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

Abstract

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.

1. Introduction

The interplay between energy consumption and economic growth has become one of the central issues in contemporary economic and environmental research. This nexus not only shapes the trajectory of long-term economic performance but also has direct implications for sustainability, energy security, environmental protection, and policy design for future generations. Energy serves as a fundamental input into the production process, sustaining industrial activity and supporting living standards. Since the industrial revolution, fossil fuel use has increased steadily, driving economic expansion but also generating severe environmental externalities. Rising levels of pollution, global warming, and air quality deterioration have emerged as critical threats to sustainable growth, underscoring the dual challenge of meeting energy needs while mitigating long-term risks. As the global economy undergoes structural transformation, with rising energy demand and increasing pressure to decarbonize, the question of how different energy sources influence growth has acquired renewed significance. Notably, international policy frameworks such as the Paris Agreement and the United Nations Sustainable Development Goals emphasize the urgent need to reconcile economic growth with environmental sustainability. This global policy agenda reinforces the importance of re-examining the energy–growth nexus. Yet despite this international consensus, the empirical relationship remains complex and subject to ongoing debate.

When analysis shifts from aggregate indicators to specific energy sources, identifying the interaction between energy consumption and GDP becomes particularly challenging due to the complexity of these relationships. While certain theoretical frameworks point to a straightforward link, the evidence reported across countries is far from consistent, with results depending heavily on economic structure, stage of development, and the composition of the energy mix. Comparative studies underline these differences, and the debate therefore remains unresolved. Earlier analyses based on aggregate energy data and standard linear models provided useful reference points, yet they also obscured the divergent effects of specific energy sources [1,2,3]. This inconsistency highlights the need for approaches that are disaggregated, context-sensitive, and capable of capturing nonlinear dynamics, thereby offering more reliable insights for policies aimed at sustainable development.

Another major challenge in the literature arises when empirical analyses move beyond aggregate measures and attempt to differentiate energy sources and country contexts. The distinction between fossil fuels and renewables has produced markedly different findings. Fossil fuels often generate short-term output gains through established industrial linkages yet impose long-term costs via environmental degradation and external dependence [1,4,5]. In contrast, renewable energy is emphasized both in endogenous growth theory [6,7] and in empirical studies [3,8,9,10,11] as a driver of sustainable, innovation-led growth. Yet the evidence remains far from uniform: several studies point to bidirectional causality between renewables and GDP [1,4,12], while others document weak or even negative relationships in specific regional contexts [13]. These inconsistencies become even more evident when regional and national heterogeneity is considered. In particular, differences in development stages, energy security constraints, institutional quality, and economic structure give rise to heterogeneous patterns across OECD members [2,3], resource-dependent MENA economies [4], and African and emerging markets [11,13,14]. Even within a single country, such as the United States [15], regional heterogeneity has been observed. These findings accord with classical and neoclassical perspectives emphasizing resource endowments [16,17], while also aligning with endogenous-growth arguments that stress technological progress and diffusion of clean energy [6,7]. In addition, classical hypotheses in the literature, namely the growth, conservation, feedback, and neutrality hypotheses, offer distinct explanations for the causal direction between energy use and GDP, helping to clarify why results vary across contexts.

A further set of limitations arises from methodological considerations. Strictly linear econometric specifications, while having contributed important insights, are not well suited to capturing nonlinearities, threshold effects, and high-dimensional interactions. Recent advances in machine learning (ML) techniques, including artificial neural networks and other flexible nonlinear regressors, have demonstrated strong capabilities in prediction and classification by uncovering complex dynamics without imposing restrictive parametric assumptions. These methods have improved forecast performance and revealed interactions among energy use, GDP dynamics, carbon emissions, and environmental outcomes, underscoring the need for disaggregated, methodologically diverse, and context-sensitive analyses. Building on this trend, a growing body of research has applied ML methods across scientific and energy-related contexts. These techniques enhance forecasting accuracy and deepen understanding of the interactions between energy use, GDP, and environmental indicators. Unlike strictly linear models, such approaches can address nonlinear and high-dimensional problems due to their ability to approximate complex functional forms and capture interactions among multiple variables.

Over the past decade, data-driven models have been applied in diverse domains and are now increasingly visible in energy studies, ranging from electricity demand forecasting and renewable integration to analyses of consumption patterns [18,19,20]. Thus, compared to traditional econometric models, these approaches provide greater flexibility in capturing nonlinear interactions without restrictive parametric assumptions. As global energy systems become more diversified and dynamic, particularly with the growing share of renewables and the variability they introduce, ML models are increasingly utilized to support evidence-based decision making in energy policy and macroeconomic planning [21,22]. Early contributions such as Cogoljević et al. and Kurniawan and Managi illustrated the potential of ML for predicting energy consumption, while Magazzino et al. and extended its use to economic growth and environmental issues [19,23,24,25]. More recent studies by Sah et al. and Abd El-Aal et al. applied ML to global GDP growth, while Lu et al., Sen et al., Zhang et al., and Khan and Wyrwa emphasized hybrid approaches combining ML with econometric techniques [18,20,21,22,26,27]. Collectively, these contributions highlight the growing interest in applying ML to the energy–growth nexus, though their scope remains limited.

Against this backdrop, the present study investigates the disaggregated impact of eight primary energy sources, namely coal, oil, natural gas, nuclear, hydro, wind, solar, and other renewables, on economic growth during the period 2000–2022. The analysis is conducted across four country groups, comprising OECD founding members, all OECD members, the G20, and a broad world sample, to evaluate how the relationship varies with development levels and structural characteristics. Before proceeding with the main analyses, descriptive statistics were conducted to summarize the distributions and associations among the variables. Subsequently, a multilayer feedforward neural network (MLP) was employed to model the relationship between energy consumption and GDP. For completeness, multiple linear regression was also applied as a conventional baseline. However, due to its weak performance ($Corr$ values around 0.20), the results were only briefly referenced and not incorporated into the detailed analysis. Finally, the Dumitrescu–Hurlin panel causality test was applied to evaluate the direction of causality within this relationship, thereby capturing both predictive accuracy and causal direction.

1.1. Objectives and Contributions

The present research seeks to address key limitations in the existing literature, namely the reliance on aggregate indicators, the inconsistent findings across fossil fuels and renewables, and the strong context-dependence of the nexus. In this context, the main objective of the study is to examine, in a disaggregated manner, the effects of eight primary energy sources, including coal, oil, natural gas, nuclear, hydro, wind, solar and other renewables, on economic growth across four country groups comprising OECD founding members, all OECD members, the G20 and the global sample over the period 2000–2022, thereby providing a comparative perspective. To achieve this objective, ML analyses were employed to model the relationship between energy consumption and GDP, and a panel causality test was applied to evaluate the direction of causality within this relationship. In addition, multiple linear regression was used as a conventional benchmark to observe the extent to which the relationship can be explained through linear methods, thereby providing a contrast with the nonlinear approaches adopted in the study.

Building on the identified gaps, the present research makes several contributions to the literature by extending the scope of analysis and advancing methodological practice. The main contributions are as follows:

• Disaggregated analysis of energy sources: By moving beyond aggregate indicators and employing source-level data, the heterogeneous growth effects of the eight primary energy sources coal, oil, natural gas, nuclear, hydro, wind, solar, and other renewables are explicitly identified.
• Comparative evaluation across country groups: By conducting a cross-group comparison, the study systematically evaluates how the nexus varies across different levels of development and structural heterogeneity, ranging from relatively homogeneous developed economies to diverse global samples.
• Comprehensive advanced methodological framework: By combining conventional linear econometric models, including the Dumitrescu–Hurlin panel causality test, with nonlinear ML approaches, while also testing conventional statistical linear models, specifically multiple linear regression as a benchmark for nonlinear prediction, the study provides a robust framework that captures both predictive accuracy and causal direction, extending prior work that typically relied on a single class of models.

Beyond academic contributions, the study provides policy relevance by offering insights into renewable investment strategies, efficiency improvements, and electrification initiatives, while clarifying differences between developed and developing economies in their transition processes. In line with these contributions, the study is guided by the following research questions:

• Is there evidence of unidirectional or bidirectional causality between energy consumption and GDP across different energy sources and country groups?
• How does the relationship between energy consumption and economic growth differ across country groups (OECD founding members, all OECD members, the G20, and the global sample) given structural and institutional heterogeneity?
• To what extent do ML approaches, particularly artificial neural networks, enhance the ability to capture complex patterns and improve predictive performance compared to conventional linear regression models in heterogeneous contexts, while also complementing econometric causality tests in understanding the energy–growth nexus?

These questions highlight the need to move beyond aggregate indicators, to incorporate methodological diversity, and to explicitly address both causality and prediction in understanding the energy–growth nexus.

1.2. Rationale for the Methodological Approach

The energy–growth relationship is inherently nonlinear, multidimensional, and sensitive to the composition of energy inputs. Analyses based solely on linear models may therefore miss threshold effects, interactions among sources, and other nonlinear features. For this reason, the study employed MLP, which was well suited to capture flexible functional forms and complex patterns among disaggregated energy sources and growth outcomes. To enable comparison with conventional linear models, multiple linear regression was also applied as a baseline; however, due to its limited explanatory power, the results were only briefly referenced and not included in the detailed analysis. For transparency and to provide an overview of the data, descriptive statistics were first reported to summarize distributions and correlations among the variables. Moreover, because prediction alone cannot reveal the direction of influence, the Dumitrescu–Hurlin panel causality test was incorporated to assess whether causality runs from energy consumption to GDP, from GDP to energy consumption, or in both directions. Collectively, the adopted framework combined the exploratory value of descriptive analysis, the predictive strength of ML methods, and the causal interpretability of panel econometric testing.

1.3. Structure of the Study

The paper is structured into five main sections. The first section outlines the significance of the research topic, highlights key limitations in the existing literature, and presents the objectives and rationale of the study, thereby providing the conceptual foundation and framing the research questions. The second section reviews the theoretical and empirical literature, covering classical hypotheses and recent econometric and ML applications on the energy–growth nexus. This review situates the study within existing scholarship and clarifies the gaps the present work seeks to address. The third section describes the dataset, variables, preprocessing procedures, and model specifications, as well as reporting descriptive statistics, to provide an overview of the data, which serve as the empirical basis for subsequent analysis. This stage is essential for ensuring transparency and establishing the empirical foundation of the analysis. The fourth section presents the empirical results and discussion, including both the ML analyses and the Dumitrescu–Hurlin panel causality test. These steps highlight how predictive accuracy and causal direction are jointly evaluated, enabling a more comprehensive interpretation of the energy–growth relationship. Finally, the fifth section concludes by summarizing the main findings, discussing their theoretical and policy implications, and suggesting directions for future research on sustainable development and the energy transition. This concluding stage synthesizes the contributions and situates them within broader academic and policy debates.

2. Literature Review

From a theoretical perspective, the relationship between energy consumption and economic growth can be framed within classical and modern growth models. Classical growth theories, such as those proposed by Adam Smith and David Ricardo, highlight the role of natural resources, including energy, as fundamental inputs in production and long-term economic expansion [16,28]. The Solow–Swan neoclassical growth model further formalizes this relationship by incorporating capital, labor, and technological progress, with energy considered an augmenting input to production functions [17,29]. Endogenous growth theories, such as those developed by Romer and Lucas, emphasize technological innovation and human capital accumulation, where energy efficiency and renewable energy adoption play a crucial role in sustaining long-term economic growth [6,7]. These theoretical frameworks provide a foundation, yet empirical studies have produced highly diverse findings depending on energy type, time horizon, and regional context.

The relationship between energy consumption and economic growth has been extensively studied due to its crucial role in shaping sustainable development policies worldwide. Both renewable and non-renewable energy sources have been examined to understand their short- and long-run impacts on economic performance across diverse regions and economies. Moreover, methodological advances have enabled researchers to employ various econometric and ML techniques to capture the complex dynamics of this relationship more accurately. Within this broad literature, several influential panel studies have provided key evidence on the directionality of the nexus. A bidirectional causal relationship between renewable and non-renewable energy consumption and economic growth was identified in both the short and long term, based on a panel error correction model for developed and developing countries during 1990–2007 [1]. Similarly, Salim et al. identified bidirectional causality between economic growth and non-renewable energy, alongside a unidirectional link from renewable energy to growth, based on panel causality tests for OECD countries covering 1980–2011 [2]. In a panel analysis of 34 OECD member economies, renewable energy consumption was found to have a positive and significant impact on growth between 1990 and 2010 [3]. The evidence so far suggests that renewable and non-renewable energy sources can both exhibit bidirectional relationships with growth, but the strength and direction of these links remain highly context dependent. This diversity of findings underscores the need for approaches that explicitly account for heterogeneity across countries and energy types.

Regional-level empirical analyses reveal a feedback relationship between non-renewable energy consumption and economic growth, along with a unidirectional link from renewable energy to growth in the long term. This evidence was based on an ARDL causality analysis for Algeria covering 1980–2012 [30]. Consistent with this, Kahia et al. (2017) reported bidirectional causality between renewable and non-renewable energy consumption and economic growth across eleven MENA Net Oil Importing Countries during 1980–2012 [4]. Likewise, Shakouri and Yazdi determined bidirectional causality between renewable energy consumption and economic growth for South Africa over 1971–2015 using the Granger causality test [31]. In a similar manner, a panel analysis was conducted across 50 U.S. states over 1978–2014, revealing significant regional heterogeneity in the energy–GDP growth rate relationship. While energy consumption Granger-caused GDP in some regions (e.g., Rocky Mountains), the reverse was found in others (e.g., Southwest), suggesting that national-level policy prescriptions may overlook critical regional dynamics [15]. These findings emphasize the significance of regional heterogeneity, demonstrating that even within national boundaries, energy–growth dynamics can diverge sharply across regions. This calls for careful attention to spatial variation, which subsequent studies explored further across broader international samples.

Cross-country comparisons provide further insights into the heterogeneous nature of the nexus. Among European economies, Ntanos et al. reported a strong correlation between renewable energy consumption and economic growth through ARDL analysis for 25 European countries covering 2007–2016 [8]. In line with these results, Saad and Taleb, using Granger causality tests for 12 European Union countries between 1990 and 2014, found unidirectional causality from economic growth to renewable energy consumption in the short term, and bidirectional causality in the long term [32]. Contrasting with these positive relationships, Maji et al. found that renewable energy consumption was associated with slower economic growth in 15 West African countries, based on a panel DOLS analysis for 1995–2014 [13]. By the 2020s, Behera and Mishra also applied panel ARDL testing and found short-term causality from non-renewable energy consumption to economic growth for G7 countries (1990–2015) [5]. Extending the regional scope, dynamic OLS tests for South Asian countries (1990–2014) revealed positive effects of both renewable and non-renewable energy consumption on economic growth [33]. Can and Korkmaz concluded that renewable energy consumption was a causal factor for economic growth in Bulgaria from 1990 to 2016 through ARDL analysis [9]. This set of findings underscores the salient role of regional heterogeneity and demonstrates that national-level results may conceal significant subnational variations, with important implications for the design of context-sensitive energy policies. The accumulated evidence points to the conclusion that renewable energy often supports long-run growth, whereas the impacts of non-renewables appear more mixed and context-dependent. These mixed outcomes motivated further investigations focusing on specific countries and additional explanatory factors.

Country-specific investigations highlight how structural and institutional contexts shape the energy–growth relationship. For North African economies, Bouyghrissi et al. identified unidirectional causality from renewable energy to economic growth in Morocco for 1990–2014 [10]. Namahoro et al. applied a nonlinear autoregressive distributed lag (NARDL) model to Rwanda’s economy, providing further evidence of renewable energy’s influence on growth during 1990–2015 [14]. In addition to country-specific cases, broader regional studies have examined the issue, including a Granger causality analysis across 26 European countries between 1990 and 2018, which revealed bidirectional causality between renewable energy and economic growth, along with a unidirectional link from renewable to non-renewable energy [12]. Additional evidence comes from Ghana, where Gyimah et al. found that increased renewable energy consumption positively affected the economic growth using both Granger causality and mediation models for 1990–2015 [11]. In another study, Xie et al. validated the renewable energy-led growth hypothesis for the Next-11 economies through a non-parametric panel data approach spanning 1990–2020 [34]. More recently, Kilinc-Ata used the ARDL model to examine the link between CO₂ emissions, GDP, energy consumption, financial development, foreign direct investment, urbanization, and population in the Sultanate of Oman between 1990 and 2023. The findings indicate that urbanization and GDP reduce CO₂ emissions, while population growth, energy use, foreign direct investment, and financial development increase emissions [35]. These findings emphasize that heterogeneity operates at multiple levels: within countries, where sub-national regions may diverge sharply, and across country groups, where structural and institutional differences shape the energy–growth nexus. Rather than a uniform pattern, the evidence points to a multi-layered relationship that requires tailored analytical approaches, paving the way for subsequent studies employing advanced methodologies.

Recognizing the limitations of conventional econometric models in capturing the nonlinear and complex interactions between energy consumption and growth, recent studies have increasingly adopted ML methodologies. Among these, Cogoljević et al. developed an ML-based approach to predict GDP using energy resource mixes, reporting slight improvements in predictive accuracy [23]. Along similar lines, Kurniawan and Managi compared artificial neural networks (ANNs) and tree-based models to forecast energy consumption trajectories in Indonesia from 1971 to 2014 [24]. Their analysis (RMSE: 0.0222) concluded that tree-based models outperformed ANN in both accuracy and application potential. In another study, ANN was utilized to analyze Brazil’s renewable energy consumption and its effect on accelerating GDP growth during the COVID-19 pandemic, demonstrating the sustainability potential of renewable energy for economic growth [25]. The empirical findings of the study indicated that increasing reliance on renewable energy sources may sustain the economic growth process.

In recent studies, Kahia et al. applied ML regression techniques to Saudi Arabian data covering 1980–2020 and emphasized that increasing the share of renewable energy is essential for achieving stable economic development [4]. Building on this application of ML to national contexts, the effects of GDP and energy consumption on carbon emissions in EU countries between 2000 and 2020 were investigated using multilayer perceptron algorithms with RMSE values of 0.304 (training) and 0.298 (testing), indicating an acceptable model fit [26]. At the global level, Abd El-Aal et al. examined the influence of renewable, non-renewable, and nuclear energy consumption on GDP growth via ML algorithms, finding that renewable energy contributed the most significantly, accounting for 67.5% of growth [20]. Advancing methodological innovation, Lu et al. introduced novel energy consumption indices and employed a mixed-frequency MIDAS-LASSO approach (R2 = 71.6%), which demonstrated stable GDP growth forecasting performance even amid crises and geopolitical shocks. This provided new perspectives on energy-sector-level economic growth prediction [27]. Focusing on the role of technological change, Yuan and Liu analyzed panel data from 281 Chinese cities between 2006 and 2021 using a dual machine learning model [36]. Their findings showed that green technology advancement improved the energy consumption structure, which in turn led to green economic growth. Overall, these contributions illustrate the growing role of ML in energy–growth studies, though applications remain fragmented and often limited to specific countries or time periods.

While these regional and methodological advances provide valuable insights, the findings remain fragmented and context specific. This highlights the need for a broader, comparative approach that systematically examines multiple energy sources across diverse country groups, employing both econometric and ML methods. In particular, prior research has often relied on aggregate indicators and linear models, obscuring the heterogeneous and nonlinear dynamics that distinguish fossil fuels from renewables and that vary sharply across development contexts. Addressing these limitations by integrating disaggregated data, advanced ML models, and panel-based causality tests constitute the key contributions of the present study.

3. Materials and Methods

The methodological framework of this study integrates machine learning, linear modeling, and panel causality approaches to provide a comprehensive assessment of the energy–growth nexus. Within this framework, an ML technique, specifically a multilayer perceptron (MLP) neural network, was employed in this study to analyze the relationship between economic growth and per capita energy consumption covering coal, oil, natural gas, nuclear, hydro, wind, solar and other renewables. Subsequently, multiple linear regression analysis was conducted to benchmark the explanatory capacity of conventional linear approaches. This provided a baseline against which the added value of nonlinear models could be assessed. Finally, the Dumitrescu–Hurlin panel causality test was applied to determine the direction of causal linkages between per capita energy consumption and GDP growth, complementing both regression and ML analyses by explicitly accounting for cross-country heterogeneity.

3.1. Data Description

In the study, the relationship between energy consumption and economic growth was investigated. Growth data were obtained from the World Bank [37], while consumption data for primary energy sources were collected from Our World in Data, an open-access scientific database maintained by the Global Change Data Lab [38]. For the energy indicators, per capita consumption of coal, oil, natural gas, nuclear, hydro, wind, solar, and other renewables was measured in kilowatt-hours (kWh). The dependent variable was the annual GDP growth rate (%).

Table 1. Dependent and independent variables.

Dependent Variable (%)	Independent Variables (kWh)
Growth Rate	Coal
	Oil
	Gas
	Nuclear
	Hydro
	Wind
	Solar
	Other Renewables

summarizes the dependent and independent variables used in the analysis.

When examining the energy–growth relationship, the main reason for considering coal, oil, natural gas, nuclear, hydro, wind, solar, and other renewables as separate variables is the heterogeneity of their effects on economic performance. Fossil fuels, which have long been the primary drivers of growth in industry and transportation, entail high emissions and external dependency risks, whereas nuclear energy, despite its high capital requirements, offers a distinct dynamic for energy security through low-carbon baseload generation. Renewables such as hydro, wind, solar, and other sources contribute to growth by promoting environmental sustainability while also fostering investment, employment, and technological learning. The literature emphasizes the necessity of this distinction [39,40,41,42,43], since the direction of causality, the short- and long-term effects on growth, and even policy implications differ across energy types. In addition, the availability of international databases that classify energy consumption into these eight categories enables robust comparative and long-term analyses.

Within the scope of the study, the founding countries of the OECD, all OECD members, the G20, and a global sample covering all countries with available data were analyzed as separate groups. The OECD founding group was included because it represents advanced economies with established energy technologies, efficiency practices, and coordinated policy frameworks, reflecting long-standing efforts to develop common strategies for sustainability. The broader OECD membership was examined to capture the heterogeneity introduced by newer member states and to assess how energy–growth dynamics evolved within a more diverse bloc. The G20 group was selected as it combines both developed and emerging major economies, accounts for a substantial share of global output and energy consumption and exerts a critical influence on international energy and environmental policy. Finally, the global sample was incorporated to provide generally valid insights, enabling systematic comparisons across groups. This perspective also offers a clearer understanding of the successes and shortcomings of different policy approaches in the context of the sustainable development goals advanced by organizations such as the United Nations and the World Bank.

The datasets used in this study consist of four groups, namely OECDf, representing the 20 founding countries of the OECD, OECDa, covering all 38 member countries, G20, including the 20 member states of the G20, and World, encompassing 79 countries with available energy data. The complete list of countries belonging to each dataset is provided in Appendix A for reference. Since energy consumption data were not available for several countries before the year 2000, the analysis was restricted to the period 2000–2022, and years with no recorded production of any energy type were excluded. The sample sizes (n) of the datasets are reported in

Table 2. The number of samples for datasets.

Dataset	$\mathit{n}$
OECDf	440
OECDa	778
G20	418
World	1715

.

The scale of energy consumption varies significantly depending on the type of energy. In such cases, variables with very large magnitudes may distort the predictive accuracy of ML methods, as they tend to dominate the target variable [44]. Therefore, in data mining studies, preprocessing of the data is carried out using various methods to achieve standardization. In this study, min-max normalization was employed for data scaling (Equation (1)). This method was preferred because it preserves the relative distribution of the original data while transforming all variables into a comparable range between zero and one, which is particularly advantageous when variables measured in different units are included in the same model [45].

$$x_{norm}={\displaystyle \frac{x_i-x_{min}}{x_{max}-x_{min}}}$$

(1)

In Equation (1), $x_{norm}$ represents the normalized value of the data $x_i$, while $min$ and $max$ indices indicate the respective minimum and maximum values in the dataset. Another preprocessing step involves data cleaning. This entails identifying and eliminating data points (outliers) that may arise from errors in data collection or other factors, potentially leading to inaccurate conclusions from the data. The Median Absolute Deviation (MAD) method was utilized for outlier detection. This method computes the median of the absolute deviations of data points from the median itself, resulting in the MAD value. Subsequently, outliers were identified and removed using the MAD value as a threshold. MAD was chosen because of its robustness to noise, its effectiveness in handling heterogeneous data distributions, and its suitability for detecting extreme values in large datasets [46].

To establish baseline insights, multiple linear regression analysis was performed to model the relationship between independent variables and the growth rate. However, due to the complex nonlinear nature of the data, where hidden dependencies and nonlinear interactions often dominate the data-generating process, an ML approach was employed as an alternative to traditional regression. Despite challenges such as noisy and missing data, as well as multidimensional and nonlinear patterns, neural networks can effectively extract complex relationships within datasets without prior assumptions. Their ability to learn and generalize allows them to approximate highly nonlinear functional forms, which makes them particularly suitable for modeling economic and energy systems. In this study, a multilayer feedforward neural network trained by the Levenberg–Marquardt backpropagation algorithm was selected for its reliable performance in modeling realistic nonlinear multiple relationships, even on relatively small datasets [47]. All methods were implemented using MATLAB R2017b [48].

3.2. Descriptive Statistics and Correlation Analysis

To establish a baseline, descriptive statistics were computed (mean, median, standard deviation, and range) to summarize central tendency, dispersion, and distributional features for nine variables: per capita consumption of coal, oil, gas, nuclear, hydro, wind, solar, and other renewables, and annual GDP growth. This preliminary step provided an overview of the data structure and variability across countries before the implementation of machine learning models. Building on these univariate summaries, then Pearson product–moment correlations (two-tailed) were estimated to quantify the strength and direction of pairwise linear associations among the nine indicators.

Table 3. Descriptive statistics for G20 countries ¹.

Variable	M	SD	Median	Q1	Q3	Min	Max
Coal per capita (kWh)	7900.000	7620.000	5720.000	1490.000	11,900.000	0.000	32,200.000
Oil per capita (kWh)	16,200.000	13,000.000	12,700.000	5880.000	23,800.000	1191.000	61,800.000
Gas per capita (kWh)	10,900.000	9530.000	9190.000	2000.000	15,100.000	195.000	32,700.000
Nuclear per capita (kWh—equivalent)	2930.000	4540.000	470.000	0.000	5230.000	0.000	20,600.000
Hydro per capita (kWh—equivalent)	3000.000	6510.000	1620.000	238.000	2410.000	0.000	34,400.000
Wind per capita (kWh—equivalent)	428.000	732.000	82.100	2.780	551.000	0.000	4160.000
Solar per capita (kWh—equivalent)	184.000	391.000	6.000	0.218	156.000	0.000	3150.000
Other renewables per capita (kWh—equivalent)	399.000	450.000	209.000	35.500	653.000	0.000	1980.000
GDP growth	2.890	3.730	2.730	1.240	5.030	−11.000	14.200

¹ M: Mean, SD: Standard deviation, Q1: First quantile, Q3: Third quantile, Min: Minimum, Max: Maximum.

reports the descriptive statistics for the independent variables (per capita energy consumption) and the dependent variable (GDP growth). An examination of the mean values indicates that G-20 nations, on average, consume the most oil (M = 16,200.000 kWh) and gas (M = 10,900.000 kWh) per capita. The lowest average per capita consumption is observed in solar (M = 184.000 kWh) and other renewables (M = 399.000 kWh). For the outcome variable, the average GDP growth rate for the group is 2.890%.

The correlation analysis among the variables is presented in

Table 4. Correlation analysis for G20 countries ¹.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Coal per capita (kWh) (1)	1	0.188 ***	0.038	0.061	−0.003	0.083 *	0.145 ***	0.100 **	0.059
Oil per capita (kWh) (2)		1	0.758 ***	0.303 ***	0.336 ***	0.130 ***	0.053	0.206 ***	−0.158 ***
Gas per capita (kWh) (3)			1	0.191 ***	0.451 ***	0.203 ***	0.059	0.190 ***	−0.170 ***
Nuclear per capita (kWh—equivalent) (4)				1	0.247 ***	0.146 ***	−0.016	0.171 ***	−0.154 ***
Hydro per capita (kWh—equivalent) (5)					1	0.160 ***	−0.053	0.279 ***	−0.075
Wind per capita (kWh—equivalent) (6)						1	0.660 ***	0.732 ***	−0.204 ***
Solar per capita (kWh—equivalent) (7)							1	0.570 ***	−0.196 ***
Other renewables per capita (kWh—equivalent) (8)								1	−0.299 ***
GDP growth (9)									1

¹ Level of significance: *** p-value < 0.01, ** p-value < 0.05, * p-value < 0.10.

. The primary finding indicates a consistent and significant negative association between GDP growth and six different types of energy consumption. The analysis shows that higher per capita consumption of other renewables (r = −0.299, p < 0.01), wind power (r = −0.204, p < 0.01), solar power (r = −0.196, p < 0.01), gas (r = −0.170, p < 0.01), oil (r = −0.158, p < 0.01), and nuclear power (r = −0.154, p < 0.01) are all associated with lower GDP growth. This pattern indicates that greater reliance on these sources coincides with weaker growth performance in the G20 sample. Beyond their link to GDP growth, the matrix also reveals significant relationships among the independent variables themselves. There are strong positive correlations between the consumption of different fossil fuels, most notably between oil and gas (r = 0.758, p < 0.01). Likewise, a very strong positive link exists between wind and solar power consumption (r = 0.660, p < 0.01). These clusters suggest that national energy strategies often evolve around complementary resource pairs, a point that is pertinent for subsequent predictive modeling.

Table 5. Descriptive statistics for OECDa countries ¹.

Variable	M	SD	Median	Q1	Q3	Min	Max
Coal per capita (kWh)	7580.000	7400.000	5240.000	2430.000	10,300.000	0.000	38,200.000
Oil per capita (kWh)	19,200.000	11,400.000	17,200.000	11,700.000	23,800.000	2915.000	80,400.000
Gas per capita (kWh)	9320.000	6630.000	8040.000	4680.000	11,500.000	0.000	31,300.000
Nuclear per capita (kWh—equivalent)	3670.000	5100.000	225.000	0.000	7030.000	0.000	23,900.000
Hydro per capita (kWh—equivalent)	8540.000	19,800.000	1820.000	260.000	4920.000	0.000	112,000.000
Wind per capita (kWh—equivalent)	837.000	1290.000	215.000	26.200	1150.000	0.000	7360.000
Solar per capita (kWh—equivalent)	197.000	364.000	7.760	0.312	258.000	0.000	3150.000
Other renewables per capita (kWh—equivalent)	1850.000	5610.000	538.000	194.000	1250.000	0.000	43,200.000
GDP growth	2.310	3.410	2.420	1.070	3.960	−14.600	24.400

¹ M: Mean, SD: Standard deviation, Q1: First quantile, Q3: Third quantile, Min: Minimum, Max: Maximum.

presents the descriptive statistics for OECDa countries for all eight energy consumption types. The mean values show that, on average, OECDa nations consume the most oil (M = 19,200.000 kWh) and gas (M = 9320.000 kWh) per capita, while solar (M = 197.000 kWh) and wind (M = 837.000 kWh) remain the lowest. The dependent variable indicates an average GDP growth rate of 2.310% across these economies.

The correlation analysis reported in

Table 6. Correlation analysis for OECDa countries ¹.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Coal per capita (kWh) (1)	1	−0.041 *	−0.150 ***	0.163 ***	−0.054 **	0.052 **	0.110 ***	0.015	−0.022
Oil per capita (kWh) (2)		1	0.403 ***	0.039	0.092 ***	0.024	0.040 *	0.085 ***	−0.014
Gas per capita (kWh) (3)			1	−0.081 ***	−0.078 ***	−0.077 ***	−0.026	−0.078 ***	0.072 ***
Nuclear per capita (kWh—equivalent) (4)				1	0.068 ***	0.125 ***	0.105 ***	0.053 **	−0.112 ***
Hydro per capita (kWh—equivalent) (5)					1	0.068 ***	−0.059 **	0.733 ***	−0.071 ***
Wind per capita (kWh—equivalent) (6)						1	0.392 ***	0.080 ***	−0.131 ***
Solar per capita (kWh—equivalent) (7)							1	0.001	−0.154 ***
Other renewables per capita (kWh—equivalent) (8)								1	−0.058 **
GDP growth (9)									1

¹ Level of significance: *** p-value < 0.01, ** p-value < 0.05, * p-value < 0.10.

for OECDa countries demonstrates a consistent and significant negative association between GDP growth and most renewable and nuclear energy sources. Specifically, higher per capita consumption of solar power (r = −0.154, p < 0.01), wind power (r = −0.131, p < 0.01), nuclear power (r = −0.112, p < 0.01), hydro power (r = −0.071, p < 0.01), and other renewables (r = −0.058, p < 0.05) coincides with weaker economic growth. By contrast, gas consumption exhibits a significant positive relationship with GDP growth (r = 0.072, p < 0.01), suggesting that, unlike the other sources, greater per capita gas use is associated with stronger growth performance in this context. In addition, strong positive correlations are observed among the independent variables, particularly between hydro and other renewables (r = 0.733, p < 0.01) and between oil and gas (r = 0.403, p < 0.01), reflecting the clustering of energy strategies around related sources.

As reported in

Table 7. Descriptive statistics for OECDf countries ¹.

Variable	M	SD	Median	Q1	Q3	Min	Max
Coal per capita (kWh)	5040.000	4090.000	3880.000	2280.000	6410.000	0.000	22,300.000
Oil per capita (kWh)	23,100.000	12,500.000	19,400.000	15,700.000	29,900.000	5029.000	80,400.000
Gas per capita (kWh)	10,800.000	7950.000	9570.000	4670.000	14,600.000	0.000	31,300.000
Nuclear per capita (kWh—equivalent)	4040.000	5820.000	224.000	0.000	6820.000	0.000	23,900.000
Hydro per capita (kWh—equivalent)	12,900.000	25,200.000	1970.000	481.000	12,700.000	6.500	112,000.000
Wind per capita (kWh—equivalent)	1260.000	1510.000	683.000	157.000	1890.000	0.000	7360.000
Solar per capita (kWh—equivalent)	227.000	359.000	12.800	1.020	342.000	0.000	1710.000
Other renewables per capita (kWh—equivalent)	2430.000	7240.000	680.000	292.000	1360.000	0.000	43,200.000
GDP growth	1.910	3.370	1.990	0.823	3.250	−11.300	24.400

¹ M: Mean, SD: Standard deviation, Q1: First quantile, Q3: Third quantile, Min: Minimum, Max: Maximum.

, the descriptive statistics for OECDf countries show that, on average, (M = 23,100.000 kWh), hydro (M = 12,900.000 kWh), and gas (M = 10,800.000 kWh) dominate per capita energy use, whereas solar (M = 227.000 kWh) and wind (M = 1260.000 kWh) remain comparatively limited. The lowest average per capita consumption is seen in solar (M = 227.000 kWh) and wind (M = 1260.000 kWh). The dependent variable indicates an average GDP growth rate of 1.910% for this group. Overall, the descriptive profile highlights the predominance of conventional energy sources, with renewables such as solar and wind playing only a minor role in the energy mix.

The correlation results provided in

Table 8. Correlation analysis for OECDf countries ¹.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Coal per capita (kWh) (1)	1	−0.041 *	−0.150 ***	0.163 ***	−0.054 **	0.052 **	0.110 ***	0.015	−0.022
Oil per capita (kWh) (2)		1	0.403 ***	0.039	0.092 ***	0.024	0.040 *	0.085 ***	−0.014
Gas per capita (kWh) (3)			1	−0.081 ***	−0.078 ***	−0.077 ***	−0.026	−0.078 ***	0.072 ***
Nuclear per capita (kWh—equivalent) (4)				1	0.068 ***	0.125 ***	0.105 ***	0.053 **	−0.112 ***
Hydro per capita (kWh—equivalent) (5)					1	0.068 ***	−0.059 **	0.733 ***	−0.071 ***
Wind per capita (kWh—equivalent) (6)						1	0.392 ***	0.080 ***	−0.131 ***
Solar per capita (kWh—equivalent) (7)							1	0.001	−0.154 ***
Other renewables per capita (kWh—equivalent) (8)								1	−0.058 **
GDP growth (9)									1

¹ Level of significance: *** p-value < 0.01, ** p-value < 0.05, * p-value < 0.10.

for OECDf countries reveal a mixed yet systematic set of relationships between energy consumption and GDP growth. A consistent negative association emerges for most renewable and nuclear sources, as higher per capita consumption of solar power (r = −0.154, p < 0.01), wind power (r = −0.131, p < 0.01), nuclear power (r = −0.112, p < 0.01), hydro power (r = −0.071, p < 0.01), and other renewables (r = −0.058, p < 0.05) is linked to weaker economic growth. Conversely, gas consumption shows a significant positive link with GDP growth (r = 0.072, p < 0.01), indicating that reliance on gas aligns with stronger growth performance in this group. Beyond the relationship with GDP growth, strong positive correlations also appear among the independent variables, most notably between hydro and other renewables (r = 0.733, p < 0.01) and between oil and gas (r = 0.403, p < 0.01). This context is valuable for understanding the interplay of different energy sources within these selected OECDf countries.

Table 9. Descriptive statistics for World countries ¹.

Variable	M	SD	Median	Q1	Q3	Min	Max
Coal per capita (kWh)	7580.000	7400.000	5240.000	2430.000	10,300.000	0.000	38,200.000
Oil per capita (kWh)	19,200.000	11,400.000	17,200.000	11,700.000	23,800.000	2915.000	80,400.000
Gas per capita (kWh)	9320.000	6630.000	8040.000	4680.000	11,500.000	0.000	31,300.000
Nuclear per capita (kWh—equivalent)	3670.000	5100.000	225.000	0.000	7030.000	0.000	23,900.000
Hydro per capita (kWh—equivalent)	8540.000	19,800.000	1820.000	260.000	4920.000	0.000	112,000.000
Wind per capita (kWh—equivalent)	837.000	1290.000	215.000	26.200	1150.000	0.000	7360.000
Solar per capita (kWh—equivalent)	197.000	364.000	7.760	0.312	258.000	0.000	3150.000
Other renewables per capita (kWh—equivalent)	1850.000	5610.000	538.000	194.000	1250.000	0.000	43,200.000
GDP growth	2.310	3.410	2.420	1.070	3.960	−14.600	24.400

¹ M: Mean, SD: Standard deviation, Q1: First quantile, Q3: Third quantile, Min: Minimum, Max: Maximum.

presents the descriptive statistics for worldwide energy consumption and GDP growth data. The mean values reveal that, on average, oil (M = 19,200.000 kWh) and gas (M = 9320.000 kWh) per capita. The lowest average per capita consumption is seen in solar (M = 197.000 kWh). For the outcome variable, the average GDP growth rate across this global sample is 2.310%, reflecting more moderate expansion compared to the G20 and OECD groups.

Table 10. Correlation analysis for World countries ¹.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Coal per capita (kWh) (1)	1	0.123 ***	0.368 ***	−0.007	−0.187 ***	−0.079 *	−0.134 ***	−0.099 **	0.05
Oil per capita (kWh) (2)		1	0.606 ***	−0.011	0.121 **	−0.247 ***	−0.140 ***	0.094 **	0.077
Gas per capita (kWh) (3)			1	−0.042	−0.229 ***	−0.101 **	0.029	−0.303 ***	−0.006
Nuclear per capita (kWh—equivalent) (4)				1	−0.096 **	−0.106 **	−0.081 *	−0.119 **	−0.021
Hydro per capita (kWh—equivalent) (5)					1	−0.184 ***	−0.245 ***	0.721 ***	0.021
Wind per capita (kWh—equivalent) (6)						1	0.342 ***	−0.111 **	−0.031
Solar per capita (kWh—equivalent) (7)							1	−0.112 **	−0.159 ***
Other renewables per capita (kWh—equivalent) (8)								1	0.017
GDP growth (9)									1

¹ Level of significance: *** p-value < 0.01, ** p-value < 0.05, * p-value < 0.10.

denotes the relationships between the variables. The primary finding is that on a global scale, fewer energy sources show a significant link to economic growth compared to specific economic blocs. The analysis shows a significant negative relationship for solar power (r = −0.159, p < 0.01), where higher consumption is associated with lower GDP growth. In contrast, gas consumption is the only source to exhibit a significant positive relationship with GDP growth (r = 0.077, p < 0.10). In addition to their connection with GDP growth, the correlation matrix highlights noteworthy links among the predictor variables. Some positive associations exist between different energy types, particularly between hydro and other renewables (r = 0.721, p < 0.01) and between oil and gas (r = 0.606, p < 0.01). These associations highlight that global energy strategies often develop around clusters of interrelated sources, which is an important consideration for more advanced modeling.

3.3. Multilayer Perceptron Neural Network

ANNs, inspired by the human brain and the biological nervous system, are among the earliest and most widely applied machine learning methods capable of learning from input data. An ANN is structured with three or more layers, consisting of interconnected processing that link consecutive layers. Each connection in the network is associated with a numerical weight. An example of a four-layered neural network is depicted in Figure 1. In ANNs, intermediate layers are referred to as hidden layers.

In a multilayer feedforward neural network (multilayer perceptron/MLP), which is one of the ANN models, input samples from the neurons in the previous layer are combined through weighted sums (net) and transmitted to the next layer via an activation function, denoted as $f\left(net\right)$ (Figure 2). Nonlinear functions such as sigmoid or hyperbolic tangent are commonly used as activation functions [49].

The output layer contains neurons equal to the size of the output vector, and each neuron processes the information coming from the previous layers to generate an output ($\widehat{y}$) value for the respective input sample. The weights ($w$) are iteratively updated until the error between the obtained actual output values ($y$) and the predicted ones ($\widehat{y}$) is minimized [50]. This iterative updating process, known as the system’s training process, characterizes the learning capability of the artificial network.

For each input example of a dataset with an output vector $y\in R^s$, the error function ($J)$ calculated at each iteration ($t)$ is given by the formula in Equation (2).

$$J\left(w\right)={\displaystyle \frac{1}{2}}\sum _{k=1}^s{\left(y_k-{\widehat{y}}_k\right)}^2$$

(2)

The most common algorithm used for training MLPs is the backpropagation algorithm. In this algorithm, the error function is minimized by updating the weights in the layers through gradient-based backward propagation (Equation (3)).

$$w_{kj}^{t+1}=w_{kj}^t-{\displaystyle \frac{\partial J}{\partial w_{kj}^t}}$$

(3)

where $\eta$ represents the learning rate and $w_{kj}$ is the weight connecting the $kth$ neuron in one layer to the $jth$ neuron in the previous layer. Among the well-known variants of backpropagation, the Levenberg–Marquardt algorithm is frequently employed in training multilayer perceptrons, as it inherently operates in batch mode and adaptively adjusts the step size through the damping factor (µ) rather than using a fixed learning rate.

3.4. Dumitrescu–Hurlin Panel Causality Test

The Dumitrescu–Hurlin panel causality test offers a robust framework for detecting causal linkages in multi-country datasets [51]. Unlike approaches that treat all units identically, this method accounts for heterogeneous fixed effects, recognizing that individual countries may display distinct economic behaviors. Such heterogeneity is critical, as economic phenomena rarely manifest uniformly across nations. The test exploits the richness of panel structures by combining multiple time periods (T) and cross-sectional units (N), thereby enhancing the ability to detect causal relationships beyond what single-country time series analysis can capture. An important implication is that causal patterns identified in some economies may also reflect broader dynamics in others, albeit with varying intensities.

4. Results and Discussion

The empirical analysis was designed in two stages to evaluate the link between disaggregated energy consumption and GDP growth across G20, OECDf, OECDa, and World datasets. As an initial benchmark, multiple linear regression was employed to test the predictive validity of conventional linear models. However, the results revealed relatively weak associations, with $Corr$ values of 0.220 for OECDf, 0.240 for OECDa, 0.248 for the World sample, and a modest 0.383 for the G20. To move beyond these linear associations, a machine learning approach was introduced to capture potentially nonlinear and high-dimensional predictive relationships; for this purpose, a multilayer perceptron (MLP) neural network was employed. Finally, to assess the direction of influence between energy consumption and growth, Dumitrescu–Hurlin panel causality tests were applied, allowing the identification of whether energy sources merely follow economic activity or also act as drivers of growth.

4.1. Machine Learning Analysis

During the machine learning analysis, a three-layer feedforward neural network was trained using the Levenberg–Marquardt backpropagation algorithm. The input layer of the neural network consisted of independent variables representing disaggregated energy sources, specifically coal, oil, gas, nuclear, hydro, wind, solar, and other renewables, which served as inputs to the network. For training, the Levenberg–Marquardt backpropagation inherently operates in batch mode and adaptively adjusts the step size through the damping factor (µ) rather than employing a fixed learning rate. The maximum number of epochs was set to 1000, which proved sufficient since extending the training further did not alter the results. To determine the optimal number of nodes in the hidden layer for each dataset; however, a series of runs was conducted on each dataset. In the trial runs, the number of hidden-layer nodes was varied from 4 to 40 in increments of 4 [52]. Since the performance remained high for values between 12 and 32, a finer search was conducted by setting the increment value to 1 for further testing. The optimal number node numbers, determined based on the training set performance, were 15 for the World dataset, 28 for OECDa, 26 for OECDf, and 29 for G20.

To evaluate the predictive performance of the MLP model in linking energy consumption to economic growth, both Pearson’s correlation coefficient ($Corr$) and the intraclass correlation coefficient ($ICC$) were analyzed across four datasets: G20, OECD founding members (OECDf), all OECD members (OECDa), and a global subset (World). The results are presented in

Table 11. MLP model performance: correlation and reliability metrics ¹.

Data	Train			Test
	$\mathit{C}\mathit{o}\mathit{r}\mathit{r}$	$\mathit{I}\mathit{C}\mathit{C}$	95% CI	$\mathit{C}\mathit{o}\mathit{r}\mathit{r}$	$\mathit{I}\mathit{C}\mathit{C}$	95% CI
G20	0.94	0.97	0.95–0.98	0.83	0.91	0.76–0.97
OECDf	0.88	0.93	0.87–0.96	0.82	0.90	0.62–0.97
OECDa	0.80	0.88	0.82–0.92	0.77	0.87	0.65–0.95
World	0.89	0.95	0.93–0.96	0.78	0.87	0.75–0.94

¹ CI = Confidence Interval.

, and the corresponding regression plots for training and testing phases are shown in Figure 3 and Figure 4. In light of Table 11, the model’s predictions align closely with actual GDP growth rates across datasets. The MLP model demonstrates robust predictive performance in estimating the relationship between energy consumption and GDP growth across all country groups, as evidenced by both correlation coefficients and intraclass reliability metrics.

For the G20 dataset, training phase predictions exhibited near-perfect alignment with actual growth rates ($Corr$ = 0.94, $ICC$ = 0.97 [95% CI: 0.95–0.98]), reflecting the model’s capacity to capture energy–growth dynamics in large, structurally diverse economies as visually confirmed in Figure 3a, where data points closely align with the identity line during both training and testing phases. This high reliability persisted during testing ($Corr$ = 0.83, $ICC$ = 0.91 [0.76–0.97]). These findings are consistent with Cogoljević et al. [23], who reported improved GDP predictive accuracy by integrating energy resource mixes through a ML approach. Similarly, strong predictive performance was observed for OECD founding members (OECDf: training $Corr$ = 0.88, $ICC$ = 0.93 [0.87–0.96]; testing $Corr$ = 0.82, $ICC$ = 0.90 [0.62–0.97]), where institutional and economic homogeneity likely contributed to stable energy–growth linkages. As illustrated in Figure 3b, predicted values remain tightly clustered around the target line in both training and test phases, affirming the model’s robustness for this relatively uniform group. Given the relatively higher share and stable integration of renewable energy in several OECDf countries, this result may also reflect the positive contribution of renewables to economic performance. This parallels the positive impacts of renewable energy on economic growth reported by Inglesi-Lotz in OECD countries, who found a significant growth effect from renewables in panel data analysis [3].

The superior performance of the model for the G20 and OECDf datasets may be attributed to the relatively mature and stable energy consumption patterns in these economies, often characterized by the dominance of fossil fuels (coal, oil, gas). In such contexts, consumption trends tend to exhibit a stronger historical coupling with GDP growth. This stronger coupling likely enhances the model’s ability to capture energy–growth relationships accurately, reflecting more predictable patterns than in regions undergoing rapid renewable-energy transitions. Apergis and Payne identified strong bidirectional causality in developed economies with dominant fossil fuel consumption, supporting our finding that such energy structures aid model performance [1]. This is further supported by Mahalingam and Orman, who demonstrated substantial regional differences within the United States, where the direction and strength of the energy–GDP growth relationship varied across states and regions, highlighting the importance of localized energy structures in determining economic outcomes [15].

The enhanced performance is underpinned by the structural stability of their energy–growth linkages. The high performance of G20 and OECDf countries stems from the more stable and predictable energy consumption patterns of these countries. Such economies have established a strong and consistent link between energy consumption and growth over many years, thanks to their high levels of industrialization and stable energy infrastructure. Because the model easily captures this consistent link, the $Corr$ and $ICC$ values remain high. Furthermore, the presence of institutionalized and organized datasets in OECDf and G20 countries allows the MLP to capture patterns more accurately. In summary, because growth in G20 and OECDf countries is largely based on fossil fuel consumption, these energy types have historically had a strong correlation with economic growth. This strong and stable energy–growth relationship stands out as a critical element for policymakers in G20 and OECD countries to consider when planning their energy strategies. Therefore, taking steps to diversify energy sources while maintaining current growth dynamics is crucial. Policymakers in G20 and OECD countries should consistently phase out fossil fuel dependency. They should increase the share of renewable energy sources to reduce carbon emissions. Investments in energy efficiency should reduce carbon emissions without undermining the existing strong energy–growth link.

In contrast, the expanded OECD dataset (OECDa), encompassing newer members with divergent energy policies, showed moderately lower, yet still strong agreement (training $Corr$ = 0.80, $ICC$ = 0.88 [0.82–0.92]; testing $Corr$ = 0.77, $ICC$ = 0.87 [0.65–0.95]). As shown in Figure 4a, the regression line remains evident, although a broader spread of residuals appears during testing. This broader spread of residuals and wider confidence intervals for the OECDa dataset can be attributed to multiple forms of unobserved heterogeneity within this diverse group. These factors include (i) the contrast between fossil fuel-dependent members (e.g., Poland) and those undergoing rapid renewable transitions (e.g., Denmark); and (ii) the inclusion of countries that are highly susceptible to external economic shocks, such as the 2008 global financial crisis, because of their significant energy import dependencies. Such diverse energy structures and vulnerabilities to external shocks can severely disrupt established energy–growth relationships, leading to increased prediction variability and lower model performance. It is similarly noted that diverse energy policies can weaken model consistency, reflecting our observed variability in OECDa [2,20]. Additionally, the World dataset’s relatively lower performance can be partly explained by data quality issues, notably sparse pre-2010 solar and wind energy records, which likely increased prediction errors. Notably, the global dataset (World) achieved high training-phase reliability ($Corr$ = 0.89, $ICC$ = 0.95 [0.93–0.96]), but its testing performance ($Corr$ = 0.78, $ICC$ = 0.87 [0.75–0.94]) revealed limitations in generalizing to countries with sparse energy data or volatile growth drivers (e.g., commodity-export-dependent economies). This aligns with findings by Maji et al., who observed that insufficient renewable-energy data led to weaker growth linkages in West African countries, highlighting how data sparsity can diminish model accuracy [13]. The trend is also reflected in Figure 4b, which shows a steeper slope in the training phase and greater deviation in testing, likely due to data quality issues.

To better understand the reasons behind this reduced performance, it is essential to consider the institutional and structural heterogeneity within the OECDa and global samples. The lower performance of OECDa and World datasets reflects significant institutional and economic heterogeneity among member states. For example, sharp contrasts exist between countries such as Mexico or Türkiye and highly industrialized economies like Germany or the United States. In the global data, the coexistence of developed and developing countries weakens the consistency of the energy–growth relationship. As heterogeneity increases, the common patterns captured by the model weaken, leading to more scattered results. Furthermore, while some countries globally and within the OECDa are rapidly transitioning to renewable energy, others still rely heavily on fossil fuels. This transition process makes the energy–growth relationship more volatile and difficult to predict. These structural differences in the energy–growth relationship and differences in transition processes not only affect model performance but also necessitate different approaches in policy design across countries and regions. In this context, policymakers in OECDa countries should differentiate their energy policies on a country-by-country basis. While some member countries remain dependent on fossil fuels, others are undergoing rapid renewable energy transitions. In brief, policymakers should implement flexible framework policies, for example, applying renewable energy incentives at different intensities depending on each country’s current energy structure, rather than a common policy. Policymakers worldwide should prioritize strengthening energy data infrastructure. Therefore, in addition to country-specific policies within the OECDa, coordinated measures and capacity-building mechanisms at the global level are critically important to support the energy transition. On a global scale, developed countries should facilitate the transition of developing countries to renewable energy through technology transfer and financial support mechanisms. Policymakers should increase predictability in the energy–growth relationship by improving institutional capacity.

Overall, the consistently high $ICC$ values (>0.87 across all testing sets) confirm that between-country differences, including institutional frameworks, energy mix composition, and development stages, constitute the primary source of predictive variance rather than measurement error. Unobserved factors such as geopolitical shocks and varying subsidy policies likely contribute to residual variance, particularly in datasets with diverse country compositions. This aligns with existing literature emphasizing national context in energy–growth nexuses. In this vein, as emphasized by Asiedu et al. emphasize that institutional and policy heterogeneity across European countries significantly influence energy–growth dynamics [12]. However, it is important to note that the $Corr$-$ICC$ gap observed in some cases (e.g., OECDf testing: $∆Corr- ICC$ = 0.08) may hint at systematic biases or uncaptured nonlinear interactions between specific energy types and growth within the model. For instance, the model might tend to overestimate growth in coal-reliant economies during periods of aggressive decarbonization, suggesting a potential area for further model refinement.

The findings underscore the ANN’s utility as a tool for identifying directional trends in energy–growth relationships, particularly for stable, data-rich economies. Nevertheless, small prediction deviations in some instances caution against interpreting outputs as precise point estimates, especially for countries undergoing rapid structural changes. While the MLP model generally demonstrates strong predictive capability for energy–growth relationships under normal economic conditions, two key considerations must be acknowledged. First, the wider confidence intervals and increased residual spread observed in the testing phase, particularly during periods of global volatility, suggest that models based on annual growth rates may not fully capture the effects of abrupt macroeconomic shocks. Second, persistent between-country variability—quantified by $ICC$-based variance partitioning—highlights the role of unmodeled institutional and geopolitical factors, especially in developing economies. Similar concerns have been raised in recent studies, which indicate that even advanced ML models can be sensitive to geopolitical instability and structural disruptions, particularly under volatile macroeconomic conditions [15,26].

4.2. Panel-Based Bidirectional Causality Analysis

To complement the correlation- and reliability-based evaluation of the ANN model, the analysis was extended with a panel causality approach to uncover the directional dynamics between disaggregated energy sources and economic growth. For this purpose, the Dumitrescu–Hurlin panel causality test was applied, enabling a more nuanced assessment of whether energy consumption merely follows economic expansion or also acts as a driver of growth across different country groups. In this respect, the test directly engages the classic growth–conservation–feedback–neutrality hypotheses summarized in these surveys, allowing the present results to be read against well-established causal patterns in the literature [39,40,41].

The results of the Dumitrescu–Hurlin panel causality tests for G20 countries are presented in

Table 12. Panel causality tests for G20 countries ¹.

Null Hypothesis	W-Stat.	Zbar-Stat.	p	Decision
Coal does not cause GDP growth	1.544	−0.993	0.321	Fail to reject
GDP growth does not cause Coal	7.733 ***	12.494	0.000	Reject
Oil does not cause GDP growth	1.162 *	−1.826	0.068	Reject
GDP growth does not cause Oil	4.055 ***	4.478	0.000	Reject
Gas does not cause GDP growth	1.914	−0.187	0.852	Fail to reject
GDP growth does not cause Gas	2.961 **	2.094	0.036	Reject
Nuclear does not cause GDP growth	0.899 **	−2.400	0.016	Reject
GDP growth does not cause Nuclear	3.904 ***	4.149	0.000	Reject
Hydro does not cause GDP growth	1.147 *	−1.860	0.063	Reject
GDP growth does not cause Hydro	3.384 ***	3.017	0.003	Reject
Wind does not cause GDP growth	1.306	−1.512	0.131	Fail to reject
GDP growth does not cause Wind	6.907 ***	10.695	0.000	Reject
Solar does not cause GDP growth	1.318	−1.486	0.137	Fail to reject
GDP growth does not cause Solar	6.703 ***	10.249	0.000	Reject
Other renewables does not cause GDP growth	1.851	−0.325	0.745	Fail to reject
GDP growth does not cause Other renewables	2.774 *	1.687	0.092	Reject

¹ Level of significance: *** p-value < 0.01, ** p-value < 0.05, * p-value < 0.10.

, revealing important insights into the relationship between various energy sources and GDP growth.

The findings indicate bidirectional causality between GDP growth and oil per capita, nuclear per capita, and hydro per capita. This reciprocity suggests that increases in these energy sources can stimulate economic activity, while economic expansion simultaneously raises demand for them. A parallel appears in aggregate panel evidence, which reports two-way feedback between renewable/non-renewable energy use and growth in mixed-country samples [1]. The two-way relationship implies that G20 countries rely on these energy sources for their economic development, and conversely, economic growth necessitates increased energy consumption in these sectors. Additionally, there is unidirectional causality from GDP growth to coal per capita, gas per capita, wind per capita, solar per capita, and other renewables per capita. This indicates that economic growth in G20 countries leads to increased consumption of these energy sources, but the reverse causality does not hold. The result suggests that while economic expansion drives demand for these energy types, their consumption does not significantly contribute to GDP growth in the sample countries. Notably, no causality is observed from coal, gas, wind, solar, and other renewables to GDP growth. This implies that increases in these energy sources do not have a significant direct impact on economic growth in G20 countries. The unidirectional relationship from GDP growth to renewable energy sources (wind, solar, and other renewables) particularly suggests that renewable energy adoption in these countries is more a consequence of economic development rather than a driver of it. This, in turn, implies that renewable energy investments in G20 countries are still in developmental stages or that their economic impact has not yet translated into a significant growth contribution. Providing external support, short-run European evidence in which economic activity precedes renewable uptake [32].

The results of the Dumitrescu–Hurlin panel causality tests for OECDa countries are presented in

Table 13. Panel causality tests for OECDa countries ¹.

Null Hypothesis	W-Stat.	Zbar-Stat.	p	Decision
Coal does not cause GDP growth	1.102 ***	−2.693	0.007	Reject
GDP growth does not cause Coal	3.126 ***	3.379	0.001	Reject
Oil does not cause GDP growth	1.111 ***	−2.667	0.008	Reject
GDP growth does not cause Oil	3.064 ***	3.191	0.001	Reject
Gas does not cause GDP growth	1.037 ***	−2.889	0.004	Reject
GDP growth does not cause Gas	2.050	0.149	0.881	Fail to reject
Nuclear does not cause GDP growth	0.437 ***	−4.689	0.000	Reject
GDP growth does not cause Nuclear	2.384	1.152	0.249	Fail to reject
Hydro does not cause GDP growth	0.961 ***	−3.117	0.002	Reject
GDP growth does not cause Hydro	2.066	0.197	0.844	Fail to reject
Wind does not cause GDP growth	1.165 **	−2.506	0.012	Reject
GDP growth does not cause Wind	3.319 ***	3.958	0.000	Reject
Solar does not cause GDP growth	2.341	1.024	0.306	Fail to reject
GDP growth does not cause Solar	4.869 ***	8.608	0.000	Reject
Other renewables does not cause GDP growth	1.089 ***	−2.734	0.006	Reject
GDP growth does not cause Other renewables	2.088	0.265	0.791	Fail to reject

¹ Level of significance: *** p-value < 0.01, ** p-value < 0.05.

, revealing distinct patterns in the energy–growth nexus compared to G20 countries.

The findings demonstrate bidirectional causality between GDP growth and coal per capita, oil per capita, and wind per capita. At a broader OECD/European scale, panel evidence reports similar bidirectional or context-dependent links between energy use and growth [2,8]; moreover, long-run feedback for renewables has been observed [32]. This two-way relationship suggests that these energy sources both drive and are driven by economic growth in OECDa countries. The bidirectional link implies that coal and oil consumption remains integral to economic activities in these developed economies, while simultaneously, economic expansion increases demand for these conventional energy sources. Notably, wind energy also exhibits bidirectional causality, indicating that renewable wind power has matured sufficiently in OECDa countries to both contribute to and benefit from economic growth. Furthermore, there is unidirectional causality from gas per capita, nuclear per capita, hydro per capita, and other renewables per capita to GDP growth. This indicates that increased consumption of these energy sources significantly contributes to economic growth in OECDa countries, but economic growth does not necessarily drive their consumption. Corroborating this direction, comparable one-direction effects of conventional energy on growth are reported for G7 and South Asia [5,33]. In particular, this finding is particularly interesting for nuclear and hydro power, suggesting these energy sources serve as important drivers of economic development rather than merely responding to economic demands.

The unidirectional causality from gas to GDP growth indicates its crucial role as a transitional fuel in supporting economic activities in OECDa economies. Additionally, there is unidirectional causality from GDP growth to solar per capita, with no reverse causality observed. It follows that solar investments are still dependent on economic capacity and policy support rather than being economically competitive enough to independently stimulate growth. This pattern is mirrored by short-run EU panel evidence points to a growth-to-renewables channel [32], which indicates that solar energy adoption in OECDa countries is primarily driven by economic prosperity rather than serving as a growth driver itself. Notably, no causality is observed between GDP growth and other renewables in the reverse direction, suggesting that while other renewable sources can influence economic growth, their consumption levels are not significantly affected by economic expansion in OECDa countries. Such cross-country differences are consistent with institutional and policy heterogeneity documented for Europe [12].

The Dumitrescu–Hurlin panel causality test results for selected OECDf countries are displayed in

Table 14. Panel causality tests for OECDf countries ¹.

Null Hypothesis	W-Stat.	Zbar-Stat.	p	Decision
Coal does not cause GDP growth	0.923 **	−2.408	0.016	Reject
GDP growth does not cause Coal	4.069 ***	4.627	0.000	Reject
Oil does not cause GDP growth	0.614 ***	−3.099	0.002	Reject
GDP growth does not cause Oil	2.879 **	1.965	0.049	Reject
Gas does not cause GDP growth	0.618 ***	−3.091	0.002	Reject
GDP growth does not cause Gas	2.071	0.159	0.874	Fail to reject
Nuclear does not cause GDP growth	0.442 ***	−3.483	0.001	Reject
GDP growth does not cause Nuclear	2.751 *	1.680	0.093	Reject
Hydro does not cause GDP growth	0.780 ***	−2.727	0.006	Reject
GDP growth does not cause Hydro	2.692	1.547	0.122	Fail to reject
Wind does not cause GDP growth	0.617 ***	−3.092	0.002	Reject
GDP growth does not cause Wind	4.974 ***	6.649	0.000	Reject
Solar does not cause GDP growth	0.710 ***	−2.885	0.004	Reject
GDP growth does not cause Solar	6.481 ***	10.020	0.000	Reject
Other renewables does not cause GDP growth	1.087 **	−2.041	0.041	Reject
GDP growth does not cause Other renewables	2.748 *	1.673	0.094	Reject

¹ Level of significance: *** p-value < 0.01, ** p-value < 0.05, * p-value < 0.10.

, providing valuable insights into the dynamics between different energy sources and economic growth in this subset of developed economies. The analysis reveals bidirectional causality between GDP growth and several energy sources including coal per capita, oil per capita, wind per capita, and solar per capita. This reciprocal relationship indicates that consumption of both conventional (coal and oil) and renewable (wind and solar) energy sources simultaneously influences and responds to economic growth patterns in these selected OECDf nations. Accordingly, these two-way links align with the ‘feedback’ hypothesis synthesized in survey work [39,40] and are plausible under documented institutional heterogeneity across European economies [12]. The bidirectional nature suggests these energy types are deeply integrated into the economic structure, where economic prosperity drives energy demand while energy availability supports continued growth. The results also show bidirectional causality between GDP growth and nuclear per capita as well as other renewables per capita. This mutual relationship demonstrates that nuclear energy and other renewable sources have achieved sufficient maturity and scale in these countries to both benefit from and contribute to economic expansion. The two-way causality for nuclear power particularly highlights its established role as a baseload energy source that both supports and is supported by economic activities. In contrast, unidirectional causality runs from gas per capita and hydro per capita to GDP growth, without significant reverse effects. This suggests that natural gas and hydroelectric power serve primarily as drivers of economic growth rather than being demand-driven by economic expansion. Comparable one-direction effects of conventional energy on growth are reported for G7 and South Asia [5,33].

The one-way relationship indicates these energy sources function as foundational inputs to economic production in the selected OECDf countries, with their consumption levels determined more by availability and infrastructure than by economic cycles. Remarkably, all energy sources exhibit significant causal links with GDP growth, underscoring the critical importance of diverse energy portfolios in sustaining economic development in these advanced economies. This comprehensive energy–growth relationship suggests that selected OECDf countries have successfully integrated various energy sources into their economic frameworks, with each contributing meaningfully to overall economic performance.

The panel causality test results for several countries worldwide are presented in

Table 15. Panel causality tests for World countries ¹.

Null Hypothesis	W-Stat.	Zbar-Stat.	p	Decision
Coal does not cause GDP growth	1.210 ***	−3.534	0.000	Reject
GDP growth does not cause Coal	3.691 ***	7.561	0.000	Reject
Oil does not cause GDP growth	1.024 ***	−4.363	0.000	Reject
GDP growth does not cause Oil	2.657 ***	2.938	0.003	Reject
Gas does not cause GDP growth	1.191 ***	−3.617	0.000	Reject
GDP growth does not cause Gas	2.237	1.059	0.290	Fail to reject
Nuclear does not cause GDP growth	0.641 ***	−6.079	0.000	Reject
GDP growth does not cause Nuclear	2.019	0.085	0.933	Fail to reject
Hydro does not cause GDP growth	0.886 ***	−4.982	0.000	Reject
GDP growth does not cause Hydro	2.108	0.484	0.629	Fail to reject
Wind does not cause GDP growth	1.126 ***	−3.910	0.000	Reject
GDP growth does not cause Wind	3.756 ***	7.853	0.000	Reject
Solar does not cause GDP growth	1.431 **	−2.545	0.011	Reject
GDP growth does not cause Solar	4.878 ***	12.873	0.000	Reject
Other renewables does not cause GDP growth	1.205 ***	−3.555	0.000	Reject
GDP growth does not cause Other renewables	2.420 *	1.878	0.060	Reject

¹ Level of significance: *** p-value < 0.01, ** p-value < 0.05, * p-value < 0.10.

, offering a comprehensive global perspective on the energy–growth relationship across diverse economies. The findings demonstrate bidirectional causality between GDP growth and multiple energy sources, including coal per capita, oil per capita, wind per capita, solar per capita, and other renewables per capita. This reciprocal causality suggests a strong interdependence between energy consumption and economic development at the global level. This world-level reciprocity resonates with evidence from the Next-11 and from global ML applications highlighting the growth contribution of renewables [20,34]. The two-way relationship indicates that worldwide, these energy sources not only respond to economic expansion but also actively contribute to driving economic growth. The bidirectional link for renewable sources (wind, solar, and other renewables) is particularly noteworthy, signaling that renewable energy has reached a sufficient global scale to both stimulate and be stimulated by economic activities.

Moreover, the results indicate unidirectional causality from gas per capita, nuclear per capita, and hydro per capita to GDP growth, with no significant reverse causality detected. This one-way relationship suggests these energy sources function primarily as catalysts for economic development rather than being consumption patterns driven by economic prosperity. More generally, the coexistence of energy-to-growth and growth-to-energy channels matches the mixed patterns summarized in broader surveys [39,41]. Natural gas, nuclear, and hydroelectric power appear to serve as fundamental economic inputs across countries worldwide, with their availability and infrastructure determining usage levels rather than economic demand cycles. It is worth noting that all examined energy sources demonstrate significant causality toward GDP growth, highlighting the universal importance of energy access and diversity for economic development regardless of a country’s development stage. This comprehensive pattern underscores that energy remains a critical factor in global economic performance, whether from conventional fossil fuels or emerging renewable sources. The absence of reverse causality from GDP growth to gas, nuclear, and hydro consumption suggests these energy sources face supply side constraints or infrastructure limitations that prevent their consumption from readily expanding with economic growth, particularly in developing nations where such infrastructure may be lacking or underdeveloped.

By complementing the ANN-based predictive and reliability analysis with the Dumitrescu–Hurlin panel causality tests, a more comprehensive picture of the energy–growth nexus emerges. The ANN results demonstrated that disaggregated energy consumption patterns provide robust predictive alignment with GDP growth, particularly in structurally stable economies such as the G20 and OECDf groups. The complementary panel causality tests added a directional dimension, revealing which energy sources not only co-move with economic activity but also actively drive it. The combined evidence underscores that conventional sources such as coal, oil, and gas continue to underpin growth trajectories, while certain renewables, especially wind and solar in OECD settings and globally, have begun to exert reciprocal growth effects, albeit unevenly across regions. These findings highlight that the energy–growth nexus is both predictive and causal in nature, with implications extending beyond statistical fit to concrete policy design. For policymakers, this dual perspective suggests that while fossil fuels remain deeply entrenched as growth drivers, the gradual but strengthening bidirectional role of renewables signals the necessity of policies that accelerate their integration without destabilizing established growth structures. This synthesis sets the stage for the concluding section, where the broader implications for sustainable development and energy transition strategies are further elaborated.

5. Conclusions

The dynamic and multifaceted relationship between energy consumption and economic growth remains a central focus in economic and environmental research. This nexus, however, has proven difficult to characterize, given its nonlinear features, strong contextual dependence, and heterogeneous effects across economies. Prior work has frequently relied on aggregate energy indicators and linear specifications, which provide useful baselines but often conceal the distinct roles of individual energy sources. To address these limitations, the study examined the heterogeneous impacts of eight disaggregated energy sources including coal, oil, natural gas, nuclear, hydro, wind, solar, and other renewables, on economic growth across four distinct country groups (OECD founding members, all OECD members, the G20, and a global sample) over the period 2000–2022. To address this complexity, a machine learning approach was introduced to capture nonlinear patterns and predictive dynamics; for this purpose, a multilayer perceptron (MLP) was employed. Multiple linear regression was also implemented as a conventional benchmark, enabling a direct comparison between linear statistical methods and nonlinear ML approaches. Finally, the Dumitrescu–Hurlin panel causality test was applied to clarify the directionality of energy–growth linkages. This integrated design aimed to combine predictive accuracy with causal interpretability, thereby providing a more comprehensive perspective on the energy–growth nexus. Model performance was rigorously assessed using both $Corr$ (Pearson correlation) and $ICC$ (intraclass correlation).

The findings unequivocally demonstrated the MLP model’s robust predictive capability in linking energy consumption to economic growth across all investigated country groups. High correlation coefficients ranging from 0.80 to 0.94 in training phases, and ICC values consistently above 0.87 in testing phases, reaffirm the ANN’s strength in identifying directional trends in these complex relationships. Notably, the model exhibited superior performance for more homogenous and structurally stable economies such as the G20 and OECDf groups, where energy consumption patterns tend to be more predictable. These findings underscore the ANN’s ability to capture directional trends in energy–growth dynamics rather than precise point estimates. However, the analysis also unveiled critical nuances and limitations, particularly in the OECDa and World datasets. The observed wider confidence intervals and increased spread of residuals in the testing phases underscored areas where the model’s predictive accuracy showed greater deviation. This suggests that models based on annual growth rates may be challenged in fully capturing abrupt macroeconomic shocks or outlier events, such as major financial crises, which can temporarily decouple energy-demand linkages. Furthermore, the persistent between-country variability, as robustly quantified by ICC variance partitioning, highlighted the considerable influence of unmodeled institutional, policy, or geopolitical factors, especially pronounced in developing economies navigating complex energy transitions. The overall results underline the effectiveness of ML approaches, specifically ANNs, as a powerful tool for analyzing the intricate energy–growth nexus and providing valuable insights beyond traditional linear methods. While the model demonstrated strong predictive performance under normal economic conditions, it also highlighted the need for further refinement to address the complexities introduced by systemic shocks and unmodeled heterogeneity across diverse economies.

Beyond the predictive performance of the ANN model, the Dumitrescu–Hurlin panel causality tests were employed to further examine the directionality of the energy–growth relationship, offering complementary insights into how specific energy sources interact with economic expansion across different country groups. The Dumitrescu–Hurlin panel causality tests further complemented the ANN-based results by clarifying the directionality of the energy–growth nexus across different country groups. For the G20, the bidirectional causality observed between GDP and oil, nuclear, and hydro consumption aligns with earlier findings that conventional energy sources remain central to industrial expansion and economic performance [40,41]. At the same time, the unidirectional link from GDP growth to renewables suggests that renewable energy in these economies still functions more as a consequence of prosperity than as a growth driver, echoing the conclusions of Bhattacharya et al. on the developmental stage of renewable markets [43]. In OECD countries, coal and oil continued to show reciprocal causality with GDP, consistent with Stern, who emphasized the persistent dependence of advanced economies on fossil fuels despite transition efforts [41]. However, the emergence of bidirectional causality between wind energy and GDP indicates that certain renewable technologies have matured sufficiently to contribute to growth, supporting the findings of Apergis and Payne on the growth-enhancing role of renewables in developed economies [1]. For selected OECD members, the evidence of widespread bidirectional causality across nearly all energy types points to a deeper structural integration of energy into economic systems, a pattern rarely observed in developing economies. At the global level, the bidirectional causality between renewables (wind, solar, other renewables) and GDP highlights a turning point: clean energy sources have begun to play an active role in stimulating growth worldwide. This complements the ANN evidence on their rising importance. Overall, these results confirm the heterogeneous nature of the energy–growth relationship across development levels and resonate with the broader literature stressing the importance of context-specific policies to balance growth, sustainability, and energy security. Viewed jointly, the predictive evidence from the ANN analysis and the directional insights from the panel causality tests provide a complementary perspective, underscoring that the energy–growth nexus is both nonlinear and causal in nature. The findings highlight the heterogeneous role of different energy sources, where fossil fuels and nuclear generally exhibit limited or negative growth effects, natural gas shows a positive association, and renewables display mixed patterns. These results underscore the importance of tailoring energy policies to country-specific contexts and the critical role of diversification for sustainable growth.

From a policy perspective, these results suggest differentiated strategies across country groups In G20 economies, the findings suggest that policies could prioritize diversifying the energy mix, strengthening efficiency measures, and expanding green financing instruments, while allowing flexible transition pathways for fast-growing members such as India and Indonesia. Among OECD founding members, the evidence indicates that accelerating carbon-neutrality targets, advancing renewable integration through storage and grid modernization, and sustaining innovation leadership in hydrogen and carbon capture technologies could be central policy directions. For the wider OECD membership, the results point to the need for country-specific approaches and targeted support mechanisms for less advanced members in order to balance growth with sustainability goals. At the global level, the analysis highlights universal energy access, just-transition programs, and stronger international cooperation in clean-energy financing and technology transfer as continuing priorities. The study further shows that while the energy–growth relationship remains strong worldwide, low-income countries should prioritize secure and affordable access to energy. Results also imply that energy investments ought to advance environmental sustainability in parallel with economic expansion. International collaboration in climate finance, technology exchange, and renewable deployment could be further reinforced to accelerate the transition. Finally, in fossil-fuel-dependent economies, employment-transition initiatives are recommended to safeguard social and economic cohesion during decarbonization.

The empirical findings also address the research questions posed at the outset. Regarding the first question, evidence of both unidirectional and bidirectional causality was observed, with mutual reinforcement between GDP and conventional energy sources (such as coal, oil, and nuclear) in the G20 and OECD founding members, while renewables still tend to follow economic expansion in most cases. In broader and more diverse samples, these relationships became less uniform, yet at the global level renewables increasingly exhibit bidirectional links with growth, underscoring their emerging role in economic development. Addressing the second question, the comparative design revealed that homogeneous country groups (G20 and OECDf) displayed stronger and more stable energy–growth interactions, whereas the inclusion of more heterogeneous economies (OECDa and World) reduced predictive accuracy, reflecting structural and institutional differences. Finally, in response to the third question, the results confirm that nonlinear machine learning methods, particularly ANNs, substantially outperform conventional linear approaches in capturing the complex and context-dependent nature of the energy–growth nexus. This validates the use of advanced computational techniques in this domain.

For future research, this study highlights clear avenues for enhancing model robustness and generalizability. Incorporating explicit variables such as crisis dummy variables, more granular policy indicators, or even transitioning to higher-frequency datasets like monthly energy data could significantly improve the model’s ability to account for nonlinear shock effects and subtle within-country dynamics. Such advancements would not only refine the model’s precision but also enhance its utility in informing policy decisions and understanding energy–growth relationships under a broader spectrum of global circumstances, thereby extending the practical relevance of the current findings. While the present study offers new insights into the heterogeneous energy–growth nexus by employing disaggregated energy data and ML techniques, some limitations should be noted. First, the models focus solely on the link between energy use and GDP, without incorporating additional explanatory variables such as capital formation, institutional quality, or policy indicators. Future research could enrich the framework by integrating these factors to better isolate the independent role of energy consumption. Furthermore, although artificial neural networks capture nonlinear dynamics effectively, the model remains largely opaque in terms of interpretability. Future work may incorporate interpretive ML techniques, such as feature selection, sensitivity analysis, or SHAP values, to clarify the relative contribution of each energy source to growth. This would complement the statistical and causal approaches applied here and enhance the transparency of ML-based findings.