How to choose inputs and output when using DEA model is debated in the academic literature. The choice of inputs and output will influence the efficiency value evaluated, so we need to think thoroughly beforehand and choose the most important ones. Basically, there is a common consensus in the choice of inputs and output while calculating efficiency values
Step1: Delete 36 local branches of foreign banks
Step2: Delete 16 non-commercial banks
Step3: Delete 5 banks with more branches in any
individual city other than Taipei 81 banks served in
Taiwanese banking market
45 domestic Taiwanese banks
29 domestic Taiwanese commercial banks
24 domestic Taiwanese commercial banks in our final list of DMUs
production approach. In our paper, we choose some important financial ratio indices to capture the performances of banks assessed. 25 financial ratios, can be divided into five parts including, are Main Financial and Performance Ratios for domestic banks collected by the CBC (Central Bank of China, Taiwan) which are summarized in Appendix 4. All of these 25 indices are important but not all of them can be included into our model. We include three key factors as output to evaluate performance, which are Profitability, Asset Quality and Growth Ability, although the conventional intermediation or production approaches have not taken the measurement of risk and growth ability into account.
It goes without saying of the importance of Earning Indices, so we have chosen ROE, ROA, P/L and Margin rate, all four of these are popular in practice as measurements of earning performance. Bertrand Rime et al. (2003) have mentioned that “the most obvious way to compare the performance of different size institutions is to look at familiar accounting ratios like ROA, ROE.” Muhammet Mercan et al. (2003) have used ROE as an indictor to measure the profitability. Dean Amel et al. (2002) have mentioned that “The simplest
approach consists of comparing balance sheet ratios that describe costs (e.g., operating costs over gross income) and profitability (e.g., return on assets or on equity).” George E. Halkos et al. (2004) have employed ROE, P/L and ROA as profitability indicators. Hugh Crowford et al.
(2004), in THE ART OF BETTER RETAIL BANKING, have mentioned that ROE is the most widely used and ROA is a common used performance measurement. In addition, the two indices are high-level and catch all measurements of performance. In fact, ROA and ROE may be treated as similar indices, however if banks are listed in order of their ROE(s), which is an approximation to a listing from best to worst, it is not the same order as their ROA(s).
(p.28) Note that Margin rate is a percentage that how many net-earnings earned by firms from
$100 dollar operational revenue, so we can realize the net-earning structure in operational revenue. Furthermore, the higher the Margin rate is, the more the cost efficient it is, thus to a certain extent, we can regard the Margin rate as a cost efficiency index.
We can’t obtain the finest picture of a bank’s performance if we don’t include risk into consideration. In fact, authorities have focused on the risk control since 1998, because of the eruption of many crucial financial events and bankruptcy in financial sectors which were blamed to their poorer performance in risk control. In addition, authorities have given some incentives to encourage banks to reduce their Non-performing loan ratio. Therefore, we used the Non-performing loan ratio (NPL) to capture the concept of risk assessment in this paper, although NPL only captures Credit Risk of loans, not all risks faced by banks. The main reason we didn’t include all the risks is because we can’t explain those risk ratios in only one side. Take Leverage Rate as an example. According to Vasconcelos (2003), the Leverage rate expresses the institution’s ability in “circulating” more money without increasing by the same proportion its own capital, or rather, its capacity in levering assets by third party’s resources.
The higher the leverage rate, the greater is the liquidity risk borne by the institution. Thus, a higher leverage rate indicates a less risk-averse institution. It is, however, more prone to insolvency if assets fall abruptly and in great numbers. By the introduction of the Leverage rate, we can understand that we can’t judge a higher leverage rate as good or bad because it may be explained by higher risk (bad) and more profit potential (good), therefore, we can’t use it as the output in the DEA model. Similar stories also happened in other risk ratios, so we don’t take them as output in our DEA model. Note that the NPL ratio is negative as related to other output values, so we should do some adjustments which will be discussed in the next section.
Finally, according to (Dyson 2001) what about the so-called Target and Objectives which we have used as goals to evaluate efficiency of units of assessment usually has
influenced a manager’s behaviors, and furthermore, it ultimately changes the performance of a firm. However, profitability indices are common targets for banks, although they are short-run operating outcomes. In order to make balances between long-term and short-term objectives when we measure performance of units assessed, managers should consider both long-run and short-run cases. In this thesis, we choose growth ratios of deposits and loans into
regulated by the CBC and we only selected two of them, since the most important and conventional activities of banks are deposits and loans businesses. Therefore we intuitively characterize banks as outstanding performers if their market share of loans and deposits are larger. In other words, the proportion of deposits and loans to the entire market and the market share of deposits and loans, can be treated as monopoly indicators. The higher of these two ratios would indicate higher profitability. The higher of the growth rate of these two ratios would indicate higher profitability prospects. As a result, we include growth rates of loans and deposits as output. In summary, we include three parts of performance measurement indices, which are asset quality, profitability and growth, and seven indicator ratios in our final list of choices of inputs and output as described below:
1. Asset quality:
Non-performing loan ratio (NPL) (%)
=Non-performing loans6 divided into total loans 2. Profitability:
(1) Income 7-to-Average Equity (ROE) (%) (2) Income-to-Average Asset (ROA) (%)
(3) Income-to- Operating Revenue (Margin) (%)
(4) Income-to-number of Employee (PL) (thousand NT dollars / per employee) 3. Growth Ability:
(1) Growth rate of Deposit (GDR) (%) (2) Growth rate of Loan (GLR) (%)
3.2.2 Examinations and Adjustments of Output Data
6 The use of the new definition of NPLs has started from 1 July 2005. We know the old definition of NPLs before 30 June 2005 from the website of the CBC (Central Bank of China, Taiwan). According to the new definition of NPLs regulated by the CBC since 1 July 2005, the items of new NPLs’ definition includes loans which the repayment of principal or interest have been overdue for more than 3 months and any loan of which the principal debtors and surety has been disposed, although the repayment of principal or interest have not been overdue for more than 3 months.
7 Income before tax
The efficiency values can be easily obtained by using the DEA Excel Solver provided in Cooper, Seiford and Tone (2000). However, there are several adjustments should be done before we run the DEA Excel Solver software, when certain situations described below occur:
(1) Negative values exist in data set, (2) The data set violated the basic correlation assumption required by DEA model, and this two situations can be found in our data set.
Descriptive statistic of original data for year of 2005 has calculated and shown in Appendix 5. We can find out negative values and negative correlation in our output data. As shown in Appendix 5, values of ROE, ROA, Margin, PL, GDR, and GLR exit negative values, so we have paralleled the negative values to solve the negative value problem. Take ROE as an example, the parallel steps include: (1) Adding the modulus of minimum value of ROE to all ROE data; then (2) Adding one to all adjusted ROE data. There are no negative values in our data set after this adjustment process has been done.
Appendix 6 is shown the coefficient correlation of the original data set for the year of 2005. It’s clearly that NPL data is negative related to all the other data, because
Non-performing Loans are undesirable outputs for banks. We have done several adjustment processes by the suggestion of Seiford and J Zhu (2002, 2005): (1) Calculate the maximum value of NPL and minus all NPL to obtain a set of new data; then (2) Adding 1 to all NPL data.
There are positive relationships between any of two outputs in our data set since the adjustment has been done.
EMPIRICAL RESULTS
4.1 DESCRIPTIVE STATISTICS AND CORRELATION COEFFICIENTS OF THE