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Table 6 Regression result of the estimated Trans-log cost function (Eq. A23)

From: Impact of learning through credit and value creation on the efficiency of Japanese commercial banks

\(lnTC\) Coef St.Err t-value p-value [95% Conf Interval] Sig
\(ln\varnothing\) 2.1343 0.1325 16.11 0.000 1.875 2.394 ***
0.5*\(\left({ln\varnothing }^{2}\right)\) − 0.0052 0.0123 − 0.42 0.674 − 0.029 0.019  
\({\mathrm{ln}w}_{1}\) − 0.0740 0.0453 − 1.63 0.102 − 0.163 0.015  
\({\mathrm{ln}w}_{2}\) 0.0631 0.0344 1.83 0.067 − 0.004 0.131 *
\({\mathrm{ln}E}_{k}\) 0.0162 0.0818 0.20 0.843 − 0.144 0.176  
t − 0.0090 0.0056 − 1.61 0.107 − 0.020 0.002  
\(0.5\times {{(\mathrm{ln}w}_{1})}^{2}\) 0.0102 0.0052 1.96 0.050 0.000 0.020 *
\(0.5\times {{\mathrm{ln}w}_{2}}^{2}\) 0.0169 0.0032 5.26 0.000 0.011 0.023 ***
\(0.5\times {{(E}_{k})}^{2}\) − 0.0078 0.0012 − 6.61 0.000 − 0.010 − 0.005 ***
\(0.5\times {T}^{2}\) 0.0006 0.0001 6.30 0.000 0.000 0.001 ***
\(ln\varnothing \times {\mathrm{ln}w}_{1}\) 0.0051 0.0053 0.96 0.338 − 0.005 0.016  
\(ln\varnothing \times {\mathrm{ln}w}_{2}\) − 0.0235 0.0068 − 3.47 0.001 − 0.037 − 0.010 ***
\(ln\varnothing \times {\mathrm{lnE}}_{k}\) 0.0021 0.0050 0.41 0.682 − 0.008 0.012  
\(ln\varnothing \times t\) 0.0010 0.0003 3.20 0.001 0.000 0.002 ***
\({\mathrm{ln}w}_{1}\times {\mathrm{ln}w}_{2}\) 0.0059 0.0031 1.87 0.061 − 0.000 0.012 *
\({\mathrm{ln}w}_{1}\times {\mathrm{lnE}}_{k}\) − 0.0094 0.0052 − 1.81 0.071 − 0.020 0.001 *
\({\mathrm{ln}w}_{2}\times {\mathrm{lnE}}_{k}\) 0.0159 0.0067 2.38 0.017 0.003 0.029 **
\({\mathrm{ln}w}_{1}\times t\) − 0.0003 0.0005 − 0.54 0.591 − 0.001 0.001  
\({\mathrm{ln}w}_{2}\times t\) − 0.0026 0.0003 − 7.68 0.000 − 0.003 − 0.002 ***
\(Cons.\) − 0.9030 0.6352 − 1.42 0.155 − 2.148 0.342  
\(/mu\) − 2.7213 17.0605 − 0.16 0.873 − 36.159 30.717  
\(/Insigma2\) − 1.6087 5.9322 − 0.27 0.786 − 13.236 10.018  
\(/ilgtgamma\) 5.3698 5.9595 0.90 0.368 − 6.311 17.050  
\(sigma2\) 0.200144 1.1873    1.79E − 06 22,432.45  
\(gamma\) 0.995367 0.027485    0.001814 1  
\(sigma\_u2\) 0.199216 1.1873    − 2.12785 2.526281  
\(sigma\_v2\) 0.000927 3.24 E− 05    0.000864 0.000991  
\(Mean\,dependent\,var\) 29.4652 \(SD\,dependent\,var\) 2.2258  
\(Number\,of\,obs\) 1800 \(Chi-square\) 609,337.6989  
\(Prob>chi2\) 0.0000 \(Akaike\,crit.\,(AIC\)) −6994.4018  
  1. *** p < 0.01, ** p < 0.05, * p < 0.1