a conceptual framework for and survey of banking efficiency study

A CONCEPTUAL FRAMEWORK FOR AND SURVEY OF BANKING EFFICIENCY STUDY1 Hamim Syahrum Ahmad Mokhtar Central Bank of Malaysia, Malaysia [email protected]

Syed Musa AlHabshi International Institute of Islamic Finance Inc., Malaysia [email protected]

Naziruddin Abdullah AlHosn University, United Arab Emirates. [email protected], [email protected]

ABSTRACT This paper provides a conceptual framework for the banking efficiency study and a survey of the previous banking efficiency literature. The discussions include the concept of efficiency measurement, different types of efficiency, methodology as well as the approaches of input and output variables. The possible bank efficiency determinants or factors that could explain the differences in efficiency of the bank are also discussed. The findings show that no estimation techniques dominate over the other with DEA widely used to measure the technical efficiency while SFA mostly used to measure the cost efficiency. The paper also found that the intermediation approach is the common approach used to decide the appropriate input and output variables.

KEYWORDS: Bank Efficiency, Conceptual Framework, Data Envelopment Analysis (DEA) , Stochastic Frontier Approach (SFA).

INTRODUCTION

Since the 1990s, studies that were focused on the efficiency of financial institutions have become an important part of banking literature (Berger & Humphrey, 1997). One of the important aspects of the banking efficiency studies is that efficiency measures are indicators of success, by which the performance of individual banks, and the industry as a whole, can be gauged. Greater efficiency implies that individual banks can adapt better to a different operating environment via their improved ability to combine and utilise inputs. This development could lead, for example, to improved financial products and services, a higher shareholder value, a higher volume of funds intermediated and more economic growth if funds are channelled into more productive investments. The efficiency study can also be used to investigate the potential impact of government policies on banking efficiency. It is of the interest of regulators to know the impact of their policy decision to 1 Parts of this paper have been presented in the 2005 National Conference of Young Scholar, 12-13 December 2005, Istana Hotel, Kuala Lumpur, Malaysia.

UNITAR E-JOURNAL Vol. 2, No. 2, June 2006

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the performance and efficiency of the banks, as they will hugely affect the economy. Berger and Humphrey (1997) noted, “the information obtained from efficiency studying could be used” (p.175). 1. To inform governments on their policy by assessing the effects of deregulation, mergers or market structure on efficiency; 2. To address research issues by describing the efficiency of an industry, ranking firms, or checking how measured efficiency may be related to different efficiency techniques employed; 3. To improve managerial performance by identifying ‘best practices’ and worst practices’ associated with high and low measured efficiency, respectively, and encouraging the former practices while discouraging the latter. The main objective in writing this paper is to discuss the conceptual framework for the bank efficiency study and survey the previous literature on bank efficiency. The paper is divided into seven parts. Following this introduction, section two defines the efficiency while section three explains briefly the concept of efficiency. Section four then proceeds with the framework on bank efficiency. Section five analyses the previous banking efficiency studies and section six examines the possible determinants of bank efficiency. Lastly, section seven contains our concluding remarks.

EFFICIENCY DEFINITION

In general, the efficiency analysis of a production or service unit refers to the comparison between the outputs and inputs used in the process of producing a product or services. For lucidity, the process is shown in Figure 1.

Figure 1 The Efficiency Analysis Framework Environment Factors

Inputs

Firm transforms inputs into outputs

Outputs

Efficiency Source: Adapted from Chu & Lim (1998); Ahmad Mokhtar, Abdullah & Alhabshi (2005).

Efficiency measurement is one aspect of a firm’s performance. Efficiency can be measured with respect to maximization of output, minimization of cost or maximization of profits. In general, efficiency is divided into two components (Kumbhakar & Lovell, 2003). A firm is regarded as technically efficient if it is able to obtain maximum outputs from given inputs or minimise inputs used in the production of given outputs. The objective of producers here is to avoid waste. According to Koopmans (1951), “a producer is considered technically efficient if, and only if, it is


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impossible to produce more of any output without producing less of some other output or using more of some input”. On the other hand, allocative efficiency relates to the optimal combination of inputs and outputs at a given price. The objective of producers might entail the production of given outputs at minimum costs or the utilisation of given inputs to maximise the revenue, or the allocation of inputs and outputs to maximise profit. This is also what we call economic efficiency and the objective of producers becomes one of attaining a high degree of economic efficiency (cost, revenue or profit efficiency). According to Berger and Mester (1997), the two most important economic efficiency concepts are cost and profit efficiency.

THE CONCEPT OF EFFICIENCY

The concept of measuring efficiency was first discussed by Farrell (1957). Drawing inspirations from Koopmans (1951) and Debreu (1951), Farrell was first to measure the efficiency empirically. According to Farrell (1957), the concept of efficiency measurement can be divided into two components, technical efficiency (TE) and allocative efficiency (AE). According to him, technical efficiency is the firm’s ability to obtain maximal output from a given set of inputs while allocative efficiency means the firm’s ability to use inputs in optimal proportions, given their respective prices and production technology.

Figure 2 Overall, Technical & Allocative Efficiency

.P

X2/y

S

A

R

..

Q

.

Q’

S’

O

A’

X1/y

Source: Coelli et al. (1998, p.135).

Based on his concept, the combinations of two components will produce overall economic efficiency (OE). The concept is illustrated in Figure 2. Assuming a firm, ABC, is using only two inputs, x1 and x2 to produce a single output (y) at point P. SS’ slope shows the possible combinations of inputs the firm can produce if it is perfectly efficient. The slope AA’ represents the input price ratio and it shows the various combinations of inputs that require the same level of expenditure. If the firm’s production is efficient, it should occur at point Q’, which indicates the cost


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minimisation. That is where SS’ and AA’ slope intersect, which means the input combinations Q’ is both technically and allocatively efficient. Since the ABC firm produces using the combination of input at point P, two types of inefficiency arise. First, it is technically inefficient, since by moving to point Q, it could produce the same output with fewer inputs. In order to measure the magnitude of a firm’s technical efficiency (TE), the ratio is calculated as OQ/OP, which is equal to one minus QP/OP. Second, it is allocatively inefficient. Producing at point P shows that the firm made an incorrect choice as to the combination of inputs at the given prices, therefore incurring more cost than if it had produced at point Q’. To measure the allocative efficiency (AE), the ratio is calculated as OR/OQ. Then, we would be able to measure the Overall Efficiency (OE), since we have the ratio calculation for TE and AE. According to Farrell, OE is TE multiplied by AE. O E = TE

X

A E = (O Q /O P )

X

(O R /O Q )

(1)

Where, Overall Efficiency (OE) equals to Technical Efficiency (TE) multiplied by Allocative Efficiency (AE). Farrell’s original ideas were illustrated in input-oriented measures under the assumption of constant returns to scale. This input-oriented measure addresses the question of “by how much can input quantities be proportionally reduced without changing the output quantities produced?” One could also ask another question; “by how much can output quantities be proportionally expanded without altering the input quantities used?” This is, according to Coelli (1996), an outputoriented measure as opposed to the input-oriented measure as discussed by Farrell above.

BANKING EFFICIENCY ANALYSIS FRAMEWORK

The aim of this section is to discuss framework of the bank efficiency study. Figure 3 shows the conceptual framework of the bank efficiency study. The framework demonstrates what is needed and what you need to know in analysing the banking efficiency. As shown in the Figure 3, the conceptual framework is divided into five (F1-F5) steps or stages. In substance, the figure spells out the steps one has to follow in order to measure the efficiency of a production unit. In step one (F1), for example, one has to illustrate or identify the main objectives of the study, which is to examine the efficiency of the bank. The measurement of efficiency would enable us to know the status of the individual banks’ efficiency and how it is compared among them. It is noted that while extensive literature has been developed to examine banking efficiency in the US and Europe (Berger & Humphrey, 1997; Goddard, Molyneux & Wilson, 2001), there is only limited literature on developing countries (Elzahi Saaid, 2002; Hussein, 2003). Step two (F2) in Figure 3 shows the type of efficiency used in the frontier efficiency measurement, which are technical and allocative efficiency. The allocative efficiency can be further divided into two main types of allocative efficiency: cost and profit efficiency. We reiterate here that a producer or service provider is considered technically efficient if he/she can produce more outputs from a given set of inputs or use less input to produce a given level of output (Kumbhakar & Lovell, 2003). We also note that a producer or service provider is considered cost efficient if he/she is able to produce a given output at a minimum cost. Similarly, he/she is deemed revenue efficient if he/she is able to maximise revenue from the utilisation of given inputs. In the same vein, he/she is regarded as profit efficient if he/she is able to maximise profit from the allocated inputs and outputs.


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Figure 3 Conceptual Framework of Banking Efficiency

Objective- to measure efficiency of the banks

F1

F2

Type of efficiency Technical efficiency (Farell, 1957)

Allocative/ Economic Efficiency (Farell, 1957, Leibenstein, 1966)

Cost efficiency (Berger & Mester, 1997)

F3

Profit efficiency (Berger & Mester, 1997)

Estimation Techniques Non-Parametric Approach

Parametric Approach

SFA (ALS, 1977, MVB, 1977)*

DFA (Berger, 1993)

TFA (Berger & Humprey, 1991, 1992)

DEA (Charnes, Cooper & Rhoedes, 1978)*

F4

FDH (Deprins et. al, 1984)

Definition of input output variables Production Approach (Cobb & Douglas, 1928)

Intermediation Approach (Sealey and Lindley, 1977)

Environmental variables Regulatory-specific variables

F5

Efficiency results & Findings

Bank-specific variables

Previous Empirical Research

US & Europe (e.g. Berger & Humprey, 1997)

Asia & Middle East (e.g. Abd. Karim, 2001)

* ALS: Aigner, Lovell, and Schmidt (1977); MVB: Meusen and Van Den Broeck (1977).

Next, step 3 (F3) in Figure 3 shows the two general methodologies that are commonly used to measure efficiency. They are: parametric approach using econometric techniques; and, nonparametric approach utilising linear programming method. Both differ mainly in how they handle the random error and their assumptions regarding the shape of the efficient frontier. Each of the techniques has its own strengths and weaknesses.


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The parametric approach has the advantage of allowing noise in the measurement of inefficiency. However, the approach needs to specify the functional form for the production, cost or profit function. Non-parametric is simple and easy to calculate since it does not require specification of functional form (Coelli, 2004). However, it suffers from the drawback that all deviations from the best-practice frontier are attributed to inefficiency since it does not allow for noise to be taken into account. Common parametric methods are the Stochastic Frontier Approach (SFA), the Thick Frontier Approach (TFA) and the Distribution Free Approach (DFA), while the common nonparametric techniques are the Free Disposal Hull analysis (FDH) and the Data Envelopment Analysis (DEA). Berger and Humphrey (1997) found that out of 130 applications, more than half used nonparametric techniques and 60 were parametric which suggest no approaches dominate the other. McAllister and McManus (1993), Mitchell and Onvural (1996) and Wheelock and Wilson (2001) test and reject the translog specification of bank cost functions, and suggest seminonparametric or nonparametric methods for estimating bank costs. In contrast, Bauer et al. (1998) have found nonparametric techniques do not meet some of their consistency conditions and therefore some cautions should be taken before using them. The examples of DEA and SFA models are discussed in the Appendix. Most of the studies use either non-parametric or parametric techniques in their respective bank efficiency studies. This might be because both techniques are altogether different in terms of their approaches in analysing the efficiency. The evidence of consistency between the two techniques is limited and scarce as only a few studies have been performed to test the robustness of the results generated by the two frontier techniques apart from the studies by Resti (1997), Bauer et al. (1998) and Sturm and Williams (2004). It is suggested both parametric and nonparametric techniques are used in order to strengthen the findings and to make the study more robust (Favero & Papi, 1995; Intarachote, 2001; Nghia, 2003; Mohamed, 2003). Ideally, if the majority of the findings from the two different techniques are similar, then one can be sure that the findings are not being driven by chance or luck. After the type of efficiency and the measurement techniques, one has to decide the input and output variables. Specifically, step 4 (F4) in Figure 3 demonstrates the decision that a service provider has to undertake before measuring the bank’s efficiency. Any decision made, however, will essentially be subject to banks’ treatment of the money they received from the depositors as well as the money they extended to the creditors. In relation to this, two main approaches can be found in the literature. They are: the intermediation approach; and, the production approach The production approach defines the bank activity as production of services and views the banks 2 as using physical inputs such as labour and capital to provide deposit and loan accounts . While the intermediation approach views banks as the intermediator of financial services and assumes that banks collect deposits, using labour and capital, then intermediate those sources of funds into loans and other earning assets (Sealey & Lindley, 1977). This intermediation approach is argued to be particularly appropriate for banks where most activities consist of turning large deposits and 3 funds purchased from other financial institutions into loans or financing and investments (Favero & Papi, 1995). In practice, the intermediation approach is the most widely used in the banking literature (Kwan, 2002). In choosing the appropriate approach, Berger and Humphrey (1997) suggested that the intermediation approach is the most appropriate for evaluating the entire bank because it is inclusive of interest expense (income paid to depositors), which often accounts for one-half to twothird of total costs. Meanwhile, he recommended that the production approach is more appropriate for evaluating the efficiency of the bank’s branches because branches process customer documents for the banks as a whole.

2 3

Cobb and Douglas (1928) explained about the theory of production. The term financing is for Islamic banks, which is equivalent to the loans for conventional banks.


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Figure 4 Input-output relationship in banking (intermediation approach) INPUT VARIABLES

Operation Process Banking

Labour Capital

Financial Aspect

Deposits

OUTPUT VARIABLES Loans, Advances & Financing Investment & Trading Securities

An example of the intermediation approach is illustrated in Figure 4. In this case, the banking operation process produces joint-outputs. That is to say, banks produced different outputs from the same set of inputs. To give but one example, the same staff, office space and deposits and funds (for brevity, they are called inputs) are used to provide financial assistance to corporate or retail clients. At the same time they are used to conduct other business dealings like investment and trade, which generate returns for the banks and subsequently depositors. Finally, after going through all the process discussed earlier, you will get the efficiency results (step 5 in Figure 3). A value of 1 or 100% indicates full efficiency and operations on the frontier. A value of less than 1 or 100% reflects operations below the frontier. The wedge between 1 and the value observed measures the inefficiency.

SURVEY OF THE PREVIOUS BANK EFFICIENCY STUDY

The studies of efficiency using “frontier” approaches on banking did not start until Sherman and Gold (1985) initiated their study. They applied the frontier approaches to the banking industry by focussing on operating efficiency of branches of a savings bank. Since then, there have been extensive studies on bank efficiency done in the US and European countries and most of the studies focused on conventional banking (Berger & Humphrey, 1997; Goddard et al., 2001). This paper analysed the previous bank efficiency study to link with the conceptual framework highlighted in the previous section. The works written on global banks’ efficiency are summarised in Table 1. Specifically, the table provides an understanding of the frequency, and type of inputs and outputs used by the studies on banks’ efficiency for the period between 1985 and 2005. All in 4 all, during the period there were 47 bank efficiency studies included .

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The detail of analysis on the previous studies is available upon request.


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Table 1 Input and Output Variables, its Approaches, and Techniques Used: Inputs variables Labour (Physical) Capital (core) deposits Interest expense Non-interest expense Purchased Funds Time and Savings Deposits Borrowed Funds/Money Operating Expense Demand Deposits Customer Funds Expenditure on Materials Financial Capital Transactions Deposits Non-transactions Deposits Occupancy Costs Total Inputs and Outputs Approaches Intermediation Production Value-Added User Cost Asset Total

Frequency 39 32 15 10 8 6 6 6 5 3 3 3 3 2 2 2 145 Frequency 34 5 5 3 2 49

Outputs Variables Investment Securities Net/ total loans Commercial Loans Real Estate Loans Consumer Loans or Loans to individuals Non-interest Income Other Loans Interest Income Demand/savings Deposits Time Deposits Earning Assets Deposits Placements Securities in Trading Commitment & Contingencies Short Term Loans Long Terms Loans Instalment Loans Total

Frequency 15 14 13 13

Estimation Techniques

Frequency

DEA SFA DFA TFA FDH Total

13 12 10 7 7 7 5 5 4 4 3 3 2 137

32 23 5 2 1 63

Sources: Authors’ own updates. Note: These results were found to be used in a review of 47 bank efficiency studies. Take note that the total number of techniques used in the previous studies are more than 47 studies since there are studies which used more than one technique. The same goes to the other findings.

Based on the analysis in Table 1, one can safely conclude that labour, physical capital, various kinds of deposits (core deposits, time and savings deposits, demand deposits, purchased funds, borrowed funds) and interest expenses are the most widely used input variables. Likewise, the most commonly used outputs are investment securities, different kinds of loans (such as real estate loans, commercial loans, consumer loans or loans to individuals, total or net loans and other loans), interest income and non-interest income. It is also obvious from the table that the intermediation approach, the frequency of which 34 as opposed to value-added (5) and production (5), is the most frequently employed technique to define the banks’ inputs and outputs. Table 1 also shows the number of estimation techniques used in bank efficiency studies. Of the studies conducted over the 1985-2005 period, 32 studies utilised data envelopment approach (DEA), while 31 others utilised other techniques ranging from stochastic frontier technique with the frequency of 23 to free disposal hull (FDH) technique with the frequency of 1.


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Table 2 Types of efficiency analysed by different estimation techniques No. 1.

Estimation Techniques DEA

2.

Type of Efficiency Technical Efficiency Cost Efficiency Allocative Efficiency

Number of Times 23 6 3

SFA

Technical Efficiency Cost Efficiency Profit Efficiency Revenue Efficiency

3 15 4 1

3.

DFA

Cost Efficiency Profit Efficiency

4 1

4.

TFA

Cost Efficiency Profit Efficiency

1 1

5.

FDH

Technical Efficiency

1

Sources: Authors’ own updates. Note: These results were found in a review of 47 bank efficiency studies.

Meanwhile, Table 2 is the extension of Table 1. It shows the types of efficiency that are analysed using different estimation techniques. As evident from Table 2, DEA is the most widely used estimation technique to measure the efficiency of the banks. However, a closer look reveals that DEA was mostly used to measure the technical efficiency, while SFA was more frequently used to measure the cost efficiency.

FRAMEWORK ON DETERMINANTS OF BANKING EFFICIENCY

The process of producing outputs from inputs can also be influenced by environmental variables or explanatory variables such as location, which are often not controllable by producers or service providers (see Figure 1 and Step 4 of Figure 3). This section commented on possible environmental or explanatory variables that may explain the differences in efficiency of the bank. The approach is to take into account both regulatory-specific variables and bank-specific variables in explaining the variations in bank’s efficiency estimates (Figure 5).


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Figure 5 Determinants of Banking Efficiency Regulatory-specific variables

Dependent variable

Bank-specific variables Size (Berger & Mester, 1997).

Bank Type (Al-Jarrah & Molyneux, 2003)

Capital Adequacy (Girardone et al., 2004)

Time (Bhattacharya et al. 1997).

Efficiency Ownership Status (Sturm & Williams, 2004).

Loan Quality (Berger & Mester, 1997). Expenses (Bauer et al., 1998)

Geographical region (Abdul Karim, 2001)

Bank Age (Mester, 1996).

In Table 3, the details of each familiar regulatory-specific variables, which are categorical in nature and can be found in the literature, are shown. They are; time trend, bank type, ownership status and geographical region.

Table 3 Regulatory-specific variables

Explanation of the variables

Previous studies

1. Time trend • Time trend will show how bank efficiency evolves through time relative to the base year. • It can also be used to indicate the impact of changes in the regulatory environment. • A positive co-efficient of time implies that banks became more efficient as they slowly adapted to the competition within the banking environment Bhattacharya et al. (1997).

• Kwan and Eisenbeis (1996) found that the average inefficiency appears to be declining over time. • Bhattacharya et al. (1997) reported a declining trend of efficiency for commercial banks in India during the 1986-1991 period. • Casu and Molyneux (2000) found a slight improvement in efficiency levels through time for European banks with the exception of the banks in Italy.


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Explanation of the variables 2. Bank type • An analysis of different bank type will indicate whether there is any difference in efficiency between the types of banks.

3. Ownership status • An analysis of different ownership status will indicate whether there is any efficiency difference in different kinds of ownership status. • Common ownership status is a comparison between domestic or local banks with foreign banks (Sturm & Williams, 2004).

4. Geographical region • An analysis by geographical region is to test whether there is any difference in efficiency in different geographical region.

Previous studies • Al-Jarrah and Molyneux (2003) reported that Islamic banks (0.98) appear to be more cost efficient than commercial (0.940.95) and investment banks (0.93). They studied the cost and profit efficiency of 82 banks in Jordan, Egypt, Saudi Arabia and Bahrain during the period of 1992-2000. • Elyasani and Mehdian (1992) found that both minority and non-minority owned banks in the US had closed efficiency with an average of 0.89 and 0.87 respectively. Elyasani and Mehdian (1992) used DEA techniques to measure the technical and allocative efficiency. • Zaim (1995) found that foreign banks are the most efficient banks, followed by state banks, which were more efficient than private banks. • Sturm and Williams (2004) reported that foreign banks are more technically efficient than domestic banks in Australia during the period from 1988 to 2001. • Favero and Papi (1995) found that Southern Italy has lesser efficiency results than Northern and Central Italy. • Abdul Karim (2001) reported that Thailand banks are the most efficient banks, followed by Malaysian banks, Indonesian banks and finally the Philippines banks.

Sources: Authors’ own updates

Table 4, on the other hand, summarises the bank-specific variables. They are also used in many studies on bank efficiency. The bank-specific variables normally consist of bank size, capital adequacy or strength of the bank, bank’s expenses, bank’s loan quality and the age of the bank. The bank-specific variables can also assist us to explain the differences in efficiency for a different type of bank and ownership status.


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Table 4 Bank-specific variables Explanation of the variables Bank size • To examine whether size would be the determinants of bank efficiency. • The natural log of total assets is used to examine the relationship between efficiency and bank size. • Previous studies also categorised the bank by different sizes; e.g. large, medium and small banks.

Capital Adequacy • Capital adequacy can be proxy by the ratio of equity to total assets (EQTA). • EQTA indicates capital strength or bank safety and soundness. • Positive correlation is expected as high capitalised banks tend to be more efficient since efficient banks tend to have more profits, which in turn strengthen their capitalisation status (Isik & Hassan, 2003). Bank Expenses • The ratio of total costs to total assets (TCTA) can be used to analyse the relationship between bank expenses and efficiency. • A negative correlation between TCTA and efficiency is expected, since banks with higher expense may overutilise inputs and therefore be less efficient. Loan Quality • The ratio of loan loss reserve to total loans (LLRTL) can be used to measure loan quality (Molyneux et al., 1996). • The larger the ratio, the poorer the loan quality. As Intarachote (2001) points out, LLRTL is expected to be negatively related to efficiency, since greater loan losses increase financial risk and would reflect passive risk management, which should lead to lower efficiency.


Previous studies • Most of the studies used asset size, but no consistent results emerge of its relationship with efficiency (Berger & Mester, 1997). • Abdul Karim (2001) reported that larger banks tend to be more cost efficient compared to their smaller rivals. • Abdul Majid et al. (2003) found that size had positive relationship with the efficiency of the banks. • Kaparakis et al. (1990) and Elyasani et al. (1994) reported a positive correlation between capital to asset ratio and efficiency. • Mester (1993), Mester (1996) and Girardone et al. (2004) found a negative correlation between capital adequacy ratio and inefficiency.

• Berger and Mester (1997) and Bauer et al. (1998) studies reported a negative correlation between bank efficiency and proportions of cost to total assets.

• A general finding is that more efficient banks have lower levels of non-performing loans (Berger & Mester, 1997). • Similarly, Kwan and Eisenbeis (1996) reported that the inefficient bank is associated with higher loan losses.

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Explanation of the variables

Previous studies

Bank Age • Bank Age is assessed by the number of years the bank has been in operation. • According to learning by doing hypothesis, the older the bank, the more experience they have, therefore the bank could better manage their operations and might become more efficient, (Mester, 1994, 1996). • A positive relationship with efficiency might also suggest that more efficient banks are more likely to survive (Mester, 1994, 1996).

• Mester (1994, 1996) found that inefficient banks tend to be younger in her study of 214 third district banks. • However, Isik and Hassan (2003) found insignificant negative relationship between the bank age and efficiency.

Sources: Authors’ own updates

CONCLUSION

One of the best ways to learn about the banking efficiency is to learn from the experiences of others. Many efficiency studies have been conducted in recent years that you can read and learn from before you embark on your empirical analysis. This paper provides conceptual framework for the bank efficiency study and a survey of previous banking efficiency literature. The findings show that no estimation techniques dominate the other with DEA widely used to measure the technical efficiency while SFA was mostly used to measure the cost efficiency. The paper also found that the intermediation approach is the common approach used to decide the appropriate input and output variables. While there has been extensive literature examining the efficiency of US and European conventional banking over the recent years (Berger & Humphrey, 1997; Goddard et. al, 2001), the empirical work on developing countries is still lacking. The study on Islamic Banking efficiency is also in its infancy apart from a few studies (Hassan, 2003; Elzahi Saaid, 2002; Brown & Skully, 2003). Typically the studies on Islamic banks have focussed on theoretical issues, and empirical work has relied mainly on the analysis of descriptive statistics rather than rigorous statistical estimation (El-Gamal & Inanoglu, 2003). These are the gaps in the bank’s efficiency study. A contribution of the present paper is that it provides the framework of the banking efficiency study as a reference for the researcher on banking efficiency. The present paper basically provides you the step that you need to follow in analysing the “frontier” efficiency. The interested researcher can also refer to Coelli, Rao and Battese (1998) and Kumbhakar and Lovell (2003) for a much more rigorous overview of the efficiency methods and conceptual issues. Besides that, the SFA and DEA programmes can be downloaded free from this web site (http://www.une.edu.au/econometrics/cepa.htm), which was developed by Tim Coelli, one of the prominent scholars on efficiency study.

Acknowledgement The authors would like to thank Associate Professor Dr. R. Ravindran, two anonymous referees, and the editors of this journal for useful comments on previous drafts of this paper. The usual caveats apply.


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APPENDIX

DEA MODELLING FRAMEWORK

This section provides the mathematical formulation for technical and cost efficiency using DEA techniques. Following Coelli et. al (1998) and Coelli (2004), we assume N firms or banks, each has K inputs and M outputs. For the i-th firm, xi and yi represent the column vectors of input and output respectively. For N firms, X represents the K*N input matrix and Y is the M*N output matrix. For example, the VRS input-oriented technical efficiency of each bank is estimated by solving a linear programming problem. The mathematical formulation is as follows:

m i n θ ,λ θ s u b je c t to

− yi + Y λ ≥ 0,

(2)

θ xi − X λ ≥ 0, N 1'λ = 1 λ ≥ 0 where

λ

is N*1 intensity vector of constants and

estimated value of

θ

θ

is a scalar. N1 is an N*1 vector of ones. The

is the efficiency score for each of the N firms. The estimate will satisfy the

restriction θ ≤ 1 with a value θ = 1 indicating a technically efficient firm. The problem has to be solved N times, once for each firm, to derive a set of N technical efficiency scores. Note that the convexity constraints ( N 1' λ = 1 ) ensures that an inefficient firm is benchmarked against firms of a similar size and the projected point of that firm on the DEA frontier will be a convex combination of observed firm.

The cost efficiency, according to Coelli et. al (1998) and Coelli (2004), is defined as the ratio of the minimum possible cost to the observed cost for the i-th firm. DEA cost efficiency can be estimated by solving a linear programming problem. In this example, the problem is to choose input quantities to minimise costs holding constant input prices and output quantities. The mathematical formulation is as follows:

m i n λ , X i*

w i'xi *

s u b je c t to

− yi + Y λ ≥ 0,

(3)

x − X λ ≥ 0, * i

N 1'λ = 1 λ ≥ 0 where

wi is a vector of input prices for the i-th firm and Xi* is the cost-minimising vector of input

quantities for the i-th firm, given the input price ( wi ) and the output quantities ( for firm i is calculated as the ratio of

'

*

'

yi ). Cost efficiency

'

wi xi / wi xi , where wi is the transpose of firm i’s input price

vector. Thus, cost efficiency (CE) is the ratio of frontier costs of firm i’s output vector, given the set of its input prices, to its actual cost, where 0 ≤ CE ≤ 1 , and CE=1 for fully efficient firms or banks.


18

SFA MODELLING FRAMEWORK

This example shows the parametric cost efficiency model which is derived from a cost function. The cost function can be written in a natural logarithm form as the following:

ln ΤC = f (Y, W) + ln U c + ln Vc

(4)

ln ΤC is the total cost, f denotes some functional form, Y is the vector of quantities of output variables, W is the vector of price input variables, ln U c is the inefficiency factor that Where

may raise cost above the best-practice optimal cost and

ln Vc is the random error incorporated to

capture the measurement error and luck, which may temporarily increase or decrease a bank’s costs. Basically, the cost function above describes the relationship between the cost variable with prices of input variables, quantities of output variables plus the inefficiency and random error. For parametric techniques, the inefficiency and random error components of the composite error term are disentangled by making explicit assumptions about their distributions. For the composite error-term component in the equation 1.3, it can be written as,

E = U +V

(5)

Following Aigner, Lovell and Schmidt (1977), the study normally assumes the distribution of the error term or statistical noise, V , to be two-sided normal distribution while the inefficiency term, U , is assumed to be one space (half normal distribution). Note that the cost function can take various functional forms in bank efficiency study. The functional forms (f) for the majority of cost-based studies are translog cost function. An example of a standard translog cost function is shown as: m

n

ln TC = α 0 + ∑ α i ln Yi + ∑ β j ln W j i =1

j =1

1

m

m

2

i =1 l =1

n

n

+ [∑∑ δ il ln Yi ln Yl + ∑∑ γ jk ln W j ln Wk ] m

j =1 k =1

(6)

n

+ ∑∑ ρij ln Yi ln W j + Ei i =1 j =1

where,

lnTC

is the natural logarithm of total costs,

lnY

quantities; lnWj is the natural logarithm of input prices; Ei =

γ

whereas α , β , δ , and

ρ are coefficients to be estimated.


is the natural logarithm of output

V + U is as defined in equation 1.4;

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