Kuen-Horng Lu*

Int. J. Business Performance Management, Vol. 9, No. 1, 2007

Copyright © 2007 Inderscience Enterprises Ltd.

22

Measuring the operating efficiency of domestic banks with DEA

Kuen-Horng Lu* Department of Asia-Pacific Industrial and Business Management, National University of Kaohsiung, No. 700, Kaohsiung University Road, Nan Tzu District, Kaohsiung 811, Taiwan, ROC E-mail: [email protected] *Corresponding author

Min-Li Yang Department of Business Administration, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan, ROC E-mail: [email protected]

Feng-Kai Hsiao and Hsin-Yi Lin Department of Human Resource Development, National Kaohsiung University of Applied Sciences, Kaohsiung 811, Taiwan, ROC

Abstract: This study employed the CCR model of Data Envelopment Analysis (DEA) and the slack variable analysis to evaluate the operating efficiency of the domestic banks in Taiwan from 1998 to 2004. The operating efficiency of domestic banks was measured using interest expenses, fixed assets, deposits and number of employees as input variables. Interest income, non-interest income, investments and loans were used as the output variable. The results revealed significant differences in the average of fixed assets, deposits and loans between the high and low efficiency groups. This study found that the Non-Performing Loans/Gross Loans (NPL/GL) ratio of the high efficiency group is significantly lower than that of the low efficiency group. This study also found room for improvement in non-interest income and investments in each year and made suggestions for banks to adjust all the variables in order to enhance their overall operating efficiency.

Keywords: domestic banks; operating efficiency; Data Envelopment Analysis; DEA.

Reference to this paper should be made as follows: Lu, K-H., Yang, M-L., Hsiao, F-K. and Lin, H-Y. (2007) ‘Measuring the operating efficiency of domestic banks with DEA’, Int. J. Business Performance Management, Vol. 9, No. 1, pp.22–42.

Biographical notes: Dr. Kuen-Horng Lu is a Professor in the Department of Asia-Pacific Industrial and Business Management, National University of Kaohsiung. He received his PhD form the Institute of Management Science,

Measuring the operating efficiency of domestic banks with DEA 23

National Chiao Tung University. His current research interests are performance management, collaborative planning, forecasting and replenishment. He had published several papers in International Journal of Electronic Business Management, Quality Engineering, International Journal of Information and Management Sciences, International Journal of Libraries and Information Services, Journal of Management and System, Quality World Technical Supplement, Production and Inventory Management Journal, etc.

Min-Li Yang is currently a Senior Lecturer in the Department of Business Administration, National Kaohsiung University of Applied Science, Taiwan. She completed her Doctorate in School of Business and Management, University of Glasgow, UK. Her current research interest is strategic management and marketing management.

Feng-Kai Hsiao is a Graduate student in the Department of Human Resource Development, National Kaohsiung University of Applied Sciences.

Hsin-Yi Lin is a Graduate student in the Department of Human Resource Development, National Kaohsiung University of Applied Sciences.

1 Introduction

The banking sector serves as a financial intermediary in the economy, transferring capital from suppliers to demanders, so that the latter can obtain the operating capital. The slowdown of economy, outward migration of corporations and the chaotic political and economic circumstances in recent years, however, has tremendously changed the domestic supply and demand of capital. In response to the dynamic trend of financial liberalisation and the entry into the World Trade Organization, the government of Taiwan has deregulated many restrictions since 1989. The government has, for instance, encouraged the establishment of new commercial banks, increased their operations and actively promoted the privatisation of government-owned banks. An increase in the number of banks has resulted in higher competition between local banks forcing them to lower the loan rates and increase the interest rates to attract capital. This has consequently narrowed the differences between the rates and led to a decrease in profits. Domestic banks in Taiwan are now limited in size, have relatively higher Non-Performing Loans-Gross Loans (NPL/GL) ratio, and are not very competitive.

In response to this, the government has committed to improve the financial environment through implementation of a series of financial reforms. By amending relevant financial regulations, the government has encouraged financial institutions to merge in order to enhance the competition. The government is also formulating regulations to facilitate the market exit mechanism for the poorly managed financial institutions to ensure stability of the financial system. The pressure of market competition has driven domestic banks to enhance their operating efficiency. It is therefore imperative that every bank is completely aware of its operating efficiency and employs an effective optimal operating strategy.

Financial Ratio Analysis (FRA) is one of the traditional approaches used to measure the operating efficiency of a bank. This approach measures only the input and output ratio of a single item for a bank rather than the operating capability of a bank, thereby revealing effective use of resources and the operating efficiency of each bank in relation

24 K-H. Lu et al.

to other banks. Data Envelopment Analysis (DEA) is a methodology for analysing the relative efficiency and managerial performance of productive (or response) units, having the same multiple inputs and multiple outputs. It allows the comparison of relative efficiency of banks by determining the banks that span the frontier. It is a non-parametric linear programming technique that computes a comparative ratio of outputs to inputs for each unit (bank), which is reported as the relative efficiency score. The efficiency score is usually expressed as a number between zero and one. A Decision-Making Unit (DMU) with a score less than one is deemed as inefficient relative to other units. In addition, DEA’s main usefulness is its ability to generate potential improvements for inefficient banks and identifying the efficient banks to benchmark. On the basis of the DEA’s advantages, the researchers were motivated to measure the operating efficiency of the domestic banks with DEA approach and propose suggestions to the domestic banks regarding the potential improvements (achievable targets) of all the variables.

To sum up, this research aims to apply the CCR model of DEA to measure the relative operating efficiency of all the domestic banks to determine those that are efficient (which are the banks to be benchmarked) and those that are inefficient and need to be improved. The Quartile approach and ANOVA were adopted to divide the relative efficiency of banks in each year into four groups according to the efficient scores obtained from DEA analysis. The correlations between the input/output variables and high/low efficiency banks were examined from the cross-sectional and longitudinal aspects. The analysis of slack variable was also employed to explore why the inefficient banks have relatively low operating efficiency. Moreover, the correlations between the effectiveness of DEA’s measurement and the traditional financial indicators were also explored. Finally, some suggestions were made to demonstrate how each variable should increase (or lower) its efficiency in order to effectively enhance the overall operating efficiency of the bank.

2 Literature review

Efficiency, as an economic term, focuses on the correlation between the input item and output item of a company’s production. Production function further reflects the technical relationship between the input and output. A bank is considered as a company with multiple inputs and outputs. The efficiency of a bank lies in the correlation between its input and output. Over the recent years, FRA, Regression Analysis (RA) and Frontier Analysis (FA) have been the three major methods used to evaluate operating efficiency of a bank. Each method has differentials of model hypotheses and research limitations, and researchers tend to adopt the method best suited for their research objectives and methodology. The FRA is used to analyse the company’s efficiency by using the variables of RAO and ROE. RA was adopted by researchers like Rhoades (1993) and De Young and Hasan (1998).

The FA developed from Farrell’s (1957) efficient concept connects each point that has the highest efficiency and creates a production frontier. Many researchers employ frontier efficiency models primarily because they can produce an objectively determined quantified measure of relative performance that removes the effects of many exogenous factors. The gap between any single production point and the production frontier is the relative value of lower efficiency. On the basis of the gap, a researcher can come up with an improved value for the production point of low efficiency. Furthermore, the


researcher can adopt quantitative measures to calculate the production cost or profit function of the company in order to analyse the company’s technical, allocative and cost efficiency. Previous studies of banks’ financial efficiency have examined efficiency and performance from several different aspects. Table 1 (Aly et al., 1990; Barr et al., 2002; Lin et al., 2004; Miller and Noulas, 1996; Sherman and Franklin, 1985; Siems, 1992; Yue, 1992) summarises the principal articles by using DEA in efficiency analysis of banks.

3 Mathematical foundations for DEA

DEA is a technical efficiency measure of the multiple-output/multiple-input developed by Farrell. DEA optimises each individual observation with the objective of calculating a discrete piecewise linear frontier determined by the set of Pareto-efficient DMUs. Using this frontier, DEA computes a maximal performance measure for each DMU in relation to all other DMUs. Each DMU lies on the efficient (external) frontier or can be enveloped within the frontier. The DMUs that lie on the frontier are the best practice institutions and retain a value of 1. Those enveloped by the external surface are scaled against a convex combination of the DMUs on the frontier facet closest to it and have values somewhere between 0 and 1.

In this study, the DEA has been used as the method for developing the efficient frontier because it focuses solely on productive efficiency and does not require the explicit specification of the form of the underlying production relationship. Its usefulness in benchmarking is adopted here to provide an analytical quantitative tool for measuring relative productive efficiency among banks.

To guide this discussion, there are 60 banks to be evaluated. Each bank utilises several inputs to produce four different outputs. Specifically, bank j uses amounts Xj = {xy} of inputs and produces amounts Yj = {yrj} of outputs r = 1, …, s. We assume that the observed values are positive, so that xij > 0 and yrj > 0. The s⋅n matrix of output measures is denoted by Y and the m⋅n matrix of input measures is denoted by X.

A constrained-multiplier, CCR input-oriented DEA model was used to reduce the multiple-input, multiple-output situation for each bank to a scalar measure of efficiency (Charnes et al., 1978). Consider the following ratio form of the model:

CCR Model

1

1

maxs

rk rkrk m

ik iki

U YE

V X=

=

= ∑∑

(1)

s.t.

1

1

1, 1, ,s

r rjrm

i iji

U Yj n

V X=

=

≤ =∑∑

…

, 0, 1, , 4, 1, , 4rk rkU V r iε> > = =∑ ∑ … …

26 K-H. Lu et al.

Table 1 Principal articles on use of DEA in efficiency analysis of banks


Table 1 Principal articles on use of DEA in efficiency analysis of banks (continued)

28 K-H. Lu et al.

Table 1 Principal articles on use of DEA in efficiency analysis of banks (continued)


where Ek represent the relative efficiency score of bank k, Xik represent the observed amounts of the ith input variable of the kth DMU, X1k represent the observed amounts of the interest expenses of the kth DMU, X2k represent the observed amounts of the fixed assets of the kth DMU, X3k represent the observed amounts of the deposits of the kth DMU, X4k represent the observed amounts of the employees number of the kth DMU, Yrk represent the observed amounts of the rth output variable of the kth DMU, Y1k represent the observed amounts of the interest income of the kth DMU, Y2k represent the observed amounts of the non-interest income of the kth DMU, Y3k represent the observed amounts of the loans of the kth DMU, Y4k represent the observed amounts of the investments of the kth DMU, Vi represent the weights of the ith input, Ur represent the weights of the rth output, n represent the numbers of domestic banks of each year (1998–2004) and ε is a non-archimedean constant that is smaller than any positive-valued real number (ε = 10−6).

4 Results

4.1 Analysis of the overall efficiency of all the banks

On the basis of the year-end data collected from 1998 to 2004, this research has measured the operating efficiency of banks in Taiwan with the CCR model in DEA. Interest expenses, fixed assets, deposits and number of employees are treated as input variables while interest income, non-interest income, loans and investments are treated as output variables. The definition of input and output variables is described in Table 2. By using the Pearson’s correlation test, the inputs and outputs are found to be significantly correlated. The results of Pearson’s correlation test correspond to the isotonicity that the DEA model requires. Thus the input and output variables could be used for this research to measure the operating efficiency.

Table 2 Definition of input/output variables

Variance Define

Interest expenses Deposits interest, borrowing funds interest, other interest expenses

Fixed assets Property and equipment Deposits Check deposits, demand deposits, time deposits, saving deposits,

foreign currencies deposits, government deposits Employees number Total employees Interest income Loan and discount interest, interest due from banks, bonds interest,

other interest income

Non-interest income Gain on sales of securities, gain on sales of stocks, commission and service fees, currency exchange gains

Loans Discounts, import bills purchased, overdrafts, short-term loans, medium- and long-term loans, medium- and long-term loans, export bills purchased, non-accrual loans

Investments Cash, due from banks, government securities, other investments

In order to understand the operating efficiency of all banks in Taiwan, this research applied the CCR model to work out the overall operating efficiency for each domestic bank in each year. The score of each DMU in each year is given in Table 3. See Appendix 1 for the list of banks.

30 K-H. Lu et al.

Next, the results of this study are analysed from the cross-sectional and longitudinal aspects.

Table 3 Operating efficiency score of each DMU in each year

1998 1999 2000 2001 2002 2003 2004

DMUs Score DMUs Score DMUs Score DMUs Score DMUs Score DMUs Score DMUs Score

1 100 48 100 48 100 50 100 48 100 48 100 50 100

2 100 50 100 49 100 48 100 3 100 50 100 48 100

3 100 2 100 20 100 3 100 50 100 54 100 44 100

4 100 3 100 50 100 21 100 6 100 11 100 51 100

5 100 18 100 3 100 10 100 7 100 26 100 54 100

6 100 5 100 21 100 7 100 4 100 3 100 26 100

7 100 7 100 10 100 6 100 21 95.68 35 100 3 100

8 100 6 100 7 100 4 99.36 18 94.25 21 100 10 100

9 99.82 11 98.98 6 99.98 5 95.84 5 92.95 7 100 35 100

10 99.02 4 97.02 11 97.05 8 94.92 35 91.59 4 100 18 100

11 98.92 17 96.95 5 96.59 45 91.27 13 89.73 53 100 30 100

12 97.24 1 96.92 4 93.22 13 90.66 52 89.69 5 99.7 4 100

13 97.12 16 96.81 2 92.68 18 88.36 8 88.48 18 98.86 7 100

14 97.09 22 95.82 12 91.28 32 85.31 36 85.23 12 97.18 53 100

15 97.08 9 95.81 26 90.42 14 84.02 16 84.98 51 96.3 13 100

16 97.08 26 95.66 45 89.56 16 83.6 22 84.44 30 94.4 20 99.54

17 96.88 13 95.53 1 89.3 19 83.6 45 84.35 55 93.8 14 98.8

18 96.75 19 95.21 18 89.24 15 83.4 10 83.78 13 92.92 5 98.18

19 96.45 12 94.37 13 88.73 22 83.3 14 83.43 29 90.7 22 97.92

20 96.36 15 93.86 16 86.45 31 81.75 49 82.69 41 90.69 21 97.58

21 95.67 32 90.93 15 85.33 30 80.2 32 82.44 14 90.27 33 97.53

22 95.4 25 90.85 30 85.04 40 77.35 15 81.29 40 87.65 37 97.28

23 95.24 45 90.63 17 84.77 35 76.9 30 80.82 32 87.43 11 97.18

24 95.17 39 90.27 32 84.53 12 76.69 54 79.69 16 87.13 41 96.77

25 95.15 8 90.09 22 84.07 1 76.42 19 79.67 47 86.56 55 96.67

26 94.14 27 89.79 14 83.67 2 75.22 31 78.86 22 85.76 29 96.33

27 93.78 31 89.65 19 82.84 43 74.86 26 78.62 10 84.35 24 94.69

28 93.3 51 89.53 31 82.62 11 74.77 33 77.93 49 82.57 16 94.49

29 91.91 30 89.49 23 82 28 74.65 12 76.42 58 82.41 60 94.09

30 91.9 41 88.81 35 81.37 51 74.56 40 76.33 33 82.08 56 93.89

31 91.77 35 88.47 41 81.31 23 74.37 29 76.25 15 81.41 40 91.88

32 91.63 23 87.92 39 81.01 24 74.13 9 76 20 80.26 32 91.68

33 89.99 14 87.71 40 79.24 36 73.21 56 75.62 19 79.99 47 91.2

34 89.3 21 87.08 43 78.62 9 72.73 28 74.63 31 78.78 12 91.18

35 89.08 10 86.49 56 78.58 29 72.01 24 74.02 36 78.71 45 90.88

36 89.02 24 86.34 51 77.53 26 71.45 41 72.79 8 78.62 58 90.5

37 87.84 42 86.2 8 77.27 41 71.28 51 71.54 34 76.64 28 88.85

38 87.65 29 85.83 25 77.13 49 70.42 37 71.14 45 75.63 15 85.9


Table 3 Operating efficiency score of each DMU in each year (continued)

1998 1999 2000 2001 2002 2003 2004

DMUs Score DMUs Score DMUs Score DMUs Score DMUs Score DMUs Score DMUs Score

39 87.42 40 85.72 29 76.37 58 68.73 11 70.85 59 75.22 59 83.7

40 87.28 43 85.61 28 76.26 33 68.42 55 70.77 28 74.57 25 82.77

41 87.08 28 85.5 9 75.84 37 67.51 58 69.62 24 72.57 46 82.35

42 86.87 56 83.6 24 74.53 42 67.19 20 69.16 56 71.71 57 81.44

43 86.76 37 81.92 36 74.06 25 66.77 59 69.07 44 67.77 19 80.72

44 83.53 47 81.52 37 73.19 20 66.54 47 67.67 25 67.59 34 79.7

45 83.21 20 80.62 47 71.9 56 66.43 27 66.32 37 67.58 31 78.75

46 81.34 33 80.03 33 71.6 47 66.34 25 65.94 42 63.61 36 78.39

47 80.84 36 78.2 42 71.02 17 65.55 42 64.57 46 55.54 8 75.37

34 75.34 38 70.89 27 65.04 44 63.02 27 49.95 27 29.28

44 74.77 27 69.86 44 64.56 46 60.49 38 45.87

38 73.85 44 67.95 46 59 34 60.09

46 67.5 34 65.41 34 55.85 38 52.27

46 61.24 38 55.57

4.1.1 Cross-sectional analyses

There are eight efficient banks in 1998 which are DMU1 to DMU8; but comparably there are 39 inefficient banks. In 1999, there are eight efficient banks which are DMU2, DMU3, DMU5, DMU6, DMU7, DMU18, DMU48 and DMU50. At the same time, there are 43 inefficient banks, which are mainly the medium- to small-sized enterprise banks. The results show that these banks require more improvement in operating efficiency.

In 2000, there are eight banks, which are considered as the efficiently operating enterprises, and 44 inefficient operating banks. The efficiently operating banks are DMU3, DMU7, DMU10, DMU20, DMU21, DMU48, DMU49 and DMU50.

The efficient banks in 2001 are DMU3, DMU6, DMU7, DMU10, DMU21, DMU48 and DMU50 compared to 44 inefficient banks. There are six efficient banks in 2002, which are DMU3, DMU4, DMU6, DMU7, DMU48 and DMU50, compared to 45 banks considered as inefficient.

In 2003, DMU3, DMU4, DMU5, DMU7, DMU11, DMU21, DMU26, DMU35, DMU48, DMU48, DMU50, DMU53 and DMU54 are the efficient bank, with 38 inefficient banks.

There are 15 efficient banks in 2004, which are DMU3, DMU4, DMU7, DMU10, DMU13, DMU18, DMU26, DMU30, DMU35, DMU44, DMU48, DMU50, DMU51 DMU53 and DMU54 in comparison to 33 inefficient banks.

On the whole, from 1999 to 2004, there are four banks (DMU48, DMU50, DMU3 and DMU7), which are considered to be operating with high efficiency. DMU48 and DMU50 have joined the financial sector in 1999. They top the list in operating efficiency from 1999 to 2004. DMU3 and DMU7 enjoy the highest operating efficiency from 1998 to 2004 as well. In contrast, DMU27, DMU38 and DMU46 have the lowest operating efficiency. From the result, it has shown that the medium- to small-sized enterprise banks are mainly the low efficient banks. This also means that the medium- to small-sized enterprise banks still have room to improve their operating efficiency. This research

32 K-H. Lu et al.

suggests that DMU16 cuts down its operational size, DMU38, DMU33 and DMU34 expand their operating scope, and DMU37 adjusts the management to improve its operating efficiency.

4.1.2 Longitudinal analyses

The changes in overall efficiency from 1998 to 2004 are given in Table 4. And the number of efficiently operating banks has increased from 6 to 15 from 2001 to 2004, given in Table 3. This is a great improvement. This is probably because consumers start to use credit cards and cash cards as the credit expanding instrument rather than the payment tools when a large number of credit cards and cash cards are issued to compete with each other. The loans made through credit cards and cash cards are unsecured loans. Therefore, the banks have faced the higher risk and low collection rate. As a result, the loans are likely to become non-performing loans to the banks. Consequently, the government of Taiwan has since the end of 2001, started to clear up the bad debts of the financial institutions in order to strengthen the competitiveness of the financial sector. A series of financial reforms implemented by the government are likely to trigger significant improvements in the operating efficiency of domestic banks.

Table 4 Overall average efficiency of each year

Year 1998 1999 2000 2001 2002 2003 2004

Average efficiency

93.45 89.87 84.07 78.66 79.71 83.06 90.32

4.2 Input and output measures

On the basis of the results given in Table 3, according to the overall efficiency of each bank in each year, these banks are classified into four different groups by using quartile method. The results were given in Table 5. The Q1 group includes the top 25% of banks that have the highest efficiency with the average efficiency of 0.98. The Q2 group includes the top 26–50% of the banks with the average efficiency of 0.89. In 2004, there are fifteen efficient banks. This indicates that over 25% of the banks are efficient. This research classified fifteen efficient banks in 2004 as Q1 group while the remaining banks are sorted into three groups according to their efficiency. These four groups are compared by the efficiency trend with the variables and examined to see if there are any significant differences. One-way ANOVA was used to test whether there are significant differences in the inputs and outputs of four groups with different efficiency.

Table 5 Four quartile of each year’s efficiency

1998 1999 2000 2001 2002 2003 2004

Q1 0.9958 0.9897 0.9842 0.9695 0.9556 0.9989 1

Q2 0.9635 0.9298 0.8711 0.806 0.8244 0.9125 0.9762

Q3 0.9174 0.8763 0.7968 0.7286 0.7478 0.8096 0.9212

Q4 0.8543 0.7903 0.7106 0.6421 0.6492 0.6563 0.7622

Average 0.9358 0.8965 0.8407 0.7866 0.7943 0.8443 0.9149


4.2.1 Input measures

There are four variables in the input measure. Each of them is analysed separately:

• Interest expenses: the results of one-way ANOVA test show that there is only one significant difference between Q1 group and Q4 group in 2002 based on the ratio of the Interest expenses to Average Assets (I/AA). There is no significant difference in the remaining six years. Overall, the average of interest expenses in Q1 group is smaller than that of Q4 group every year. The I/AA of each group decreases progressively in each year. See Figure 1(a) for the interest expenses in each efficiency group.

• Fixed assets: for the fixed assets variable, part of the results show a significant difference while part of the results show no major difference between Q1 group and Q4 group, as shown in Figure 1(b). The results revealed that there are significant differences between Q1 group and Q4 group from 1999 to 2001, and 2003. Moreover, the averages of fixed assets of Q4 group are larger than those of Q1 group in each year.

• Deposits: as shown in Figure 1(c), the deposits variable between different efficiency groups has found to have significant differences in each year except in 2004. The results also show that the averages of deposits of Q1 group are greater than those of Q4 group from 1999 to 2004.

• The number of employees: the results shown in Figure 1(d) revealed that there is only one significant difference between Q1 group and Q4 group in 1998 with regard to the number of employees. The results showed that there are significant differences between Q1 group and Q4 group from 1999 to 2001, and 2003. Moreover, the average of fixed assets of Q4 group is larger than those in Q1 group every year.

Figure 1 Comparing (a) the interest expense between each group, (b) the fixed assets between each group, (c) the deposits between each group and (d) the number of employees between each group

34 K-H. Lu et al.

Figure 1 Comparing (a) the interest expense between each group, (b) the fixed assets between each group, (c) the deposits between each group and (d) the number of employees between each group (continued)

Note: *Represented there is a significant difference between Q1 and Q4 at p < 0.05.

The significant difference in the total number of employees of companies in each group is only found in 1998. The total number of employees of the companies in Q1 group has been slightly increasing since 2001. The total number of employees of the companies in Q4 group jumps from 1269 in 2003 to 3102 in 2004. Each group has crossed with each other in 2004.

4.2.2 Output measures

There are four variables in the output measure. Each of them is analysed separately:

• Interest income: as shown in Figure 2(a), the results revealed that there are no significant differences between each group. But from the graph, we found that there is a trend that the ratio of interest income to average assets is progressively declining in each year.

• Non-interest income: in this variable, the results shown in Figure 2(b) revealed that there is only one important difference between Q1 group and Q4 group in 2003. Although, there are no major differences between each group in other years, the figure showed that there is a reasonable gap between Q1 group and Q4 group. Furthermore, the Q4 group non-interest income has been increasing since 2002.

• Loans: part of the results show a significant difference while rest of the results show little difference between Q1 group and Q4 group, as shown in Figure 2(c). The results revealed that there are significant differences between Q1 group and Q4 group from 2000 to 2002. The average of loans in Q1 group is noticeably smaller than those in Q4 group; and the average of loans in Q4 group has a substantial decline in 2004. In 2004, the ratio of loans has risen in Q1 and Q3 groups. In the contrary, a decrease has occurred in Q2 and Q4 groups with an intersection point in 2004.


• Investments: as shown in Figure 2(d), there is a gap between Q1 group and Q4 group. However, a decrease has occurred in Q4 group and has an intersection with Q1 group in 2004. In addition, the graph shows that there were bigger changes between Q2 group and Q3 group.

Figure 2 Comparing (a) the ratio of interest income to average assets between each group, (b) the ratio of non-interest income to average assets between each group, (c) the ratio of loans to average assets between each group and (d) the investment between each group


36 K-H. Lu et al.

4.3 Comparison of the financial ratios in each group

In this section, we launched the comparison between the effectiveness of DEA measurement and the traditional financial analysis.

• Asset liability ratio: this is a measure of the risk level of a bank. Effective allocation of assets and liabilities can help maximise the net interest income of a bank and control the risk exposure. As shown in Figure 3(a), significant differences between the asset liability ratios of each group are only seen in 2003 while Q4 shows an obvious upward trend.

• ROAA: ROAA is the ratio of pretax profit divided by average total assets and also an indicator of measuring the profitability of a bank. As a business, pursuing profits is one of the objectives of a bank’s operation. Therefore, profitability is not only an indicator of a bank’s operating efficiency but also crucial to its sustenance. As shown in Figure 3(b), the significant differences of the ROAA in the groups are only shown in 2000 and 2001. Q1 group has a higher ROAA while Q4 group has a lower ROAA. In 2002, each group shows an obvious decline in ROAA.

• NPL/GL: NPL/GL ratio is the non-performing loans divided by total gross loans. As NPL/GL ratio is used to measure the asset quality, the bank with higher NPL/GL ratio is more likely to have bad debts, which may result in losses and lower the operating efficiency. As shown in Figure 3(c), the only two years that have not showed significant differences in NPL/GL ratio among all the efficiency groups are 2003 and 2004. Between 1998 and 2002, Q1 group has lower NPL/GL ratio comparing to Q4 group. This shows that banks with higher efficiency tend to have lower NPL ratios. Q4 group has showed an apparent increase of NPL/GL ratio in 2001. This is possibly because consumers start to use credit cards and cash cards as an instrument for credit expansion instead of an instrument for payment when a large number of credit cards and cash cards are issued to compete with each other. Loans obtained through credit cards and cash cards are unsecured and face higher risk and low collection rate. As a result, they are likely to become non-performing loans for the banks.

Figure 3 (a) The asset liability ratio of each group, (b) the ROAA ratio of each group and (c) the NPL/GL ratio of each group


Figure 3 (a) The asset liability ratio of each group, (b) the ROAA ratio of each group and (c) the NPL/GL ratio of each group (continued)


5 Overall extent of possible improvement

Slack variable is the indicator provided in the CCR model. It represents the extent that the input should decrease or the output should increase when the inefficient DMUs attempt to have the same efficiency of the resource useful with those of efficient DMUs. The slack variable analysis aims to examine the inefficient DMUs through slack variables and efficiency values. The results can indicate the extent to which the inefficient DMUs can improve its input resources and output quantities to reach the same level of efficiency.

The following slack variables model is a duality model, which transformed from Equation (1):

1 1min

m s

k i ri r

h S Sθ ε − +

= =

= − + ∑ ∑ (2)

s.t.

1

1

0

, , 0, 1, , , 1, , 4, 1, , 4

n

j ij ik ij

n

j rj r rkj

j i r

X X S

Y S Y

S S j n i r

λ θ

λ

λ

−

=

+

=

− +

− + =

− =

≥ = = =

∑

∑… … …

where θ and ( 1, , )λ = …j j n are the dual variables of the linear program model

(Equation (3.1)).

38 K-H. Lu et al.

The scalar variable θ is the (proportional) reduction that should be applied to all inputs of DMU in order to make it efficient. The dual variable λj represents the amount by which inputs and outputs of unit j should be multiplied to create the composite unit. The slack variables ( iS− , rS+ ) are standard linear programming terminology for

additional variables added to the model in order to convert inequality constraints to equality constrains. Therefore, the optimisation can be achieved in two steps: first the maximal reduction of inputs is computed (by the optimal θ*), then movement on the efficient frontier is achieved using slack variables –

iS and .rS+ Improper selection of a

value for ε can result on serious errors as indicated by computational testing. DMU is efficient if and only if θ * = 1 and all slacks are zero. θ * < 1 and non-zero slacks indicate the sources and amount of inefficiencies. We can calculate the relative efficiency score from the above model. We can further estimate the targeted value for each output/input of each banks. That is: * *

ik ik ikX X Sθ= − and *jk jk jkY Y S+= + where θ * is the solution

of θ; *jkS+ , *

ikS are the solutions of jkS+ and ,jkS− respectively. Xjk and Yjk represent the

targeted value for the input/output of kth bank. Xik and Yjk mean the corresponding actual value of banks. In addition, we can compute the magnitude of potential improvement for specific output and input for each inefficient bank. That is: i i iX X X∆ = − and

.i i jY Y Y∆ = − We can also compute the figure of ( / ) %100i i iW X X= × and

( / ) %100j j jR Y Y= × , which represents the percentage of improvement for specific

input and output of each inefficient bank, respectively. Table 6 lists the percentage of possible improvement for each input variable and

output variable in each year. This is achieved by adding up the potential improvements for each unit – no weightages are applied. Table 6 also indicates that the non-interest income and investments are the output variables that require more improvement in each year. In other words, inefficient banks need to focus on non-interest income and investments. Regarding to the input variables, no particular improvements are required for any variable.

Table 6 Percentage of total potential improvements

Total potential improvements

1998 1999 2000 2001 2002 2003 2004

Interest expenses

−2.56% −2.37% −7.63% −8.83% −6.35% −4.15% −6.18%

Fixed assets −8.84% −3.54% −4.02% −11.98% −14.37% −5.56% −14.94%

Deposits −4.87% −4.95% −2.91% −4.89% −11.93% −6.98% −8.75%

Employees number

−6.64% −2.47% −3.28% −5.74% −8.13% −5.84% −9.87%

Interest income

0.64% 0.03% 0.01% 0.36% 0.45% 0.51% 1.26%

Non-interest income

58.14% 47.46% 32.23% 41.69% 16.98% 59.16% 44.17%

Investments 18.01% 38.52% 48.4% 25.07% 38.48% 17.45% 12.85%

Loans 0.31% 0.65% 1.52% 1.45% 3.28% 0.35% 1.99%


6 Conclusions

This research adopted the CCR model of DEA to measure the operating efficiency of banks in Taiwan. We have examined how the inputs, outputs and financial ratios of the banks correlate to their performance in the high efficiency and low efficiency groups. Eventually, the overall extent of possible improvements in each year is suggested. The following are the conclusions from the cross-sectional and time series aspects.

6.1 Inputs and outputs measures

Among the input and output variables of each year, the variables of fixed assets, deposits and loans have demonstrated marked differences in the high efficiency group and low efficiency groups for several years. The variable of fixed assets shows significant differences between the high efficiency group and low efficiency groups in five years out of seven years and the value of fixed assets for high efficiency group is smaller than that for low efficiency group in each year. The variable of deposits shows considerable differences in six out of seven years, and the value of deposits for high efficiency group is smaller than that for low efficiency group in each year. The variable of loans shows significant differences in three out of seven years, and the value of loans for high efficiency is smaller than that for low efficiency group in each year.

6.2 Financial ratios

It is a general concept that an efficient bank has better asset quality, higher profitability and lower risk level. This research has divided the banks into four groups according to their efficiency and verified that efficient banks have lower asset liability ratio, higher ROAA ratio, and lower NPL/GL ratio. Among them, NPL/GL ratio shows significant differences for several years. Efficient banks have low NPL/GL ratio while inefficient banks have high NPL/GL ratio.

6.3 Total potential improvements

By using slack variable analysis, we have obtained the percentage of potential improvement for each input and output variables in each year. The results revealed that the non-interest income and investments variables for most banks have more room to improve. However, the measuring results are the relative efficiency value, not the absolute efficiency value. In other words, even the banks that are evaluated to be the efficient banks will change their efficiency scores when different objectives or different input or output variables are chosen. Therefore, the efficient banks in this study still have to check their weaknesses frequently, and learn from other competitors in order to maintain their operating efficiency. For the inefficient banks, they can refer the results of the slack analysis to improve their inefficient performance.

40 K-H. Lu et al.

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Appendix 1

List of banks

DMUs The name of banks

1 Cathay United Bank

2 Da An Commercial Bank

3 Central Trust of China

4 Chinatrust Commercial Bank

5 The International Commercial Bank of China

6 Formerly UWCCB

7 Chiao Tung Bank

8 Bank of Taiwan

9 Grand Commercial Bank

10 Shanghai Commercial & Savings Bank Ltd.

11 The Chinese Bank

12 Far Eastern International Bank

13 Land Bank of Taiwan

14 E.Sun Bank

15 Hua Nan Commercial Bank Ltd.

16 Taiwan Business Bank

17 Union Bank of Taiwan

18 Taishin International Bank

19 First Commercial Bank Ltd.

20 Taichung Commerical Bank

21 Fubon Commercial Bank

22 Chang Hwa Bank

23 Asia Pacific Bank

24 Sunny Bank

25 Bank of Overseas Chinese

26 Entie Commercial Bank

27 Chung Shing Commercial Bank

28 Hsinchu International Bank

29 International Bank of Taipei

30 The Farmers Bank of China

31 Bank of Taipei

32 Taiwan Cooperative Bank Ltd.

33 Enterprise Bank of Hualien

34 Tai-Tung Business Bank

35 Cosmos Bank

36 Macoto Bank

37 Tainan Business Bank

42 K-H. Lu et al.

Appendix 1 (continued)

DMUs The name of banks

38 Bank of Kaohsiung

39 Baodao Commercial Bank

40 Chinfon Bank

41 Ta Chong Bank

42 Pan Asia Bank

43 Bank SinoPac

44 Lucky Bank Taiwan, Inc.

45 Bank of Kaohsiung

46 Kao Shin Commercial Bank

47 Bank of Panhsin

48 Industrial Bank of Taiwan

49 United-Credit Commercial Bank

50 China Development Industrial Bank

51 Cota Commercial Bank

52 Union Bank

53 Cathay-Union Bank

54 Union Bank of Taiwan

55 Fuhwa Bank

56 Hwatai Bank

57 Bowa Bank

58 Jih Sun International Bank

59 Bank SinoPac

60 Taiwan Shin Kong Commercial Bank

Kuen-Horng Lu*

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