## 4 Results
** \\ \hline LOGATM & 0.188631 & 0.046479 & 4.058386 & 0.0001 \\ LOGBANKEMPL & \(-\)0.323770 & 0.056521 & \(-\)5.728280 & 0.0000 \\ LOGDESI\_HC & 0.926947 & 0.202242 & 4.583349 & 0.0000 \\ LOGDESI\_IDT & \(-\)0.921624 & 0.096607 & \(-\)9.539929 & 0.0000 \\ LOGDIGINCL & 2.296045 & 0.371943 & 6.173118 & 0.0000 \\ LOGEBANK & \(-\)0.289611 & 0.065868 & \(-\)4.396819 & 0.0000 \\ LOGGDP & \(-\)0.281414 & 0.099263 & \(-\)2.835022 & 0.0053 \\ RD & 0.245810 & 0.035356 & 6.952406 & 0.0000 \\ MOMENT1 & 0.418840 & 0.048837 & 8.576286 & 0.0000 \\ MOMENT2 & 0.428785 & 0.023229 & 18.45944 & 0.0000 \\ C & \(-\)3. In parallel, the period-weighted specification (Table 7b) maintained strong performance, with an R-squared of 0.8051 and adjusted R-squared of 0.7910. The F-statistics remained significant (F = 56.99, \(p\) = 0.000), and the model converged after 11 iterations. The heteroskedasticity test again returned a \(p\)-value of 0.0000, validating the correction mechanism. Although the Durbin-Watson statistics dropped to 1.33, suggesting some residual autocorrelation, the model still effectively mitigates structural heteroskedasticity. The use of panel EGLS (Table 7c) directly responds to the problem of cross-sectional and period-based heteroskedasticity. The likelihood ratio tests included in the analysis unequivocally reject the null hypotheses of homoskedasticity at the 1% level for both cross-sectional (\(p\) = 0.0000) and period-based (\(p\) = 0.0000) residuals. This demonstrates the presence of significant heteroskedasticity within the dataset, validating the application of generalized least squares estimators. The weighted estimation ensures more efficient and unbiased coefficient estimates under the assumption of heteroskedastic and contemporaneously correlated errors, thus adhering to the robustness requirements advocated by the reviewer. Moreover, the panel EGLS results exhibit high levels of explanatory power (R\({}^{2}\) = 0.977 cross-section; R\({}^{2}\) = 0.805 period-based), and all key automation and digitalization variables retain statistical significance at conventional levels. This corroborates the strength and reliability of the findings, while the use of robust estimation methods further enhances the empirical validity of the causal inferences. The residual diagnostics (Table 6) confirm significant heteroskedasticity across both dimensions (Likelihood Ratio Tests with \(p\) < 0.0001), thus validating our choice of EGLS as a remedial technique. The EGLS results yielded consistent and significant coefficients aligned with the MMQR estimations, particularly for variables such as LOGDESI_HC, LOGATM, and RD, thereby reinforcing the reliability of our findings across quantiles. The cross-section weighted model (Table 7a) achieved an exceptionally high R-squared value of 0.9772 and an adjusted R-squared of 0.9755, indicating a highly explanatory model. This robustness check strengthens the credibility of our causal inferences, especially in light of the complex, multi-dimensional nature of automation and banking performance. In conclusion, the application of both MMQR and EGLS not only strengthens our estimation strategy against violations of homoskedasticity and normality but also ensures that the core results remain robust and generalizable. These methods together serve the dual function of methodological rigor and empirical resilience.