5. Empirical results
5.3 Lerner index
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0.6820 for Luxembourg to 0.8791 for Switzerland. Comparing to Table 8, we see that the mean CE score derived from the case of multiple outputs tends to be lower than that from the single output case. This implies that the aggregation of multiple outputs is apt to distort the estimates of cost efficiency.
The overall average TGRs of CSSFM and LP equal 0.9527 and 0.6837, respectively, which are both lower than those in Table 8. Aggregating outputs here is inclined to under-estimate the average TGR. CSSFM still gives quite similar average TGRs among the five countries, while LP suggests that banks in the sample countries adopt quite different technologies. The standard deviation of CSSFM is smaller than that of LP for each country, as expected. The component of TGR of CSSFM is on average larger than that of CE, but the reverse is true for LP.
5.3 Lerner index
Table 10 reports the summary statistics of the Lerner indices for the outputs of loans and investments and for the single output case across countries estimated by CSSFM and conventional models. As far as the loan market is concerned, the Swiss banking market is the most competitive among the five sample countries, as its average
L
New is the lowest, followed by France, Luxembourg, Italy, and Germany.8 German and Italian banks appear to enjoy stronger market power than the remaining three nations.The average
L
Old gives the same ordering, as shown in the last 5 column of the table.Moreover, the new Lerner index measures tend to be higher than the conventional ones, except for Germany, due partially to the fact that some of the
L
Old estimates are negative. Consequently, the conventional model inclines to underestimate the index such that the degree of market competition is exaggerated.
8 The pairwise differences in the average new Lerner index among these countries are all significant at the 1% level, except for the difference between Germany and Switzerland in the investment market and the difference between Germany and Luxembourg in the single output case.
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Table 9 Various Efficiency Scores for a Single Output
CSSFM LP
Mean Min. Max. SD Mean Min. Max. SD
FRA FRA
CE 0.8463 0.2166 0.9058 0.0633 CE 0.8391 0.1783 0.9807 0.0725 TGR 0.9543 0.8234 0.9614 0.0102 TGR 0.6709 0.0481 0.9557 0.1663 CEM 0.8077 0.1910 0.8708 0.0603 CEM 0.5645 0.0364 0.8614 0.1493
GER GER
CE 0.7070 0.3225 0.8740 0.0719 CE 0.7420 0.2079 0.9817 0.1502 TGR 0.9501 0.8975 0.9614 0.0083 TGR 0.7380 0.0675 0.9498 0.1020 CEM 0.6717 0.3079 0.8403 0.0686 CEM 0.5485 0.0324 0.7981 0.1377
ITA ITA
CE 0.8613 0.5302 0.9050 0.0512 CE 0.8035 0.1972 0.9794 0.1220 TGR 0.9588 0.8534 0.9614 0.0073 TGR 0.8194 0.2730 1.0000 0.2122 CEM 0.8259 0.5097 0.8701 0.0497 CEM 0.6591 0.1625 0.9363 0.1389
LUX LUX
CE 0.8317 0.5023 0.9205 0.0661 CE 0.6820 0.1780 0.9744 0.2025 TGR 0.9450 0.8903 0.9614 0.0123 TGR 0.5873 0.0388 1.0000 0.2320 CEM 0.7859 0.4741 0.8850 0.0633 CEM 0.4117 0.0145 0.9428 0.2146
SWI SWI
CE 0.8883 0.4329 0.9349 0.0529 CE 0.8791 0.3525 0.9828 0.0664 TGR 0.9537 0.8980 0.9614 0.0064 TGR 0.6231 0.0177 0.8809 0.2134 CEM 0.8472 0.4110 0.8989 0.0506 CEM 0.5481 0.0160 0.8228 0.1929
Overall Overall
CE 0.8270 0.2166 0.9349 0.0915 CE 0.8038 0.1780 0.9828 0.1391 TGR 0.9527 0.8234 0.9614 0.0096 TGR 0.6837 0.0177 1.0000 0.1883 CEM 0.7880 0.1910 0.8989 0.0884 CEM 0.5510 0.0145 0.9428 0.1801
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Table10 Summary Statistics of the Lerner Index Measure
Mean of
L
New Mean ofL
Old France are nearly perfectly competitive, as their average values ofL
New fall short of 0.08. The remaining three markets may be characterized as monopolistic competition.Again, the new Lerner index measures are all higher than the conventional ones across our sample countries. This time, three out of the five countries have negative values of the
L
Old measure, arising from large negative estimates that may result due to adverse random shocks. Conversely, ourL
Newmeasure is able to avoid such a problem, as it is internally built into the simultaneous equations model.In the context of the single output case, the largest value of the new Lerner index is Switzerland (0.2549), followed by France, Italy, Germany, and Luxembourg. The new Lerner index is on average larger than the conventional Lerner index with the exception of Italy. One is led to conclude that these financial markets can be classified as monopolistic competition. Our estimates of
L
New andL
Old are close to past works, e.g., Berger et al. (2009) and Carbó et al. (2009).‧ 國
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According to Table 11, the overall mean value of MCGR is equal to 0.3848 for the loan market in the five countries as a whole. The same measures vary among the sample countries from 0.0857 for Luxembourg to 0.6835 for Switzerland, indicating that the potential increase in profit for banks in the two countries is 8.57% and 68.35%, respectively, provided they adopt the most advanced technology in the production of loans. The average value of MCGR is equal to 0.5338 for the entire investment market, lying in the range between 0.3127 for Germany and 0.9866 for Luxembourg. Banks in Germany and Switzerland can earn additional profit rates up to 31.27% and 98.66%, respectively, when adopting the potential advanced technology. Our results imply that banks should first allocate scarce resources to promote their production technology in investments, since the potential profitability from investments is larger than that of loans. Improving the production technology of investments is capable of a larger profit rate relative to enhancing the production technology of loans.
Under the single output case, the mean value of MCGR is merely 0.0335 for the asset market. Italian banks have the highest value of 0.0620, followed by Luxembourg (0.0605), Germany (0.0490), France (0.0119), and Switzerland (0.0111). These numbers are substantially lower than the multiple output case, implying that the single output case is apt to under-estimate the measure of MCGR.
Recall from equation (29) that the sum of
L
New and MCGR is referred to as the potential Lerner index. The single output case still under-estimates theLerner
p measure in comparison to the multiple output case. In the loans market, German, Italian, and Luxembourg banks can substantially increase their profit by setting higher lending rates over their MCs, as theirL
New measures exceed MCGRs, while banks in France and Switzerland are suggested to lower their country-specific MCs as close as possible to the meta-frontier MCs, as their MCGRs are larger than theL
New measures.‧
Table 11 Estimates of the Potential Lerner Index
Loan FRA GER ITA LUX SWI TOTAL
Lerner
p 0.8902(0.1668)
Lerner
p 0.8394(0.2305)
Lerner
p 0.2055(0.0894)
Note: Numbers in parentheses are standard deviations.
In the investments market, German and Switzerland banks can effectively increase their profits by setting a higher price of investments, but banks in the remaining three countries should reduce their MC in order to largely improve profits. In the single output case, all banks in the sample countries are recommended to exert their market power by raising the output price, rather than by reducing their MC, as the
L
New measures are all larger than MCGRs.‧ 國
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