5. Empirical Results and Analysis
5.3 Global Views on the Trend
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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.
5.3 Global Views on the Trend
An interesting issue may be raised, i.e., whether the financial integration of the Single Market in European Union (EU) helps promote bank efficiencies.6 Table 12 summaries the measures of CE, TGR, and MCE derived from the SMF95 over the sample period and Figure 5 draws the trends of these efficiency scores. The mean values of CEs exhibit a gradual upward trend varying from 0.887 to 0.904 in the period of 1996 to 2000, followed by a slow downward trend from 0.893 to 0.871 in the period of 2000 to 2010. Measure MCE has a similar trend to CEs, which ranges from 0.813 to 0.838 in the first four years, and then goes down all the way to 0.786, especially after the subprime crisis of 2007-2010, starting from the U.S. This suggests that such a more integrated financial market is at least initially able to enhance banking efficiency. This outcome is in congruent with, e.g., Casu and Girardone (2004), Weill (2007), and Kondeas et al. (2008). Although the financial integration might increase banks’ cost efficiency, bank manages might choose to take up more risk to reflect a higher regulatory burden, which could ultimately affect banks’
performance. For example, loose and easy credit conditions, during 2002-2008, result
6 The Single Market for Financial Services in the EU was established on January 1, 1993.
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Table 12 Summary statistics of relevant efficiency scores over time (SMF95-FF)
Period CE TGR MCE
Note: SMF95, stochastic metafrontier with Battese and Coelli (1995) specification.
in higher risk-taking of lending and borrowing activities. As noted by Fiordelisi et al.
(2011), banks with lower levels of efficiency tend to have a moral hazard incentive to undertake risky business, such as the less intensive monitoring of credit in an attempt to boost returns. Moreover, the exposure of higher risk is possibly to lessen a bank’s efficiency, because this bank has a higher probability to consume large amounts of resources coping with the increased non-performing loans. The downward trends of CEs and MCEs are indeed corresponding to the recession period of global economies after 2000 and the trends deteriorate after the subprime crisis starting from late 2007.
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Different trending is traced out by the other two models, due possibly to their different treatments with respect to cost inefficiency and country heterogeneity. For SMF92, the means of the relevant efficiency scores are provided in Appendix C. Table C1 shows that the mean MCEs has a gradual upward trend from 1996 to 2000, followed by a slight downward trend from 2001 to 2003, a subsequently upward trend from 2004 to 2006, and then a downward trend again from 2007 to 2010. Based on the significantly estimated positive coefficient of
η
, the TGRs is expected to grow with time, which is confirmed by Table C1 and Figure C1, with a few exceptions.Different from the results of SMF95, these findings largely provide evidence in favor of technology improvements during the sample period. Since the SMF92 model excludes other important factors from the TGR, its average value of the TGR is apt to be underestimated and difficult to precisely describe the evolutions of technology innovations with economic shocks, occurred in European banks.
According to Table C2 and Figure C2 in Appendix C, the QP model and the two SMF models reveal considerable differences in the various efficiency measures and their time trends. Specifically, the average MCE and TGR fluctuate synchronously.
That is, the mean MCEs (TGRs) exhibit a slow upward trend between 0.545 (0.617) and 0.627 (0.702) during 1996- 2005 and then turn into a downward trend varying from 0.618 (0.690) to 0.571 (0.567). Kontolaimou and Tsekouras (2010) reach the similar results of the convergence process in Western European banking over the period of 1994 to 2003 based on a nonparametric metafrontier analysis. Huang et al.
(2011a) adopt the QP method to obtain similar upward sloping trends for commercial banks in Western European nations over the period of 1994 to 2003. It is noteworthy that these results are likely to be confounded with random shocks, particularly in a long panel like ours. As the programming technique is deterministic in essence without considering random disturbances, it is unable to separate time effect and
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country heterogeneity from random shocks in the explanation of the technology gap.
Any time effect and unobserved heterogeneity are ascribable to the gap of technology, which tends to bias the estimation results.
Another difference in the source of cost inefficiencies is also noteworthy. To understand what causes inefficiencies, it is useful to analyze the components of the MCE. On the basis of Figure 5, where the SMF95 is employed to gauge banks’
efficiency scores, the CE component is lower than the TGR component, which indicates that the managerial inability constitutes the primary source of inefficiencies, rather than the technology adopted. This result suggests that banks should make efforts to improve their managerial efficiency. However, different source is traced out by the other two metafrontier models, i.e., the SMF92 and QP. According to Figures C1 and C2 when the environmental heterogeneity is not considered, the TGR component is lower than the CE component, implying that the major source of inefficiencies comes from adopting inferior technology, instead of the managerial inability.
As in the case of translog specification, Table 13 and Figure 6 demonstrate the results of the efficiency measures based on the SMF95. The patterns of TGRs and MCEs are roughly the same with the results of FF specification during the period 1996-2007. After 2007, these measures exhibit a dramatic decline and then turn up slowly. Since the translog function is inferior to the FF cost structure, the results here may be doubtful. As regards the other two models, Figures C3-C4 and Tables C3-C4, Appendix C, provide the numerical and graphic representations. For the models without considering the environmental heterogeneity, the trends are essentially flat over time, which are consistent with those FF specifications. These measures seem not to be able to reflect the complex macroeconomic conditions, confirming that the consideration of environmental variables is essential when assessing bank efficiency.
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Table 13 Summary statistics of relevant efficiency scores over time (SMF95-TL)
Period CE TGR MCE
Mean S.D. Mean S.D. Mean S.D.
1996 0.874 0.080 0.888 0.097 0.774 0.100 1997 0.875 0.082 0.899 0.091 0.785 0.100 1998 0.878 0.077 0.905 0.083 0.793 0.095 1999 0.878 0.079 0.909 0.077 0.797 0.093 2000 0.883 0.080 0.917 0.072 0.809 0.092 2001 0.872 0.089 0.923 0.070 0.804 0.097 2002 0.874 0.092 0.917 0.074 0.801 0.101 2003 0.878 0.096 0.913 0.076 0.801 0.106 2004 0.877 0.103 0.913 0.103 0.801 0.104 2005 0.869 0.099 0.913 0.073 0.792 0.104 2006 0.871 0.099 0.901 0.087 0.784 0.113
2007 0.868 0.115 0.888 0.114 0.770 0.112
2008 0.854 0.106 0.884 0.102 0.752 0.117 2009 0.855 0.102 0.888 0.104 0.757 0.116 2010 0.849 0.105 0.898 0.090 0.760 0.109 96-98 0.875 0.080 0.897 0.091 0.784 0.099 99-01 0.877 0.082 0.916 0.073 0.803 0.094 02-04 0.876 0.092 0.915 0.077 0.801 0.104 05-07 0.869 0.097 0.901 0.087 0.782 0.110 08-10 0.853 0.104 0.890 0.099 0.756 0.115 Average 0.871 0.091 0.904 0.087 0.786 0.105
Note: SMF95, stochastic metafrontier with Battese and Coelli (1995) specification.
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Table 14 Summary statistics of relevant efficiency scores by asset sizes, return on
assets and the ratio of equity to total assets (SMF95-FF)Class Obs. CE TGR MCE
Panel A. Total Assets
SIZE1 below 100 758 0.90208 0.92118 0.83039
SIZE2 100-200 1,100 0.89761 0.93222 0.83632
SIZE3 200-400 1,368 0.89494 0.92728 0.82950
SIZE4 400-800 1,403 0.89718 0.92063 0.82568
SIZE5 800-2,000 1,700 0.89564 0.91803 0.82171
SIZE6 2,000-5,000 1,179 0.88448 0.91042 0.80407 SIZE7 5,000-15,000 793 0.87694 0.88964 0.77848 SIZE8 above 15,000 888 0.87490 0.89650 0.78223
Notes: SMF95, stochastic metafrontier with Battese and Coelli (1995) specification. The values of total assets are measured in millions of US dollars to save space.
increasing rends in the various efficiency measures are found with the increase in banks’ profitability. Figure 8 depicts similar trends. It is clear that banks’ profitability, managerial performance, and the level of technologies undertaken are interrelated,
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Tables D1-D2, Appendix D, and Figures D1-D6 present the results obtained from the SMF92 and QP models. The former model has the patterns roughly consistent with those obtained by SMF95, but more volatile. However, the QP model gives quite different patterns from both SMF92 and SMF95 models. Figure D4 draws an inverted U-shape for the average TGR and MCE curves against size classes, where they increase as the bank size grows initially, and decrease starting from the fourth asset size. On the basis of the profit levels, Figure D5 displays that the average efficiency curves cycle up and down, failing to show a clear relationship between efficiency scores and profits. Figure D6 detects a similar inverted U-shape across different ETA classes to that of asset sizes. In summary, there appears to have no clear patterns between efficiency scores, derived by the QP model, and a bank’s size, profitability, and risk attitudes. This may be ascribed to the failure of the QP model to split random shocks from the related efficiency measures.
Finally, it is important to understand whether different specification on cost structure yields conflicting evidence on the impact of bank characteristics on various efficiency scores. Table 15 and Figures 8-10 illustrate the trends as bank size grows, and profitability improvements, as well as risk attitude changes for the SMF95. When the data are used to fit translog cost frontiers, the foregoing conclusion regarding the effect of bank characteristics continues to be held in general. Figures 7-12, Appendix D, summarize the results for the other two models. Similar patterns are found by the SMF92 estimation. In the case of QP measures, there are no apparent trends in efficiency scores as bank characteristics change. Overall, these results are robust against different functional forms and the stochastic metafrontier procedure is more appropriate to evaluate bank’s efficiency.
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Table 15 Summary statistics of relevant efficiency scores by asset sizes, return on
assets and the ratio of equity to total assets (SMF95-TL)Class Obs. CE TGR MCE
Panel A. Total Assets
SIZE1 below 100 758 0.88819 0.91868 0.81636
SIZE2 100-200 1,100 0.88357 0.92705 0.81850
SIZE3 200-400 1,368 0.87737 0.92139 0.80779
SIZE4 400-800 1,403 0.87785 0.90925 0.79734
SIZE5 800-2,000 1,700 0.87288 0.90541 0.78901
SIZE6 2,000-5,000 1,179 0.85919 0.89337 0.76544
SIZE7 5,000-15,000 793 0.84876 0.86666 0.73220
SIZE8 above 15,000 888 0.84928 0.86800 0.73348
Panel B. ROA (%)
ROA1 below 0 879 0.83638 0.90253 0.75387
ROA2 0-0.15 870 0.86679 0.88500 0.76511
ROA3 0.15-0.3 1,148 0.86840 0.88757 0.76897
ROA4 0.3-0.5 1,581 0.87746 0.90373 0.79175
ROA5 0.5-1 2,029 0.86771 0.90353 0.78223
ETA6 12-20 1,514 0.87354 0.92919 0.81107
ETA7 20-30 591 0.89037 0.93348 0.83120
ETA8 above 30 641 0.91705 0.91532 0.83967
Notes: SMF95, stochastic metafrontier with Battese and Coelli (1995) specification. The values of total assets are measured in millions of US dollars to save space.
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Figure
re 10. Trend
e 11. Trends
ds in CE, TG
s in CE, TG
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GR, and MC
GR, and MC
CE by size c
CE by ROA
class (SMF9
class (SMF
95-TL)
95-TL)
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Figuree 12. Trends in CE, TG
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GR, and MCCE by ETA cclass (SMF995-TL)
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6. Conclusion
This paper successfully extends the deterministic metafrontier translog cost function to the more general SMF Fourier flexible cost function that has several advantages. Unlike the use of conventional two-step procedure, e.g., Battese et al.
(2004), O’Donnell et al. (2008), and Huang et al. (2011a), which combines the stochastic frontier approach with the mathematical programing technique, the stochastic metafrontier is formulated and applied for estimating the technology gap ratio, instead of the programming technique, such that the first and the second step of the study are compatible. It is therefore of great benefit that the statistical inferences can be drawn, on the basis of a regression model, without relying on simulation or bootstrapping. Furthermore, composed errors can be incorporated to handle random shocks and possible production inefficiency. This avoids the criticism aimed at mathematical programming. Most importantly, our new model specifies the TGR to be a function of some exogenous variables. That is, the group-specific environmental differences are allowed to be included in the second-step estimation procedure. The environments faced with a bank usually impose some restrictions on bank managers, which may limit their ability to optimize the allocation of resources among different uses. This helps characterize the sources of a bank’s production inefficiency, on the one hand, and reduce the problem of heteroskedasticity, on the other hand.
Using the newly developed formulas, this paper devoted to uncovering new evidence on the cost efficiency of Western European banks during the period of 1996 to 2010 and to broaden our capacity for illustrating the usefulness of the proposed estimation approach and comparing with the results of various competing metafrontier models. The empirical application discloses that the TGR and MCE exhibit a gradual upward trend initially during 1996-2000 and then fluctuate with a downward trend reflecting market movements, especially after the subprime crisis of 2007-2010.
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These results show that a single and competitive banking market not only contributes to greater cost efficiencies, but also shrinks the technology gap within the member states of European Union. A representative bank in Western Europe attains a remarkable efficiency improvement after the financial markets become more competitive and integrated due to the creation of a single market in 1993. However, the wave of international economic integration is usually inevitably accompanied by higher degree of risk exposure. The subsequently downward trends reflect this factor during the recession period of global economies after 2000 and are found to have deteriorated after the global financial crisis which started in late 2007.
In seeking further evidence on the role played by the bank’s size, profitability, and risk attitude on relevant efficiency score, several implications can be drawn from the empirical results. First, smaller banks appear to outperform the larger ones in terms of MCE and TGR. On the other words, banks with smaller assets size are able to benefit more from the cost efficiency and advanced technology. Second, higher profitability is connected with greater efficiency. Banks with higher profitability tend to be more cost efficient and to adopt more advanced technology than poor profitable banks. Finally, more conservative banks are related to greater efficiency. Banks with higher values of capital ratio are inclined to enhance cost efficiency and to adopt more advanced technology. This result might be ascribable to the fact that risk-averse bank managers are frequently engaged in monitoring and supervising activities that help reduce the exposure of risks.
As in the case for the other two competing metafrontier models, the choice of methodology seems to influence the estimation results and its associated policy implications derived from the analyses. Not only the parameter estimates considerably differ from each other, but also the so-derived efficiency scores show dissimilar distribution and patterns. The deterministic metafrontier programming techniques
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tends to underestimate the TGR and MCE measures and these estimates exhibit larger variation, probably due to specification error, i.e., the estimates are inclined to be confounded with shocks, and lack of considering environmental variable. Although the SMF92 appear to be better choices due to its ability to incorporate random shocks, it is also apt to underestimate these measures and exhibit larger variation in contrast to the SMF95. Moreover, when we adopt deterministic metafrontier programming techniques to deal with further insights on the effect of assets size, profitability, and risk attitude, there is little evidence to suggest that the widely accepted results.
Therefore, the proposed stochastic metafrontier specification, which includes group-specific environmental variable as determinants of technology gap, should be preferable and consistent with reality.
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