## 3 Materials and Methods
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  
As the process of innovation and technological adaptation is significantly influenced by the level of investment in research and development, the proposed model also incorporates R&D expenditure (R&D expenditure, by sectors of performance), a variable that indicates the level of investment in innovation and the ability of the financial sector to adopt emerging technologies. This variable helps to explain national differences in the adoption of emerging technologies, influencing both the automation of banking processes and the competitiveness of financial institutions. In addition to these explanatory variables, GDP per capita is used as a control variable, as it indirectly influences the level of digitalization and accessibility of financial technologies, and the number of employees in the banking sector allows for assessing the effects of automation on employment. In Table 1, the H3 hypothesis is operationalized through the inclusion of two key variables. Firstly, R&D--Research and Development Expenditure: this variable is a direct proxy for national-level investment in innovation and technological advancement. It reflects the intensity of resources allocated to research and is measured as a percentage of GDP. Within the framework of H3, RD serves as the primary indicator of innovation input. Secondly, DESI_IDT--Digital Economy and Society Index-Integration of Digital Technology: this variable captures the degree to which businesses and the broader economy have integrated digital tools and infrastructure. It represents the initial level of digitalization mentioned in the hypothesis, reflecting a country's readiness to absorb and effectively implement innovation. The DESI_IDT is thus the moderator in the hypothesized relationship. The interaction between these two variables is central to H3. Specifically, the hypothesis suggests that the effectiveness of R&D in enhancing banking sector performance (measured through ROE) is conditional on the digital maturity of the economy, as captured by DESI_IDT. This allows the model to assess whether innovation investments are more productive in digitally advanced environments compared to less developed ones. While ROE is the dependent variable through which this effect is ultimately measured, and thus essential to the empirical test of the hypothesis, RD and DESI_IDT are the variables most directly and conceptually tied to H3. No other variables in the table serve the same conceptual or operational role for this hypothesis. Furthermore, the study incorporates instrumental variables represented by MOMENT1 and MOMENT2, in alignment with the MMQR framework as proposed by [PERSON] and [PERSON] [115]. These variables are designed to capture unobservable processes and mitigate simultaneity bias, thereby enhancing the reliability of causal inference. Thus, the use of moment conditions in the MMQR framework addresses potential endogeneity and omitted variable bias while ensuring valid inference across conditional quantiles of ROE. The selection of return on equity (ROE) as the primary dependent variable is rooted in its direct relevance to shareholder value and strategic banking decisions. Unlike Return on Assets (ROA), which captures operational efficiency, ROE integrates both profitability and leverage, providing a more comprehensive reflection of performance outcomes influenced by technological and organizational transformations, especially those tied to automation and digitalization. Net Interest Margin (NIM), while valuable, is more sensitive to monetary policy and interest rate environments, and less so to operational or digital efficiency. Our conceptual framework, aligned with the recent literature (e.g., [59; 60]), prioritizes ROE due to its sensitivity to structural shifts in bank strategy catalyzed by automation technologies.