## 4 Results
While we confirm a long-term relationship among variables, we acknowledge that cointegration does not prove causality. This is why we have incorporated Granger causality analysis. The Granger causality analysis (Table 13a-e and Figure 4) reveals a web of significant predictive relationships across macroeconomic, digital, and institutional banking indicators. By applying a 1-lag structure over the 2017-2022 sample period, the test identifies several causality directions that inform the dynamics of bank performance, technological diffusion, and economic behavior. The results indicate that macroeconomic growth, as measured by GDP, precedes and significantly predicts return on equity (ROE), suggesting a fundamental influence of broader economic performance on bank profitability. Moreover, ROE itself emerges as a strong antecedent of R&D investment and digital integration (DESI_IDT), implying that more profitable institutions may channel resources into innovation and digital transformation initiatives. This reinforces the view that successful banking institutions become engines of innovation through endogenous reinvestment mechanisms. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**(a)**} \\ \hline
**Causal Relationship** & **Direction** & **F-stat** & \(\mathbf{p}\)**-Value** & **Significance** \\ \hline LOGGDP \(\Rightarrow\) LOGROE & Unidirectional & 8.063 & 0.0053 & *** 1\% \\ LOGROE \(\Rightarrow\) RD & Unidirectional & 4.605 & 0.0340 & *** 5\% \\ MOMENT1 \(\Rightarrow\) LOGROE & Unidirectional & 7.779 & 0.0062 & *** 1\% \\ MOMENT2 \(\Rightarrow\) LOGROE & Unidirectional & 5.332 & 0.0228 & *** 5\% \\ LOGROE \(\Rightarrow\) LOGBANKEMPL & Unidirectional & 2.751 & 0.0999 & * 10\% \\ LOGROE \(\Rightarrow\) LOGCDESI\_IDT & Unidirectional & 5.937 & 0.0163 & ** 5\% \\ \hline \multicolumn{3}{c}{**(b)**} \\ \hline
**Causal Relationship** & **Direction** & **F-stat** & \(\mathbf{p}\)**-Value** & **Significance** \\ \hline LOGCDESI\_HC \(\Rightarrow\) LOGATM & Unidirectional & 4.810 & 0.0301 & *** 5\% \\ LOGCDESI\_IDT \(\Rightarrow\) LOGATM & Unidirectional & 8.072 & 0.0052 & *** 1\% \\ LOGDIGINCL \(\Rightarrow\) LOGATM & Unidirectional & 6.823 & 0.0101 & *** 5\% \\ LOGGDP \(\Rightarrow\) LOGATM & Unidirectional & 15.438 & 0.0001 & *** 1\% \\ RD \(\Rightarrow\) LOGATM & Unidirectional & 3.161 & 0.0778 & * 10\% \\ LOGATM \(\Rightarrow\) MOMENT2 & Unidirectional & 3.136 & 0.0793 & * 10\% \\ \hline \multicolumn{3}{c}{**(c)**} \\ \hline  & **Direction** & **F-stat** & \(\mathbf{p}\)**-Value** & **Significance** \\ \hline LOGCDESI\_HC \(\Rightarrow\) & Unidirectional & 4.100 & 0.0449 & *** 5\% \\ LOGBankKEMPL & Unidirectional & 5.434 & 0.0213 & *** 5\% \\ LOGBankKEMPL & Unidirectional & 5.857 & 0.0169 & *** 5\% \\ LOGGDP \(\Leftrightarrow\) LOGBankKEMPL & Bidirectional & 5.409 / 4.192 & 0.0216/0.0426 & *** 5\% \\ RD \(\Rightarrow\) LOGBankKEMPL & Unidirectional & 4.448 & 0.0368 & *** 5\% \\ \hline \multicolumn{3}{c}{**(d)**} \\ \hline
**Causal Relationship** & **Direction** & **F-stat** & \(\mathbf{p}\)**-Value** & **Significance** \\ \hline LOGCDESI\_IDT \(\Leftrightarrow\) & Bidirectional & 8.659 / 4.419 & 0.0038/ 0.0374 & ***/** \\ LOGCDESI\_HC & Unidirectional & 3.893 & 0.0506 & *** 5\% \\ LOGEBANK \(\Rightarrow\) LOGCDESI\_IDT & Unidirectional & 7.567 & 0.0068 & *** 1\% \\ LOGEBANK \(\Rightarrow\) LOGCDP & Unidirectional & 3.125 & 0.0794 & * 10\% \\ \hline \multicolumn{3}{c}{**(e)**} \\ \hline
**Causal Relationship** & **Direction** & **F-stat** & \(\mathbf{p}\)**-Value** & **Significance** \\ \hline LOGGDP \(\Leftrightarrow\) RD & Bidirectional & 5.443 / 3.703 & 0.0212/ 0.0565 & **/* \\ MOMENT1 \(\Rightarrow\) LOGGDP & Unidirectional & 4.802 & 0.0305 & *** 5\% \\ MOMENT2 \(\Rightarrow\) LOGGDP & Unidirectional & 2.973 & 0.0874 & * 10\% \\ MOMENT2 \(\Leftrightarrow\) MOMENT1 & Bidirectional & 5.266 / 2.969 & 0.0236/ 0.0877 & **/* \\ \hline \hline \end{tabular}
\end{table} 
Table 13: **(a)** Significant Granger causality links. **(b)** Banking infrastructure drivers.