5. Empirical Results and Analysis
5.2 Cost Efficiencies and Technology Gaps
國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
41
5.2 Cost Efficiencies and Technology Gaps
Table 10 presents the summary statistics of the calculated TGR, CE, and MCE measures for all countries, based on the three methodologies mentioned in the previous subsection. Note that those estimated CEs are not comparable across countries. The average values (standard deviation) of measure CE vary from roughly 0.812 (0.072) in Spain to 0.930 (0.041) in Germany with an overall average value of 0.891 (0.077). A representative bank in Spain is able to save its production costs by improving its managerial ability up to 19.8%. In contrast, the potential cost saving of Germany banks is merely 7%, whose actual costs lie closer to the cost frontier for a given bundle of output.
The average values (standard deviation) of TGR range from 0.807 (0.099) in Luxembourg to 0.960 (0.013) in Denmark with an overall mean value of roughly 0.916 (0.070). Recall that the larger the value of the TGR, the more advanced technology the country adopts. Banks in Luxembourg are found to assume inferior technology, since its cost frontier is apart farther from the metafrontier than other countries’ frontiers. This result may be attributed to the fact that Luxembourg has the largest value of deposit density (see Table 5), which is negatively correlated with TGR.
Conversely, Danish banks take on the most advanced technology, whose cost frontier is the nearest to the metafrontier. This is partially ascribable to its having the third lowest value of deposit density contributing to TGR. Besides Danish and British banks also have access to the most advanced technology. A common feature of these two countries worth mentioning is that Denmark and the United Kingdom, the member states of European Union, have opt-outs from joining by reasons of economic sovereignty. This result is possibly reasonable, because the both countries have modern, extremely open and developed market economy. They believe that limiting
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
42
Table 10 Summary statistics of relevant efficiency scores for various competing metafrontier models based on FF specification Stochastic Metafrontier
with τ (SMF95)
Stochastic Metafrontier
without τ (SMF92) Metafrontier (QP)
Mean Min Max S.D. Mean Min Max S.D. Mean Min Max S.D.
Technology gap ratio (TGR)
Austria 0.924 0.258 1.000 0.085 0.850 0.290 1.000 0.118 0.659 0.085 1.000 0.184 Belgium 0.900 0.559 0.976 0.071 0.814 0.484 0.966 0.116 0.580 0.146 0.876 0.157 Denmark 0.960 0.870 1.000 0.013 0.920 0.760 1.000 0.040 0.720 0.280 1.000 0.107 France 0.933 0.364 1.000 0.047 0.819 0.335 0.990 0.080 0.685 0.030 1.000 0.172 Germany 0.911 0.375 1.000 0.053 0.811 0.348 1.000 0.075 0.649 0.039 0.999 0.141 Italy 0.946 0.399 1.000 0.035 0.919 0.536 1.000 0.063 0.760 0.162 1.000 0.131 Luxembourg 0.807 0.463 1.000 0.099 0.712 0.448 1.000 0.122 0.513 0.044 1.000 0.189 Spain 0.911 0.509 0.980 0.070 0.863 0.436 0.996 0.096 0.662 0.099 0.986 0.181 Switzerland 0.932 0.664 0.978 0.029 0.852 0.505 0.991 0.084 0.687 0.078 1.000 0.172 United Kingdom 0.948 0.578 1.000 0.039 0.859 0.383 1.000 0.099 0.680 0.109 1.000 0.176 All countries 0.916 0.258 1.000 0.070 0.834 0.290 1.000 0.105 0.662 0.030 1.000 0.175
Group-Specific cost efficiency (CE)
Austria 0.892 0.428 0.979 0.070 0.892 0.428 0.979 0.070 0.892 0.428 0.979 0.070
Belgium 0.901 0.757 1.000 0.044 0.901 0.757 1.000 0.044 0.901 0.757 1.000 0.044
Denmark 0.866 0.682 0.992 0.035 0.866 0.682 0.992 0.035 0.866 0.682 0.992 0.035
France 0.887 0.226 0.983 0.072 0.887 0.226 0.983 0.072 0.887 0.226 0.983 0.072
Germany 0.930 0.286 1.000 0.041 0.930 0.286 1.000 0.041 0.930 0.286 1.000 0.041
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
43
Italy 0.840 0.210 1.000 0.122 0.840 0.210 1.000 0.122 0.840 0.210 1.000 0.122 Luxembourg 0.919 0.691 0.983 0.035 0.919 0.691 0.983 0.035 0.919 0.691 0.983 0.035 Spain 0.812 0.684 1.000 0.072 0.812 0.684 1.000 0.072 0.812 0.684 1.000 0.072 Switzerland 0.904 0.120 1.000 0.075 0.904 0.120 1.000 0.075 0.904 0.120 1.000 0.075 United Kingdom 0.845 0.193 1.000 0.112 0.845 0.193 1.000 0.112 0.845 0.193 1.000 0.112 All countries 0.891 0.120 1.000 0.077 0.891 0.120 1.000 0.077 0.891 0.120 1.000 0.077
Metafrontier cost efficiency (MCE)
Austria 0.824 0.162 0.940 0.099 0.758 0.202 0.956 0.123 0.589 0.053 0.963 0.172 Belgium 0.811 0.528 0.947 0.073 0.734 0.448 0.942 0.117 0.522 0.139 0.837 0.143 Denmark 0.831 0.652 0.955 0.035 0.796 0.617 0.946 0.048 0.623 0.244 0.915 0.094 France 0.828 0.204 0.963 0.077 0.727 0.184 0.948 0.093 0.609 0.028 0.963 0.162 Germany 0.847 0.222 0.982 0.062 0.754 0.199 1.000 0.079 0.604 0.035 0.933 0.135 Italy 0.795 0.202 0.968 0.117 0.772 0.188 0.985 0.123 0.641 0.129 0.954 0.148 Luxembourg 0.742 0.413 0.962 0.098 0.655 0.353 0.962 0.119 0.472 0.043 0.961 0.177 Spain 0.739 0.435 0.975 0.079 0.700 0.390 0.941 0.091 0.538 0.082 0.884 0.152 Switzerland 0.843 0.115 0.943 0.075 0.770 0.098 0.958 0.102 0.622 0.051 0.951 0.170 United Kingdom 0.802 0.178 0.937 0.111 0.728 0.148 0.948 0.134 0.576 0.051 0.960 0.171 All countries 0.816 0.115 0.982 0.090 0.742 0.098 1.000 0.109 0.590 0.028 0.963 0.164
Notes: SMF95, stochastic metafrontier with Battese and Coelli (1995) specification; SMF92, stochastic metafrontier with Battese and Coelli (1992) specification; QP, quadratic programming model.
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
44
the ability to conduct an independent monetary policy in European economic and monetary union would be detrimental to their economies.
Moreover, the average TGRs in these countries are quite close to one another, with the exception of Luxembourg. This indicates that banks operating in a relatively mature market and a more integrated market, like Western European countries, tend to undertake quite advanced and analogous technology in such a way as their cost frontiers do not deviate away from the metafrontier very much. In other words, the integration of EU economies is beneficial, because liberalization of cross-border trade of financial services stimulates innovation and technological progress.
To examine potential connection between cost efficiency and technology level, Figure 3 illustrates the scatter diagram for the average values of the both measures for each country. The figure exhibits that they are negatively correlated with each other, which is confirmed by running a simple regression model. The correlation coefficient is equal to -0.12, suggesting that a higher value of TGR is accompanied by a lower value of CE. However, the negative correlation is not very strong. Similar negative relationship is found by Battese et al. (2004) and Huang et al. (2010).
A direct efficiency comparison among nations can be conducted using MCE, instead of CE scores. The average values of the MCE in the ten sample countries lie in the range from 0.739 to 0.847, with an overall mean value of 0.816. An interesting question immediately arises, i.e., which element of the CE and TGR plays a more important role in determining the MCE. Table 10 shows that the CE components in most countries are lower than those components of TGR, implying that the primary source of inefficiencies derives from managerial inability, rather than assuming inferior technology. Banks in Germany (0.847), Switzerland (0.843), and Denmark (0.831) are the most efficient in terms of the MCE, while banks in Spain (0.739), Luxembourg (0.742), and Italy (0.795) are the least efficient. This finding is
‧
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
46
efficient. Although this connection requires further investigation, it confirms the current trend towards the universalization of banking system.
Figure 4 depicts that the mean values of the TGR in all sample countries derived from the QP method are less than those from the SMF methods, resulting in lower average values of the MCE. In other words, the programming method tends to underestimate banks’ TGR and MCE, together with larger variations in the parameter estimates. This evidence is in accordance with the previous studies.5 Berger and Mester (1997) note that the above result is partially arisen from the inclusion of some random errors into the efficiency score. Hence, the SMF appears to be the desirable model.
We now turn our attention to compare the results of SMF95 with those of the SMF92. Table 9 supports that the macroeconomic environmental conditions are important determinants on the technology gap of
U
Mjit in equation (11). For the SMF92 model, the average values (standard deviations) of the TGR range from 0.712 (0.122) in Luxembourg to 0.920 (0.040) in Denmark, with an overall mean value of 0.834 (0.105). For the model of the SMF95, the average values (standard deviations) of the TGR are between 0.807 (0.099) in Luxembourg and 0.960 (0.013) in Denmark, with an overall mean value of roughly 0.916 (0.070). The SMF92 is inclined to underestimate the TGR measures and exhibit larger variations. This may be attributed to the exclusion of environmental variables that impact the TGRs, causing a possible misspecification. The SMF95 is suggested to account for environmental differences.To be more convincing, the relevant efficiency scores are also calculated by using the parameter estimates from the translog functional form (Table B4). Different approaches are compared by evaluating the efficiency scores for each sample country
5 See Berger and Humphrey (1997) for a comprehensive survey.
‧
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
48
Table 11 Summary statistics of relevant efficiency scores for various competing metafrontier models based on TL specification Stochastic Metafrontier
with τ (SMF95)
Stochastic Metafrontier
without τ (SMF92) Metafrontier (QP)
Mean Min Max S.D. Mean Min Max S.D. Mean Min Max S.D.
Technology gap ratio (TGR)
Austria 0.899 0.362 1.000 0.094 0.797 0.424 1.000 0.111 0.648 0.081 1.000 0.153 Belgium 0.921 0.496 0.974 0.063 0.758 0.338 0.916 0.101 0.642 0.106 0.984 0.161 Denmark 0.963 0.862 1.000 0.011 0.869 0.723 1.000 0.043 0.773 0.478 1.000 0.077 France 0.913 0.269 0.981 0.058 0.781 0.336 0.985 0.077 0.634 0.019 1.000 0.153 Germany 0.878 0.355 1.000 0.062 0.768 0.525 1.000 0.070 0.616 0.037 1.000 0.122 Italy 0.938 0.642 1.000 0.032 0.895 0.531 1.000 0.070 0.752 0.156 1.000 0.115 Luxembourg 0.748 0.496 1.000 0.100 0.645 0.419 1.000 0.109 0.455 0.029 1.000 0.171 Spain 0.929 0.365 0.985 0.072 0.899 0.418 0.995 0.097 0.739 0.161 1.000 0.180 Switzerland 0.955 0.641 0.983 0.024 0.801 0.533 0.979 0.092 0.593 0.056 0.904 0.148 United Kingdom 0.927 0.583 1.000 0.056 0.815 0.497 1.000 0.080 0.660 0.128 1.000 0.154 All countries 0.904 0.269 1.000 0.087 0.790 0.336 1.000 0.108 0.629 0.019 1.000 0.167
Group-Specific cost efficiency (CE)
Austria 0.870 0.262 0.969 0.085 0.870 0.262 0.969 0.085 0.870 0.262 0.969 0.085
Belgium 0.876 0.779 1.000 0.045 0.876 0.779 1.000 0.045 0.876 0.779 1.000 0.045
Denmark 0.854 0.593 0.975 0.046 0.854 0.593 0.975 0.046 0.854 0.593 0.975 0.046
France 0.863 0.130 1.000 0.089 0.863 0.130 1.000 0.089 0.863 0.130 1.000 0.089
Germany 0.906 0.358 1.000 0.043 0.906 0.358 1.000 0.043 0.906 0.358 1.000 0.043
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
49
Italy 0.815 0.173 1.000 0.143 0.815 0.173 1.000 0.143 0.815 0.173 1.000 0.143 Luxembourg 0.915 0.684 0.981 0.038 0.915 0.684 0.981 0.038 0.915 0.684 0.981 0.038 Spain 0.710 0.610 1.000 0.080 0.710 0.610 1.000 0.080 0.710 0.610 1.000 0.080 Switzerland 0.893 0.124 1.000 0.080 0.893 0.124 1.000 0.080 0.893 0.124 1.000 0.080 United Kingdom 0.826 0.171 1.000 0.115 0.826 0.171 1.000 0.115 0.826 0.171 1.000 0.115 All countries 0.871 0.124 1.000 0.091 0.871 0.124 1.000 0.091 0.871 0.124 1.000 0.091
Metafrontier cost efficiency (MCE)
Austria 0.782 0.125 0.944 0.113 0.694 0.114 0.959 0.122 0.565 0.065 0.881 0.146 Belgium 0.806 0.472 0.962 0.068 0.665 0.321 0.885 0.103 0.562 0.101 0.835 0.146 Denmark 0.822 0.575 0.956 0.045 0.742 0.569 0.956 0.055 0.660 0.376 0.934 0.076 France 0.788 0.115 0.972 0.095 0.674 0.103 0.954 0.097 0.550 0.017 0.863 0.148 Germany 0.795 0.293 0.985 0.068 0.696 0.243 1.000 0.076 0.558 0.036 0.946 0.115 Italy 0.763 0.168 0.975 0.134 0.727 0.169 0.975 0.133 0.614 0.123 0.975 0.142 Luxembourg 0.685 0.417 0.950 0.097 0.591 0.310 0.957 0.106 0.418 0.027 0.928 0.160 Spain 0.658 0.257 0.961 0.081 0.636 0.292 0.928 0.085 0.525 0.109 0.905 0.139 Switzerland 0.853 0.122 0.956 0.078 0.715 0.101 0.916 0.106 0.529 0.051 0.865 0.142 United Kingdom 0.766 0.139 0.929 0.116 0.674 0.132 0.914 0.119 0.548 0.071 0.911 0.156 All countries 0.786 0.115 0.985 0.105 0.686 0.101 1.000 0.109 0.546 0.017 0.975 0.150
Notes: SMF95, stochastic metafrontier with Battese and Coelli (1995) specification; SMF92, stochastic metafrontier with Battese and Coelli (1992) specification; QP, quadratic programming model.
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
50
efficiency scores. For example, the mean value of MCE under translog specification is equal to 0.786, while the same measure is equal to 0.816 under FF specification. In other words, the average potential cost savings are about 21.4% and 18.4%, respectively. Furthermore, the translog cost function gives relatively unstable ranking results in comparison to the FF cost function. Such a difference may be ascribed to the fact that the FF cost function can approximate the underlying cost structure more accurately than the translog cost function.