The Role of Human Capital and Energy Transition in Driving Economic Growth in Sub-Saharan Africa

Abstract

This research investigates the role of fossil fuel energy, renewable energy, and education in terms of years of schooling and mean years of schooling on the economic growth of 19 selected Sub-Saharan African countries. The primary objective is to assess whether renewable energy and educational attainment serve as viable long-term drivers of economic development in a region still heavily reliant on fossil fuels. We employed the newly developed and robust econometric estimators, including “Residual Augmented Least Squares (RALS) co-integration”, to estimate long-term links among the facets of study. Moreover, “Pooled Mean Group–Autoregressive Distributed Lag model (PMG-ARDL) and Quantile Autoregressive Distributed Lag (QARDL)” econometric estimator was employed to estimate the long and short coefficients of the antecedents of study. The estimations obtained from the PMG-ARDL and QARDL estimators provide evidence that the coefficients of fossil fuel energy and renewable energy on economic growth are positive. But surprisingly, the magnitude of renewable energy is greater than fossil fuel energy in Sub-Saharan countries that still depend on fossil fuels. Moreover, human capital and capital stock boost economic growth in the countries studied. The outcomes reveal that not only quality but also quantity of education play a vital role in boosting economic development. To deepen the understanding of the observed effects, the study also explores the transmission channels through which renewable energy and education foster economic growth. Renewable energy contributes by lowering the marginal cost of electricity, encouraging green industrial transformation, and serving as a catalyst for technological innovation. Concurrently, improvements in education—measured by both expected and mean years of schooling—elevate labor productivity and facilitate the absorption and diffusion of new technologies across sectors, thereby stimulating sustained economic performance. The empirical results provide valuable insights for government officials and policymakers in specific Sub-Saharan African countries.

1. Introduction

The global economies have experienced significant economic expansion since the onset of the industrial revolution. Nevertheless, the increasingly pressing environmental concerns resulting from economic progress, such as the phenomenon of global warming and the subsequent rise in sea levels, have considerably compromised both human well-being and societal progress [1]. However, in recent decades, there has been an increase in competition for sustainable economic growth on a global scale, driven by trends in energy consumption, education, and economic development. Policymakers and scholars have looked at the interactions and contributions of energy and education in achieving the desired economic development because of the connections among these three factors. Additionally, a rise in industrial output of commodities and overall economic growth might result in an increase in energy usage [2]. Fossil fuel energy serves as a vital component of the industrialized economy and has played a significant role in driving economic growth [3]. However, a dependence on fossil fuel sources has resulted in an ongoing increase in energy consumption, posing a major danger to the environment [4,5,6]. Moreover, according to [7], due to their high carbon content, limited availability, and non-renewability, the excessive use of fossil fuels undermines energy security. The excessive reliance on fossil fuels for worldwide economic progress entails significant drawbacks in terms of energy security and environmental quality, primarily due to the substantial carbon emissions associated with these fuels and their finite and non-renewable nature.

Therefore, the world is in an energy transition process from fossil fuels to renewable energy and investing green finance in clean energy projects to meet the existing demand of energy by any economy [8]. Renewable energy pertains to the energy derived from naturally occurring resources, including sunlight, wind, rain, and geothermal heat. These sources are considered renewable as they are not depleted upon utilization [9]. Renewable energy resources serve as viable alternatives to fossil fuels, thereby safeguarding the planet against the adverse effects of climate change and global warming [10], while simultaneously fostering economic growth [11]. On the contrary, it has been evidenced by some research studies such as [7,12,13,14] that although renewable energy has positive impact on the environment, it adversely affects economic growth. Therefore, it is necessary to understand the impact of renewable energy and fossil fuel energy on economic growth, particularly in the selected Sub-Saharan African countries. According to [1], enhancing access to renewable energy not only supports environmental sustainability but also complements human development indicators such as education, thereby reinforcing economic growth prospects in the long term.

Furthermore, in accordance with the human capital theory and economic growth theory [15], for example, there exists a motivation to invest in individuals in order to cultivate a workforce that possesses knowledge and expertise, thereby playing a crucial role in driving economic advancement [16]. Subsequently, there has been a heightened discourse surrounding the significance of human capital, encompassing not only its impact on education but also its influence on various domains ranging from health to economic development. Moreover, the assertion made by [17] that the impact of schooling on economic growth is primarily determined by its quality rather than its quantity is primarily supported by the statistical findings derived from their economic growth models. This assertion has been supported by some of the earlier researchers [18,19]. However, some researchers [20,21,22] have rejected the assertion of [17]. Therefore, the subject of quantity or quality of education requires more inquiry to drive a unanimous collusion. Hence, to understand economic growth volatility, we have developed a model testing the role of fossil fuel energy, renewable energy, human capital, capital stock, and quality of schooling—measured as years of schooling and mean years of schooling—on economic growth, particularly in the selected Sub-Saharan African countries.

Furthermore, we have selected the sample of 19 Sub-Saharan African countries based on following facts: According to the World Economic Forum, fossil fuels continue to be extensively used in the Sub-Saharan African region, where an estimated population of over 500 million individuals lacks access to electricity (“Energy: Should fossil fuels be banned in sub-Saharan Africa? | World Economic Forum (weforum.org)”). Nevertheless, there is a contention among experts that Sub-Saharan Africa should be granted equitable access to the global carbon budget and should not face prohibition in using fossil fuels (“Sub-Saharan Africa needs fair access to global carbon budget | World Economic Forum (weforum.org)”). Conversely, several forecasts indicate that the year 2023 may mark a significant turning point in the realm of power production, whereby renewable sources such as solar and wind have the potential to surpass fossil fuels on a worldwide scale (“We’re close to a new era of renewable power generation | World Economic Forum (weforum.org)”). Furthermore, as reported by the World Bank, the economic growth of Sub-Saharan Africa had a decline from 4.1% in 2021 to 3.6% in 2022, and it is projected to further decrease to 3.1% in the year 2023 (“Africa Overview: Development news, research, data | World Bank”). Third, the area experienced further economic disruptions as a consequence of the Russian incursion into Ukraine (“Sub-Saharan African Growth Slows Amid Ongoing and New Economic Shocks (worldbank.org)”). Fourth, according to the World Bank, Sub-Saharan Africa has seen advancements in human capital in recent years. However, the region continues to encounter several obstacles, including inadequate levels of education, healthcare, and gender parity (“The Human Capital Project in Sub-Saharan Africa: Stories of Progress (worldbank.org)”). The decision to focus on renewable energy and education in Sub-Saharan Africa is rooted in the region’s dual challenge of achieving sustainable economic development while addressing chronic deficits in energy access and educational infrastructure.

In this study, we aim to empirically investigate the interconnected roles of energy consumption patterns—both fossil-based and renewable—and educational attainment in shaping long-run economic growth across the 19 Sub-Saharan African countries. The primary objective is to determine whether renewable energy and expanded access to education serve as effective engines of growth in these countries, many of which remain reliant on fossil fuels and face significant educational challenges. By integrating human capital theory with modern energy transition frameworks, this research endeavors to offer a nuanced understanding of how energy diversification and educational expansion interact to influence economic outcomes in one of the world’s most developmentally complex regions.

While this study investigates 19 Sub-Saharan African countries due to the availability of consistent and complete data across the selected indicators, it is important to acknowledge that Sub-Saharan Africa encompasses a far broader set of nations with considerable heterogeneity in economic structures, resource endowments, and institutional capacities. The selected sample, though analytically robust, may not capture the full spectrum of socioeconomic diversity across the region. As such, the findings should be interpreted with an understanding of these limitations, particularly regarding the generalizability of results in the entire Sub-Saharan African context. Future research should consider expanding the sample size as data availability improves to enhance the representativeness and policy relevance of empirical conclusions.

Our research contributes in the following ways: Theoretically, to our limited knowledge, none of the studies have investigated the role of fossil fuel energy, renewable energy together with human capital, capital stock, and education on the economic growth in the case of the 19 selected Sub-Saharan countries. Furthermore, methodologically, to the best of the author’s knowledge, this research is the first instance of using the most current, freshly designed, and enhanced approach such as “Residual Augmented Least Squares (RALS) cointegration, Pooled Mean Group–Autoregressive Distributed Lag model (PMG-ARDL), and Quantile Autoregressive Distributed Lag (QARDL)” econometric approach. The RALS cointegration technique is selected due to its inherent benefits and superior performance compared to traditional cointegration tests. One key advantage is its increased power and robustness, achieved by effectively incorporating information from non-normal errors [23]. The RALS procedure circumvents the use of nonlinear estimating approaches by using “nonlinear moment conditions linked to non-normal errors”. Nonlinear cointegration tests may suffer power loss if the functional form is misidentified. However, this issue can be mitigated by using the “RALS cointegration technique”. In situations where information on nonmorality is lacking, the efficacy of RALS-based tests may be deemed equivalent to that of other “single equation-based cointegration tests” [23,24].

Moreover, the PMG-ARDL methodology has a novel strategy that effectively addresses issues associated with the estimation of short time-series data, hence enhancing accuracy and preventing potential difficulties. In addition to the PMG-ARDL approach, we have employed newly developed “Quantile Autoregressive Distributed Lag (QARDL) approach” to estimate long run coefficients of antecedents. Previous scholarly investigations in the field of literature have mostly concentrated on conventional and commonplace methodologies, thus neglecting the temporal dimension of the “Quantile Autoregressive Distributed Lag (QARDL) approach”. Therefore, the use of the RALS cointegration technique, PMG-ARDL, and the QARDL methodology sets this study apart from past research, as it yields more dependable, significant, and impartial results. These conclusions are crucial for policymakers in formulating a robust policy framework that can effectively address the sustainable development objectives by the year 2030.

The subsequent sections of the research are organized as follows: Section 2 provides a comprehensive summary of the current body of knowledge. Section 3 is structured into three sub-sections, each of which offers a comprehensive examination of the theoretical framework, data, and methodologies used in the study. Section 4 of the study focuses on the comprehensive examination and elucidation of the empirical data. Section 5 concludes the study and examines the potential policy consequences.

2. Literature Review

2.1. Renewable Energy, Fossil Fuel Energy, and Economic Growth

In light of increasing global environmental awareness, the pursuit of an appropriate means of energy that aligns with both economic growth and environmental preservation objectives has emerged as a significant concern for numerous nations. A variety of studies revealed that various forms of energy boost economic growth and environmental quality. For instance, Ref. [25] revealed that renewable energy promotes economic growth and environmental quality in the case of 24 nuclear energy countries. Moreover, they argued that renewable energy is replacing fossil fuel energy source (Oil, Gas, natural resources) consumption in these countries as they are believed to be dirty sources contributing to environmental degradation along with economic growth. Ref. [26] employed the CSARDL economic estimator to estimate the link between fossil fuels and economic growth and suggested that fossil fuels speed up economic growth. Similar estimations have been observed by [3] in China, Ref. [27] in Nigeria, Ref. [6] in Saudi Arabia, Ref. [14] in “East Asia–Pacific region” and Ref. [28] in 42 Countries.

Moreover, to answer the question whether renewable energy promotes the economy is not straightforward. As such, Ref. [29] in France, Ref. [26] in Pakistan, Ref. [30] in China, Ref. [6] in Saudi Arabia, Ref. [31] in Vietnam, Ref. [11] in South Africa, Ref. [32] in China, and Ref. [25] in OECD countries utilized several econometric estimators such as “Fully Modified Ordinary Least Square (FMOLS), Generalized Movement Method (GMM), Wavelet Coherence (WC), Autoregressive Distributed Lag Model (ARDL), and Nonlinear Autoregressive Distributed lag model (NARDL)” to estimate the role of “renewable energy consumption on the economic growth”. The aforementioned research investigations altogether showed that the use of renewable energy sources is of utmost importance in fostering economic development and enhancing environmental sustainability.

In contrast, Ref. [7] in the case of West Africa, utilized “Panel-Corrected Standard Errors (PCSE) and the Feasible Generalized Least Squares estimators” (FGLS) to “gauge the relationship between renewable energy and economic growth”. The estimated findings suggest that the utilization of renewable energy sources may impede economic growth. Furthermore, they argued that West Africa underuse renewable energy. The primary contributing factors to this phenomenon can be attributed to a limited level of consciousness, financial limitations, an unfavorable institutional framework, and insufficient technological progress within the area. Also, [12] employed the MMQR estimator on the data in the case of N-11 states. They established that “renewable energy consumption boosts economic growth in the short run only however, renewable energy consumption has negative impact on economic growth in medium and long-term”. Similarly, [13] studied the link in “Low–Middle–High-income countries” by using the “FOLS and Threshold Panel Model” and proposed that “REC association is significant with GDP in high income group countries; however, it has N shaped and U-shaped nexus in medium and low-income group countries”. Additionally, Ref. [9] portrayed the nonlinear association “between renewable energy and economic growth”. The above discussion witnessed that there is no consensus on the association between renewable energy and economic growth.

2.2. Education and Economic Growth

Ref. [17] conducted a thorough examination of the body of research pertaining to the influence of cognitive abilities on economic progress. The authors provide substantial evidence in favor of the proposition that the cognitive abilities of individuals, primarily developed through formal education, have a significant impact on the increase in income, both at an individual and societal level. Similar results have been extracted by [19] in their review on education quality and economic growth, Ref. [33] in their research study on “Alternative school policies and the benefits of general cognitive skills”, and Ref. [18] in their research study “Schooling, Labor-Force Quality, and the Growth of Nations”. These research studies support the idea that the quality of education measure in terms of “scores on international tests of math and science skills”, rather than schooling quality measured in terms of “years of schooling or average years of schooling”, is the central focus of economic development. On the other hand, an increasing number of scholarly works highlight the distinction between schooling and learning [20,21,34]. Additionally, several studies have reported that economic growth is not centered on the quality of education but education quantity as well. Similarly, many research studies have found positive links between years of education and economic growth [34,35,36]. Hence, it has been evidenced that the hypothesis derived by [17] needs more inquiry to accept it or reject it.

2.3. Human Capital, Capital Stock, and Economic Growth

In recent times, economists have increasingly turned their attention towards intelligence as a metric for assessing human capital, aiming to elucidate the factors contributing to economic growth [37]. For instance, Ref. [38] used Granger Causality in the microstates and found crucial influence of human capital on economic advancement. Similarly, Ref. [39] in Sub-Saharan countries, Ref. [40] in Nigeria, Ref. [41] in BRICS nations, Ref. [42] in Indonesia, Ref. [37] in Mexico, Ref. [43] in N-11 nations, Ref. [44] in South Asian nations, Ref. [45] in China, Ref. [46] in European nations, Ref. [16] in Bangladesh, Ref. [47] in 141 developing and developed countries, Ref. [48] in Bangladesh, Ref. [49] in Brazil, and Ref. [50] in G-7 nations used multiple econometric methods such as “Autoregressive Distributed Lag Model (ARDL), Path analysis, Ordinary Least Square (OLS), Fully Modified Ordinary Least Square (FMOLS), Augmented Mean Group (AMG), Vector Autoregressive (VAR), Moment Method Quantile Regression (MMQR), and Systematic Generalized Moment Method (SGMM)” to estimate the prudential effect of “human capital on the economic growth”. They all concluded that skilled, effective, and efficient human capital is a vital component to boost the economic progress in the studied nations.

Moreover, the stock of human capital contributes to the production of more physical capital, stronger investment returns, and greater technological adoption [51]. Therefore, the nexus between capital stock and economic growth have been estimated by many researchers such as [52] in Europe, Ref. [53] in “Latin American and Caribbean countries”, Ref. [54] in BRI nations, Ref. [51] in Pakistan, Ref. [55] in China, Ref. [56] in Greece. They used my econometric models such as “Autoregressive Distributed Lag Model (ARDL), Diff-in-Diff regression method (DID), Perpetual Inventory Method (PIM), Fully Modified Ordinary Least Square (FMOLS), Panel Vector Autoregressive model (VAR), Generalized Moment Method (GMM), and Granger Causality”, to drive the link between two facets. The estimates of these studies present that capital stock boosts the economic development in the nations studied. Hence, keeping in view the importance of human and stock capital we have added these facets to the study to prevent the model from omitted biasness. Furthermore, the synthesis of the scholarly works is provided in

Table A1. Literature review.

Authors	Country	Methodology	Results
[48]	Bangladesh	ARDL	HC + ve EG
[42]	Indonesia	Path Analysis	HC + ve EG
[37]	Mexico	OLS	HC + ve EG
[46]	European Countries	Pooled OLS	HC + ve EG
[40]	Nigeria	ARDL	HC + ve EG
[41]	BRICS	FMOLS	HC + ve EG
[43]	N-11 Countries	AMG	HC + ve EG
[44]	South Asian Countries	ARDL	HC + ve EG
[16]	Bangladesh	ARDL	HC + ve EG
[49]	Brazil	ARDL	HC + ve EG
[45]	China	MRW	HC + ve EG
[77]	Microstates	Granger Causality	HC + ve EG
[39]	Sub-Saharan Countries	SGMM	HC + ve EG
[47]	141 developing and developed countries	SGMM	HC + ve EG
[50]	G7 Countries	MMQR	HC + ve EG
[55]	China	ARDL	CN + ve EG
[70]	African Countries	DID	CN + ve EG
[56]	Greek Economy	PIM	CN + ve EG
[52]	Europe	Granger Causality	CN + ve EG
[51]	BRICS Countries	DH Causality	CN + ve EG
[53]	Latin American and Caribbean countries	PVAR	CN + ve EG
[54]	BRI Countries	GMM	CN + ve EG
[13]	Low–Middle–High-income countries	FMOLS Threshold Panel Model	CN + ve GDP(104 Countries) CN + ve GDP (HI Group) CN − ve GDP (MI Group) CN + ve GDP (LI Group)
[31]	Vietnam	ARDL	CN + ve GDP
[9]	European Countries	TVFE, FE	CN + ve EG
[26]	Asian Countries	CSARDL	FF + ve EG
[3]	China	FE	FF Inverted U shaped in Eastern Region FF + ve U shaped in Central Region
[27]	Nigeria	ARDL	FF + ve EG
[6]	Saudi Arabia	WC	FF + ve GDP
[14]	East Asia–Pacific region	NARDL, WC	FF (+ve Shock) + ve EG FF (−ve Shock) − ve EG
[28]	42 Countries	FGSE PCSE	FF + ve EG
[78]	Pakistan	NARDL	FF (+ve Shock) + ve GDP REC (−ve Shock) − ve GDP
[71]	24 Nuclear energy countries	FMOLS & DH causality	Natural Gas + ve EG Oil + ve EG Coal − ve EG REC + ve EG
[7]	West Africa	PCSE and FGLS	REC − ve EG
[9]	European Countries	TVFE, FE Model	REC nonlinear association with EG
[32]	China	GMM	REC + ve GDP
[6]	Saudi Arabia	WC	REC + ve GDP
[31]	Vietnam	ARDL	REC + ve GDP
[12]	N-11	MMQR	REC + ve GDP (Short Run) REC + ve GDP (Long Run)
[11]	South Africa	ARDL	REC + ve GDP
[30]	China	ARDL	REC + ve GDP
[13]	Low–Middle–High-income countries	FOLS Threshold Panel Model	REC + ve GDP(104 Countries) REC association is significant with GDP (HI Group) REC association with GDP inverted N shaped (MI Group) REC association is U shaped with GDP (LI Group)
[25]	OECD	Threshold Panel Model	REC + ve GDP
[72]	Rwanda	NARDL	REC + ve GDP REC (+ve Shock) + ve GDP REC (−ve Shock) no effect on GDP
[14]	East Asia–Pacific region	NARDL, WC	REC − ve EG
[78]	Pakistan	NARDL	REC (+ve Shock) − ve GDP REC (−ve Shock) + ve GDP
[29]	France	ARDL	REC + ve EG
[74]	Developed and Developing Countries	GMM, FE	MYS insig EG (GMM) MYS + ve EG (FE)
[75]	46 Countries	Linear regression	MYS + ve EG
[22]	33 Countries	GMM, POLS	LAYS + ve EG MYS + ve EG
[73]	30 Countries	Linear regression	MYS + ve EG
[76]	Multiple groups of countries	Perpetual Inventory system	EYS + ve EG
[21]	Multiple groups of countries	PISA, TIMSS	LAYS + ve EG MYS + ve EG

Note: ARDL = Autoregressive Distributed Lag Model; OLS = Ordinary Least Square; FMOLS = Fully Modified Ordinary Least Square; AMG = Augmented Mean Group; MMQR = Moment Method of Quantile Regression; DID = Difference in Difference; MRW = Mankiw-Romer-Weil; SGMM = Systematic Generalized Moment Method; PVAR = Panel Vector Autoregressive; GMM = Generalized Moment Method; PIM = Perpetuity Inventory Management; TVFE = Time-Varying Fixed Effects; FE Model = Fixed-Effect Model; CSARDL = Coress Sectional Autoregressive Distributed Lag Model; NARDL = Nonlinear Autoregressive Distributed Lag Model; FGSE = Feasible Generalized Least Square Panel; PCSE = Corrected Standard Errors model; DH Causality = Dumitrescu–Hurlin Panel Granger Causality; PISA = Program for International Student Assessment; TIMSS = Trends in International Mathematics and Science Study; WC = Wavelet Coherence; HC = Human Capital; EG = Economic Growth; CN = Capital Stock; GDP = Gross Domestic Product; HI = High Income; LI = Low Income; MI = Middle Income; FF = Fossil Fuel; REC = Renewable Energy; MYS = Mean Average Years of Schooling; LAYS = Learning Average Years of Schooling; EYS = Years of Schooling.

, which can be found in Appendix A.

3. Methodology

3.1. Data

This study empirically assesses the impact of human capital, capital stock, fossil fuel energy consumption, renewable energy consumption, expected years of schooling, and mean years of schooling on economic growth across 19 Sub-Saharan African countries during the period 2000–2019. To enable consistent scaling and interpretation of elasticities, all variables are transformed into their natural logarithmic forms. The baseline econometric model is specified as follows in Equation (1):

$${Ln(GDP}_{it})=\mathsf{\alpha }+{{\beta }_{1}Ln(CN}_{it})+{{\beta }_{2}Ln(EYS}_{it})+{{\beta }_{3}Ln(FOSSIL}_{it)}+{{\beta }_{4}Ln(HC}_{it})+{{\beta }_{5}Ln(MYS}_{it)}+{{\beta }_{6}Ln(REC}_{it})+{\in }_{it}$$

(1)

where $LnGDP$ is “logarithm of gross domestic product presenting economic growth measured as GDP per capita, PPP (constant 2017 international $)”, $LnCN$ is “logarithm of capital stock measured as capital stock at current PPPs (in mil. 2017US$)”, $LnEYS$ refers to “logarithm of expected years of schooling measured as the number of years of schooling a child is expected to receive”, $LnFOSSIL$ depicts “logarithm of fossil fuel energy measured as fossil fuel energy consumption (% of total)”, and $LnHC$ refers to the “logarithm of human capital measured as number of persons employed”. $LnMYS$ presents the “logarithm of mean years of schooling measured as geometric average of mean years of schooling (average number of years of education received by people aged 25 and older”, and $LnREC$ refers to the logarithm of renewable energy measured as “renewable energy consumption (% of total final energy consumption)”. The dual inclusion of Expected Years of Schooling (EYS) and Mean Years of Schooling (MYS) captures both the forward-looking and retrospective dimensions of educational attainment. EYS reflects a country’s investment in future human capital and the education system’s capacity to retain students, while MYS indicates the realized educational stock of the adult population. Employing both indicators mitigates the risk of omitting relevant information and allows for a more comprehensive analysis of how education—both as a flow and a stock variable—influences economic growth. Moreover, $\mathsf{\alpha }$ is intercept and ${\beta }_1$ to ${\beta }_6$ represents the coefficients of CN, EYS, FOSSIL, HC, MYS, and REC, respectively. However, I and t present the number of countries such as the 19 selected Sub-Saharan African countries “(Angola, Benin, Botswana, Cameroon, Congo, Ethiopia, Gabon, Kenya, Mauritius, Mozambique, Namibia, Niger, Nigeria, Senegal, South Africa, Sudan, Togo, Zambia, Zimbabwe)” selected on the basis of the availability of data. The data for the variable of the study range from 2000 to 2019 and have been extracted from World Bank, Penn World Table (PWT10.01), and UNDP-HDR sources.

Table 1. Data description.

Variables	Abbreviations	Measurement Units and Definitions	Sources
Economic Growth	GDP	“GDP per capita, PPP (constant 2017 international $). GDP per capita based on purchasing power parity (PPP). PPP GDP is gross domestic product converted to international dollars using purchasing power parity rates. An international dollar has the same purchasing power over GDP as the U.S. dollar has in the United States”. “GDP at purchaser’s prices is the sum of gross value added by all resident producers in the country plus any product taxes and minus any subsidies not included in the value of the products. It is calculated without making deductions for depreciation of fabricated assets or for depletion and degradation of natural resources”.	World Bank
Human Capital	HC	“Number of persons employed. A Labor stock data is adjusted by human capital index to deal with the heterogeneity of Labor productivity in relation to education across countries (Labor stock = Labor employed × human capital index). (Human capital index, based on years of schooling and returns to education”	Penn World Table (PWT10.01)
Capital Stock	CN	“Capital stock at current PPPs (in mil. 2017US$)”	Penn World Table (PWT10.01)
Fossil Fuel Energy	FOSSIL	“Fossil fuel energy consumption (% of total). Fossil fuel comprises coal, oil, petroleum, and natural gas products”.	World Bank
Renewable Energy	REC	“Renewable energy consumption (% of total final energy consumption). Renewable energy consumption is the share of renewable energy in total final energy consumption”.	World Bank
Expected years of schooling	EYS	“Expected years of schooling (the number of years of schooling a child is expected to receive)”.	UNDP-HDR
Mean years of schooling	MYS	“Geometric average of mean years of schooling (average number of years of education received by people aged 25 and older”.	UNDP-HDR

Source: Authors’ compilation.

below shows the summary of the data.

3.2. Model Estimations

First, we investigated the stability of variables by utilizing “Augmented Dickey–Fuller (ADF) and Residual Augmented Least Squares ADF (RALS-ADF) stationary tests, as recommended by [57]”. Additionally, the “Engle and Granger (EG) cointegration test” proposed by [58] and the “RALS-EG cointegration test” proposed by [23] are used to examine cointegration among study variables. The special advantages of the RALS cointegration approach that are not included in standard models led to its selection. First, unlike other tests addressed in the literature, the cointegration analysis based on the RALS approach takes into account the useful information included in non-normal errors. Second, when non-normality is present, the use of greater moment information increases the power of “RALS-based unit root tests and RALS-based cointegration tests” in comparison to more traditional techniques. Thirdly, in comparison to tests based on linear frameworks, nonlinear cointegration tests demonstrate diminished statistical power when faced with errors that do not follow a normal distribution. The “RALS estimator mitigates power loss by employing a linear model framework that relies on conventional least square estimation” when confronted with non-normal errors.

The Engle–Granger (EG) test was developed as a “two-step cointegration test based on the residual framework and standard t-statistics” proposed by [58]. The initial phase of the examination involves the computation of the stationary integration level, followed by the estimation of “Ordinary Least Squares (OLS) regression” in the subsequent step, provided that the variables were integrated of order one I (1). The following model provides a summary of this step as follows:

$$y_t={\partial Z}_t+{\cup }_t$$

(2)

The “Augmented Dickey–Fuller (ADF) unit root test” is performed on the residuals $\left({\widehat{\cup }}_t\right)$ that are acquired in order to determine the level of integration in the system.

$${∆\widehat{\cup }}_t={\partial }_0+{\partial }_1{\widehat{\cup }}_{t-1}+{\sum }_{i-1}^p{\partial }_{i+1}{\Delta \widehat{\cup }}_{t-1}+{\varnothing }_t$$

(3)

If the test equation errors follow a non-normal distribution, higher residual moments will suggest that the residuals themselves are non-normal. Ref. [59] used the RALS approach to leverage the “additional high-moment information available in nonnormal errors in linear model frameworks”. The RALS approach has the potential to provide conclusions that are more powerful, more reliable, as well as more resilient when the error term has a non-normal distribution. Ref. [23] employed the RALS methodology as a supplementary tool to augment the “EG cointegration test”. By merging the “second and third moments of the residuals obtained from conventional cointegration tests”, the method that has been provided offers an original concept. In order to carry out the RALS method, Equation (3) is supplemented by the following term

$${\widehat{\omega }}_t==\rho \left({\widehat{\cup }}_t\right)-\widehat{\in }-{\widehat{\cup }}_t{\widehat{\phi }}_t, \mathrm{t}=1, 2, 3, 4, 5....,T$$

where ${\widehat{\cup }}_t$ represents the residuals that are obtained from Equation (3) presented before.

$$\rho \left({\widehat{\cup }}_t\right)=[{\widehat{\cup }}_t^2, {\widehat{\cup }}_t^3], \widehat{\in }={\displaystyle \frac{1}{T}}{\sum }_{i=1}^T\rho {(\widehat{\cup }}_t), {\widehat{\phi }}_t={\displaystyle \frac{1}{T}}{\sum }_{i=1}^T\rho \prime {(\widehat{\cup }}_t)$$

Additionally, the following equation represents the “RALS term advanced by [60]”.

$${\widehat{\omega }}_t=\left[{\widehat{\cup }}_t^2-{\mathbb{m}}_2,{\widehat{ \cup }}_t^3-{\mathbb{m}}_3-{3\mathbb{m}}_2{\widehat{\cup }}_t\right]$$

(4)

where ${\mathbb{m}}_i$ = ${\mathrm{T}}^{-1}\sum _{i=1}^T{\widehat{\cup }}_t^j$. In addition, the RALS cointegration regression is shown in Equation (5) as shown below by including ${\widehat{\omega }}_t$ in Equation (3).

$${\mathsf{\Delta }\widehat{\cup }}_t={\partial }_1{\widehat{\cup }}_{t-1}+\sum _{i-1}^p{\partial }_{i+1}{\mathsf{\Delta }\widehat{\cup }}_{t-1}+{\widehat{\omega }}_t\pi +{\varnothing }_t$$

(5)

The traditional t-test is used to analyze the null hypothesis, which states that there is “No Cointegration among Examined Variables”, if ${\partial }_1$ = 0. In addition, in order to construct the “three different asymptotic distributions of t-statistics”, Equation (6) is applied.

$$t^{\ast }\to \rho .t+\sqrt{1}-{\rho }^2.Z$$

(6)

3.3. PMG-ARDL Model

In our study, we utilized the PMG-ARDL methodology as suggested by [61]. As with “panel dataset models with individual effects”, ARDL estimation cannot reduce bias due to the “connection between the white noise term and the mean differenced independent variables”. Consequently, an effective solution can be achieved by employing a combination of the “PMG estimator [62] and the ARDL model”. Mathematically, the PMG-ARDL model is present as under:

$${ly}_{it}={\phi }_i{ECT}_{it}+{\sum }_{j=0}^{q-1}{∆lX}_{it-j}{\mathsf{\gamma }}_{ij}+{\sum }_{j=1}^{p-1}{\delta }_{ij} \ast {∆ly}_{it-j}+{\epsilon }_{it}$$

(7)

$${ECT}_{it}=y_{it-1}-X_{it}\partial$$

(8)

In the above equations, y represents the regressed variable that, in the case of our study, is economic growth (GDP), X denotes the regressors in our study, which are human capital (HC), capital stock (CN), fossil fuel energy (FOSSIL), renewable energy (REC), “expected year of schooling (EYS), and mean years of schooling (MYS)”. Moreover, q refers to the number of lags for the cross-sectional units represented by i and t refers to the time period. Moreover, $\phi$ refers to the adjustment coefficient, $∆$ refers to the difference operator, $\partial$ refers to the long run coefficient that generates the $\mathsf{\gamma }$ and $\delta$ estimates after the convergence is reached, and $\epsilon$ denotes the white noise.

In addition, as a robustness check, this research study investigates the long-term stability nexus across quantiles by using the recently established “Quantile Autoregressive Distributive Lag (QARDL)” proposed by [63]. The QADRL model performs better than linear models for three different reasons. First, as indicated by [64,65,66,67], the model takes into account “locational asymmetry, findings and components may vary depending on the context of the dependent variable, in our case economic growth within its conditional distribution”. Second, the QARDL approach considers long-term nexus as our case of human capital, capital stock, fossil fuel energy, renewable energy, “expected years of schooling, mean years of schooling”, and economic growth. Third, the QARDL technique is preferable than linear approaches (ARDL) because it accommodates locational asymmetry and considers both long-term and short-term associations across quartiles of conditional distribution. In addition, it performs better than nonlinear methods such as NARDL [68], in which nonlinearity is determined exogenously since the threshold is set to zero rather than being selected via a data-driven process. Furthermore, it outperforms nonlinear methods such as NARDL [68]. Because of these factors, the QARDL is a strong candidate for modeling the nonlinear and asymmetric links that exist among the research aspects in a more detailed manner. The traditional ARDL approach, as presented by [69], is as follows:

$$\begin{array}{ll}{lnGDP}_{it}=& {\alpha }_0+\sum _{i=1}^p{\varnothing }_{it}{lnCN}_{it-1}+\sum _{i=0}^q{\omega }_{it}{lnEYS}_{it-1}+\sum _{i=0}^r{\lambda }_{it}ln{FOSSIL}_{it-1}+\sum _{i=0}^s{\mathsf{\gamma }}_{it}{lnHC}_{it-1}+\sum _{i=0}^t{\theta }_{it}ln{MYS}_{it-1}\\ & +\sum _{i=0}^u{\partial }_{it}{lnREC}_{it-1}+{\pi }_t\end{array}$$

(9)

where ${\pi }_t$ shows “error term” defined as ${GDP}_t-E$ [ ${\displaystyle \frac{{GDP}_{it}}{{\mathrm{\pounds }}_{it-1}}}$ ]. The ${\mathrm{\pounds }}_{it-1}$ is the lowest ϱ—field produced by [ ${GDP}_{it},{CN}_{it},{EYS}_{it},{FOSSIL}_{it},{HC}_{it},{MYS}_{it},{REC}_{it},\dots \dots ]$ and p, q, r, s, t, and u, are “lag orders presented by Bayesian information criteria”.

In addition, we changed the ARDL model Equation (9) into the QARDL model equation that is shown in the following equation, as proposed by [63].

$$\begin{array}{ll}{\mathcal{Q}\Delta GDP}_{it}=& \alpha (\tau )+\sum _{i=1}^p{\varnothing }_{it}(\tau ){GDP}_{it-1}+\sum _{i=0}^q{\omega }_{it}(\tau ){CN}_{it-1}+\sum _{i=0}^r{\lambda }_{it}{(\tau )EYS}_{it-1}+\sum _{i=0}^s{\gamma }_{it}{(\tau )FOSSIL}_{it-1}\\ & +\sum _{i=0}^t{\theta }_{it}{(\tau )HC}_{it-1}+\sum _{i=0}^u{\partial }_{it}{(\tau )MYS}_{it-1}+\sum _{i=0}^v{\vartheta }_{it}(\tau ){REC}_{it-1}+{\pi }_{it}(\tau )\end{array}$$

(10)

where ${\pi }_{it}(\tau )$ = ${GDP}_{it}-{\mathcal{Q}\Delta GDP}_t\left({\displaystyle \frac{\tau }{{ʆ}_{it-1}}}\right)$ is “error correction term defined and is the $\tau -th$ quantile as proved by of ${GDP}_t$ depending on the information set ${ʆ}_{t-1}$ and 0 > τ ˂ 1”. To exclude any possibility of a possible serial correlation, the QARDL estimate Equation (10) may be further explained as shown below.

$$\begin{array}{ll}{\mathcal{Q}\Delta GDP}_{it}=& \alpha \left(\tau \right)+{\rho GDP}_{it-1}+{\mathsf{\gamma }}_{cn}{CN}_{it-1}+{\mathsf{\gamma }}_{eys}{EYS}_{it-1}+{\mathsf{\gamma }}_{fossil}{FOSSIL}_{it-1}+{\mathsf{\gamma }}_{hc}{HC}_{it-1}+{\mathsf{\gamma }}_{mys}{MYS}_{it-1}+{\mathsf{\gamma }}_{rec}{REC}_{it-1}\\ & +\sum _{i=1}^p{\varnothing }_{it}(\tau ){GDP}_{it-1}+\sum _{i=0}^q{\omega }_{it}(\tau ){CN}_{it-1}+\sum _{i=0}^r{\lambda }_{it}{(\tau )EYS}_{it-1}+\sum _{i=0}^s{\mathsf{\gamma }}_{it}{(\tau )FOSSIL}_{it-1}+\sum _{i=0}^t{\theta }_{it}{(\tau )HC}_{it-1}\\ & +\sum _{i=0}^u{\partial }_{it}{(\tau )MYS}_{it-1}+\sum _{i=0}^v{\vartheta }_{it}(\tau ){REC}_{it-1}+{\pi }_{it}(\tau )\end{array}$$

(11)

In addition to this, Ref. [63] states that the QARDL estimation Equation (11) may be rewritten in ECM form as follows:

$$\begin{array}{ll}{\mathcal{Q}\Delta GDP}_{it}=& \alpha \left(\tau \right)+{\rho (\tau )GDP}_{it-1}+{\beta }_{cn}\left(\tau \right){CN}_{it-1}+{\beta }_{eys}\left(\tau \right){EYS}_{it-1}+{\beta }_{fossil}\left(\tau \right){FOSSIL}_{it-1}+{\beta }_{hc}{HC}_{it-1}+{\beta }_{mys}{MYS}_{it-1}\\ & +{\beta }_{rec}{REC}_{it-1}\\ & +\sum _{i=1}^p{\varnothing }_{it}(\tau ){GDP}_{it-1}+\sum _{i=0}^q{\omega }_{it}(\tau ){CN}_{it-1}+\sum _{i=0}^r{\lambda }_{it}{(\tau )EYS}_{it-1}+\sum _{i=0}^s{\mathsf{\gamma }}_{it}{(\tau )FOSSIL}_{it-1}\\ & +\sum _{i=0}^t{\theta }_{it}{(\tau )HC}_{it-1}+\sum _{i=0}^u{\partial }_{it}{(\tau )MYS}_{it-1}+\sum _{i=0}^v{\vartheta }_{it}(\tau ){REC}_{it-1}+{\pi }_{it}(\tau )\end{array}$$

(12)

The long-term cointegration of previous $CN$, EYS, FOSSIL, HC, MYS, and REC parameters is determined by beta (β) and employed by following formula as ${\beta }_{{co2}^{\ast }}$ = −${\displaystyle \frac{{\rm Y}CN}{\rho }}$, ${\beta }_{{fdi}^{\ast }}$ = −${\displaystyle \frac{{\rm Y}EYS}{\rho }}$, ${\beta }_{{rem}^{\ast }}$ = −${\displaystyle \frac{{\rm Y}FOSSIL}{\rho }}$, ${\beta }_{{inf}^{\ast }}$ = −${\displaystyle \frac{{\rm Y}HC}{\rho }}$, ${\beta }_{{gfcf}^{\ast }}$ = −${\displaystyle \frac{{\rm Y}MYS}{\rho }}$, and ${\beta }_{{tr}^{\ast }}$ = −${\displaystyle \frac{{\rm Y}REC}{\rho }}$, respectively. Where is the variable that represents the parameter for altering the speed, which must be substantial and negative. Additionally, this research study employs the “Shapiro–Wilk normality test” to assess the normality of data.

In this study, the selection of econometric models—RALS cointegration, PMG-ARDL, and QARDL—is motivated by their distinct methodological strengths and their alignment with the characteristics of the data and research objectives.

The Residual Augmented Least Squares (RALS) cointegration technique, developed by [23], offers enhanced statistical power by incorporating higher-order moment conditions from non-normal error distributions. Unlike traditional cointegration methods, RALS is particularly robust when normality assumptions are violated—an issue common in macroeconomic panel data involving heterogeneous countries. By leveraging additional information from the skewness and kurtosis of residuals, RALS improves efficiency in estimating long-run relationships, especially in the presence of structural breaks or outliers. This makes it especially suitable for Sub-Saharan African countries where data irregularities may be prevalent.

The Pooled Mean Group–Autoregressive Distributed Lag (PMG-ARDL) estimator, originally proposed by [62], is employed to estimate both short-run dynamics and long-run equilibrium relationships in panel data settings. The model allows short-run coefficients, adjustment dynamics, and error variances to vary across cross-sectional units, while constraining the long-run coefficients to be homogeneous. This is particularly appropriate for the 19 Sub-Saharan African countries under study, which may differ in short-term policy implementation or economic shocks but share similar long-term structural characteristics. Additionally, the PMG-ARDL approach is adept at handling variables integrated in mixed orders (I(0) and I(1)), reducing the risk of model misspecification.

To complement the PMG-ARDL analysis and provide robustness across the conditional distribution of the dependent variable, we also employ the Quantile Autoregressive Distributed Lag (QARDL) model introduced by [63]. Unlike linear ARDL models that estimate average effects, QARDL captures heterogeneous effects of regressors at different quantiles of the outcome variable—in this case, economic growth. This is crucial for understanding asymmetric relationships, especially when policy impacts differ for countries at varying growth levels. Moreover, the QARDL model allows for long-run and short-run dynamics to differ across quantiles, offering a more nuanced interpretation of how renewable energy, education, and human capital affect countries at lower versus higher performance levels. This approach outperforms traditional nonlinear models like NARDL by using a data-driven quantile structure instead of arbitrarily chosen thresholds.

Overall, the integration of RALS, PMG-ARDL, and QARDL estimators ensures methodological rigor, mitigates potential estimation biases, and provides a multifaceted understanding of the dynamic interplay between energy, education, and economic growth across diverse Sub-Saharan countries.

4. Results

The correlation heatmap (Figure 1) reveals that GDP has a strong positive relationship with fossil fuel usage (0.77) and human capital (0.64), while it is negatively correlated with renewable energy usage (−0.69). This suggests that higher economic output is currently associated with greater reliance on fossil fuels and human capital, rather than renewable energy. Fossil fuel and renewable energy use are strongly inversely related (−0.77), indicating a trade-off between the two. Education variables, such as mean and expected years of schooling, show weak negative correlations with GDP and other factors, suggesting limited direct influence in this dataset. Overall, the data highlights a traditional energy–growth dependency and a potential gap between educational investment and immediate economic or environmental outcomes.

We conducted the “ADF and RALS-ADF unit root test” to assess the stationarity of the variables. The outcomes presented in

Table 2. Unit root test results.

Variables	ADF	RALS-ADF	${\mathsf{\rho }}^2$
GDP	0.61	−2.98	0.87
CN	−2.25	−5.12 ***	0.68
HC	0.99	1.5	0.64
EYS	−0.74	−2.35	0.47
MYS	−2.87 *	−3.61 **	0.91
FOSSIL	−0.25	−1.81	0.8
REC	−2.93 *	−7.29 ***	0.96
∆GDP	−3.87 ***	−8.05 ***	0.82
∆HC	−2.63 *	−3.35 **	0.87
∆EYS	−3.16 **	−17.1 ***	0.74
∆FOSSIL	−3.04 **	−3.43 **	0.72

Note: ***, **, and * indicate significance at 1%, 5%, and 10%, respectively. The 1%, 5%, and 10% critical values for the ADF are −3.58, −2.93, and −2.60, respectively. The 1%, 5%, and 10% critical values for the RALS-ADF are −3.75, −3.30, and −3.05, respectively.

show that MYS and REC are stationary at the level; however GDP, CN, HC, EYS, and FOSSIL are stationary at the first difference. Moreover, RALS-ADF estimates indicate that CN, MYS, and REC are stationary at the level; however, GDP, EYS, FOSSIL, and HC are stationary at the first difference. Additionally, we assess the normality in the dataset by utilizing Shapiro–Wilk test. The estimates of Shapiro–Wilk test suggest that p-values of all facets (GDP, HC, CN, MYS, EYS, FOSSIL, and REC) are less than 0.1. This reveals that the null hypothesis of existence of normality in the data is rejected. Furthermore, it can be observed from Figure 2 that the graphical distribution of all the variables under investigation deviates from the expected theoretical distribution. Hence, The RALS-EG cointegration test is considered to be a more effective method for identifying cointegration relationships between variables, particularly in situations where nonstationary is present. Moreover, the QARDL is the best estimator to predict long-run estimations.

In addition to that, the estimations of the “EG and RALS-EG cointegration test” are presented in

Table 3. RALS cointegration test results.

Methods	K	Test Statistics	${\mathsf{\rho }}^2$
EG	0	−5.11 ***	−
RALS-EG	0	−4.53 **	0.98

Note: *** and ** indicate the significance at 1% and 5% respectively; K shows the optimum lag length found using recursive statistics; the 1% and 5% critical values for the EG test are −5.02 and −4.32 respectively; the 1% and 5%critical values for the RALS-EG test are −4.80 and −4.19, respectively.

. The estimation of the EG estimator for the cointegration test is −5.11, which is less than critical threshold (5.02) at the 1% significance level. Therefore, it discloses that the null hypotheses suggesting the absence of cointegration are rejected. Furthermore, the RALS-EG test statistic result is −4.53, which, at a 5% level of significance, is less than the crucial value of (−4.19) and thus disproves the null hypothesis. In conclusion, the findings of the “EG and RALS-EG test” provide empirical support for the presence of a cointegration relationship among GDP, HC, CN, EYS, MYS, FOSSIL, and REC.

Moreover, the type and scale of the short–long-run relations among economic growth, human capital, capital stock, renewable energy, estimated years of schooling, mean years of schooling, fossil fuel energy, and renewable energy are estimated by the PMG-ARDL econometric model. The PMG-ARDL estimator’s estimations are presented in

Table 4. PMG-ARDL results (Dependent variable: LOG(GDP)).

Variable	Coefficient	Std. Error	t-Statistic	Prob.
Long-run Coefficients
LOG(CN)	0.22	0.12	1.83	0.04 **
LOG(EYS)	0.04	0.01	6.13	0.00 ***
LOG(FOSSIL)	0.22	0.06	3.78	0.00 ***
LOG(HC)	1.59	0.19	8.44	0.00 ***
LOG(MYS)	0.02	0.01	2.57	0.01 **
LOG(REC)	0.53	0.12	4.48	0.00 ***
C	7.95	0.74	10.80	0.00 ***
Short-run Coefficients
ECM (−1)	−0.09	0.03	−3.06	0.00 ***
DLOG(FOSSIL)	0.06	0.04	1.68	0.07 *
DLOG(HC)	1.25	0.67	1.87	0.06 *

Note: ***, **, and * indicate the significance at 1%, 5%, and 10% respectively.

. The statistical significance of the error correction term (ECT) is observed to be at a significance level of 1% for all estimation results. This finding suggests that there is a significant speed of adjustment in correcting the long-term balance, as presented in Table 4.

The PMG-ARDL estimates produce that coefficient (1.59) of human capital is positive and significant with economic growth at 1% level of significance in the long run. However, the coefficient (1.25) of human capital is positive and significant with economic growth at 10% level of significance in the short run. Particularly, a 1% increase in human capital boosts economic growth by 1.59% and 1.25%, respectively, in the case of the 19 selected Sub-Saharan African countries. It has been observed from the outcomes that the scale of effect of human capital on economic growth is more in the long run as compared to the short run. Our empirical findings reveal that human capital significantly enhances economic growth, with its impact more pronounced over the long term. This suggests that the accumulation of human capital through improved educational systems and labor market readiness yields compounded benefits that manifest more clearly over extended periods. Such dynamics align with the endogenous growth theory, which emphasizes sustained investment in education and skill development as fundamental to long-run productivity gains.

Moreover, the PMG-ARDL estimator evidenced that the coefficient (0.22) of capital stock is positive and significant with economic growth at 5% level of significance in the long run. Particularly, a 1% increase in the capital stock lifts the economic growth by 0.22% in the case of the 19 selected Sub-Saharan African countries. Furthermore, the findings showed that the coefficient (0.22) of fossil fuel energy is positive and significant, with economic growth at 1% level of significance in the long run. However, in the case of the short run, the PMG-ARDL estimator showed that coefficient (0.06) of fossil fuel energy is positive and significant with economic growth at 10% level of significance. Particularly, a 1% increase in the capital stock lifts economic growth by 0.22% and 0.06% in the long and short run, respectively, in case of the 19 selected Sub-Saharan African countries. It has been demonstrated that the magnitude of the effect of fossil fuel energy consumption on economic growth is greater in the long run as compared to the short run. Likewise, the study found that coefficient (0.53) of renewable energy consumption is positive and significant with economic growth at 1% level of significance in the long run. Particularly, a 1% increase of the capital stock lifts the economic growth by 0.53% in the case of the 19 selected Sub-Saharan African countries.

Furthermore, the outcomes of PMG-ARDL show that the coefficient of expected years of schooling (0.04) and mean years of schooling (0.02) are positive and significant with economic growth in long run, in case of the 19 selected Sub-Saharan African countries. It is evidenced that a 1% rise in the expected years of schooling and mean years of schooling accelerate economic growth by 0.04% and 0.02%, respectively. Moreover, it has been revealed that a boost in economic growth, in terms of magnitude, is greater with expected years of schooling as compared to mean years of schooling.

The outcomes of the normality estimator are presented in

Table 5. Shapiro–Wilk normality test.

Variables	W	p-Values
GDP	0.96	4.36 × 10−9
HC	0.96	2.28 × 10−9
CN	0.92	5.17 × 10−13
FOSSIL	0.95	2.05 × 10−9
REC	0.76	2.20 × 10−16
MYS	0.68	2.20 × 10−16
EYS	0.66	2.20 × 10−16

.

Robustness Test Estimations

We utilized the QARDL estimator to check the robustness of outcomes obtained from the PMG-ARDL estimator. The QARDL estimates are shown in

Table 6. Results of the Quantile Autoregressive Distributed Lag (QARDL).

$\mathbf{Q}\mathbf{u}\mathbf{a}\mathbf{n}\mathbf{t}\mathbf{i}\mathbf{l}\mathbf{e}\left(\mathsf{\tau }\right)$	${\mathsf{\alpha }}_0\left(\mathsf{\tau }\right)$	$\mathsf{\pi }\left(\mathsf{\tau }\right){\mathit{G}\mathit{D}\mathit{P}}_{\mathit{i}}$	${\mathsf{\gamma }}_{\mathit{i}1}\left(\mathsf{\tau }\right)\mathit{H}\mathit{C}$	${\mathsf{\gamma }}_{\mathit{i}2}\left(\mathsf{\tau }\right)\mathit{C}\mathit{N}$	${\mathsf{\gamma }}_{\mathit{i}3}\left(\mathsf{\tau }\right)\mathbf{F}\mathit{O}\mathit{S}\mathit{S}\mathit{I}\mathit{L}$	${\mathsf{\gamma }}_{\mathit{i}4}\left(\mathsf{\tau }\right)\mathbf{R}\mathit{E}\mathit{C}$	${\mathsf{\gamma }}_{\mathit{i}5}\left(\mathsf{\tau }\right)\mathit{M}\mathit{Y}\mathit{S}$	${\mathsf{\gamma }}_{\mathit{i}6}\left(\mathsf{\tau }\right)\mathbf{E}\mathit{Y}\mathit{S}$
0.05	0.01 *	0.99 *	0.71 *	0.05 *	0.14 *	0.02 *	0.01 *	0.01 *
0.2	0.01 *	0.99 *	0.61 *	0.04 *	0.12 *	0.04 *	0.01 *	0.01 *
0.4	0.01 *	1.00 *	0.68 *	0.03 *	0.08 *	0.05 *	0.01 *	0.01 *
0.6	0.02 *	1.00 *	0.67 *	0.01 *	0.06 *	0.03 *	0.01 *	0.01 *
0.8	0.03 *	1.00 *	0.65 *	0.03 *	0.04 *	0.02 *	0.02 *	0.01 *
0.95	0.02 *	0.98 *	0.53 *	0.06 *	0.06 *	0.03 *	0.01 *	0.01 *

Source: Authors’ estimation. * Represents 5% significance level.

. All quintiles exhibit significantly positive long-term $\mathsf{\pi }$ economic coefficient values. This observation demonstrates that the current state of economic growth in the selected countries is primarily determined by the historical levels of economic growth experienced by all quintiles. Moreover, long-run coefficients of ${\mathsf{\gamma }}_{\mathit{i}1}\left(\mathsf{\tau }\right)\mathit{H}\mathit{C}$, ${\mathsf{\gamma }}_{\mathit{i}2}\left(\mathsf{\tau }\right)\mathit{C}\mathit{N}$, ${\mathsf{\gamma }}_{\mathit{i}3}\left(\mathsf{\tau }\right)\mathbf{F}\mathit{O}\mathit{S}\mathit{S}\mathit{I}\mathit{L}$, ${\mathsf{\gamma }}_{\mathit{i}4}\left(\mathsf{\tau }\right)\mathbf{R}\mathit{E}\mathit{C},{\mathsf{\gamma }}_{\mathit{i}5}\left(\mathsf{\tau }\right)\mathit{M}\mathit{Y}\mathit{S}$, and ${\mathsf{\gamma }}_{\mathit{i}6}\left(\mathsf{\tau }\right)\mathbf{E}\mathit{Y}\mathit{S}$ across all quantiles are positive and significant. Therefore, estimations of the QARDL support and validate the estimations derived by PMG-ARDL by witnessing the positive and significant link of human capital, capital stock, fossil fuel energy consumption, renewable energy consumption, years of schooling, and mean years of schooling with economic growth in the case of the 19 selected Sub-Saharan African countries. It is interesting to point out the fossil fuel energy consumption throughout the quantile is decreasing, thus suggesting the 19 selected Sub-Saharan African countries are reducing the dependence on fossil fuel energy consumption and diverting the direction of energy demand to the clean energy to meet the desired objective climate change committed in the Paris agreement.

5. Discussion

The findings indicate that human capital plays a crucial role in driving economic growth, with its influence becoming increasingly evident over longer time horizons. It suggests that human capital is more beneficial in the long run as compared to the short run. The outcomes of our study are in line with the previous literature such as [16,37,38,40,41,42,43,45,46,47,48,50]. Therefore, it is evident that human capital has emerged as a crucial element in the development process within some of the 19 selected Sub-Saharan African countries. It is evident that the presence of human capital, which encompasses the combined skills, knowledge, and innovative capabilities of individuals, plays a significant role in the production process and subsequently contributes to economic growth. In addition to the production process, the presence of skilled individuals plays a crucial role in driving economic growth. These individuals contribute to the effective utilization of human capacity, thereby functioning as valuable human capital within the growth equation [44]. Moreover, the involvement of human capital in the economic process can be observed through its role as a productive factor in production, as well as its function as a crucial catalyst for the introduction, dissemination, and adoption of technological innovations in the studied countries. However, it is important to note that while economic growth can contribute to the deterioration of environmental quality, human capital can play a significant role in mitigating these negative effects on the environment. Our outcomes support the prevailing theory of human capital, according to which, the expansion of human capacities contributes to the generation of economic value, which subsequently leads to increased labor productivity and, consequently, higher rates of economic growth.

Moreover, the results evidenced that capital stock is positive and significant with economic growth in the long run. The outcomes of the study are in line with the previous literature such as [9,31,52,53,54,55,56,70]. The findings of our study indicate that a comprehensive analysis of the economic development in the 19 selected Sub-Saharan African countries necessitates a thorough comprehension of the role played by capital stock in driving economic progress. According to [54], the capital stock generally impacts the procurement of a novel manufacturing facility, as well as machinery, equipment, and all forms of productive capital assets. The role of capital stock in economic growth is of significant importance. The notion of a deliberate and strategic approach to player engagement has consistently been regarded as a prevailing perspective in the 19 selected Sub-Saharan African countries. Moreover, the augmentation of capital is indicative of the adoption of advanced technology, while the establishment of infrastructure facilitates the attainment of sustainable economic growth. Therefore, in order to attain sustainable economic growth, it is imperative for future policymakers to formulate and implement effective policies within the 19 selected Sub-Saharan African countries.

Also, the results showed that fossil fuel energy has a positive and significant effect on economic growth. The outcomes of our study are in line with the previous literature such as [3,6,14,26,27,28,71]. This finding indicates that the unrestricted utilization of fossil fuels serves as a catalyst for economic expansion. The correlation between fossil fuel production and economic performance in some of the 19 selected Sub-Saharan African countries provide additional evidence supporting the notion of energy dependency. Moreover, on the flip side, the utilization of fossil fuels energy produces pollutants in the environment such as greenhouse gases, which harm the environmental quality. Under the Paris agreement, the world must take major initiatives to reduce dependence on fossil fuels to keep the environment green and clean. Hence, based on the evidence, the 19 selected Sub-Saharan African countries must use alternative sources of the energy such as clean and green energy to produce sustainable and green economic growth.

Likewise, renewable energy consumption is positive and significant with economic growth. The outcomes of our study are in line with the previous literature such as [6,9,11,25,29,30,31,32,72]. The utilization of renewable energy sources is advantageous for fostering economic growth and mitigating the release of carbon dioxide (CO₂) emissions, thereby ensuring sustainable development in the long run. Moreover, according to [26], renewable energy sources have the potential to generate economic advantages while simultaneously attaining a state of zero carbon emissions. This suggests that renewable energy sources are of significant importance in the process of transitioning to a more sustainable energy system, and it is imperative to actively promote these sources of energy in the case of the selected countries in this study. Therefore, it is imperative for the selected countries to establish a comprehensive national and regional policy that encompasses the adoption and development of renewable energy (REC). The legislative body of the different governments in the region has the authority to implement measures aimed at creating a comprehensive renewable energy (REC) policy framework that effectively tackles the current obstacles hindering the widespread adoption of renewable energy. Policies may encompass various measures, such as incentives and the creation of a conducive environment, aimed at promoting the robust development of renewable energy (REC) technologies and their associated components at the local level. Overall, in order to promote the efficient utilization and widespread acceptance of renewable energy (REC), policymakers in the studied countries are required to implement a range of strategic measures.

The negative and statistically significant relationship between renewable energy consumption and economic growth observed in the long run may be attributed to several underlying mechanisms. First, the integration of renewable energy technologies reduces dependency on imported fossil fuels, thereby improving energy security and stabilizing input costs for industries. This, in turn, enhances firm-level competitiveness and investment potential. Second, renewable energy deployment often necessitates infrastructure development and stimulates domestic innovation ecosystems, particularly in areas such as grid modernization, battery storage, and clean technology manufacturing. These dynamics generate employment, promote technological spillovers, and lead to the creation of new economic sectors, altogether fostering economic expansion.

Similarly, the observed significance of both expected and mean years of schooling as determinants of economic growth highlights the multifaceted contribution of human capital to development processes. Beyond the accumulation of formal educational years, these indicators capture the broader enhancement of cognitive and productive capacities within the labor force. This development of human capital translates into improved labor productivity, facilitating technological adoption, innovation, and, ultimately, sustained economic expansion. On another level, education serves as a foundation for innovation and technological assimilation; better-educated populations are more likely to adopt, adapt, and create new technologies, which in turn propels productivity and economic diversification. Importantly, the study’s findings challenge the previously held notion that only education quality matters; rather, it indicates that increasing access and overall duration of schooling is also vital in generating long-term growth dividends, particularly in developing regions.

Finally, this study shows that expected years of schooling and mean years of schooling are positive and significant to economic growth. The outcomes of our study are in line with existing studies such as [21,22,73,74,75,76]. Hence, the findings of the studies indicate that increasing both the duration and average level of education will enhance the caliber of the workforce. This, in turn, will lead to the development of advanced skills, foster creativity, and facilitate the assimilation of crucial technologies that are essential for economic progress in the countries examined in the selected studies. In addition to this, the outcome of this study rejects the notion of Hanushek and Woessmann’s statistical analysis [17], that states “schooling quality, not quantity, affects economic growth or increases in the quality rather than the quantity of schooling are what contribute to economic growth”.

6. Conclusions and Policy Recommendation

This study estimated the role of fossil fuel energy, renewable energy, human capital, capital stock, expected years of schooling, and mean years of schooling in economic growth across the 19 Sub-Saharan African countries. The time span of the study ranges from 2000 to 2019. We have used the latest and updated methodologies such as RALS unit root and cointegration estimators to estimate the stationary and long-term links among the antecedents, respectively. Moreover, to estimate the long- and short-term coefficient values of facets in our case fossil fuel energy, renewable energy, human capital, capital stock, years of schooling, and mean years of schooling, this study employed PMG-ARDL and QARDL estimators.

The estimations of the PMG-ARDL and QARDL witnessed the positive link between fossil fuel energy consumption, renewable energy consumption, human capital, capital stock, years of schooling, and mean years of schooling. The PMG-ARDL estimates reveal the magnitude of renewable energy effect is greater than fossil fuel energy. Therefore, suggesting that fossil fuel used by the selected Sub-Saharan African countries enhances their economic growth, but it harms the environmental quality. Hence, to tackle the environmental effects of fossil fuel, to obtain the desired sustainable economic development, and to meet the sustainable development goals (SDGs) the Sub-Saharan African countries are in an energy transection process as they are shifting their demand of energy consumption from fossil fuels to renewable and clean energy. While fossil fuel consumption contributes to short-term economic gains, it simultaneously deteriorates environmental quality through greenhouse gas emissions and pollutant discharge. In contrast, renewable energy not only delivers long-term growth but also significantly curtails carbon emissions, promotes cleaner air, and reduces reliance on depleting and geopolitically sensitive fossil fuel reserves. Embracing renewables enables Sub-Saharan African countries to pursue a development pathway that harmonizes economic and environmental priorities, supporting global climate objectives while securing sustainable domestic prosperity. Moreover, human capital boosts the productivity of the studied countries, because transformed human capital, in terms skills, innovative capabilities, and knowledge occupies a substantial part in the production process to accelerate the economy. Additionally, the relationship between capital stock and economic growth in Sub-Saharan countries is statistically significant, indicating that the acquisition of a new factory, machinery, equipment, and other productive capital goods plays a role in this relationship. Moreover, substantial effect of years of schooling and mean years of schooling on economic growth presented by the estimators rejects the “Hanushek and Woessmann’s statistical analysis HW’s hypothesis that schooling quality, not quantity, affects economic growth” [17]. Hence, the outcomes suggest that, along with quality, the quantity of schooling affects economic growth in the countries examined in this study.

Our findings suggest the potential for interaction effects between education and energy variables. For instance, education may facilitate the adoption of renewable technologies by improving labor force competencies, while access to reliable and clean energy supports educational infrastructure and student outcomes. Thus, rather than treating education and energy in isolation, policymakers should recognize the mutual reinforcement between these domains when designing long-term growth strategies.

Based on the estimations of the estimators of this study, we have proposed and suggested the following policy recommendations and implementation.

• Sub-Saharan African countries should accelerate the transition process of energy from fossil fuels to renewable energy to meet the sustainable economic development as fossil fuel energy is environmental unfriendly. In order to achieve this, the Sub-Saharan countries in question have to establish high-tech parks, which serve as platforms for manufacturers to produce their own supplies and machinery. This approach will enhance the management of investment expenses, consequently leading to a reduction in the overall costs associated with renewable energy. Moreover, as the energy business has significant investment costs, banks are required to invest less in fossil fuels and more in climate mitigation to provide financing and tax incentives for renewable energy. Renewable energy must be risk-free to boost economic development.
• Furthermore, it is imperative to ensure the availability of a wide range of invested capital for the continuous support of renewable energy generation endeavors. In order to fully benefit from renewable energy sources, a substantial financial commitment is required. Furthermore, the involvement of the private sector is of utmost importance in the initiation of environmentally sustainable investment initiatives. In order to engage the private sector in green investment endeavors, it is imperative to provide accessible green financing options that are specifically tailored to the needs of potential investors, as opposed to offering generic credit opportunities.
• It is advisable to engage in the study of countries in order to facilitate the reform of prevailing education policies and ensure their effective and efficient implementation, monitoring, and control. This is because the reform of education will not only enhance the rate of enrollment in secondary education but also improve the quality of education. Consequently, this will undeniably augment the impact of education on the economic growth rate within the nation. Future research endeavors can draw valuable insights from the policy implications.

Our study is limited to the 19 selected Sub-Saharan African countries due to the unavailability of data. Researchers can study the existing model of study in all Sub-Saharan African countries if they access the data. Moreover, this research model can be investigated in individual countries or other groups of countries such as OECD countries, N-11, BRICS, and low-, middle-, and high-income countries, etc. Furthermore, the model of our study can be expanded and amended by the introduction of other antecedents such as technological innovation, financial development, banking sector development, and green finance by using other robust methodologies.