3. RESEARCH DESIGN
3.2. Variables and Data
3.2.1 Variables
This research follows the model developed by Lins et al. (2003) in that it chooses a single output and multiple inputs to measure the efficiency score. Drake et al. (2006) introduce a profit-oriented model with revenue components as outputs and cost components as inputs in a banking efficiency study. Banks pursue their profit maximisation goal by increasing revenue and reducing cost. In the securities industry, an individual SF pursues the goal of market share maximisation by innovating itself as an e-broker or e-trader. Thus, this output-oriented ZSG-DEA model chooses market share as the single output. Drake and Hall (2003) adopt general and administrative expenses and fixed assets as the two inputs of the DEA model. Berger and Mester (1997) indicate that another important aspect of efficiency measurement is the treatment of financial capital. A bank’s financial capital that is available to absorb possible losses helps reduce its insolvency risk.
Accordingly, the study adopts fixed assets, in which the SFs increase their fixed assets by investing in computer hardware, financial capital as well as general and administrative expenses as the three inputs of the ZSG-DEA model.
3.2.2 Data
A panel dataset covering the period 2001-2005 includes 266 ISFs in Taiwan.
During 2002, eight SFs were merged and one foreign-affiliated SF established branches in Taiwan. In 2003, four SFs were merged and one foreign-affiliated
institution joined the securities market in Taiwan. Appendix B lists the number of observations from 2001-2005. Since the data cover five years, several variables, including three inputs, which are exogenous variables in the 2SLS, are deflated with the gross domestic product (GDP) deflator (2001=100) to avoid the distortion caused by inflation (Bierlen and Featherstone, 1998; Li et al., 2004). Market share is the trading amount in brokerage and proprietary trading of an individual firm divided by the total trading amount of all securities’ brokers and dealers. The firm-level data for the exogenous variables in the 2SLS are the trading amounts, fixed assets, general expenses, financial capital, total assets, and profits. All variable data are obtained from the reports of the Taiwan Stock Exchange Corporation during the 2001-2005 period (http://www.tse.com.tw/ch/statistics/statistics_list.php?tm=03&stm=004, accessed April 4, 2007). The descriptive statistics for all the variables are shown in Table 3-1.
TABLE 3-1. Descriptive Statistics for the BCC-DEA, ZSG-DEA and 2SLS
Variables Yr. Obs. Average Min Max σ
Inputs
x1: Fixed assets (NT$Mn) 2001 61 932.13 5.74 4455.02 1074.12 2002 54 1006.18 1.84 4306.02 1132.26 2003 51 1067.66 0.00 4413.71 1259.69 2004 50 1135.49 0.00 6203.25 1439.44 2005 50 1141.64 0.00 6692.11 1482.82 x2: Financial capital (NT$Mn) 2001 61 1637.57 48.70 7815.06 1733.19 2002 54 5112.88 151.29 24689.52 5439.46 2003 51 5594.04 154.58 25382.95 5958.09 2004 50 6163.88 156.84 31988.93 6822.10 2005 50 6284.13 157.81 33559.95 7069.14 x3: Expenses (NT$Mn) 2001 61 4413.48 150.00 22315.20 4730.23 2002 54 1935.13 10.64 10560.52 2323.28 2003 51 2126.09 11.12 8587.78 2555.90 2004 50 3010.77 21.18 14008.10 3757.83 2005 50 3213.83 26.80 12772.28 3682.73 Output
y: Market share (%) 2001 61 1.64 0.05 8.66 1.89
2002 54 1.85 0.02 10.48 2.42
2003 51 2.02 0.01 11.01 2.53
2004 50 2.00 0.02 9.39 2.51
2005 50 2.00 0.02 7.63 2.31
Exogenous Variables
Asset : Total Assets (NT$Bn) 2001 61 13.69 0.24 91.03 17.59
2002 54 16.34 0.25 103.37 20.66
2003 51 19.31 0.22 120.35 24.55
2004 50 21.96 0.35 127.17 28.72
2005 50 23.93 0.58 149.49 31.55
Profit: Profits (NT$Bn) 2001 61 0.36 -0.80 2.96 0.65
2002 54 0.25 -0.57 3.87 0.69
2003 51 0.57 -0.58 6.11 1.05
2004 50 0.43 -0.60 2.29 0.70
2005 50 0.19 -1.18 1.44 0.50
Note: 1. Variables are deflated with the gross domestic product (GDP) deflator (2001=100) to avoid the distortion caused by inflation.
2. Data Sources: Taiwan Stock Exchange Corporation
(Website: http://www.tse.com.tw/ch/statistics/statistics_list.php?tm=03&stm=004).
fourteen securities firms in Taiwan. The firm-specific financial data are collected from peers’ data exchange among the securities firms and the reports of the Taiwan
Stock Exchange Corporation (Website:
http://www.tse.com.tw/ch/statistics/statistics_list.php?tm=03&stm=004). For the fiscal year of 2002, some of these ISFs were committed themselves as an FHC’s subsidiary in 2003. This period offers to measure the technical efficiency and managerial efficiency before imposing the impact of FHC. Each of these ISFs is treated as a DMU under the DEA model. Two guidelines are commonly applied on the number of DMUs. One is that the total number of inputs and outputs should be less than one third that the number of DMUs in the DEA model. (Friedman and Sinuany-Stern, 1998) Another is that the number of DMUs should be at least two times the number of inputs multiplied by the number of outputs (Dyson et al., 2001).
In our model there are two inputs and two outputs. The number of DMUs in a year is hence more than triple the total number of input and output items.
In order to increase the homogeneity of DMUs, the ISFs with the top twelve to fourteen asset values are selected. As Table 3-2 shows, these selected ISFs account for more than 70 percent of the total assets of the entire ISF sectors in Taiwan.
TABLE 3-2. The Asset Value (NT$Bn) of Top-14 ISFs in Taiwan
Securities Firms 2002 Ranking 2005# Ranking
1. Fubonf 65.012 2 62.639 7
2. Taiwanf 48.895 5 52.259 12
3. KGI 38.264 11 90.776 2
4. Yuanta Core Pacific 102.490 1 148.224 1
5. Capital 45.910 6 72.677 4
6. President 41.741 8 53.487 10
7. Polaris 42.397 7 70.531 5
8. MasterLink 40.012 9 70.391 6
9. SinoPacf 49.346 4 53.826 9
10. Grand Cathayf 51.415 3 77.436 3
11. Jih Sunf 38.718 10 57.848 8
12. Taiwan International 22.582 13 41.379 13
13. Fuhwaf 23.143 12 30.825 14
14. Megaf 18.792 14 51.903 11
Subtotal for top-14 firms 628.720 71.86%a 895.520 78.74%a
Total Assets for ISFs 874.859 934.202
Note: 1.frepresents this ISF is the subsidiary of an FHC;
2. a Total asset value of the observation ISFs accounts for 71.9% and 78.7% of the total ISF’s population in 2002 and 2006, respectively;
3.#Asset value has been divided by GDP deflator (2002 = 100);
4. Data Sources: Taiwan Stock Exchange Corporation (website:
http://www.tse.com.tw/ch/statistics/statistics_list.php?tm=03&stm=004).
The top twelve ISFs have exchanged data such as market share and brokerage revenue for peer comparison since 2001. Fuhwa Securities and Mega Securities did not exchange financial data with peers due to the smaller assets of Mega and unavailable data of Fuhwa in 2002. Mega Securities merged with another ISF to increase its asset by almost triple compared with its assets in 2002. Two more ISFs joined the exchange pool in 2003, making fourteen securities firms available for DEA.
The top twelve ISFs have exchanged data such as market share and brokerage revenue for peer comparison since 2001. Fuhwa ISF and Mega ISF did not exchange financial data with peers due to the smaller assets of Mega and unavailable
data of Fuhwa in 2002. Mega ISF merged with another ISF to increase its asset by almost triple compared with its assets in 2002. Two more ISFs joined the exchange pool in 2003, making fourteen securities firms available for DEA.
This study further employs a profit-oriented, non-parametric model, which uses revenue components as outputs, and cost components as inputs. Drake et al. (2006) use this profit-oriented DEA model to investigate the bank efficiency in Hong Kong.
The first stage input-oriented DEA model includes physical inputs and outputs in the strict production theory sense. There are two outputs: market share of brokerage business (MS) and revenue (BR), which includes the fee income and service charge in the brokerage business. The market share of the brokerage business is an important factor to evaluate performance for senior managers. This research is the first one to introduce market share as an output to evaluate an ISF’s efficiency score.
Revenue from the brokerage business accounts for roughly 70 % of total revenue of the top-10 Taiwanese Securities firms. Revenue from the brokerage business as an output is shown on the existing literature.
Two inputs are used to produce brokerage services: branches (BO) and the discounted expense amount of the brokerage business (DE). BR and DE have been divided by GDP deflator (2002 = 100). Table 3-3 presents the definition and explanation of variables.
TABLE 3-3. Definition and Explanation of Variables for the Four-Stage DEA Variable Definition
MS = y1 Market share for brokerage business (%) BR = y2 Brokerage revenue (NT$100Mn)
BO = x1 Branch offices
DE = x2 Discounted expenses (NT$100Mn)
Goldberg et al. (1991) also adopted branch office as one of the inputs in the literature. In practice, high discounted expenses provide benefits to customers.
When the discounted amount is more, then it motivates customers to trade equities with this ISF. It also benefits the broker’s market share. This research is the first one to adopt the discounted expense amount as one input for research. Market share of the brokerage business is measured in percentage terms. Brokerage revenue and the discounted expenses are measured in NT$100 million. Table 3-4 displays descriptive statistics of the raw data.
TABLE 3-4. Descriptive Statistics of ISFs for the Four-Stage DEA
Variables 2002 2003 2004 2005
Avg SD Max Min Avg SD Max Min Avg SD Max Min Avg SD Max Min
BO 42.5 18.6 88.0 20.0 46.7 17.3 93.0 20.0 51.0 19.4 107.0 26.0 49.5 18.2 99.0 26.0
BO-FHC 43.8 14.5 61.0 21.0 47.1 11.3 64.0 31.0 52.3 10.8 64.0 34.0 50.6 12.6 65.0 27.0 BO-Non
-FHC 41.6 22.2 88.0 20.0 46.3 22.8 93.0 20.0 49.7 26.4 107.0 26.0 48.4 23.6 99.0 26.0
DE 6.9 2.5 10.4 2.4 6.7 2.8 11.6 2.5 10.0 3.4 15.1 4.3 8.9 3.3 14.8 4.0
DE-FHC 7.3 2.9 10.3 3.9 6.8 3.0 10.4 3.7 10.2 3.8 14.9 6.0 9.1 3.7 14.8 5.2
DE-Non
-FHC 6.5 2.4 10.4 2.4 6.6 2.8 11.6 2.5 9.8 3.3 15.1 4.3 8.6 3.2 14.7 4.0
Note: 1. The sample size is 54;
2. BR and DE (NT$100Mn) have been divided by GDP deflator (2002 = 100);
3. Data Sources: Taiwan Stock Exchange Corporation
(website:http://www.tse.com.tw/ch/statistics/statistics_list.php?tm=03&stm=004).
Four environmental variables are introduced to measure the effect of input utilization. Annual sales volume is the exchanged data among the top-14 ISFs.
Durations are calculated by each firm’s registration date in the Taiwan Market Post Information System and asset values are the annual report data listed in the Taiwan Securities and Futures Bureau.