combination of inputs X1 and X2 at point N to produce output Y. By using different combinations of inputs X1 and X2, PP’ is the isoquant that indicates the output level Y for fully efficient bank (technically efficient). For example, if the bank under this study uses the combinations of inputs X1 and X2 at point M. So we can conclude it is technically efficient. On the other hand, the distance MN represents the inefficiency of bank. Thus, the ratio of the distance from origin to point M over the distance from origin to point N can measure the technical efficiency of the bank which shown below: TE: OM / ON

The value of technical efficiency lies between zero to one. If the bank is fully efficient the value is one. In contract, if the value closes to zero, it means the bank is more inefficient. For example, a bank got a value 0.9, means that bank is 90% efficient and it can produce the same level of output by using 10% less quality of inputs.

To measure the bank efficiency of banking sector, there are two types of techniques that have been widely used, parametric and nonparametric techniques. Parametric techniques which include Distribution Free Approach (DFA), Stochastic Frontier Approach (SFA) and Thick Frontier Approach (TFA) Berger and Humphrey (1997). For non-parametric approach total factor productivity indices and Data Envelopment Analysis (DEA) are being widely adopted for measuring the bank efficient. Each method has its own advantages and disadvantages. Berger and Humphrey (1997) surveyed 130 studies which used frontier efficiency analysis to financial institutions in 21 countries, out of these 130 studies, 58 studies used DEA to measure the efficiency frontier which shows how popular people use the DEA. Moreover, DEA can handle multiple outputs and multiple inputs that don’t require the assumption of functional form relating inputs to outputs. The other major advantage of DEA is that inputs and outputs can have and use different units. For example, one input can be the numbers of employees while the other input can be the dollar amount. So in this approach, I prefer DEA as my methodology to complete this research. During my research, I will use the DEA to different commercial banks operating in Hong Kong as to measure the technical efficiency starting from 2005 to 2009. There are several papers studied measuring the efficiency of banking industry in various countries by adopting DEA. Lin (2002), Jemric and Vujcic (2002), Halkos and Salamouris (2004), Lim and Randhawa (2005), Brown and Skully (2006), Drake et al. (2006), Havrylchyk (2006), Ozkan – Gunay and Tektas (2006), Ariff and Can (2007), Chiu and Chen (2008), Huet al. (2008), Istk (2008).

3.1 Data Envelopment Analysis (DEA)

Farrell (1957) was one of the researchers who initiated the theoretical development of DEA. To measure the efficiency of decision making units, Charnes et al. (1978) used DEA which is based on linear programming. Later on, the model was developed by Charnes, Cooper and Rhodes (1978), henceforth the CCR model. Data Envelopment Analysis (DEA) is a Linear Programming methodology to measure the relative performance and efficiency of multiple Decision Making Units (DMUs) when the production process presents a difficult structure of multiple inputs and outputs. The benefits of DEA are as follow: (1) There are not necessary to explicitly specify a mathematical from the production function. (2) It is proven that it is useful in uncovering relationships may remain hidden for other methods. (3) It is capable to handle multiple inputs and outputs. (4) With any input and output measurement, it is capable to used. (5) For every evaluated unit, the sources of inefficiency can be analyzed and quantified.

In the DEA methodology formely developed by Chames Cooper and Rhode (1978) (CCR) efficiency is defined as a weight sum of outputs to a weighted sum of input, where the weights structure is calculated by means of mathematical programming and constant returns to scale (CRs) are assumed in 1984, Banker, Chames and cooper developed a model (BCC) with variable returns to scale (VRS).

To understand more about the characteristics of DEA model developed by Charnes Cooper and Rhodes, assume there are N number of banks that convert I input into J inputs. As proposed by Charnes et al. DEA measures the efficiency of such a bank by figuring out the maximum of ratio of weighted outputs to weighted inputs. We can explain as follows:

(1)

Subject to:

Where:

= The efficiency score of bank under consideration

c = A specific bank to be evaluated

= The amount of output j from bank r

= The amount of input i to bank r

= Weight chosen for output j

= Weight chosen for output i

N = Number of banks

K = Number of outputs

m = Number of inputs

The above model is a non – linear; it can be transformed into linear form as the following model:

(2)

Subject to:

Primal problem is the original problem in linear programming and corresponding to this, a dual of the problem may exist. It means that if primal problem involves maximization of the objective function then dual problem involves minimization and vice versa. By using the dual theorem to the above linear programming problem (2), it takes the following model:

Subject to:

Where:

λ = Column matrix having order N*1 and containing vector of constants only while is a scalar

When compared to the original problem, this dual problem has fewer constraints. Besides, is the efficiency score of a particular bank which ranges between zero to one. By solving this problem, we need to find out the value of for each bank in the sample by N times. Assume that all the banks are operating under constant returns to scale in the above DEA model. In fact, it is not the situation in reality. In later period, Banker et al. (1984) suggested the extension of DEA model to account for variable returns to scale. To modify the constant returns to scale to variable returns to scale of the dual of original DEA model. It’s simply by adding a convexity constraint.

Subject to:

Where:

K = A matrix of order N*1 having ones and it envelopes data more tightly than the constant returns to scale specification of DEA. Scale efficiency equals to technical efficiency under constant returns to scale () divided by technical efficiency under variable returns to scale ().

SE = /

Where since . If SE equals to 1, that means that firm is scale efficient. In contrast, all values less than 1 reflects the scale inefficiency. When the scale inefficiency exists (SE < 1), then the source of inefficiency results at either increasing non-increasing returns to scale (NI) smaller than variable returns to scale (VR) or decreasing (NI=VR) return to scale.

Chapter 5. Data and the Specification of Bank Inputs and Outputs

Chapter 8. Bibliography

Chen X., Skully M., Brown K. (2005) Banking efficiency in China: Application of DEA to pre- and post-deregulation eras: 1993–2000, China Economic Review 16: 229–245

Jim Wong, Tom Fong, Eric Wong, Ka-fai Choi (2007) Determinants of the Performance of Banks in Hong Kong. Retrieved 25 April 2007 from The Hong Kong Monetary Authority Working Papers 06/2007: http://www.info.gov.hk/hkma/

Jackson P. M. and Fethi M. D. (2000) Evaluating the technical efficiency of Turkish commercial banks: An Application of DEA and Tobit Analysis, the International DEA Symposium, University of Queensland, Australia.

Muharrami S. A., Matthews K., and Khabari Y. (2006) Market Structure and Competitive Conditions in the Arab GCC Banking System. Retrieved November 2010 from Cardiff Economics Working Papers: http://www.cardiff.ac.uk/carbs/econ/workingpapers

Pasiouras F. (2008) Estimating the technical and scale efficiency of Greek commercial banks: The impact of credit risk, off-balance sheet activities, and international operations, Research in International Business and Finance 22: 301–318

Muhammad Usman, Zongjun Wang, Faiq Mahmood, Humera Shahid (2010) Scale Efficiency in Banking Sector of Pakistan, International Journal of Business and Management Vol. 5, No.4, April 2010

Tahir I. M., Bakar N. M. A., & Haron S. (2009) Estimating Technical and Scale Efficiency of Malaysian Commercial Banks: A Non-Parametric Approach, International Review of Business Research Papers, 5 (1):113- 123.

Wu C. R., Tsai H.Y and Wang Y. M. (2008) Efficiency Comparison of Operational and Profitability: A Case of Hong Kong Commercial Banks, Journal of Social Sciences 4 (4): 280-287

Zhu J. (2003) Quantitative Models For Performance Evaluation And Benchmarking, Data Envelopment Analysis with Spreadsheets and DEA Excel Solver, Kluwer Academic Publishers

Data Envelopment Analysis Online Software http://www.deaos.com/login.aspx?ReturnUrl=%2fWelcome.aspx

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