DETERMINANTS OF BANK EFFICIENCY DIFFERENCES IN THE NEW EU MEMBER COUNTRIES
7 ESTIMATION OF THE COST FUNCTION
In order to perform a cross-country comparison of cost efficiency, we construct a pooled data set for the 1996-2003 period, and employ a common frontier function in the form of a translog function.
The translog functional form is specified as follows:
where C – is total cost, yk – is the k-th output, wi – is the i-th input price, z – is the equity capital,
v – is measurement error term, u – is the inefficiency term.
The duality theorem requires the cost function to be linearly homogeneous in input prices and for the second-order parameters to be symmetric (Altunbas et al., 2001).5 Therefore, the following restrictions apply to the parameters of the cost function:
The maximum likelihood method was applied for estimation. The inefficiency effects are incorporated in the error term. The error term in a stochastic cost frontier model is assumed to have two components. One component is assumed to have a symmetric distribution (measurement error, vit ) and the other is assumed to have a strictly non-negative distribution (inefficiency term, uit ). The estimation technique we use is based on the Battese-Coelli (1992) parameterisation of time effects in the inefficiency term and accordingly the inefficiency term is modelled as a
for all i for all k
for all i, j for all k, m
truncated-normal random variable multiplied by a specific function of time. The idiosyncratic error term is assumed to have a normal distribution. As is always the case when implementing frontier estimation techniques, the efficiency score acquired from the frontier function measures the efficiency of a specific bank relative to the best-practice or most efficient bank.6
In the process of constructing the cost function we tried different normalisations of cost and input prices (normalisation with personnel costs vs. normalisation with price of physical capital) and different specifications of the function (three vs. four product variables). Ultimately, we identified a three-product cost frontier function (loans, other earning assets, deposits), normalised with price of physical capital, as a preferred cost function. The inclusion of off-balance-sheet items as a fourth product variable turned out to significantly reduce the total number of observations, whereas the normalisations with personnel costs decreased the number of statistically significant coefficients. Following some other studies (e.g. Berger and Mester, 1997), we employ also a normalisation of cost and output variables in order to control for heteroskedasticity and avoid the skewness of the variables for large banks.
We report the estimation results of our preferred translog model specification in the Appendix and selected summary statistics in Table 4. The parameters and represent the distributions parameters of the inefficiency effects, parameter is the decay parameter in modelling the inefficiency effects as in Battese and Coelli (1992) and indicates the time dynamics of measured inefficiencies. Parameter indicates the proportion of the variance in disturbance that is due to inefficiency, , i.e. the value shows the contribution of the u efficiency term to the dichotomous term v + u. The value is always between 0 and 1.
Since the estimated value in our case is 0.59 we conclude that the variation of inefficiency is more important than any other stochastic variation in the frontier.
Table 4: Selected estimation results for the translog cost function specification
Coefficient Std. Err.
Ln( ) -2.6098 0.1947
0.1000 0.0260
Log likelihood 80.7607
0.0434 0.0149
0.0301 0.0024
0.5903 0.0905
Source: Authors’ calculations.
As the objective of our study is not to investigate the reasons for cost (in)efficiencies within individual banks, the results presented in Table 5 and Figure 1 explain average cost efficiency levels in individual countries. The variability of bank efficiency within each country can be observed, which sheds light on cost efficiency differentials in the new EU member countries.
The average efficiency scores calculated for the entire sample of countries/banks and for individual countries are reported in Table 5. The average efficiency score for every country is obtained as a weighted average of individual banks’ efficiency scores as predicted by the estimated translog
6 Cost efficiency can take values between zero and one. For example, a bank with cost efficiency of 0.80 is 80% efficient. In other words, the bank could improve its cost efficiency, i.e. reduce its costs, by 25%. The bank’s cost inefficiency is 1-0.80=0.20.
cost function. The relative importance of the total equity of specific banks is used as a weight for the bank when calculating average efficiency score. We consider the weighting approach to be essential for the correct interpretation of the average efficiency results for specific sub-regions.
Table 5: Weighted average efficiency scores for the sample and by individual countries (mean value, standard deviation, coefficient of variation, 25th, 50th and 75th percentile)
Mean Sd Cv P25 p50 p75
Czech Republic 0.7078 0.0946 0.1336 0.6347 0.7046 0.7706
Estonia 0.7830 0.0907 0.1159 0.7121 0.8206 0.8508
Hungary 0.8420 0.0608 0.0722 0.8185 0.8513 0.8739
Lithuania 0.7910 0.0753 0.0951 0.7513 0.8105 0.8422
Latvia 0.8366 0.0916 0.1095 0.7683 0.8460 0.9265
Poland 0.8730 0.0397 0.0454 0.8499 0.8793 0.9014
Slovenia 0.8429 0.0655 0.0777 0.8063 0.8595 0.8876
Slovakia 0.9125 0.1160 0.1271 0.9020 0.9515 0.9842
Sample 0.8202 0.0977 0.1191 0.7706 0.8499 0.8885
Source: Authors' calculations
As presented in Table 5, the average cost efficiency of banks included in the sample was 82%, indicating that on average banks could reduce their cost by 22% if compared with the most cost efficient bank in the sample. The median cost efficiency score for the entire sample was 85%
and the cost efficiency score for the 75th percentile was 89%, suggesting that the distribution of efficiency scores is skewed to the right from the centre. The standard deviation and the coefficient of variation of the cost efficiency score indicate a moderate variability in efficiency score among banks in the sample.
Presentation of data by individual countries reveals some noticeable differences in average cost efficiency. The highest average efficiency score was achieved by banks in Slovakia (91%), followed by banks in Poland (87%), Slovenia (84%), Hungary (84%) and Latvia (83,6%). The lowest average efficiency score had banks in the Czech Republic (71%), Estonia (78%) and Lithuania (79%). Comparing mean and median values of average efficiency scores we can observe that most of the countries experienced an asymmetric distribution of efficiency scores, mostly skewed to the right with the exception of the Czech Republic, where mean and median efficiency score were almost identical.
Variability of the measured average efficiency score by country also differed significantly. The lowest variability was measured with Polish (CV = 4.5) and Hungarian banks (CV = 7.2), while in four out of eight countries the coefficient of variation exceeded value of 10.
Graphical representation of efficiency scores by country clearly reveals the discrepancies in average efficiency among countries and even more importantly also the variability of efficiency scores across countries. Particularly for the most efficient banking sectors (Slovakia, Poland, Slovenia and Hungary) it is typical that their interquartile ranges7, as denoted by the height of the box, are relatively narrow and their “whiskers”8 relatively short. Both characteristics are a sign of lower variability of individual banks’ cost efficiency score.
7 Interquartile range is confined to the central 50% of the sample in each country, bounded by the 25th and 75th percentile.
8 Vertical lines, denoting the lower and the upper adjacent value.
Figure 1: Boxplot of individual banks’ efficiency scores by country (median, 25th percentile, 75th percentile and lower and upper adjacent value)
Source: Authors' calculations
Another important aspect of bank efficiency studies that needs to be addressed is the time dynamics of bank efficiency. The time varying decay model developed by Battese and Coelli (1992) models inefficiency effects as: . The estimated coefficient provides information on the time dynamics of inefficiency effects. When > 0, the degree of inefficiency is decreasing over time and when > 0, the degree of inefficiency is increasing over time. The coefficients for the entire sample, turned out to be significant at p>1%, with the value of 0.10. A positive value of the coefficient indicated an increase of average efficiency of banks in the period under observation.