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					         Marketing and Operational Efficiency of Financial Holding
      Companies in Taiwan: The Application of Slacks-Based Measure

Cheng-Ru Wu1,*, Ya-Mei Wang2 , Che-Wei Chang3 , Hsin-Yuan Chang4
      Graduate Institute of Business and Management, Yuanpei University, 306 Yuanpei
St., Hsin Chu 30015, Republic of China, Taiwan.
  Department of Information Management, Yuanpei University, 306 Yuanpei St., Hsin
Chu 300, Taiwan, R.O.C.
    Insurance and Financial Management Department, Takming University of Science
and Technology ,56, Sec.1, Huanshan Rd., Nei Hu, Tai Pei 11451, Taiwan, R.O.C.

        The aim of this paper is to explore Taiwan's Financial Holding Companies

(FHCs) operating efficiency; a two-stage model, which evaluate banks marketing

efficiency (ME) and operational efficiency (OE). The study period covered

2003-2006, using data envelopment analysis (DEA), to explore Taiwan Financial

holding companies for bank’s operating efficiency. However, results showed that

large-sized and old banks were generally more efficient than small and new ones in

the marketing model. While large FHC banks were relatively poor in technical

efficiency, they were improving the decrease of returns to scale. Most large FHC

banks are classified by star ratings including the Chang Hwa, Cathay United banks,

Mean that large-sized FHC banks have better competitive power than the small ones.

Key word: Date envelopment analysis; Bank efficiency; Financial Holding

              Companies, Efficiency, Slacks-Based Measure

*Corresponding author. Tel.: + 886-3-6102315-6; fax: +886-3-6102317

E-mail address: (C.-R. Wu), (Y.-M. Wang) (c.-w. Chang), Chang)

1. Introduction
  Financial Holding Company (FHC) Act was implemented to induce reformation of

the industry from 2001. Taiwan has 14 Financial Holding Companies, demonstrating

the financial industry’s consolidation towards the larger trend. However, the financial

holding company of Taiwan's the main business model is none other than the pursuit

of greater scope of business and make more profit. Thus, Facing a highly competitive

environment, the formulation of competition strategy, strengthening of corporate

operations and upgrading of the quality of service have become essential for survival.

In formulating competition strategies, one major problem is the measurement of

management performance in the industry, prior to an assessment of advantages and

disadvantages. Another problem encountered the determination of factors that affect

managerial efficiency.

  According to the two-stage data envelopment analysis (DEA), we used multiple

inputs and outputs to measure the FHC banks managerial efficiency. While two-stages

of marketing efficiency (ME) and operational efficiency (OE) compared the banks

performance. It will analyze the efficiency differences among different characteristics

of the firms will be investigated and comparisons made of the efficiency of old and

new banks, and different sized banks. In addition, management performance was not

restricted to production efficiency or cost minimization, but was a more general level,

involving management and marketing services and sales. However, Banks provide

financial services, through use of non-price competition model to meet the needs of

customers with high quality services. Development of a bank's investment portfolio

will help the bank’s overall operating performance.

     Based on the measurement of managerial efficiency, a management decision

matrix is developed to serve as a basis for an assessment of the competitive strategy

of the 14 banks in Taiwan. So that each bank within the industry will aid

understanding of the gap between the banks and improve operational efficiency by

providing future operational strategies through analysis. The research methods were

aimed at the individual bank's financial performance computing, the results of further

understanding inferior to value for the performance of banks to be analyzed. Finally,

empirical results of the conclusions, recommendations and follow-up research


2. Literature review
     Because of application data envelopment analysis method have many literature,

this study only to discuss the bank operating efficiency. There have been several of

journals published regarding DEA on the banking industries efficiency levels, such as

the Journal of Economics and business 1998, the Journal of Banking and Finance

1993, the European Journal of Operations Research 1997, the Management Science

1999, and Journal of Econometrics 1990. The efficiency approach has been applied to

numerous settings over several years, including the financial services sector. Since the

first application of DEA for banking efficiency, by Sherman and Gold (1985), many

subsequent studies have been conducted. Since the traditional one-stage DEA method

is incapable of providing reflecting sufficient management information about a

company’s production process, the production process by dividing the actual

sequential process into two and treating the outputs of the first stage as the inputs for

the second stage. The same concept can be applied in this accounts, the outputs of the

second stage can be treated as the inputs of the third stage to develop a continuous

production process; this is the so-called multiple-stage DEA. Which was first by

Seiford and Zhu (1999) suggest using the two-stage DEA method and divided a

commercial bank’s production process into two stages, marketability and profitability.

Subsequently, Lu and Lo (2006) employ a two-stage production process including

profitability and marketability performance, using DEA.

     Furthermore, when factor-specific measure and BCC (Banker-Charnes-Cooper)

models were combined, they identified the inputs/outputs, which were most important

as well as distinguish those FHC’s which could be treated as benchmarks. That result

showed that large-sized FHC’s were generally more efficient than small-sized ones,

however, small efficient FHCs may easily become benchmarks, which the large

efficient FHCs were deemed as competitive niche players, indicating that further

mergers and acquisitions among FHCs should be considered in order to achieve

economies of scale. Luo (2003) apply DEA to a sample of 245 large banks; this study

provided evidence that large banks were achieving relatively low levels of marketing

efficiency. There are 34 (about 14%) banks, which had achieved higher levels of

profitability performance, but lower levels of marketing performance. Results also

indicated that the geographical location of the banks seemed not related to either the

profitability or marketability efficiency levels.

     Overall technical efficiency (OTE) of the profitability performance may predict

the likelihood of bank failures. Manandhar and Tang (2002) combines the

Service-profit chain into their research model and had a conclusion that the

profitability of a firm will ultimately increase when a firm improves its service quality

delivered to customers because good service quality will have good effects on

customer satisfaction and then indirectly have positive influence on profitability. Chan

(2002) assesses the management performance of banks in Taiwan, incorporating

operating efficiency, marketing efficiency, and financial achievements in the studied,

the results showed significant differences between the pre-calculated efficiencies.

Banks in public ownership exhibited superior performance of profitability, whereas

privately owned banks tended to perform better with regard to operational capabilities.

Furthermore, the relatively large banks exhibited superior performance on

profitability; whereas the smaller banks tended to perform better with regard to

operational capabilities Roth and Van (1991) highlight the importance of linking

marketing efficiency and operational efficiency. Halkos and Salamouris (2004)

explore the efficiency of Greek banks using a number of suggested financial

efficiency ratios and found that the banks with the larger total assets had the higher

efficiency levels, and wide variation of performance showed that increases in

efficiency were accompanied with less small banks due to mergers and acquisitions.

Zhu (2000) calculate through the DEA method, the efficiency of 364 companies and

finds     that   revenue-top-ranked   companies   do    not    necessarily   hold   the

performance-top-rankings in profitability and marketability.

        Numerous other studies have used the DEA method include Oral, Kettani, and

Yolalan, (1992); Grifell and Knox (1999); Sathye (2003); Lozano, Pastor, and Pastor,

(2002); Kao and Liu (2004); Uri (2003, 2006) and Chen, Yang and Yen (2007). In

addition, the Sathye (2001) study offered the important conclusion that government

deregulation and leadership strategies of merging banks provided operations with

significant impact. Yue (1992) propose that banking inefficiencies were due to many

input and output deficiencies, which indicated that the banks and not the rating scale

were at fault. This study referred to the relevant literature and the DEA method for a

two-stage approach to analyze Taiwan's FHC’s.

3. Methodology
3.1 Defining input-output factors

  Banks input and output definitions very according to different research perspective,

however, the most commonly used method for the Production Approach and the

Intermediation Approach. The production approach suggests that the bank use the

labor and capital from different capitol accounts, witch provide working output

capitol, excluding interest payments. The intermediation approach treats banks as

intermediary bodies, were non-depository account offer businesses financial resources,

which they may borrow against in the form of business loans, in order to make a

profit. Thus many lenders invest their money through banks, investing for the duration

of projects by paying various costs, such as costs, interest charges and the cost of

funds for projects, in which banks have invested. Most scholars have used the

intermediation approach because the project is relatively easy to calculate, the

information is easily obtained, and it can show the bank’s asset by type, size

differences, and multiple output characteristics. However, it should be noted that the

definition and measurement of bank inputs and outputs has long been debated among

researchers and there is no definite, commonly agreed choice (Soteriou and Zenios,

1999; Sathye, 2001). This study adopted the intermediation approach for definition of

input and output variables. In this study we measured managerial efficiency in

two-stages; marketing efficiency (ME) and operational efficiency (OE). These types

of efficiency are respectively based on the two-stage service provision process, which

describes two essential departments of bank operations. This paper was divided into

two stages with eight factors being expressed as inputs and outputs in each stage.

  The first stage addressed the measurement of marketing efficiency, a bank’s ability

to generate output in terms of its current personnel expenses and operating expenses,

using data based on 2003-2006 yearly average values. The input and output data were

extracted from the Taiwan Economic Journal (TEJ) data bank. The TEJ data bank is

commonly deemed valid, reliable, and available to the public. Thus, the operational

efficiency model had the following two output variables; total deposits and fee

income. The second stage measured operational efficiency with input in terms of its

current total deposits and fee income, the operational efficiency model has two

outputs: interest revenue and non-performing loan. Two-stage were as follows:

Stage I: (Marketing efficiency)

I.      Input factors

        (a). Total Deposits: With savings deposits, time deposits, demand deposits,

             check deposits, remittances, foreign currency deposits, and trust funds to

             handle Securities Lending and deposit margin financing coupons.

        (b). Fee Income: Bank sales of goods or products on the procedures for revenue.

II.     Output factors

        (a). Labor Costs: Including staff salaries, staff training expenses, allowances

             and benefits costs, etc.

        (b). Operating expenses: Including marketing, management and other expenses.

Stage II: (Operational efficiency)

I.      Input factors

        (a). Total Deposits: With savings deposits, time deposits, demand deposits,

             check deposits, remittances, foreign currency deposits, and trust funds to

             handle Securities Lending and deposit margin financing coupons.

        (b). Fee Income: Bank sales of goods or products on the procedures for revenue.

II.     Output factors

        (a). Interest revenue: The bank's interest income data.

        (b). NPL: Non-performing Loan variables include the collection.

      Form Fig.1, the marketing performance model (stage I) measuring a FHC's banks

ability to generate revenue consists of two inputs (labor costs and operating expenses)

and two outputs (total deposits and fee income). The operational performance model

(stage II) measuring a FHC's banks attractiveness in the two inputs (total deposits and

fee income) and three outputs (Interest revenue and NPL). The output and input

factors (six financial measures) used in this study as follows. Relevant information

input and output respectively shown in Table 1 and Table 2.

     Inputs                    Outputs                  Inputs              Outputs

Labor Costs                   Total deposits        Total deposits         Interest revenue
Operating expenses            Fee income            Fee income             NPL

    Stage I: Marketing efficiency              Stage II: Operational efficiency
              Figure1. Banks Inputs and Outputs in Production Process

  This study use the data based on 2003-2006. The inputs and outputs data were

extracted from the Taiwan Economic Journal (TEJ) data bank. The TEJ data bank is

commonly deemed valid, reliable, and available to the public, Table 1 presents the

descriptive statistics for our data set.

The descriptive statistics of the inputs and outputs in each DEA stage are reported in

Table 1. For example, the mean of Total deposits is about NT$ 631 billion in the

sample. In addition, the minimum is about NT$1,009,406 and the mean is

NT$8,946,080 for NPL.

                    Table 1      Descriptive statistics for the database
                                     Mean            SD          Minimum      Maximum
Payroll expense                      4913737         2891044      1051175       10000762
Operating expenses                   9838035         6009505      1498648       26026989
Total deposits                     631691844       378235786     28807755     1237871955
Fee income                           2943986         2125998       293599        8074723
Interest revenue                     23269104       12296555      2608292        44084057
NPL                                   8946080        6848139      1009406        25773512

  This study used input variables and output variables to Pearson correlation

verification, analysis inputs and outputs between the variables related to the degree to

avoid the improper admission of variables, which will affect results are correct.

Correlation analysis results as a table 2, the correlation coefficients were related to a

certain extent.

                   Table 2 Correlation coefficients among inputs and outputs
                       Payroll    Operating Total          Fee      Interest
       Factors                                                                   NPL
                       Expense    Expenses Deposits       Income    Revenue

Payroll Expense         1.000

Operating Expenses                  1.000
                        0.944       0.774
Total Deposits                                    1.000
                       (0.000)     (0.001)
                        0.803       0.870      0.689
Fee Income                                                1.000
                       (0.001)     (0.000)    (0.006)
                        0.956       0.933      0.890       0.832
Interest Revenue                                                     1.000
                       (0.000)     (0.000)    (0.000)     (0.000)
                        0.697       0.449      0.786       0.381     0.577
NPL                                                                              1.000
                       (0.006)     (0.107)    (0.001)     (0.179)   (0.031)

   3.2 The DEA methodology

      According to the concept of efficiency for performance evaluation method, the

   main comparison was between the input-output relations. DEA efficiency assessment

   model used envelope line technology to replace the general economics of individual

   production function, whose basic theory was based Farrell (1957), from the concept of

   technical efficiency. Three scholars Charnes, Cooper and Rhodes (1978) expand the

   single input single output model into the concept of multiple inputs-multiple output to

   create a form used to assess the decision-making units (decision making unit, DMU)

   relative efficiency, which can use non-identical units for a number of inputs and

   outputs various renovation to a single value, which was obtained for a value

   prefecture institutions organizational efficiency, commonly known as CCR model,

Another model has a slacks-based measure of efficiency (SBM) (Tone, 2001), which

is non-radial and deals with input/output slacks directly. The SBM returns an

efficiency measure between 0 and 1, and gives unity if and only if the DMU

concerned is on the frontiers of the production possibility set with no input/output

slacks. In that respect, SBM differs from traditional radial measures of efficiency that

do not take account of the existence of slacks.

     This study used methods for measuring efficiency levels of DEA; its theoretical

description is as follows:

3.2.1 CCR Model
  Charnes et al., (1978) pursuant to Farrell (1957) to assess the efficiency of the

theoretical basis, through two inputs, the outputs of a single model, and expand to

multiple inputs and multiple outputs model, the fixed pay scale under the assumption

that using linear programming method, the production border, and to assess each unit

for the relative efficiency, the law is known as the DEA model CCR. Suppose k

DMUs, each DMU k(k=1,⋯ ,N)Using the M input species  ik ( i=1,⋯,m;k=1,⋯,N)>

0,Production n outputs y rk (r=1,⋯,n;k=1,⋯,N)>0,As can be in a DMU k expected

that the efficiency values are as follows :

                                                     u y
                                                     r = 1
                                                             r   r k
                                Max           Hk =    m
                                                     v 
                                                     i = 1
                                                             i   i k


                                                                  u y   r       rk
                               subject to           Hk =          r=1
                                                                  v 
                                                                         i       ik

y rk :amount of the r th output for the k th DMU;

 ik :amount of the i th input for the k th DMU;

u r :the weight assigned to the r th output;

v i :the weight assigned to the i th input;

   : Non-Archimedean Quantity, is arbitrary small positive values

    Because (1) to scores-planning (Fractional Programming) model is not easy to

solve, Charnes et al., (1978) to be converted to linear programming (Linear

Programming) model, as follows:
                                    Max         k     =r
                                                         r = 1
                                                                         r k     u y        (2)

                                            n                      m
                             subject to    u y - v 
                                                     r       rk
                                                                             i    ik   0

               u r ,vi   ; i=1,    ,m ; r=1,            ,n ; k=1,                    ,N

    Formula (2) at the input items portfolio weighted average value of the one cases,

the items for output weighted average portfolio Maximum efficiency is used to

indicate the relative value. But its limitations - the number (n + k + m + l) was

significantly more than the number of variables (n + k), can use dual conversion pairs

(Duality) mode, reducing restrictions on the number of convenience-type solution, as

                                        m - n +
                       Min Hk =k -    Sik + Srk                                      (3)
                                        i=1    r=1   

                       subject            t 
                                          k = 1
                                                    k     i k    k i - -
                                                                       k       i k   +S =0


                                   
                                  k = 1
                                                    - S r k= y r k
                                                  i k

                 , k , Sik , Srk  0 ; i=1,
                          -     +
                                                                ,m ; r=1,       ,n ; k=1,   ,N

Formula (3) Sik , Sik and k for all DMU and the best allocation of DMU combination
             -     +

of linear equations, the weights θ efficiency of a practical value. Sik and Sik are the
                                                                     -       +

input and output variables variance (Slack Variable), the representative of the actual

value and the best efficiency of the difference between the value that can be used to

understand the inputs and outputs of the number of room for improvement. When θ =

    -     +
1, Sik = Sik = 0, the DMU said relatively efficient. When DMU relative efficiency,

and can be adjusted through the following and achieving optimum efficiency goals:

                                                         i* k=  *k  i-kS- *i k                (4)

                                                        y* =y rk +S+*
                                                         rk        rk

3.2.2 Slacks-based measure of efficiency (SBM)

We will deal with n DMUs with the input and output

matrices =  ij   R mxn and Y=  yij   R sxn , respectively. We assume that the data set

is positive, i.e. X > 0 and Y > 0. The production possibility set P is defined as

                               P = ( x , y  x X  ,   Y  ,
                                           )          y                                    0    (5)

Where       is a non-negative vector, in expression for describing a certain
                          n                                      n
DMU  x0 , y0  as x ij =  x ijj +si- and y rj =  y rj j -s r+ . With   0 , S-  0 and S+  0 .
                         j=1                                    j=1

The vectors S-  R m and S+  R s indicate the input excess and output shortfall of

this expression, respectively, and are called slacks. From the conditions x>0 and   0 .

Using S - and S+ , we define an index  as follows:

                                          1 m
                                       1 -  i-s / ix
                                          m i=1
                                    =                                                    (6)
                                          1 s
                                       1 +  + / ry
                                                s j
                                          s r=1

It can be verified that  satisfies the properties (i) units invariant and (ii) monotone

decreasing in input/output slacks, furthermore 0<  1 .

In an effort to estimate the efficiency of  x0 , y0  , we formulate the following

fractional program SBM in  , S - and S+ .

                                         1 m
                                      1 -  i-s / i x
                                 Min   = is = 1                                          (7)
                                      1 +  + / ry
                                                rs j
                                         s r=1
                      s u b j e c t t io
                                       j   
                                           j = 1
                                                    xi j =j -   x
                                                                i   +s    i=1,...,m


                                         yr j
                                     yj =
                                     r     
                                            j = 1
                                                           j- sr     r=1,...,s

                                           j , si- , sr+  0

The SBM can be transformed into a linear program using the Carnes Cooper

transformation in a similar way to the CCR model. Refer to Tone (2001) and Cooper

et al. (1978) for detail. Let an optimal solution for SBM be    ,   , S- , S+  . Based

on this optimal solution, we define a DMU as being SBM-efficient as follow:

Definition SBM-efficient, A DMU  x0 , y0  is SBM-efficient, if   =1 . This condition

is equivalent to S- =0 and S+ =0 i.e., no input excesses and no output shortfalls in

any optimal solution.

3.2.3 Slacks-based measure of super-efficiency (Super SBM)

     In this section, we discuss the super-efficiency issues under the assumption that

DMU  x0 , y0  is SBM-efficiency, i.e.   =1 . Let us define a production possibility set

P\  x 0 , y0  spanned by (X, Y) excluding  x0 , y0  , i.e.

                                         n               n                  
            p\(x 0 , y0 )=  x,y  x    j x j , y    j , y  0,   0                      (8)
                                       j=1,  0        j=1,  0             

Further, we define a subset

P\(x 0 , y 0 ) of P\(x 0 , y 0 ) as p\(x0 , y0 )=p\(x0 , y0 ) x  x0 and y  y0 

By the assumption X > 0 and Y > 0, P\(x 0 , y 0 ) is not empty. This distance is not less

than 1 and attains1 if and only if (x 0 , y 0 )  P\(x 0 , y 0 ) i.e. exclusion of the

DMU  x0 , y0  has no effect on the original production possibility set P.

As a weighted 1 distance from  x0 , y0  to (x 0 , y 0 )  P\(x 0 , y0 ) , we employ the

index  as defined by

                                               1 m xi
                                               m i=1 x i0
                                   Min       = s                                                   (9)
                                               1 yr
                                               s r=1 y r0

Based on the above observations, we define the super-efficiency of                     x0 , y0  as the

optimal objective function value   of the following program:

                                             1 m xi
                                             m i=1 x i0
                                   Min     = s                                                   (10)
                                             1 yr
                                             s r=1 y r0

                              subject to x       x
                                                j=1,  0
                                                            j       j

                                            y     y
                                                 j=1,  0
                                                                j       j

                                        x  x 0 and y  y 0

                                            y  0,   0

The Super SBM can be transformed into a linear programming problem using the

Charnes-Cooper transformation as linear programming
                                                 1 m xi
                                  = min  =      
                                                 m i = 1x i0

                                               1 s yr
                              subject to 1=      
                                               s r = 1y r0
                                           x      x
                                                 j=1,  0
                                                                j       j

                                           y      y
                                                 j=1,  0
                                                                j       j

                                        x  tx 0 and y  ty 0

                                           0, y  0, t >0

Let an optimal solution of linear programming be   , t  ,  , x , y  . Then we have an

optimal solution of Super SBM as expressed by   =  ,   = /t  , x  =x  /t  , y =y /t  .

     This study used methods for measuring efficiency levels of DEA; SBM model to

measure the DMU operating efficiency, we compare our method with the SBM model

proposed by Super SBM, and point out remarkable differences between them.

4. Results and Analysis
  This study used 2003-2006 year database analyzers input and output information

for the SBM model to analyze the marketing efficiency (stage I) and operational

efficiency (Stage II) of banks. In addition, the slacks-based measure of

super-efficiency (Super SBM) mode was applied, respectively, to the first and second

phases of the efficiency of banks assessed. Results of the analysis on the two stages of

the relative efficiency of the banking values, reference groups, and Super SBM

efficiency values of sequencing are shown in Table 3 and Table 4.      Efficiency values

for stage one showed the fourteen banks were relatively efficient, with borderline

levels. If the value was less than an efficient, with the intention that in the same

industry is not among the relative efficiency. While the reference groups will fall on

the efficiency of banks on the border, for example, the First banks in the first stage of

operational efficiency the reference groups, including Hua Nan and Taipei Fubon


     In regards to the study on the efficiency of banks, the Super SBM model, which

estimates its Super SBM efficiency value, states that the efficiency of its value are

greater than one. However, the higher efficiency values expressed is in comparison to

other banks, which had higher efficient performance levels, as shown in Table 3 and

Table 4 rankings. While Super SBM levels were based on the value of efficiency, in

Table 4, the phases of the operation showed the overall efficiency of the average

value of 0.73, with a standard deviation of 0.17, showed the gap between the greatest

efficiency levels.

                          Table 3 Marketing efficiency ranking
No.            Bank            SBM      Reference groups       Super SBM Ranking
D1    Chang Hwa                 0.97          D3                 0.97       4
D2    First                     0.96         D3 D8               0.96       5
D3    Hua Nan                    1            D3                 1.04       3
D4    China Development         0.25          D8                 0.25      14
D5    Mega                      0.81         D3 D8               0.81       9
D6    Chinatrust                0.63         D8 D9               0.63      11
D7    Cathay United             0.89         D3 D9               0.89       7
D8    Taipei Fubon               1            D8                 1.86       1
D9    SinoPac                    1            D9                 1.07       2
D10   E.SUN                     0.94         D3 D9               0.94       6
D11   Fuhwa                     0.82         D3 D8               0.82       8
D12   Taishin                   0.56         D8 D9               0.56      13
D13   Shin Kong                 0.62         D3 D9               0.62      12
D14   Jih Sun                   0.68         D3 D9               0.68      10
      Mean                      0.79
      S.D.                      0.21

                      Table 4 Operational efficiency ranking
No.            Bank            SBM      Reference groups       Super SBM Ranking
D1    Chang Hwa                 0.87          D14                0.87       4
D2    First                     0.61          D14                0.61      10
D3    Hua Nan                   0.59          D14                0.59      11
D4    China Development          1            D4                 1.31       2
D5    Mega                      0.63           D4                0.63       9
D6    Chinatrust                0.54           D4                0.54      13
D7    Cathay United             0.78          D14                0.78       7
D8    Taipei Fubon              0.44         D4 D14              0.44      14
D9    SinoPac                   0.65           D4                0.65       8
D10   E.SUN                     0.84          D14                0.84       5
D11   Fuhwa                     0.57         D4 D14              0.57      12
D12   Taishin                   0.91         D4 D14              0.91       3
D13   Shin Kong                 0.82          D14                0.82       6
D14 Jih Sun                      1            D14                1.34       1
      Mean                      0.73
      S.D.                      0.17

        In Figure 2 shows that except for E.SUN (the 10th DMU) whose difference

between the two-stage efficiency and the traditional one-stage efficiency is close to 0,

all the other 13 FHC’s banks have a significant difference between their marketing

and operational efficiencies. This paper also calculates the absolute value of the

difference between the marketing and operational stage efficiencies. This absolute

value can be is used to indicate differences between the two-stage efficiencies; the

bigger the absolute value, the better the two-stage DEA method is for indicating

advantages or disadvantages compared to the one-stage DEA method (see Figure 2).

        For example, in two stage division of China Development (the 4th DMU), the

difference between marketing and operational efficiency can be as high as 0.75

(=1-0.25). This suggests that although China Development may have and be

advantage in the operational, it is extremely inefficient in the net underwriting

EBITDA and Total Assets aspects.


                -0.20   1   2    3    4    5    6    7    8    9   10   11      12   13   14
                                                    Bank No.
                                     Eff. Distance between Stage1 and Stage 2
                                     Eff. Distance between Stage 1 and Stage 2
                                     Eff. Distance between Stage 2 and Single Stage
                        Figure 2 Efficiency Distance Between Two-Stage and Single Stage

        In Table 5, the mean scores of marketing and operational models were 0.79 and

0.73, respectively. The table shows that three of the banks were efficient in the

marketing performance model, in the operational performance model shows that two

banks were efficiency. From the result of the mean efficiency score, we can conclude

that marketing performance was better than operational performance for these

fourteen banks

                      Table 5 Efficiency scores of banks performance models.
                                                   Marketing              Operational                          Date
 No                 Bank name                                                                    Size
                                                    SBM                     SBM                             Established
D1      Chang Hwa                                       0.97                   0.87               Big             Old
D2      First                                           0.96                   0.61              Big             Old
D3      Hua Nan                                         1.00                   0.59              Big             Old
D4      China Development                               0.25                   1.00             Small            Old
D5      Mega                                            0.81                   0.63              Big             Old
D6      Chinatrust                                      0.63                   0.54              Big             Old
D7      Cathay United                                   0.89                   0.78              Big             Old
D8      Taipei Fubon                                    1.00                   0.44              Big             Old
D9      SinoPac                                         1.00                   0.65             Small            New
D10     E.SUN                                           0.94                   0.84             Small            New
D11     Fuhwa                                           0.82                   0.57             Small            New
D12     Taishin                                         0.56                   0.91             Small            New
D13     Shin Kong                                       0.62                   0.82             Small            New
D14     Jih Sun                                         0.68                   1.00             Small            New
        Mean                                            0.79                   0.73
        S.D.                                            0.21                   0.17
The "Big" indicates that the Total assets score is above the median. and "Small" means that the Total assets score is below the
median; Date Established in 1990 prior to is the "Old", and in 1990 after is the "New".

       . The marketing and operational model showed that large and old banks were

more efficient than the small and new banks (Table 6). The marketing model results

showed that large and old banks were more likely to generate revenue profit, etc. The

operational model can be interpreted as small-sized banks operate more efficiently

than large banks. Neither the Mann-Whitney U test nor the Kruskal-Wallis test

showed significant difference in the pure technical efficiency regarding banks size or

the date established, showing a 5% level of significance in our model.

         Table 4. Summary statistics: TE of size and for date established for fourteen FHCs
         Number          Marketing                        Operational
Category           Mamm-Whitney Kruskal-Wallis       Mamm-Whitney Kruskal-Wallis
          FHC Mean                              Mean
                    U (P-value)    χ2(P-value )       U (P-value)    χ2(P-value )
  Big         7      0.89                                   0.64
                               -1.604           2.574                  -1.983           3.931
 Small       7   0.69         (0.064)           0.109       0.83       (0.026)         (0.047)
Date Established
   Old         8     0.81                                    0.68
                               -0.778           0.605                   -1.228          1.507
  New          6     0.77     (0.245)          (0.437)       0.80      (0.114)         (0.220)
            This result also reveals that FHC's banks are facing a highly competitive

       environment in Taiwan. On the other hand, the large-sized banks are relatively SBM,

       but in the stage of constant return to scale, suggesting that large-sized and old banks

       have used managerial expertise to operate the banks in an efficiently manner. The

       larger banks, regardless of their age, showed continued lack of efficiency in technical

       areas, which were highlighted by decreasing returns to scale, suggesting that

       larger-sized FHC's banks do not perform efficiently and must become bigger to attain

       scale efficiency.

            To summarize the above results, Regardless of the banks size, the economies of

       scale are insufficient and banks should consider benefits programs. Banks must

       identify the input/output values that are most important, or distinguish the banks,

       which can be treated as benchmarks. Ranking lists of the marketing and operational

       models of all the efficient banks will be given. In Table 7 and 8 the reference-share

       measures were reported for the marketing and operational performance models, with

       the ranking in parenthesis and ordered by the average rank of the efficient banks.

       There were eight pure technical efficient banks in the marketing performance model

in Table 7. However, Hua Nan, Taipei Fubon and SinoPac bank, which is a particular

technically efficient bank, Hua Nan bank has the reference-share in Payroll Expense,

Operating Expenses and Total Deposits is therefore an important bank in

benchmarking. The percentage number is the extent to be referred for a particular

input/ output while other input/output are controlled.

              Table 7 Reference-share measure in marketing performance model
                              Input Factors                            Output Factors
No.      Banks          Payroll    Operating                      Total                   Fee
                      Expense (%) Expenses (%)                 Deposits (%)           Income (%)
D3 Hua Nan            54.33    (1)    46.50        (1)         53.23      (1)          31.59     (2)    (1.3)
D8 Taipei Fubon       29.61    (2)    30.70        (2)         27.42      (2)          50.86     (1)    (1.8)
D9 SinoPac            16.05    (3)    22.80        (3)         19.35      (3)          17.55     (3)    (3.0)
      In the operational performance model is reported in Table 8. Thus, Jih Sun bank

is a particular technically efficient banks, Jih Sun bank has the reference-share in

Total Deposits, Fee Income, Interest Revenue and NPL. And the average rank is to

first. In Table 7 and 8, Even if these banks are efficient, they are revealed as too

different in the input/output space either to be a reference to other units, or to be


          Table 8 Reference-share measure in operational performance model
                                     Input Factors                        Output Factors
No.           Banks           Total         Fee                    Interest
                                                                                         NPL (%)              Rank
                           Deposits (%) Income (%)               Revenue (%)
D4 China Development          11.91      (2) 30.81       (2)      20.67         (2)      13.12         (2)    (2.0)
D14 Jih Sun                   88.09      (1) 69.19       (1)      79.33         (1)      86.88         (1)    (1.0)
      In summary, while small efficient banks are frequently referenced, big efficient

banks can hardly become benchmarks. This result is quite reasonable since the scale

of various inputs, e.g., Total Deposits, is more easily attained for small-sized banks. It

is relatively difficult to imitate the scale of a big efficient bank. In terms of managerial

implication, this phenomenon can be explained by it being hard for big banks to be

imitated for their large scale this corresponds to the reason that the bigger the size of

banks is, the more possible they are able to survive the trend of mergers and

acquisitions. Therefore, these ranking lists give a clear and stable indication of the

banks that should be pointed out as benchmarks for others. In Table 10, the two-stage

and single stage efficiency difference compared, that use of a two-stage model is

better than the traditional one-stage model, because, in two phases can be clearly

explained the various enterprises operating phase of the advantages and disadvantages,

and can be mutually compared. However, the traditional one-stage only done a whole

did not elaborate on the assessment and comparison, in this study use two-stage under

the assessment results are there advantages or disadvantages and doing a sort. This

study use two-stage banking efficiency. In the Table 10, we find the efficiency rank of

Chang Hwa in overall and average is first. The efficiency rank of Taipei Fubon in

overall is first, but in average is tenth. The efficiency rank of Sino Pac in overall is

first, but in average is fifth.

            Table 10 Two-stage and single stage efficiency difference compared
   No.                DMU                M-SBM O-SBM Average                       Rank       Overall        Rank
    D1       Chang Hwa                      0.97         0.87        0.919           1            1             1
    D2       First                          0.96         0.61        0.783           7          0.841          10
    D3       Hua Nan                         1           0.59        0.793           6          0.890           9
    D4       China Development              0.25           1         0.624           13         0.542          14
    D5       Mega                           0.81         0.63        0.722           11         0.893           8
    D6       Chinatrust                     0.63         0.54        0.583           14         0.661          13
    D7       Cathay United                  0.89         0.78        0.836            4         0.926           6
   D8        Taipei Fubon                    1           0.44        0.721           10           1             1
   D9        Sino Pac                        1           0.65        0.827            5           1             1
   D10       E.SUN                          0.94         0.84        0.886            2         0.955           5
   D11       Fuhwa                          0.82         0.57        0.695           12         0.838          11
   D12       Taishin                        0.56         0.91        0.732           8          0.922           7
   D13       Shin Kong                      0.62         0.82        0.721           9          0.761          12
   D14       Jih Sun                        0.68           1         0.838           3            1             1
(The P-SBM is Profitability SBM; M-SBM is Marketability SBM; Average of Profitability and Marketability efficiency; the
Overall is single stage efficiency)

             In Table 11 showed that large and new banks were more efficient than the small

     and old banks. The results of average efficiency model and single-stage efficiency

     showed that large and new banks were more likely to generate revenue profit, etc.
    Table 11. Summary statistics: efficiency of size and date established for eighteen banks
        Number         Average Efficiency              Single-stage Efficiency
Category of         Mamm-Whitney Kruskal-Wallis       Mamm-Whitney Kruskal-Wallis
               Mean                              Mean
         Banks       U (P-value)    χ2(P-value )        U (P-value)     χ2(P-value )
 Large          7       0.77                                                       0.89
                                        -0.128                   0.017                             -0.129                   0.017
 Small       7   0.76                   (0.401                  (0.898)            0.86           (0.401)                  (0.897)
Date Established
  Old           8       0.75                                                       0.84
                                        -0.584                   0.017                             -0.129                   0.017
 New            6       0.78           (0.286)                  (0.898)            0.91           (0.451)                  (0.897)

             We compared the use of traditional single-stage and two-stage, the efficiency

     value of the statistical analysis results of shows use the two-stages better than

     single-stage (Table 6 and 11). Because, the two-stage can be clear that in every stage

     of the features and advantages, and clearly knows improve and maintenance best

     operational strategy will be better sustained. Therefore, when we use the two-stage

     approach is the better. In addition, Have are four cases of efficiency combinations to

     provide individual evidence of the relationship between the two kinds of efficiency in

     Table 12.

                        Table12 Four Combinations from two kinds of Efficiencies
         No          ME               OE                                           Bank Name
         1          High             High        Chang Hwa, Cathay United, E.SUN
         2          High             Low         First, Hua Nan, Mega, Taipei Fubon, SinoPac, Fuhwa
         3          Low              High        China Development, Taishin, Shin Kong, Jih Sun
         4          Low              Low         Chinatrust
      (The notation high indicates that the efficiency score is above the mean. and low means that the efficiency score is below the

     Table 12 observed that three banks are in the “stars” category, characterized by high

ME and high OE. Conversely, one bank is characterized by low ME and law OE

(group 1 and 4). It can be argued that group 4 banks should rearrange their inputs in

order to improve their performance, for example, in groups 3, included four banks,

showed characteristics of low ME and high OE, indicating that their bank services

(outputs) were unable to meet market demand. However, Use Table 9 mainly to

further distinction the important difference between marketing and operational

efficiency, a cross-tabulation is presented in Figure 3.

     The Figure 3 the marketing and operational SBM provide a two-by-two matrix to

classify the FHC banks, which fell into four quadrants: stars, cows, sleepers, and dogs,

which are similar to the classification done by the Boston Consulting Group. Splitting

half by the median was used to create high–low groups of marketing and operational

efficiency. The banks in each the groups are summarized as follows.

I.     High marketing and operational efficiency:These banks are included: Chang

       Hwa, Cathay United and E.SUN bank. That should keep their strength in

       marketing stage and operational stage by occasionally justifying their strategies

       of Payroll Expense, Operating Expenses, Total Deposits, Fee Income, Interest

       Revenue and NPL. These banks appear to be good role model, which can be

      treated as benchmarks to others.

II.   Low marketing and operational efficiency: These banks can: Increased business

      or selling products to get more income and the bank reduced overdue loans, so as

      to increase the opportunity of profitability.

III. High marketing efficiency and low operational efficiency: these banks can:

      Increase their operating efficiency with more Interest Revenue, so as to increase

      the opportunity of profitability.

IV. High operational efficiency and low marketing efficiency: these banks can: To

      reduce the amount of overdue loans and increase revenue, improve banking

      operating results. Increased sales of goods or services to get more income. And

      continue to maintain high operational efficiency.

Managerial implications
      From this analysis, it appears that each FHC's banks have its own advantages and

disadvantages in operational and profitability. In respect of good and poor

performances among the FHC's banks into four types, in each of which different

strategies are likely to enhance business efficiency (see Figure 3).

      Strategies of companies with better marketing and operational capabilities: these

banks marketing and operational were above the medians for all the banks. Banks that

belong in this category are: Chang Hwa, Cathay United and E.SUN bank. These three

banks attempt to maintain their operational advantages whilst also try to improve

enhance their profitability strategies (raise revenue to increase their profitable

opportunities). Other banks should simultaneously improve their marketability and

profitability strategies (business expansion to increase revenue, or reduce overdue

loans to increase profitable opportunities.)

Strategies of companies with less efficiency in marketing and operational: these banks

marketing and operational capabilities were below the medians for all the banks.

Banks who belongs to this category is: Chinatrust bank. This bank should try to

strengthen their marketing and operational, or their managerial efficiency is unlikely

to improve.

     Strategies of banks with better marketing yet poorer operational: banks which

belong in this category have an operational above the industry median standard, yet

profitability below this median standard. Examples of these banks are: First, Hua Nan,

Mega, Taipei Fubon, SinoPac, Fuhwa banks have good marketing but poor

operational, suggesting that these companies should improve specially their

operational strategies (Increase their operating efficiency with more Interest Revenue,

so as to increase the opportunity of profitability). The other three banks, China

Development, Taishin, Shin Kong, Jih Sun, should strengthen their marketing

strategies while also adjusting their operational strategies.

5. Conclusion and future research
  For research to assess a bank's performance of their many articles and rate their

efficiency levels is a broad discussion. Literature and DEA technology has been used

to explore this topic; however, there are still some important issues untouched.

Therefore, the purpose of this paper was to measure the marketing efficiency and

operational efficiency in Taiwan's financial holding company for banks. We include

two models, marketing and operational, with DEA analysis for the 2003-2006 years,

of fourteen banks efficient levels. Results of this study show the two-stage DEA

method of analysis can indicate managerial efficiency better and can help the FHC's

banks at various stages to understand their specific advantages and disadvantages

more thoroughly and clearly.

   It is felt that these findings should help banks practically by showing them how to

change their strategies to suit their particular circumstances. The results of this study:

We compared the use of traditional single-stage and two-stage, the efficiency value of

the statistical analysis results of shows use the two-stages better than single-stage.

Another, in regard to the marketing and operational efficiency regard to fourteen

banks, Taipei Fubon bank in the ranked first at the marketing model. But, Jih Sun

bank in the operational model ranked first. Thus, showed that bank may make other

banks as the basis targets. In addition, banks operational efficiency of the overall

average of 0.73, said the banks have 27% of the resources squandered. Non-technical

efficiency factors can be divided into purely technical inefficiency, and this is part of

the decision-making by managers errors caused by the inefficiency of the scale,

however, the non-managers in such a short time is beyond control, it must depend on

more long-term planning to improve the organization. However, at the large-sized and

old banks are generally more efficient than small-sized and new banks in the

marketing model. And, large-sized FHC’s banks are relative pure technically

inefficient, but in the stage of decreasing returns to scale. On the other hand,

large-sized FHC’s banks are classified into a zone of stars. Including the Chang Hwa,

Cathay United banks, Means that large-sized FHC's banks have better competitive

power than small ones. However, the traditional one-stage only done a whole did not

elaborate on the assessment and comparison, in this study use two-stage under the

assessment results are there advantages or disadvantages. Because, the two-stage can

be clear that in every stage of the features and clearly knows improve and

maintenance best operational strategy will be better sustained. Therefore, when we

use the two-stage approach is the best.

  Finally, Taiwan's financial system will move towards equity concentration, large

organizations, and business diversification, and the direction of the Commissioner of

transparency, the future financial holding company will continue to enhance its

operating efficiency, worthy follow-up study. Furthermore, the study was limited to

2003-2006 years, the follow-up to researchers to expand their research into the life

update information and other variables, to assess its performance.

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