5. Empirical Results and Analysis
5.1 Parameter Estimates
國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
32
5. Empirical Results and Analysis
This section presents all of our empirical results. In the first subsection we show the parameter estimates of the stochastic cost frontier for both the FF and the translog functional forms, and perform some hypothesis tests for each country. In the second subsection we analyze implications drawn from the estimated cost efficiency scores and the TGRs. The third subsection aims to provide a detailed discussion on the trending of various efficiency measures during the sample period. Finally, some further evidence about the impact of a bank’s size, profitability, and risk attitude on the efficiencies is investigated.
5.1 Parameter Estimates
Software FRONTIER 4.1 (see Coelli, 1996) is applied to yield the parameter estimates for all of the 10 country frontiers of Equation (1). Both the FF and the standard translog cost functions are estimated for the purpose of comparison. Table 6 merely summarizes the translog part of the parameter estimates of the FF cost function for each country and the estimates of Fourier series are shown in Table B1 of Appendix B. Table B2 presents the estimation results of the translog cost function. It is seen that more than half of the parameter estimates in each country reach statistical significance at least at the 10% level. The hypothesis that the parameters of all the Fourier series are joint zero is decisively rejected at the 1% level of significance by the likelihood ratio (LR) test. We, thus, claim that the FF cost function is valid to represent the sample banks’ production technologies and the underlying cost structure.
As far as the environmental conditions are concerned, Table 7 summarizes coefficient estimates of the micro-level environmental variables based on the FF cost function. The outcomes reveal that most of those estimates are significant in each sample country, but their signs are different, caused possibly by the distinct
‧
Table 6 Parameter estimates of the Fourier flexible cost frontier for the sample countries
Austria Belgium Denmark France Germany Italy Luxembourg Spain Switzerland United Kingdom
constant
-1.727 2.945 ** 3.426 -12.773 *** -4.350 *** -9.105 *** -7.976 *** 10.456 *** -0.086 -10.963 ***‧
Log-likelihood 105.923 272.526 553.276 227.496 236.092 253.407 346.905 190.023 814.589 85.147 Notes: Standard errors are given in parentheses. ***, ** and * denote statistical significance at the 1%, 5%, and 10% levels, respectively.‧
Table 7 Parameter estimates of the environmental variables
Country ETA ROA State banks Private banks
Austria -0.020 *** -0.153 *** -1.927 -0.589 ***
significantly negative 10 8 1 2
insignificant 0 2 4 3
Notes: Standard errors are given in parentheses. ***, ** and * denote statistical significance at the 1%, 5%, and 10% levels, respectively.
country-specific situations. We focus our attention only on those estimates that attain statistical significance. Variable ETA is negatively associated with the cost inefficiency term for all sample countries, implying that the higher the ETA is, the more efficient is the bank. This result is congruent with many previous studies, such as Hughes and Mester (1998), Fries and Taci (2005), Kumbhakar and Wang (2007),
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
36
Huang et al. (2011b), and Radić et al. (2012), to mention a few. With some exceptions, the coefficient of ROA is found to be significantly negative, showing that high profitability prompts banks’ cost efficiency in these countries. This finding is consistent with Cavallo and Rossi (2002) and Casu and Molyneux (2003). For the ownership dummies, the sign of the coefficient estimate for the state-owned and domestic private are significantly positive in most countries. One is led to conclude that foreign-owned banks are more cost efficient than domestic private banks and state-owned banks. This result is similar to Fries and Taci (2005) and Huang et al.
(2011b), supporting the view of global advantage hypothesis.
Table 8 reports the average estimated country-specific efficiency scores for each country, calculated by the FF and the translog cost frontiers. Figure 2 depicts these mean values. Although these CE scores are not directly comparable among the sample countries, the magnitudes of the CE scores from the translog cost function in all sample countries are smaller than those obtained by the FF cost function. The translog form tends to underestimate banks’ CE scores on average. In addition, the estimated efficiency scores of the translog specification vary wider than those of the FF form.
The FF cost function appears to be able to fit the data well and is preferred to the translog form.
Before estimating the metafrontier, it is important to test the null hypothesis that the sample banks from different countries adopt the same technology. If the hypothesis is not rejected by the data, then all banks of different countries share the same technology, implying that the estimation of the metafrontier is not necessary.
Since the LR test statistic of 983.51 exceeds the corresponding critical value at the 1%
level with the degrees of freedom 477, the hypothesis is decisively rejected. We conclude that the sample banks from different countries are indeed operating under different technologies, which validates the construction of the metafrontier.
‧
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
38
M
U
jit to be associated with an array of (macro-level) environmental variables, similar to Battese and Coelli (1995). This model is labeled as SMF95. Moreover,U
Mjit can be alternatively specified as a function of time, e.g., the one proposed by Battese and Coelli (1992). Specifically, termU
Mjit is specified asU
Mjit =U
Mji exp⎡⎣−η ( t T
−)
⎤⎦ ,where
U
Mji ~N
+( μ σ
, u2M)
and the model is labeled as SMF92.Table 9 summarizes the second-step parameter estimates for models SMF95 (column 1) and SMF92 (column 2). The estimates of Fourier series are shown in Table B3 of Appendix B. The coefficient estimates of the metafrontier in the context of quadratic programming are shown in column 3. The bootstrapping method with 1,000 replications is used to get the standard deviations of these coefficients. The coefficient estimates obtained by programming techniques deviate substantially from the ones of the SMF models, whereas the estimates of the SMF95 and SMF92 are relatively close to each other. The results reveal significant differences in both the magnitude and signs of the estimates between the SMF and QP methods. The QP estimates trend to vary larger than those of the SMF estimates.
Moreover, to justify the proposed stochastic metafrontier model, one can proceed to test whether the estimated values of
σ
u2 andσ
v2 are significant. If they areindeed significant, then the presence of
U
Mjit and vMjit is necessary, which validates the use of the stochastic metafrontier model, rather than the deterministic metafrontier model. Table 9 uncovers that the estimatedσ
u2 andσ
v2 of the both SMF models are significantly different from zero, supporting the appropriateness of our stochastic metafrontier model.Although the corresponding parameter estimates of the two SMF methods are
‧
Table 9 Parameter estimates for various competing metafrontier models (FF)
Independent SMF95 SMF92 QP
variables Coefficient S.E. Coefficient S.E. Coefficient S.D.
constant 2.073 *** 0.071 1.263 *** 0.093 2.387 0.580
Notes: SMF95, stochastic metafrontier with Battese and Coelli (1995) specification; SMF92, stochastic metafrontier with Battese and Coelli (1992) specification; QP, quadratic programming model. The standard errors of SMF are corrected by sandwich estimators. The standard errors of the QP estimators are obtained from bootstrapping. ***, **, and * indicate statistical significance at the 1%, 5%, and 10%
levels respectively.
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
40
close to each other, estimates of the SMF92 are also found to have larger variation.
The trending coefficient of
η
is estimated to be significantly positive, meaning thatM
U
jit decreases at an exponential rate such that the TGR shrinks with time. Admittedly, one potential weakness inherent in time-varying model is that the inefficiency effects of different firm at time t face the same exponential rate. It does not reflect the situations that banks might operate in a country with relatively worse technology (being relatively inefficient) at initial period but then operate in a country with relatively better technology (being relatively efficient) (Al-Jarrah and Molyneus, 2006). Turning to the SMF95 model, all of these macroeconomic environmental factors exercise significant influences on the TGRs. As expected, the coefficient estimate of variable GDPPC is significantly negative, implying that the better the economic condition, the more advanced technology the country undertakes, leading the country’s frontier closer to the metafrontier. Similarly, the significantly negative coefficient of PD uncovers that banks operating in an environment with higher PD are inclined to adopt better technology. The variable of DD is found to have a positive coefficient, suggesting that banks facing a higher level of DD tend to operate under inferior technology. The coefficient of the HHI is significantly negative, indicating that banks operating in a highly concentrated market are apt to adopt more advanced technology than those banks running in a less concentrated market.We also estimate the standard translog cost function and Table B4 of Appendix B summarizes those coefficient estimates. The finding that QP estimates deviate from the SMF estimates with larger variations is roughly similar to those obtained by FF specification. Most important, the estimates of
σ
u2 andσ
v2 are also statistically significant in both SMF models, justifying the use of the stochastic metafrontier approaches.‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
41