3.1 Dataset
The population of our research is domestic commercial banks. The examination periods are from 4th quarter 1999 to 4th quarter 2007. Since some banks were taken over by FSC, we got an unbalanced panel data in our study. At the end of September 2007, there are 40 domestic banks. However, there are only 26 banks listed in the Taiwan Stock Exchange or the OTC market during our examination periods.
Furthermore, the criteria of the sampling we adopt are (a) whether equity is negative and (b) whether the bank is taken over by FSC. The samples are eliminated if they fit the conditions of (a) and (b). Since the population of this study is the domestic commercial banks, investment banks are also eliminated.6 The Taidungbank (code:
2811) and Chunghsingbank (code: 2846) are included in the sample because they are ever listed in the Taiwan Stock Exchange.7 Finally, we adopt at most 27 samples and 840 observations in our study. Table 1 indicated the list of financial institutions and which is listed in the Taiwan Stock Exchange or the OTC market during our examination periods. Table 2 indicated that samples and observations in our study.
Samples were collected primarily by means of the panel quarterly data of commercial banks listed in the Taiwan Stock Exchange and the GreTai Securities (OTC) Market.
The information on collateralized shares and relevant financial data are collected from the Taiwan Economic Journal (TEJ) database.
The effect of mergers and acquisitions affects observations rather than samples actually. In our study, four banks (Cathay United Bank, Standard Chartered Bank, Taipei Fubon Commercial Bank and Shin Kong Commercial Bank) are in accordance with this issue. However, none of those banks are both but only one listed in the Taiwan Stock Exchange before M&A. Taking Taipei Fubon Commercial Bank for example, Before M&A, Fubon Commercial Bank was listed bank, but Taipei Commercial Bank was not. Such identical cases are Cathay United Bank and Shin
6 China Development Industrial Bank Inc. is not included in the sample because their operating mode and objective are different from the commercial bank even though it is listed banks in the Taiwan Stock Exchange.
7 The Chunghsing bank is excluded because it is taken over by FSC in 2000.
Kong Commercial Bank. The predecessor of Standard Chartered Bank is Hsinchu bank which was purchased by Standard Chartered Bank in 2006. However, it is viewed as a domestic bank after merger and we adopt it as our sample in our study.
3.2 Panel Data Model
Since OLS estimators could be inconsistent and meaningless if there were heterogeneity across individuals. To control for individual heterogeneity, the quantitative analysis of the panel data regression model was conducted. It consists of two models: the fixed-effects model and the random-effects model. They can take into account the heterogeneity across firms by allowing variable intercepts. The fixed-effects model is equivalent to introduce dummy variables to specify individual cross-sectional effects. If the regression model is specified as
'
β is constant,
α
i is the individual effects. The fixed-effects model allows us to specify individual cross-sectional effects by conducting dummy variables as' individual effect
α
i by summarizingt periods, getting mean response over t
periods and finally subtracting to each other as'
=
∑
, then the slope estimators are BLUE (Best Linear Unbiased Estimator) whenN → ∞ or T → ∞or both. However, α∧i(intercept)will be unbiased but consistent only whenT → ∞.
As opposed to the fixed-effects model treating the effects of omitted individual-specific variables are constant over time, the random-effects model, also referred to the error component model, view them as random variables and irrelevant to the error terms and the covariance structure of '
~ ~
then, the random-effects model applies the generalized least squares (GLS) method to estimate slopes and other parameters. However, contrast with the fixed-effects model, both
~
β∧ and
α
∧i are BLUE whenN → ∞ or T → ∞or both.There are three criteria used to discriminate which model is batter. First, F test can be applied to test whether OLS or the fixed-effects model is fit. The null hypothesis, the alternative hypothesis and the test statistic is shown as
0 1 2
where K is the number of explanatory variables, not including the intercept,
SSE
R andSSE are error sum of square when
UH and
0H
1 is true, respectively. It represents that individual effects do not exist whenH is true. However, oppositely, it shows that
0not all intercepts are equal and individual effects exist.
The second criterion is LM (Lagrange Multiplier) test; it can be applied to test
whether OLS or the random-effects model is fit. The null hypothesis, the alternative hypothesis and the test statistic is shown as following equation, where ε∧nt means residuals derived by OLS method. It represents that the intercept is constant when
H
0is true and individual effect exists when
H
1 is true.2
In parsimony principle, we need to specify the empirical model as sample as possible. If individuals does not exist heterogeneity, we prefer to use the OLS method to estimate unknown parameters. However, the fixed-effects model and the random-effects model can estimate parameters more precisely if heterogeneity exists and theoretically F-test and LM-test will reject null hypothesis both. Therefore, we need to specify whether the fixed-effects model or the random-effects model is batter, Hausman test namely provides a criterion to specify it. It discriminates if α and i explanatory variables were uncorrelated or not by Wald test. The null hypothesis, the alternative hypothesis and the test statistic is shown as
0 0 1 0
where K in the number of explanatory variables, if α and explanatory variables are i
uncorrelated and slope parameters derived by the fixed-effects method and by the random-effects method are both consistent, while the latter is more efficient. However, slope parameters derived by the fixed-effects method are still consistent but not by he random-effects method.