## 3 Materials and Methods
Concerning data transparency and cleaning procedures, specifically, we conducted rigorous outlier detection, inputting minimal missing values using panel-consistent mean imputation for time-invariant gaps, and excluded cross-sections with missingness above a defined threshold. All sources--IMF, Eurostat, and ECB--were cross-referenced to ensure consistency across units and temporal coverage. Also, data underwent standard cleaning procedures prior to estimation, including log-transformation for normalization, visual inspection for outliers, and listwise deletion of incomplete cases. As automation decisions are often made at the firm level, the absence of harmonized bank-level data across EU member states necessitates the use of national proxies. As argued in [PERSON] et al. [2] and [PERSON] et al. [40], national digital indices are legitimate proxies when firm-level heterogeneity is either absorbed through fixed effects or when the objective is to evaluate systemic readiness and macroeconomic impacts. Moreover, robustness checks using cross-sectional heteroskedasticity and fixed effects estimations further ensure that aggregated data do not distort inference. Thus, regarding the quantification of digitalization and automation, the study innovatively leverages proxy indicators derived from authoritative sources:  
* Chatbot adoption and AI-based tools are proxied through DESI Human Capital (HC) and DESI Integration of Digital Technology (IDT) indices, both of which capture firm-level and infrastructure readiness for advanced digital implementation across financial services;
* Digital inclusion (DIGINCL) and E-banking usage (EBANK) serve as downstream indicators of AI diffusion in customer-facing services, which inherently include conversational banking interfaces;
* While direct bank-level adoption thresholds for chatbots are not publicly available in a cross-national format, our methodology mirrors recent practices in automation impact studies [33; 40], where national-level digital readiness serves as a valid proxy for sectoral technology penetration. Automation employment implications are operationalized through the variable BANKEMPL, representing the number of employees in the banking sector. Changes in this variable over time, controlled alongside other automation indicators, enable us to infer the structural impact of automation. While detailed job role classification was beyond this study's scope, this indicator remains consistent with macro-level analyses of digital labor substitution in finance [38; 61]. The methodology applied in this study follows a structured and rigorous approach to statistical and econometric analysis, ensuring the reliability and comprehensiveness of the findings regarding the impact of automation on banking performance. Each methodological step is carefully selected to mitigate potential biases, validate estimations, and capture the complex interdependencies inherent in the dataset. Analyzing the impact of robotic automation and artificial intelligence-based solutions on the performance of the banking sector in the European Union requires a robust methodological approach capable of capturing the conditional distribution of the effects of these technologies on return on equity (ROE). In this context, the use of MMQR, following the approach proposed by [PERSON] and [PERSON] [115], allows for capturing the heterogeneity of the impact of the explanatory variables on bank performance, offering a superior alternative to the classical least squares (OLS) regression models, which only estimate the average effects of the independent variables on ROE, without capturing possible differences in the impact on lower performing banking institutions compared to the more profitable ones. Given that AI technologies and ATM automation can have asymmetric effects on banks with low, medium, or high profitability, MMQR is preferred because it provides a robust and detailed estimate of the relationships between variables across the conditional distribution of profitability.