3.1 Data Envelopment Analysis
Data Envelopment Analysis (DEA), firstly introduced by Charnes et al. (1978), is a non-parametric linear programming approach which can handle multiple control inputs and outputs.
It was initially designed to investigate the relative efficiency of non-profit organizations and is now successfully applied in diverse settings such as hospitals, schools, courts, the U.S. Air Force, rate departments, banks, etc. (Seiford 1997; Gattoufi et al., 2004; Sueyoshi et al., 2004a, 2004b).
Charens et al. (1994) collect an extensive discussion of efficiency models across a variety of industries.
We assume that the objective of each FHC is to minimize its inputs, keeping the output level constant in the CRS (constant returns-to-scale) / CCR (Charnes-Copper-Rhodes, 1978) model.
The technical efficiency of a FHCjo (jo = 1, 2, …, n) can be computed as a solution to the following linear programming (LP) problem:
1 1
is non-Archimedean infinitesimal, θ ε efficient. If TE is smaller than 1, then FHCjo is technically inefficient3.
3.2 Diversification Measure
This study uses the standard industrial classification (SIC) to compute both diversification degree and diversification type. The SIC classification is a well accepted classification system and is frequently used in the industrial organization research. And the data is readily available in the required form. In the following section, we use SIC classification codes to define the industry segments and industry groups.
SIC industries at the 2-digit level are treated as the industry groups; SIC industries at the 4-digit level are treated as the industry segment. Consider a FHC operating in N financial service industry segments. Let Pi be the ratio of the sales in ith 4-digit segment to the total sales of the FHC. A refined Herfindahl index is defined as follows to make the index increase with increasing diversification (Jacquemin and Berry, 1979):
∑
= , is added into the LP problem in Equation (1), then the technology is said to exhibit variable returns to scale (VRS) / BCC (Banker-Charnes-Cooper, 1984) model. Under the condition of VRS will produce plural FHCs having a full efficient status (TE =1) because of our small sample size. We therefore adopt CCR model rather than BCC model to avoid a great number of the FHCs to lead on the frontier. Though similar results can also be found under VRS condition but will be suppressed in our analysis.23
The entropy measurement of total diversification degree is a weighted average of the shares of the segment. This index increases with increasing of diversity. The weight for each segment is the logarithm of its inverse of its share as shown below:
Entropy Diversification
In order to further identify the direction of diversity, we define an industry group as a set of related segments. The standard industrial classification (SIC) is also used to define the related and unrelated financial services industries. Segments within a financial service industry group are deemed to be more related to one another than segments across groups. In this study, a FHC’s financial services from the same 4-digit SIC industry segment are treated as related; services from different 4-digit SIC industry segments are defined as unrelated.
We let the N segments (4-digit) if the FHC aggregates into M group (2-digit) ( N ≥M).
Related diversification is defined as a FHC’s operating in several segments within an industry group j, which can be written as the ratio of the sales in jth 2-digit group to the total sales of the FHC. A FHC’s unrelated diversification is defined as:
Unrelated Diversification
The sum of the related and unrelated component equals to the total entropy diversification (See Palepu (1985) for detailed inferences).
3.3 Data
This paper uses a sample of 14 FHCs in Taiwan. At the end of 2003, there are 14 FHCs operating, we therefore include these FHCs into our investigation. The inputs and outputs data are extracted from the Taiwan Economic Journal (TEJ) data bank. The TEJ data bank is commonly deemed valid, reliable, and available to the public, and is widely used in academia. The output and input factors (eight financial measures) used in this study are defined as follows: (1) Assets
are the FHC’s year-end total. (2) Equity is the sum of all capital stock, paid-in capital, and retained earnings at the FHC’s year-end. (3) Employees are composed of all staff members in a FHC to keep operating normally. (4) Revenues (excluding excise taxes) include consolidated subsidiaries within a FHC. (5) Profits are after taxes, after extraordinary credits or charges, and after cumulative effects of accounting charges. (6) EPS for each company is the primary earnings per share that appear on the income statement. (7) Market values are obtained by multiplying the number of common shares outstanding by the price per common share as the year end. (8) Stock prices are the prices per common share as the year end.
Table 1 presents the brief descriptive statistics for our data set. Since the DEA technique presumes the existence of a relationship among inputs and outputs data, a correlation analysis is therefore performed in Table 2. The correlation coefficients between the selected three input factors and two output factors are positive in the profitability model. These input and output factors hold an isotonical relationship, and therefore they can be included within one model.
Similar positive correlation results can also be observed in marketability model taking into two inputs and three outputs. While using the DEA model, the number of FHCs should be at least twice of the total number of input and output factors considered (Golany et al., 1989). In this study the number of FHCs is fourteen, at least twice the selected five factors for the profitability/marketability performance model. In summary, the developed DEA model in this study holds high construct validity.
[Insert Table 1 and Table 2]