Research method

In order to isolate homogenous bank groups, we have used a method of hierarchical clustering. By this method, groups are obtained recursively, as a result of joining smaller groups into larger ones, where at the starting point each bank belongs to a separate group. The advantage to this method is the possibility to illustrate interdependencies between groups. The so-called dendrograms that visualise results of the algorithm enable to determine the distances between clusters and isolation of components that are most alike within a given group as well as those that t less to the cluster in terms of the used grouping criterion.

Ward's algorithm, which minimizes distances between variables within a group (i.e. maximises the group's homogeneity) has been used to break down the banks into groups. As Ward (1963) pointed out, the purpose of his research was to nd a breakdown of population that would minimise the loss of information about the population, resulting from the grouping process. In his search for optimal grouping, Ward conned himself to procedures that, in their each step, decrease the number of groups by 1 and minimise the loss of information. Ward's approach was a compromise between the simplicity of the scheme and optimality in the broadest sense. The algorithm itself does not have any principle that would allow for termination of its operation before one group consisting of all the (components) banks is created. At the initial stage of the research the principle of cut-o has been adopted to isolate more than 1 group. The principles is based on the so-called inconsistency ratios, which measure the weight of links created among components comprising particular groups  the closer to each other two components are in terms of their isolated features (the more alike they are), the lower the inconsistency ratios are. The number of groups proved to be sensitive to the criterion level adopted. Slight changes in the cut-o level caused even a two-fold increase in the number of groups. Dening the distance level above which building of subsequent groups was

stopped turned out to be a better criterion for terminating the procedure. With regard to comparability of the results for dierent clustering criteria, the stopping level was dened as a percentage of the maximum distance between groups whose merging in the next step would result in a single group for the whole studied population. In other words, it is a percentage of the distance between groups in the case where there is no stopping criterion and, as a result of using the algorithm, there are only 2 groups left. The percentage of the distance was determined arbitrarily at 70%. The stopping level therefore denes the depth, down to which the merging of the population components into groups takes place. As the cut-o level has been selected arbitrarily, we have calculated Celinski-Harabasz's index (see Halkidi et al., 2001) in order to verify the degree of group cohesion. The use of cohesion indices does not, however, eliminate the arbitrary character of certain grouping parameters. The choice of an index usually becomes an issue of controversy.

As the research aims at a breakdown of banks into groups, which would be further used in the construction of an analytical scheme for the purpose of, inter alia, modelling the nancial result of the banking sector, two hypotheses have been veried:

• (H1) The groups created dier signicantly in terms of ROA.

• (H2) In the equations of protability regression from selected micro- and macroeconomic

variables, the estimated model parameters are more signicant for the estimation of equations for bank groups than for the total sector.

Since the breakdown into groups should help to dene dierent protability levels, return on

assets  being one of the protability measures  has been used to test the diversity of groups.82

If there were two groups with identical distributions, dierentiation between them would be of no use. The Kolmogorov-Smirnov statistics has been used (see Gajek and Kaªuszka, 2000) to verify consistence of distributions of the result from banking activity to assets ratio and the gross prot to assets ratio among groups. The null hypothesis is the equality of distributions of particular protability ratios among groups. The hypothesis has been tested for three signicance levels  0.01, 0.05 and 0.10.

Another test has been carried out on the basis of linear regression models of the average ROA and ROE of banks, depending on the average values for a particular strategic group of the following variables, which may inuence banks' earnings (similar variables and a series of other variables used in panel estimation of banks' earnings can be found in e.g. DeYoung and Rice, 2004): rate of change in GDP, spread between the interest rate on household deposits and loans, spread between the interest rate on corporate loans and the three-month WIBOR rate, spread between the interest rate on corporate deposits and loans, percentage of irregular loans, producer price index (PPI), the Warsaw Stock Exchange Index, and the dierence between banks' receivables and deposits in banks to assets ratio. Data from the period between the rst quarter of 1998 and the fourth quarter of 2004 have been used. The research has been conned to comparing the linear regression estimates with two regressors selected from the above-mentioned variables. For each pair of variables, three models of ROA dependence on the average values of variables in the whole population of analysed banks and on means in the 82_{In studies concerning testing the signicance of breakdown into groups in explanation of dierences in} protability, return on equity ratios are also used.

I Results

group of banks which in 2004 were classied into 2 selected groups have been estimated. To make things simpler, an assumption has been made that the breakdown of banks into groups has not changed over time and remained the same as in 2004. This is a strong assumption, although a sucient one for the purpose of comparison. Better estimates of models for series of mean values of variables in the obtained groups than for the mean calculated for all the banks would suggest that earnings of the banking sector should be modelled with the use of a breakdown into groups of similar banks.

As the main purpose of the research has been to explain the dierences in protability among groups of banks, the signicance of clusters has been veried only using the two tests described. Therefore it was not necessary to verify the signicance of breakdown into groups based on indices used for isolation of clusters.

Since strategic groups were analysed for multiple periods, a question about the sustainability of performance over time arises. In the verication of sustainability, the percentage of banks migrating among groups has been used.