Empirical Analysis of the Energy–Growth Nexus with Machine Learning and Panel Causality: Evidence from Disaggregated Energy Sources

The relationship between energy consumption and economic growth remains a critical and complex issue in both economic and environmental research. This study investigates the disaggregated effects of primary energy sources on GDP growth across four country groups, including G20, OECD founding members (OECDf), all OECD members (OECDa), and a global subset (World), using data from the Our World in Data and World Bank. While prior studies often rely on aggregate energy use, this study investigates the disaggregated effects of primary energy sources on GDP growth across four country groups: G20, OECD founding members (OECDf), all OECD members (OECDa), and a global subset (World). To assess these relationships, both multiple linear regression and a multilayer feedforward neural network (MLP) model were employed. While the regression model exhibited low explanatory power across all groups, the MLP offered more accurate and flexible predictions by capturing nonlinear dynamics. The model exhibited high predictive performance, with Pearson correlation coefficients ranging from 0.80 to 0.94 and intraclass correlation coefficients exceeding 0.87 across all test datasets. Predictive accuracy was strongest in more homogenous and economically stable groups such as the G20 and OECDf, while wider confidence intervals in the OECDa and World datasets indicated increased variability, likely due to heterogeneous energy structures and data quality limitations—particularly for renewables prior to 2010. These findings highlight the effectiveness of machine learning in modeling complex energy–growth relationships and underscore the importance of accounting for energy source diversity and national context in empirical analyses.