The Impact of the Renewable Energy Transition on Economic Growth in BRICS Nations

Abstract

The BRICS countries have been increasingly prioritizing electricity transition as a crucial step towards achieving sustainable growth, energy security, and mitigating climate change. As major emerging economies, the BRICS nations will play a significant role in the global energy landscape since their transition to renewable energy sources holds a significant implication for global energy markets and environmental sustainability. This study investigates the impact of the renewable energy transition on economic growth in BRICS nations from 1990 to 2023, employing a panel NARDL, DOLS, and FMOLS models. This study investigates the relationship between disaggregated renewable energy sources and economic growth. The findings show that renewable energy’s impact on economic growth varies across countries and depends on the type of renewable energy source. Specifically, hydropower, and wind power are found to have significant positive impacts on economic growth in some BRICS countries, while other renewables and trade openness have insignificant impacts. To foster economic growth and the expansion of renewable energy, it is essential for policymakers to focus on investments in hydropower and wind energy. Furthermore, they should encourage trade liberalization, as well as nuclear power development, and enhance regional collaboration. This study offers significant contributions to the current body of literature on the renewable energy–economic growth nexus, supplying crucial insights for both policymakers and researchers.

1. Introduction

The world is shifting towards a low-carbon economy, driven by climate change concerns and the need for sustainable development and economic growth. The BRICS nations, made up of Brazil, Russia, India, China, and South Africa, are at the forefront of transitioning to renewable energy and low-carbon energy sources, given their significant contribution to energy consumption and greenhouse emissions globally. As these emerging economies continue to grow, their energy demands are likely to increase, making them crucial for mitigating climate change and promoting sustainable economic growth. Recent studies have highlighted the economic benefits of the renewable energy transition, including a reduced reliance on fossil fuels, job creation, and enhanced energy security. Nonetheless, the effect of transitioning to renewable energy on economic growth within the BRICS nations continues to be a widely discussed issue. This study examines the impact of the renewable energy transition on economic growth in BRICS nations by disaggregating renewable energy sources, providing valuable insights for policymakers and stakeholders seeking to promote sustainable development and mitigate climate change.

Renewable energy refers to energy derived from naturally replenishing resources such as wind, water, and sunlight. The importance of this research stems from its role in enlightening the complex relationship between the adoption of renewable energy and economic advancement within the BRICS context. As key emerging markets and major contributors to global greenhouse gas emissions, BRICS countries have a pivotal influence on the global energy framework and combatting climate change. By examining how the transition to renewable energy affects economic progression in these nations, this study offers valuable insights for practitioners, policymakers, and researchers aiming to advance sustainable development, bolster energy security, and maintain ecological balance. The study’s outcomes can guide evidence-driven policymaking, aiding BRICS nations in tackling the complexities and advantages of transitioning to renewable energy and in attaining their sustainable development objectives.

Studies such as [1,2] did not discover a persistent connection between renewable energy and economic growth in BRICS countries, necessitating the need for further research. This study is conducted at a crucial time when signatory countries of the Paris Agreement are expected to improve efforts on combating climate change. According to [3], while there has been a decrease in greenhouse gases recently, achieving a two-degrees-Celsius reduction in global temperatures by 2030 will still be a significant challenge. This research seeks to enhance the current body of knowledge by offering fresh perspectives on how shifting towards renewable energy sources can impact sustainable economic growth differently in both the short and long terms, as well as limiting climate change.

The renewable energy industry also contributes to reducing the amount of greenhouse gas emissions, which contributes to global warming; thus, climate change impacts are reduced. Renewables show considerable strength in achieving mostly regional economic development objectives in developed and developing countries. Studies such as [4] enlighten readers with the realization that energy policies are poorly understood for climate change, even though many countries are transitioning to renewable power. Therefore, it is important to extend the discussion to other scholars who have found inconsistent results concerning the potential that alternative sources of electricity generation possess in fostering economic growth. This is particularly important, given that international and national policies support the energy transition through incentives to rely on renewable energy sources in power generation.

A capital- and technologically intensive sector, it is acknowledged as being able to influence the key parameters of macroeconomic issues. Strongly dependent on weather variables and presenting a low-level energy density, renewable energy cannot secure a continuous and renewed provision of electricity to the economy. Refs. [5,6,7,8,9] support the notion that renewable energy consumption positively contributes to economic growth. Investors are drawn to explore site-specific renewable energy niche opportunities such as wind, solar, geothermal, and hydropower. Varying levels of electricity supply highlight the need to ensure that power consumption is aligned with the generation capacity of every energy source. The positive relationship between renewable energy and economic growth is considered evidence of the renewable energy transition and economic growth, as it suggests that an increasing reliance on renewable energy sources can contribute to economic growth by creating new industries, jobs, and technological advancements.

Ref. [10] emphasizes the need for a specific investigation of each renewable energy source on economic growth and cross-country analysis of future studies to promote sustainable economic growth. This research builds upon the idea by disaggregating the sources of renewable power to explore which specific types are advantageous for economic growth within the BRICS countries [11], emphasizing the necessity of more advanced econometric models in future analyses of the renewable energy–economic growth nexus.

According to Figure 1 above, China had the highest GDP growth of any of the BRICS countries for the past two decades. However, India overtook it in the mid-2010s, and India is predicted to achieve the highest growth in the current 2020s decade. Furthermore, all five countries experienced a decline in their GDP growth during 2008’s global financial crisis and again during the coronavirus pandemic in 2020. China was the only economy that continued to grow during both crises, although India’s economy grew during the Great Recession. In 2014, [12] further explains, Brazil experienced its recession due to a combination of economic and political instability, while Russia also went into a recession due to the drop in oil prices and the economic sanctions imposed following its annexation of Crimea. As Figure 1 above shows, there is a problem of low economic growth in the BRICS nations, as evidenced by the economic growth of less than 5% for Brazil, Russia, India, and China since 2020. This might have been prompted by the impact of the COVID-19 pandemic, which had halted economic activity, including energy generation, prompting the need to fast-track the implementation of economic growth to ensure a stable electricity supply. According to [13], electricity is the backbone of any economy; therefore, it is crucial to secure stable generation and a stable supply to achieve economic growth.

This research is significant, as it takes place when these BRICS nations are required to adhere to the Paris Agreement to cut down emissions and promote sustainable development. Secondly, it contributes to the literature by providing new evidence from the five BRICS countries and focusing on which source of renewable power is beneficial for economic growth in BRICS nations on a disaggregated approach, as compared to the studies of [14,15,16,17,18] that did not do so in their study, filling the gap in the literature. The justification for disaggregating renewable energy and countries is to see which source contributes positively to economic growth in each BRICS country, so that policy formulation is based on empirical evidence.

Current studies often combine various renewable energy sources, thereby neglecting the distinct effects that individual sources like solar, wind, hydro, and others have on the economic growth of BRICS nations. To understand the complexities of the renewable energy transition, this study differentiates itself from the studies of [14,15,16,17,18] through its contribution through a comparative study of the five BRICS countries and the panel approach of PNARDL to investigate whether the results are the same in short and long-run periods and reliable for policy formulation for the study. Lastly, this research will significantly contribute to policy on the renewable energy transition and economic growth in BRICS nations based on empirical results obtained from the model with the ultimate goal of moving to renewables for electricity grid stability, minimizing load reduction, reducing electricity prizes, and spearheading the transition towards decarbonization of power sector while mitigating the negative effects of climate change.

While numerous studies explore the renewable energy–economic growth nexus, this research addresses unanswered questions regarding the most economically beneficial renewable energy source for each of the BRICS countries. Is there a sustained correlation between renewable energy and economic growth in the long term? Do symmetrical or asymmetrical relationships exist between renewable energy and economic growth in both the short and long terms? Do renewable energy’s impacts on economic growth in the BRICS nations remain consistent between short-term and long-term periods? Which source of disaggregated renewable energy contributes the most to economic growth in the BRICS countries? What are the potential policy impacts of the shift to renewable energy on the economic development of BRICS countries? The main goal of this research is to illuminate the renewable energy source that has the biggest impact on economic growth in BRICS countries. This study will guide policy choices regarding investments in renewable energy, offer an understanding of the economic advantages of certain renewable energy sources, and help in creating optimized blends of renewable energy. Disaggregating renewable energy is carried out through panel data analysis for the five BRICS nations from 1990 to 2023. The reason for selecting this timeframe is based on the scarce data available from 1990 to 2023, especially for countries like Russia. The remaining part of this research is organized in the following manner: Section 2 presents the literature, followed by the materials and methods in Section 3. Section 4 provides results, followed by a discussion in Section 5 and a conclusion in Section 6.

2. Literature Review

With the purpose of analyzing the interlinkages of energy balance and clean energy transitions on economic growth and environmental sustainability from 1990 to 2016 for Switzerland, Sweden, and Denmark, ref. [19] employed GLS, GLMM, and PCSE models and found that the trilemma energy balance, the clean energy transition, and natural resource depletion enhance economic growth, while clean energy discourages growth. Based on empirical evidence, the authors recommend reconsidering clean energy as a way of achieving the United Nations goals of energy security while enhancing economic growth and environmental sustainability. Furthermore, ref. [20] investigated whether an energy transition promotes decoupling economic growth from emissions growth in 186 countries using the decoupling index model and decomposition approach from 1990 to 2014. The study’s findings revealed that the energy transition had positively contributed to economic growth in higher-income countries but failed in middle- and lower-income countries. Based on empirical evidence, the study recommends that middle-income and lower-income countries accelerate their energy transition as a way of achieving economic growth.

Ref. [21] highlights the growing demand for green technologies such as solar panels, wind turbines, electric vehicles, and energy storage as an approach that will lead to economic growth through the energy transition. Based on the author’s findings, an energy transition negates economic growth in the short run while boosting long-run growth. Moreover, ref. [22] investigated the properties of the energy transition and clean production on China’s economic growth. The authors’ findings demonstrate that, currently, the economic growth of China is driven by fossil fuels; however, after 2045, clean energy will drive China’s economic growth. These findings will help policymakers better understand high-speed economic development in China’s energy system transition, balancing environmental protection, climate change, and the energy supply.

Ref. [23] examined the role of the energy transition from traditional non-renewables to modern renewable energy and of differential rates of innovation in the use of each of these in Sweden’s economic growth from 1850 to 1950. The econometric results reveal that, after 1890, modern energy contributed much more to economic growth than traditional energy. Simultaneously, increasing labor-augmenting technological change became the most important single driver of growth. Ref. [24] also explored the changing interplay between energy transitions, energy consumption, and sustainable economic growth among 38 IEA countries from 1995 to 2015, utilizing the AMG and CCE-MG methodologies. The findings suggest an inverse relationship between the energy transition and economic growth. However, factors such as economic sustainability, renewable energy use, non-renewable energy consumption, labor, and capital are positively associated with economic growth. The authors recommend that policymakers in IEA member states be encouraged to implement carbon pricing and taxes, continue backing research and development, and devise green trade policies to advance sustainable development.

Ref. [6] examined the impact of economic complexity on the relationship between the energy transition and economic growth across 124 countries, utilizing the weighted least squares estimation method from 2000 to 2020. The results reveal that the energy transition negatively affects economic growth, suggesting that policymakers should recognize the complex dynamics tied to shifting towards renewable energy sources and take into account the impact of economic complexity on these results. Ref. [25] analyzed the scenarios of energy transition and their economic outcomes utilizing the expanded neoclassical economic growth model. The findings from business as usual (BAU) and the sustainability strategy (SUS) indicate that, at present, the energy transition negatively impacts economic growth. Ref. [26] investigated the persistence of the energy transition changes on economic growth by incorporating the Energy Transition Policies in an augmented Solow Growth Model on a panel of 80 countries from 2000 to 2021. Using the GMM and Correia’s fixed-effects estimator, the findings show that the energy transition benefits developing economies due to primary energy demand, while developed countries face decreasing marginal returns of renewable energy investments. The study guides policymakers regarding adequate policies for the transition toward low-carbon economies while maintaining economic development and social justice for climate change.

Additionally, ref. [8] investigated the impact of nuclear energy on economic growth and carbon emissions in 24 nations by utilizing PFMOLS and the Heterogeneous D-H causality test from 2001 to 2020. The results indicate that both nuclear and renewable energy promote economic growth, suggesting that countries bolster renewable energy supply chains to hasten the energy transition across multiple sectors and thus supporting economic expansion and sustainable development. Ref. [27] examines the impact of relying on conventional energy sources on the energy transition and economic growth in 20 Sub-Saharan African nations, utilizing the Dynamic Common-Correlated Effects (DCCE) model from 2000 to 2017. The results indicate that incorporating more renewable energy sources into the energy portfolio does not necessarily support economic growth. The study advises that, although it is important to expand clean energy technologies, establishing an environment that allows for a seamless transition to clean energy is crucial to achieving the most economical growth.

Aiming to explore the link between renewable energy and economic growth, ref. [28] applied Granger causality and ARDL models. The study discovered that renewable energy enhances economic growth in China, and there is a bidirectional relationship between these variables. Employing an NARDL model on Pakistani data from 1970 to 2018, ref. [29] concluded that both increases and decreases in renewable energy significantly contribute to economic growth. On the other hand, an analysis using ARDL and Toda-Yamamoto Granger causality models in Romania, covering data from 1990 to 2014, demonstrated a one-way positive impact from renewable energy consumption on economic growth, leading [30] to suggest fostering renewable energy expansion. Similarly, investigations using ARDL and Granger causality models in Tunisia with data from 1990 to 2015 led [31] to recommend a shift towards renewable energy, as it was shown to stimulate economic growth and improve environmental protection.

Additionally, in Pakistan, ref. [32], utilizing the NARDL model on data ranging from 1990 to 2016, found that both positive and negative shifts in renewable and nuclear energy stimulate economic growth, suggesting an expansion of renewable energy for environmental sustainability. Similarly, ref. [33], employing the ARDL model on data from 1972 to 2018, concluded that renewable energy consumption drives economic growth in Pakistan and thus advised increased investment in renewable energy to achieve sustainable economic growth. Conversely, ref. [34] observed that a reduction in renewable energy enhances economic growth in Malaysia, as shown using the NARDL model on data from 1980 to 2018, and advocated for a comprehensive strategy for renewable energy development to impact economic growth. Moreover, according to [16], renewable energy promotes economic expansion in China, India, Russia, and Brazil but remains neutral for South Africa, as evidenced by the D-H causality model applied to data spanning from 1990 to 2017. Furthermore, based on a bootstrap panel causality model utilizing data from 1992 to 2013, ref. [15] recommends that BRICS nations enhance their biomass energy consumption to support environmental sustainability, foster economic growth, and lessen energy reliance.

Ref. [35] determined that, in BRICS nations, renewable energy promotes economic growth through the application of AMG and Quantile GMM models on data spanning from 1995 to 2019. Conversely, research by [36] indicated that renewable energy did not enhance economic growth in the BRICS countries based on their analysis of data from 1996 to 2015, though this might change in the future. Additionally, ref. [37] demonstrated that renewable energy contributes to economic growth across 29 European countries via DOLS and FMOLS models using data from 1995 to 2016, and the authors advocated for policies that bolster renewable energy to support sustainable economic advancement. Through the application of the ARDL model on data spanning from 2007 to 2016, ref. [38] observed that, in 25 European countries, economic growth is propelled by renewable energy, non-renewable energy, labor, and gross fixed capital formation. In another study, ref. [39] employed 2SLS, 3SLS, and GMM models on data from 1991 to 2012, finding that renewable energy contributed to economic growth in certain countries among the 17 developed and developing ones analyzed, but not in others. Additionally, ref. [40] applied OLS, DOLS, and FMOLS models on data from 1991 to 2012, concluding that renewable energy facilitates economic growth among a set of 38 leading renewable energy-consuming countries and supporting the notion of increased investment in renewable energy.

In their study, ref. [41] utilized DOLS, FMOLS, and D-H models across nine Black Sea and Balkan nations with data ranging from 1990 to 2012, concluding that renewable energy, capital, and labor contribute to economic growth, and they suggest implementing remittance policies to enhance investments in renewable energy technologies. Similarly, ref. [42] applied the ARDL model and an asymmetrical causality test to data from 1990 to 2009 for European countries, finding that renewable energy stimulates economic growth and suggesting that policies influencing renewable energy will causally impact economic advancement. Meanwhile, ref. [43] employed FMOLS, DOLS, and D-H causality models on data covering 1990 to 2014 in South Asian countries, identifying that renewable energy, non-renewable energy, and capital accelerate economic growth. Ref. [44] applied FMOLS, VECM, and Granger causality models to data spanning from 2000 to 2015 across 31 Chinese provinces, discovering a stable long-term relationship between economic growth, foreign direct investment, and renewable energy consumption. Ref. [36] used an OLS fixed-effects model on a panel consisting of 34 OECD countries, finding that capital, renewable energy, and labor contribute to economic growth, and thus, the authors recommended expanding renewable energy to promote sustainable economic growth and environmental benefits.

Ref. [45] applied FMOLS, DOLS, and Granger causality models to data from 1980 to 2012 across 11 MENO Oil Importing Countries, discovering that economic growth is stimulated using renewable energy, labor, capital, and non-renewable energy. They suggest that governments should implement a comprehensive strategy focused on the efficient utilization of renewable energy technologies for sustainable progress. Ref. [46] employed DOLS, FMOLS, and D-H causality models in 38 countries that consume renewable energy, using data from 1990 to 2018. Their findings indicated that renewable energy, non-renewable energy, labor, and capital contribute to economic growth, and they recommend enhancing investments in renewable energy technologies to ensure a sustainable environment and economic advancement. Furthermore, ref. [9] conducted an analysis on the Next-11 economies using the quantile method of moments with data spanning from 1990 to 2020, revealing that factors such as renewable energy, trade openness, gross national expenditure, and industry value added contributed to economic expansion. Likewise, ref. [47] reported that renewable energy fosters economic advancement in European nations, employing a time-varying fixed-effects model with data from 1970 to 2019. In the context of the BRICS countries, ref. [48] concluded that renewable energy promoted economic growth by applying FMOLS and Granger causality models on data from 1992 to 2014, suggesting a focus on renewable energy development for sustainable economic progress.

Analyzing data from 1990 to 2014 for 15 leading countries in renewable energy consumption, ref. [49] used the FMOLS and VECM Granger causality models and discovered that both renewable and non-renewable energy positively impact economic growth, suggesting a diversified energy policy approach. Meanwhile, ref. [50] applied a local linear dummy variable estimation method to data from 1990 to 2015 for both OECD and non-OECD countries, finding that renewable energy enhances economic growth, and suggested that developing nations could significantly influence the power sector’s transition. Moreover, ref. [51] analyzed data from 17 emerging countries spanning 1990 to 2016, utilizing the bootstrap panel causality model, and determined a neutral impact of renewable energy on economic growth. They suggest a comprehensive approach to policy development related to renewable energy. In an analysis covering BRICS countries from 1990 to 2014 employing fixed-effect panel quantile regression and D-H causality models, ref. [14] identified that renewable energy use diminishes economic growth, recommending greater energy consumption to bolster economic growth. Furthermore, ref. [17] found bidirectional causality between renewable energy and economic growth in BRICS using FMOLS and DOLS models, advocating for the widespread adoption of renewable energy to achieve both sustainable environmental and economic growth.

Ref. [7] analyzed data from 2002 to 2018 for 104 countries through a multi-threshold regression model and discovered that renewable energy enhances economic growth, advising a varied strategy for renewable energy policies across these nations. Additionally, ref. [52], employing a panel threshold model with data spanning 1997 to 2015 in 34 OECD countries, determined that renewable energy promotes economic growth, but beyond a certain limit, it hampers economic growth. Meanwhile, ref. [31] utilized an MS-VAR model and observed a unidirectional causality from economic growth to renewable energy, indicating an inverse relationship. Ref. [53] analyzed data from 1985 to 2018 across seven European nations and found no evidence of Granger causality from renewable energy consumption to economic growth, underscoring the significance of non-renewable energy prices and economic growth in the transition towards renewable energy. Ref. [54], using dynamic seemingly unrelated regression, PCSE, and FGLS models on data spanning 1995 to 2015 from 15 energy-importing countries, concluded that non-renewable and renewable energies, alongside capital and trade openness, enhance economic growth, suggesting increased investment in renewable energy technologies to achieve sustainable economic progress.

Recent research has shown that renewable energy contributes to economic growth, but a gap persists in the literature, as these studies often do not break down individual renewable sources to identify which ones most significantly impact the economic growth of BRICS countries. Moreover, many analyses either target a single nation or groups of developed countries, creating a gap in comparative research of the renewable energy transition’s effect on economic growth across all BRICS nations while examining individual renewable sources. Additionally, most studies, like [14,15,16,17,48], emphasize linear models such as FMOLS, DOLS, and ARDL, yet there is a paucity of research exploring nonlinear models, highlighting a methodological deficiency in investigating potential nonlinear relationships between renewable energy and economic growth in BRICS countries.

This research aims to fill existing literature gaps by utilizing a panel nonlinear autoregressive distributed lag model, as proposed by [55], to evaluate the influence of disaggregated renewable energy sources on the economic growth of BRICS countries. In addition, it applies both the DOLS and FMOLS models to validate the robustness of the PNARDL model outcomes. Unlike prior studies that assessed the impact of collective renewable energy sources on economic growth, this research focuses on individual energy sources, offering new insights into which source most significantly drives economic growth in BRICS nations. The empirical results will aid in shaping renewable energy policies, economic growth strategies, and climate change initiatives. Furthermore, the research underlines contributions to Sustainable Development Goals number 7 (affordable and clean energy), number 8 (decent work and economic growth), and number 13 (climate action), reinforcing global efforts towards renewable energy transition and clarifying its economic advantages. By undertaking a country-specific comparative analysis, this study will disclose the diverse effects of each renewable energy source on the economic growth across BRICS nations.

3. Materials and Methods

3.1. Research Design and Data Collection

This research employs a quantitative framework, gathering data from well-regarded secondary statistical sources online, including the World Bank and the Oxford-backed Our World in Data, as illustrated in

Table 1. Data collection and sources.

Variable	Description	Unit	Source
LEG	Annual growth rate of GDP per capita	%	The World Bank
Wind	Generation of electricity using wind energy	Terawatt-hours	Oxford’s Our World in Data
Nuclear	Production of electricity through nuclear energy	Terawatt-hours	Oxford’s Our World in Data
Hydro	Hydropower electricity production	Terawatt-hours	Oxford’s Our World in Data
Other-RE	Generation of electricity from alternative renewable energy sources	Terawatt-hours	Oxford’s Our World in Data
LK	Capital	Percentage of the gross domestic product (GDP)	The World Bank
LTO	Trade openness	Percentage of the gross domestic product (GDP)	The World Bank

Source: current authors’ compilation.

below. The dataset comprises information for the five BRICS nations, Brazil, Russia, India, China, and South Africa, covering the period from 1990 to 2023. The analysis is conducted using the econometric software EViews 10 and Stata 18.

In accordance with Table 1 above, the definitions of variables and prior research utilizing these variables are detailed below. Dependent variable: LEG signifies the annual growth rate of gross domestic product per capita, serving as an indicator of economic growth. The annual change in GDP per capita is calculated using local currencies and is divided by the midyear population. This variable was employed as a dependent variable in the research of [1,7,15,16,17,29,33,35,40,52].

Independent variables: “Wind” denotes the energy derived from wind, quantified in terawatt-hours (TWh) of total electricity output from wind energy. “Hydro” indicates hydropower, similarly, measured in TWh of electricity, derived from hydropower sources. “Nuclear” signifies energy generated from nuclear power, also gauged in TWh of total nuclear-derived electricity. “Other-RE” refers to a variety of renewable energy sources beyond the usual, such as bioenergy, with their electrical output measured in terawatt-hours (TWh). “LK” denotes the gross fixed capital formation, which involves investments in infrastructure improvements, including land development, acquisition of plants, machinery, equipment, and the construction of infrastructures like roads, railways, schools, offices, hospitals, private residences, and commercial, as well as industrial buildings. This aspect has been discussed in the literature [17,35,50]. Concurrently, “LTO” indicates trade openness, quantified as the total exports and imports of goods and services relative to the GDP. This parameter was addressed in research studies [8,9,35].

3.2. Methodology

3.2.1. Theory and Model

The commonly used neoclassical production function provides the theoretical justification for evaluating the variables in this investigation. The study’s neoclassical growth theory describes how labor, capital, and technology interact to produce a steady economic growth rate. Refs. [56,57] created and presented the long-run growth model. To calculate the rate of growth, the model first considers an external population increase; however, ref. [56] introduced technical developments into the model. According to the idea, modifying the amounts of capital and labor in the production process results in a temporary balance. Consequently, the following is a specification of the neoclassical growth theory’s production function:

$$Y = AF\left(K,L\right)$$

(1)

where A stands for the decisive degree of technology, K for the percentage of capital, L for the quantity of unskilled labor, and Y for the gross domestic product of an economy. According to this theory, economic growth depends on ongoing technical breakthroughs, and technological progress has a substantial influence on the economy, as noted by [58]. However, the short-term equilibrium is different from the long-term equilibrium, which is independent of these three variables, according to the neoclassical growth theory. According to this theory, economic growth is largely determined by how capital is accumulated and used within an economy, according to [59]. Furthermore, the relationship between labor and capital determines an economy’s production. Ultimately, ref. [60] argue that technology has the potential to increase worker productivity and production capability. Studies by [40,41] have employed the neoclassical production function; however, it was altered to accomplish the objective of the study, which was to disaggregate renewable energy sources to see their impact on economic growth in BRICS countries. Thus, the following equation specifies the empirical model based on the studies that comprise the empirical literature of this study:

$${LEG}_t = f\left({Wind}_{1t},{Hydro}_{2t},{Nuclear}_{3t},{Other-RE}_{4t},{LK}_{5t},{LTO}_{6t}\right)$$

(2)

where ${LK}_{5t}$ is capital, ${Other-RE}_{4t}$ refers to alternative renewable energy sources as biomass, ${Wind}_{1t}$ refers to wind power, ${Hydro}_{2t}$ refers to hydropower, ${LTO}_{6t}$ refers to trade openness, and ${LEG}_t$ annual increase in per capita product as an indicator of economic expansion.

3.2.2. Panel Unit Root Test

Additionally, to confirm that the variables lack a unit root, the study also conducted the [61,62] second-generation panel unit root tests. The [62] unit root test evaluates a model that incorporates individual effects without a time trend, involving a variable observed across N countries and T time periods. The LLC test investigates a model where the coefficient of the lagged dependent variable is restricted to be consistent across all panel units, as detailed further below:

$$∆y_{i,t}={\alpha }_i+\rho y_{i,t-1}+\sum _{z=1}^{{\rho }_i}{\beta }_{iz}∆y_{i,t-z}+{\epsilon }_{i,t}$$

(3)

For $i$ = 1,….,$N$ and $t$ = 1,…$T$. The errors are independent and identically distributed random variables with finite variance on a normal distribution. The null hypothesis of the unit root is given as follows: $H_0:p = 0$ against the alternate hypothesis $H_1:\rho = {\rho }_i<0$ for all $i = 1,\dots ,N$, with auxiliary assumptions about the individual effects (${\alpha }_i = 0 for all i = 1,\dots ,N under H_0)$. The study of [61] modifies the assumption of I(1) autoregressive coefficients, allowing variation in the alternative hypothesis. It employs the Fisher-ADF and Fisher-PP tests, utilizing two combined p-value statistics. The null hypothesis posits the presence of a unit root. The ADF-Fisher and ADF-Choi equations are specified as follows:

$$ADF-Fisher x^2 = -2\sum _{i = 1}^{N}log\left({\rho }_i\right)⟶x^2\left(2N\right)$$

(4)

$$ADF-Choi Z={\displaystyle \frac{1}{\sqrt{N}}}\sum _{i=1}^N{\varnothing }^{-1}\left({\rho }_i\right)\to N\left(\mathrm{0,1}\right)$$

(5)

where ${\varnothing }^{-1}$ represents the reciprocal of the cumulative function of the standard normal distribution. If the probability value of the computed statistic is less than the probability value at any level of significance (1%, 5%, and 10%), the null hypothesis is rejected in favor of the alternative hypothesis, implying that there is no unit in the variable.

3.2.3. Co-Integration Test

The research will conduct co-integration tests to assess whether long-term relationships exist among the variables. Take into account the following panel regression model:

$$y_{it} = x_{it}^{,}\beta +z_{it}^{,}\gamma +e_{it}$$

(6)

where $y_{it}$ and $x_{it}$ are I(1) and non-cointegrated. For $z_{it} = \left\{{\mu }_{it}\right\}$, ref. [63] proposed Dickey–Fuller (DF) and Augmented Dickey–Fuller (ADF) type unit root tests for $e_{it}$ as a test for the null of no cointegration. The DF and ADF types can be calculated from the fixed residuals as follows:

$${\widehat{e}}_{it}=\rho {\widehat{e}}_{it-1}+v_{it}$$

(7)

$${\widehat{e}}_{it}=\rho {\widehat{e}}_{it-1}+\sum _{j=1}^p{\vartheta }_j∆{\widehat{e}}_{it-j}+v_{itp}$$

(8)

where ${\widehat{e}}_{it} = {\tilde{y}}_{it}-{\tilde{x}}_{it}\widehat{\beta }$ and ${\tilde{y}}_{it} = y_{it}-{\overline{y}}_i.$ To test for the null hypothesis of no cointegration, the null hypothesis can be specified as follows:

$$H_0:\rho = 1$$

(9)

If the likelihood value of the calculated statistic falls below the significance thresholds (1%, 5%, and 10%), then we reject the null hypothesis in favor of the alternative hypothesis, indicating the presence of co-integration among the variables. Additionally, the study will employ the [64,65] test to examine the absence of co-integration within a panel data model that accounts for considerable heterogeneity. The initial examination involves calculating the mean of co-integration test statistics derived from time series data across several cross-sections. The alternative approach involves averaging segments, resulting in limiting distributions that depend on the limits of the numerator and denominator terms taken in pairs. The first category of statistics incorporates an average form of the [66] statistic, as shown below:

$${\tilde{Z}}_{\rho } = \sum _{i = 1}^N{\displaystyle \frac{{\sum }_{t = 1}^T({\widehat{e}}_{it-1}∆{\widehat{e}}_{it}-{\stackrel{`}{⋋}}_i)}{\left({\sum }_{t = 1}^T{\widehat{e}}_{it-1}^2\right)}}$$

(10)

When the p-value of the computed statistic is less than the significance levels (1%, 5%, or 10%), we reject the null hypothesis in favor of the alternative, suggesting that the variables are co-integrated. Furthermore, the research will perform [67], assuming the null hypothesis of co-integration, which allows for various structural breaks in both the level and trend within the panels that are co-integrated. This test is broad enough to include endogenous regressors, account for serial correlation, and handle an indeterminate number of breaks with timings that can differ across various cross-sections. Considering the multidimensional time-series variable $y_{it}$ which is observable for $i = 1,\dots \dots ,N$ cross-sectional and $t = 1,\dots ,T$ time-series observations. The following equations are specified for the data-generating process:

$$y_{it} = z_{it}^{,}{\gamma }_{ij}+x_{it}^{,}{\beta }_i+e_{it}$$

(11)

$$e_{it} =r_{it}+u_{it}$$

(12)

$$r_{it}=r_{it-1}+{\varphi }_i{u}_{it}$$

(13)

where $x_{it} = x_{it-1}+v_{it}$ is a regressor vector with k-dimensions and $z_{it}$ it is a vector of deterministic components. The hypothesis asserting that all individuals within the panel are co-integrated can be expressed as follows:

$$H_0:{\varphi }_i = 0 for all i = 1,\dots ,N$$

(14)

When the p-value of the computed statistic falls below the threshold at any significance level (1%, 5%, or 10%), the null hypothesis is discarded. This suggests the existence of heterogeneous co-integration among the variables, supporting the alternative hypothesis.

3.2.4. Panel Estimation Techniques and Robustness Checks

The research will employ the PNARDL model from [55] to conduct a short-term comparative analysis across BRICS nations and a long-term homogeneity assessment of the segmented transition to renewable energy concerning economic growth. Consequently, the nonlinear panel autoregressive distributed lags model is defined in the following manner:

$$∆Y_{it}={\theta }_i{ECT}_{it}+\sum _{j=1}^{p-1}{\lambda }_{ij}^{*}\mathsf{\Delta }{Y}_{i,t-j}+\sum _{j=0}^{q-1}({\delta }_{ij}^{*+}\mathsf{\Delta }{\mathsf{{\rm X}}}_{i,t-j}^{+}+{\delta }_{ij}^{*-}\mathsf{\Delta }{\mathsf{{\rm X}}}_{i,t-j}^{-})+{\mu }_i+{\epsilon }_{it}$$

(15)

where $Y_{it}$ is the dependent variable, $X_{it}$ shows the $(k\times 1)$ vector of explanatory variables that are decomposed into positive and negative partial sums, as given below:

$$X^{+} = {\sum }_{j = 1}^t\Delta X_{j = 1}^{+}{max}_j^{+}\left(\Delta X_j,0\right)$$

(16)

$$X^{-}={\sum }_{j=1}^t\Delta X_{j=1}^{-}{min}_j^{-}\left(\Delta X_j,0\right)$$

(17)

${ECT}_{it}={\varphi }_i{Y}_{i,t-1}-({\beta }_i^{\prime +}{X}_{i,t}^{+}+{\beta }_i^{\prime -}{X}_{i,t}^{-})$ is the error correction term that captures long-term equilibrium, ${\theta }_i$ it is the coefficient of the error correction term that quantifies how long it takes the system to converge to its long-run equilibrium in the presence of a shock. ${\mu }_i$ shows the fixed effects, ${\lambda }_{ij}^{*}$ represents the coefficient of the lagged dependent variable, ${\delta }_{ij}^{*+}$ and ${\delta }_{ij}^{*-}$ represents $(k \times 1)$ coefficient vectors of independent variables for positive and negative shocks, $t(\mathrm{1,2},\dots ,T)$ is the period, $i(\mathrm{1,2},\dots ,N)$ represents the number of cross-sections, and ${\epsilon }_{it}$ represents the stochastic error term. The study aims to use heterogeneity to conduct comparative analysis of which renewable energy sources contribute most to economic growth in each BRICS nation. Long-run homogeneity will help determine whether short-term findings align with long-term outcomes, supporting the study’s objectives. The reason for selecting the PNARDL model is its ability to estimate nonlinear relationships between renewable energy and economic growth. This model can also assess asymmetrical relationships, which is crucial as the impact of renewable energy on economic growth may differ in the short and long term. Additionally, the PNARDL model is well suited for panel data structures, as it analyzes data from various BRICS countries over time. It estimates co-integration and corrects for short-run dynamics, offering flexibility and robustness in handling diverse data types and relationships, making it ideal for this study.

This study will implement a fully modified ordinary least squares (FMOLS) method, as proposed by [66], in conjunction with a dynamic ordinary least squares (DOLS) framework outlined by [68], to evaluate the robust relationships among the variables. FMOLS offers improved estimates for cointegrating regressions by adjusting the least squares approach to tackle serial correlation and the endogeneity of regressors resulting from co-integration. This approach is particularly valuable for dealing with unit roots and cointegrating relationships, providing a standard limit theory for stationary coefficients and a combination of normal distributions for nonstationary coefficients. Conversely, DOLS aids in estimating co-integration vectors and allows for testing the presence of seasonal co-integration, showcasing its usefulness in scenarios with varying frequencies of seasonal co-integration. DOLS has several benefits, such as resilience to endogeneity, and it removes the necessity of instruments like two-stage least squares or instrumental variable regression by incorporating leads and lags of first difference exogenous regressors to manage autocorrelation. The selection of the number of leads and lags does not have a theoretical basis. DOLS is applicable to both small and large samples, and it can be used with nonstationary variables that may be co-integrated. DOLS can also be employed if regressors comprise a mixture of I(0) and I(1). Therefore, the model employed in this research is defined as follows, according to [66]:

$$Y_t = \alpha +\beta X_t+{\sum }_{j = -q}^{j = r}\delta ∆X_{t-j}+{\epsilon }_t$$

(18)

For all $i = 1,\dots ,N$ and $t = \mathrm{1,2},3,\dots ,T$ under, the assumption that adding q lags and r leads of the differenced regressors soaks up all the long-run correlation between the error terms. Consider the FMOLS estimator for the coefficient of $\beta$ of the model:

$${\beta }_{NT}^{*}-\beta = \left(\sum _{i = 1}^N{L}_{22i}^{-2}\sum _{i = 1}^T(x_{it}-{\overline{x}}_{it}{)}^2)\right)\sum _{i = 1}^N{L}_{11i}^{-1}{L}_{22i}^{-1}\left(\sum _{i = 1}^T\left(x_{it}-{\overline{x}}_{it}\right){\mu }_{it}^{*}-T{\widehat{\gamma }}_i\right)$$

(19)

where ${\mu }_{it}^{\mathrm{*}}={\mu }_{it}-{\displaystyle \frac{{\widehat{L}}_{21i}}{{\widehat{L}}_{22i}}}\mathsf{\Delta }{x}_{it},{\widehat{y}}_i={\widehat{\mathsf{\Gamma }}}_{21i}{\widehat{\mathsf{\Omega }}}_{21i}^0-{\displaystyle \frac{{\widehat{L}}_{21i}}{{\widehat{L}}_{22i}}}\left({\widehat{\Gamma }}_{22i}-{\widehat{\Omega }}_{22i}^0\right)$ and ${\widehat{\mathsf{\Gamma }}}_i$ it is a lower triangulation of ${\widehat{\mathsf{\Omega }}}_i$.

3.2.5. Residual Diagnostics Test

The influence of cross-sectional dependence in estimation is contingent upon numerous elements, like the size of the correlations between cross-sections and the characteristics of the cross-sectional dependence itself. A cross-sectional test of residuals from the study will apply the Lagrange multiplier (LM) statistic, as proposed by [69], which remains valid when N is fixed and T approaches infinity, outlined as follows:

$$LM = T\sum _{i = 1}^{N-1}\sum _{j = i+1}^N{\widehat{\rho }}_{ij}^2$$

(20)

Ref. [70] introduced a test for cross-section dependence (CD), which is widely utilized to determine whether the residuals for cross-section i at time t are correlated. According to [70], when N is substantial, whether homogeneous or heterogeneous, the subsequent equation should be applied:

$$CD = \sqrt{{\displaystyle \frac{2T}{N(N-1)}}}\left(\sum _{i = 1}^{N-1}\sum _{j = i+1}^N{\widehat{p}}_{ij}\right)$$

(21)

Moreover, under the null hypothesis that there is no cross-sectional dependence, the CD test follows a normal distribution with a mean of zero and a variance of one, given that both N and T approach infinity. Ref. [71] introduced a non-parametric test utilizing Spearman’s rank correlation coefficient, described as follows:

$$R_{AVE} = {\displaystyle \frac{2}{N(N-1)}}\sum _{i = 1}^{N-1}\sum _{j = i+1}^N{\widehat{r}}_{ij}$$

(22)

Refs. [72,73] introduced a statistic formulated on the aggregation of squared rank correlation coefficients, expressed as follows:

$$R_{AVE}^2 = {\displaystyle \frac{2}{N(N-1)}}\sum _{i = 1}^{N-1}\sum _{j = i+1}^N{\widehat{r}}_{ij}^2$$

(23)

When the p-value of the computed statistics is less than the p-value at any significant level (1%, 5%, or 10%), the null hypothesis is dismissed, indicating cross-sectional dependence in the residuals.

4. Results

According to the data in

Table 2. Descriptive and statistical analysis.

	LEG	Hydro	Nuclear	Wind	Other-RE	LK	LTO
Mean	3.0292	246.91	64.030	36.582	15.719	24.456	41.146
Median	3.0080	168.04	15.705	0.4850	1.8775	21.036	42.100
Max	13.636	1321.7	434.72	885.87	198.13	45.129	110.58
Min	−14.614	0.1460	0.0000	0.0000	0.0000	13.184	15.156
Std. Dev	4.6659	292.60	88.597	119.32	31.316	8.7539	14.568
Skewness	−0.6177	2.2517	2.0267	4.9866	3.4693	0.8725	0.5079
Kurtosis	4.0867	7.9073	7.1904	29.887	17.177	2.6071	4.6544
J-B Stat	19.175	314.24	240.76	5825.0	1764.6	22.661	26.694
p-value	0.0001	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
Observ.	170	170	170	170	170	170	170

Source: Authors’ computations.

below, only economic growth is adversely skewed; other variables, such as hydro, nuclear, wind, other-RE, capital, and trade openness, are positively skewed. Nonetheless, as the summary of descriptive statistics with the Jarque–Bera statistics indicates, the kurtosis indicates that the data may not have a normal distribution since it is leptokurtic. However, as the study considers that normality should apply to the residuals from the estimated model rather than the variables themselves, this does not endanger the study. The correlation analysis is still being conducted by the study, as shown in

Table 3. Correlation analysis.

Correlation	LEG	Hydro	Nuclear	Wind	Other-RE	LK	LTO
LEG	1.000
Hydro	0.241	1.000
Nuclear	0.053	0.636	1.000
Wind	0.130	0.788	0.701	1.000
Other-RE	0.104	0.825	0.577	0.931	1.000
LK	0.536	0.636	0.367	0.505	0.448	1.000
LTO	0.019	−0.130	0.252	−0.048	−0.158	0.044	1.000

Source: Authors’ computation.

below.

The study’s correlation analysis, presented in Table 3 above, indicates that hydro, nuclear, wind, other renewable energy, capital, and trade openness all display a positive correlation with economic growth. With correlation statistics for BRICS showing values below 0.8, a weaker linear relationship between these explanatory variables and economic growth is suggested, thus justifying the use of the nonlinear PNARDL model. To determine the integration order of the variables and avoid spurious regressions, unit root tests are continuously utilized, as depicted in

Table 4. Panel unit root test.

Variables	Levin, Lin, and Chu Unit Root Test				Im, Pesaran, and Shin Unit Root Test
	Without Trend		Trend and Intercept		Without Trend		Trend & Intercept
	Level	$∆$	Level	$∆$	Level	$∆$	Level	$∆$
LEG	−2.8640 ***	−9.5682 ***	−2.7146 ***	−8.2841 ***	−3.6071 ***	−10.518 ***	−2.7695 ***	−9.3702 ***
Hydro	0.4292	−4.5178 ***	−0.8534	−2.9088 ***	0.7062	−6.9276 ***	−1.0209	−5.4398 ***
Nuclear	2.1077	−4.0070 ***	0.2893	−4.0261 ***	2.5167	−5.3379 ***	0.6894	−4.4948 ***
Wind	8.3324	−2.1116 **	4.4288	−4.5499 ***	5.9681	−2.7221 ***	3.8523	−4.3699 ***
Other-RE	3.1213	−2.0437 **	1.9072	−3.1804 ***	3.9831	−3.2840 ***	2.3913	−2.9065 ***
LK	−1.0980	−4.9381 ***	−0.8207	−3.5438 ***	−1.4383 *	−5.6491 ***	−1.1458	−4.2130 ***
LTO	−1.5660 *	−13.328 ***	−1.7636 **	−11.832 ***	−1.7369 **	−11.220	−3.3941 ***	−10.138 ***

Source: current authors’ computation; ***, **, and *, significance at 1%, 5%, and 10% respectively.

below.

To avoid spurious regression and determine the integration order of variables, the study utilized the Levin–Lin–Chu and Im–Pesaran–Shin second-generation panel unit root tests to evaluate the model’s suitability for this analysis. According to Table 4 above, economic growth is found to be integrated at I(0), whereas variables such as hydro, nuclear, wind, other renewable energy sources, capital, and trade openness are integrated at I(1). These results justify the application of the nonlinear PNARDL model in this research to gauge the effects of transitioning to renewable energy on economic growth in BRICS nations using distinct renewable energy sources. As indicated in

Table 5. Optimal lag length criterion.

VAR Lag Order Selection Criterion Sample: 1990 to 2023
Lag	LogL	LR	FPE	AIC	SC	HQ
0	−4145.77	NA	1.32	63.8888	64.0432	63.9515
1	−2655.42	2797.28	3.09	41.7141	42.9494 *	42.2160 *
2	−2588.39	118.588	2.35	41.4368	43.7528	42.3779
3	−2519.54	114.392	1.76	41.1314	44.5283	42.5117
4	−2451.84	105.198	1.36	40.8437	45.3215	42.6632
5	−2384.76	97.0067	1.08	40.5656	46.1242	42.8242
6	−2327.63	76.4650	1.03 *	40.4405	47.0799	43.1383
7	−2278.15	60.9069	1.15	40.4330	48.1533	43.5700
8	−2214.80	71.1387 *	1.07	40.2123 *	49.0135	43.7885

Source: current authors’ computation; * significant selected lag.

below, the study is also in the process of determining the optimal lags for the model.

To determine the most suitable lags for the model, the study employed the VAR optimal lags selection criterion, as presented in Table 5 above. Although the SC and HQ criteria suggest incorporating only one lag in the model, the LR and AIC results support the use of eight lags. Nevertheless, since the SC criterion has been shown to outperform the AIC criterion in previous studies [74,75,76], this study opts for a single lag based on SC. As illustrated in

Table 6. Panel co-integration test.

Test		Statistic	Probability
Kao co-integration	Modified Dickey–Fuller t	−6.7779	0.0000 ***
	Dickey–Fuller t	−5.5244	0.0000 ***
	Augmented Dickey–Fuller t	−3.8472	0.0001 ***
	Unadjusted modified Dickey–Fuller t	−11.6787	0.0000 ***
	Unadjusted Dickey–Fuller t	−6.4371	0.0000 ***
Pedroni co-integration	Modified Phillips–Perron t	−0.1622	0.4356
	Phillips–Perron t	−6.4544	0.0000 ***
	Augmented Dickey–Fuller t	−4.7633	0.0000 ***
Westerlund co-integration	Variance ratio	−1.3136	0.0945 *

Source: current authors’ computation; ***, and *, significance at 1%, and 10%, respectively.

below, ongoing co-integration tests are conducted to identify long-term relationships within the model.

Table 6 above illustrates the results of co-integration tests conducted using the methods of Kao, Pedroni, and Westerlund. The findings suggest that we cannot reject the null hypothesis that proposes no co-integration among panels. This indicates that the model’s variables maintain long-term relationships. Therefore, the study aims to examine both the short-term and long-term relationships of these variables.

Table 7. Comparative short-run country-specific analysis relationships.

Panel Nonlinear Autoregressive Distributed Lags Model Short-Run Equation
	BRICS Country
	Brazil	Russia	India	China	South Africa
Variable	Coefficient	Coefficient	Coefficient	Coefficient	Coefficient
ECT	−1.043755 ***	−0.580778 **	−0.840271 ***	−0.016988 ***	−0.728645 ***
DHydro-POS	0.041353 ***	−0.181886 **	−0.041382 ***	−0.015463 ***	−0.028944
DHydro-NEG	0.000780	0.108869 **	0.113431 ***	0.005840 ***	−0.032417
DNuclear-POS	0.144786 *	0.383118 ***	0.128189	−0.004524	0.409936 ***
DNuclear-NEG	0.093362 **	−0.105978	−0.067747	0.112005 ***	−0.018452
DWind-POS	−0.337822 ***	−4.744947	0.864674 ***	0.038333 ***	1.537009 *
DWind-NEG	1.005292 ***	−2.945802	−0.215211	−0.002118	−0.445939
DOther-RE-POS	0.623900 **	12.05565	0.358876 **	−0.126322 ***	7.097564
DOther-RE-NEG	−0.417783 ***	−30.53595	0.659653 **	0.212045 **	−3.629348
DLTO-POS	−0.491233 ***	−0.590268 *	0.006845	0.166445 ***	0.321746 ***
DLTO-NEG	0.753346 ***	0.100026 ***	−0.210111 ***	−0.118244 ***	−0.004265
DLK-POS	0.729277 **	−0.093479	−1.087771 **	−0.364987 **	0.085499
DLK-NEG	−0.650570	−1.606529	0.162192	0.114766 **	−0.118215

Source: current authors’ computation; ***, **, and *, significance at 1%, 5%, and 10%, respectively.

below further explores these dynamics through a disaggregated approach, employing the panel nonlinear autoregressive distributed lags model, as introduced by [55], to perform a short-run comparative analysis on how transitioning to renewable energy impacts economic growth in the BRICS nations.

Table 7 clearly illustrates that the error correction terms (ECTs) are negative and statistically significant, suggesting that deviations in economic growth are annually adjusted back towards long-term equilibrium. For Brazil (−1.04), Russia (−0.58), India (−0.84), China (−0.02), and South Africa (−0.73), the ECTs indicate annual corrections towards equilibrium by 104%, 58%, 84%, 2%, and 73%, respectively. Brazil exhibits the highest adjustment speed for short-term economic growth imbalances, whereas China shows the slowest among the BRICS nations. This supports the economic theory that a negative and statistically significant error correction term is essential for verifying the study’s reliability.

In addition, positive shocks to hydropower contribute to economic growth in Brazil by 0.04%, whereas they lead to declines in economic growth in Russia, India, and China by 0.18%, 0.04%, and 0.03%, respectively, when considering a 1% increase in these shocks at a 1% level of significance. Conversely, negative hydropower shocks reduce economic output in Russia, India, and China by 0.11%, 0.11%, and 0.01%, respectively, with significance levels at 5% and 1%. However, such negative shocks have an insignificant effect on economic growth in Brazil and South Africa, and positive shocks do not significantly affect short-term growth in South Africa. This indicates that, while positive hydropower shocks boost Brazil’s economic growth, they negatively affect growth in Russia, India, and China. Within the BRICS nations, hydropower significantly fosters Brazil’s economic growth as positive hydropower events lead to growth increases.

In the context of nuclear energy, increasing positive nuclear power shocks enhance economic growth in Brazil (0.14%), Russia (0.38%), and South Africa (0.41%). This indicates that, for every 1% rise in positive nuclear power shocks, economic growth increases by 0.14% in Brazil, 0.38% in Russia, and 0.41% in South Africa at a 10% and 1% significance level, respectively. Positive nuclear shocks do not substantially affect economic growth in India and China. Conversely, rising negative nuclear power shocks adversely affect economic growth in Brazil (0.09%) and China (0.11%), suggesting that a 1% increase in negative shocks leads to a 0.09% and 0.11% decrease in economic growth in Brazil and China, respectively, at a 5% and 1% significance level. The study finds no significant negative shock impact on economic growth in Russia, India, and South Africa. These findings suggest that positive nuclear power shocks benefit economic growth in Brazil, Russia, and South Africa. Among BRICS nations, nuclear power significantly aids economic growth in South Africa, followed by Russia and, to a lesser extent, Brazil.

Positive wind power shocks exhibit a direct correlation with economic growth in India (0.86), China (0.04), and South Africa (1.54). This suggests that a 1% increase in wind power’s positive impact leads to economic growth of 0.86% in India, 0.04% in China, and 1.54% in South Africa, with confidence levels of 1% and 10%, respectively. In contrast, positive wind power shocks negatively affect Brazil’s economic growth (−0.34), indicating a significant decline of 0.34% under a 1% significance level for a 1% increase in wind power’s positive shock. Conversely, negative shocks to wind power decrease economic growth in Brazil by 1.01% with 1% significance for a 1% shock increment, whereas they have an insignificant effect on the economic growth rates of Russia, India, China, and South Africa. These findings reveal that positive wind power shocks favorably impact economic growth in India, China, and South Africa. Among the BRICS nations, South Africa benefits the most from wind power in terms of economic growth, followed by India and then China.

Positive shocks in other renewable energy sources have a favorable impact on economic growth in Brazil (0.62) and India (0.35). A 1% rise in such positive shocks increases economic growth by 0.62% in Brazil and 0.35% in India, both at a 5% significance level. Conversely, in China, these positive shocks reduce economic growth by 0.13%, significant at the 1% level. Meanwhile, negative shocks to other renewables correlate with increased economic growth in Brazil (−0.42), indicating a 1% rise in negative shocks boosts growth by 0.42% at a 1% significance level. However, similar negative shocks shrink economic growth by 0.66% in India and 0.21% in China, significant at a 5% level. For Russia and South Africa, other renewables do not significantly affect economic growth. These findings suggest that, for Brazil and India, positive shocks to other renewables support economic expansion. Within the BRICS nations, other renewable resources, such as biomass, significantly enhance Brazil’s economic growth, as indicated by the effects of both positive and negative shocks.

Table 7 presents data showing that an increase in trade openness positively impacts economic growth in China (0.17) and South Africa (0.32). Specifically, a 1% rise in positive trade shocks leads to a growth of 0.17% in China and 0.32% in South Africa, both at a 1% significance level. However, these positive trade shocks negatively affect economic growth in Brazil (−0.49) and Russia (−0.59), where a 1% increase in such shocks causes economic growth to decline by 0.49% in Brazil and 0.59% in Russia, significant at 1% and 10% levels, respectively. Positive trade shocks have an insignificant effect on India’s economic growth. On the contrary, negative trade shocks positively influence economic growth in India (−0.21) and China (−0.12), indicating that a 1% increase in negative trade shocks boosts growth by 0.21% in India and 0.12% in China, each significant at a 1% level. Meanwhile, these negative shocks have detrimental effects on Brazil (0.75) and Russia (0.10), where a 1% rise in negative trade shocks decreases growth by 0.75% and 0.10%, respectively, at a 1% significance level. South Africa’s economic growth is not significantly affected by negative shocks to trade openness. The findings suggest that positive trade shocks are beneficial for the economic growth of China and South Africa. For the BRICS nations, trade openness is particularly beneficial to South Africa and China, as demonstrated by both positive and negative trade shock impacts.

In Brazil, positive capital shocks have a beneficial impact on economic growth, with a coefficient of 0.73, indicating that a 1% increase in such shocks boosts economic growth by 0.73% at a 5% significance level, all else being equal. Conversely, in India and China, positive capital shocks have detrimental effects on growth, yielding decreases of 1.09% and 0.36%, respectively, for each 1% rise in positive capital shocks, holding statistical significance at the same level, ceteris paribus. In contrast, these positive shocks do not significantly affect economic growth in Russia and South Africa. Meanwhile, negative capital shocks adversely affect economic growth in China with a coefficient of 0.11, signifying a 0.11% reduction for every 1% increase in negative capital shocks at a 5% significance level, ceteris paribus. However, negative shocks to capital do not significantly impact economic growth in Brazil, Russia, India, and South Africa. This data suggests that positive capital shocks enhance economic growth, specifically in Brazil.

The PNARDL model presupposes that the long-term influence of different forms of renewable energy on the economic growth of BRICS nations is uniform from a theoretical standpoint. Consequently,

Table 8. Homogeneous long-run relationships.

Panel Nonlinear Autoregressive Distributed Lags Model Long-Run Equation
Variable	Coefficient	Standard Error	t-statistic	Probability
Hydro-POS	0.037123	0.025448	1.458800	0.1486
Hydro-NEG	−0.048067	0.034241	−1.403768	0.1644
Nuclear-POS	−0.289143	0.164817	−1.754334	0.0833 *
Nuclear-NEG	−0.120316	0.145253	−0.828325	0.4100
Wind-POS	0.277531	0.159946	1.735158	0.0867 *
Wind-NEG	0.293587	0.191399	1.533895	0.1291
Other-RE-POS	−0.133214	0.286697	−0.464653	0.6435
Other-RE-NEG	0.410678	0.267427	1.535664	0.1287
LTO-POS	−0.000494	0.120119	−0.004109	0.9967
LTO-NEG	−0.009208	0.111540	−0.082555	0.9344
LK-POS	1.324178	0.269182	4.919268	0.0000 ***
LK-NEG	1.578153	0.253827	6.217443	0.0000 ***

Source: current authors’ computation; *** and * significance at 1%, and 10%, respectively.

illustrates that positive disruptions in nuclear energy have a favorable effect on economic growth within these countries. Specifically, a 1% rise in positive nuclear power shocks enhances economic growth by 0.08% at a 10% significance level, all else being equal. This indicates the beneficial role of positive nuclear power shocks on the economic growth of BRICS nations. Similarly, long-term positive wind power shocks also have a positive impact, with a 1% increase boosting economic growth by 0.09% at a 10% significance level, ceteris paribus. This suggests that positive wind power shocks are advantageous for the economic growth of BRICS countries. Additionally, positive capital shocks contribute positively, while negative shocks have a detrimental effect on economic growth in these regions. A 1% rise in positive capital shocks results in a negligible increase in economic growth, whereas negative capital shocks cause a slight decrease at a 1% significance level, all else being equal. This suggests that positive capital shocks favor economic growth in BRICS countries. Overall, nuclear and wind power have the most significant long-term contributions to economic growth in these countries. Unlike the short-run outcomes, hydropower, other renewables, and trade openness do not significantly influence long-term economic growth. The analysis continues with residual diagnostics, as shown in Figure 2.

To evaluate the reliability of the model’s outcomes in forming empirically backed policies and recommendations, this research conducted the CUSUM test and the CUSUM of Squares test, as illustrated in Figure 2 above. The figures indicate that the CUSUM of Squares remains mostly within the significant boundaries, although the CUSUM sometimes exceeds them. Thus, we infer that the model is both robust and reliable for policy development related to renewable energy transition and economic growth in BRICS nations, based on these CUSUM and CUSUM of Squares test results. Furthermore, the study proceeds to perform the cross-sectional dependence test, as depicted in

Table 9. Cross-sectional dependence test.

Null Hypothesis: Cross-Sectional Independence
Test	Statistic	d.f.	Probability
Breusch-Pagan Chi-square	14.65629	10	0.1451
Pearson LM Normal	−0.076857		0.9387
Pearson CD Normal	1.898066		0.0577
Friedman Chi-square	44.22097	33	0.0918
Frees Normal	−0.025436		0.8541

Source: current authors’ computation.

below.

As illustrated in Table 9 above, a test for cross-sectional independence was conducted for the study. Based on the Breusch–Pagan Chi-square, Pearson LM Normal, Pearson CD Normal, Friedman Chi-square, and Frees Normal tests, we cannot reject the null hypothesis of cross-sectional independence at the 5% significance level. This implies that the estimated model is free from cross-sectional dependency, lending credibility to polices and recommendations connected to the shift towards renewable energy and economic growth among BRICS nations. Symmetrical tests are also carried out, as depicted in

Table 10. Short- and long-run asymmetrical test.

PNARDL Wald Test Long-Run and Short-Run Asymmetry Test
	Long-Run Asymmetries		Short-Run Asymmetries
Variable	F-Statistic	Conclusion	F-Statistic	Conclusion
Hydro	8.066480 ***	Asymmetry	10.29783 ***	Asymmetry
Nuclear	1.509847	Symmetry	3.196978 *	Asymmetry
Wind	0.419306	Symmetry	1.571000	Symmetry
Other-RE	0.563235	Symmetry	1.292771	Symmetry
LK	4.576577 **	Asymmetry	12.95356 ***	Asymmetry
LTO	9.384156 ***	Asymmetry	3.673043 *	Asymmetry

Source: current authors’ computation; ***, **, and * significance at 1%, 5%, and 10%, respectively.

below.

As shown in Table 10 above, the PNARDL Wald test was applied to examine both short- and long-term asymmetric relationships. Apart from wind power and other renewable energies such as bioenergy, the null hypothesis of symmetrical interactions cannot be accepted. Thus, in the short term, asymmetric linkages exist among hydropower, nuclear energy, capital, trade openness, and economic growth within the BRICS countries. Moreover, the long-term results reveal uneven connections involving hydropower, capital, trade openness, and economic growth among BRICS nations. These outcomes imply that, in both the short and long terms, an uneven connection exists between economic growth and the shift toward renewable power in BRICS countries. The study utilizes DOLS and FMOLS to check the robustness of the PNARDL model results, as detailed in

Table 11. Short-run DOLS and long-run FMOLS robustness check.

Variable	Panel DOLS		Panel FMOLS
	Coefficient	Probability	Coefficient	Probability
Hydro	−0.255900	0.0835 *	−0.268186	0.0000 ***
Nuclear	0.812712	0.0046 **	0.629851	0.0000 ***
Other-RE	0.927189	0.3016	−1.086451	0.0000 ***
Wind	−0.446768	0.3340	−0.298557	0.0000 ***
LTO	−0.047764	0.2369	−0.023542	0.6108
LK	0.213632	0.0008 ***	0.047110	0.0995 *
$R^2$ $\mathrm{Adjusted} R^2$	0.850922 0.656158		0.452325 0.413482

Source: current authors’ computation; ***, **, and *, significance at 1%, 5%, and 10%, respectively.

below.

Referring to Table 11, the research utilized robust checks through panel DOLS and FMOLS. The panel DOLS findings indicate a negative statistical relationship between hydropower and short-term economic growth in the BRICS nations. Specifically, a 1% rise in hydropower results in a 0.26% decrease in economic growth, all else being equal. This implies that hydropower has not positively influenced economic progress within these countries. Conversely, there is a strong positive statistical association between nuclear power and economic growth, with a 1% increment in nuclear power leading to a 0.81% boost in economic growth, ceteris paribus. This suggests that promoting nuclear energy could be beneficial for economic development. Additionally, there is a notable positive link between capital and economic growth; a 1% increase in capital stock is associated with a 0.21% rise in economic growth, with other factors being constant. These results highlight the vital role of capital in driving economic growth in the BRICS countries. On the other hand, factors such as trade openness, wind energy, and other renewables show a minimal impact on economic growth in these regions.

Given the substantial long-term correlations, the panel FMOLS indicates a significant negative correlation between hydropower and economic growth within the BRICS nations. With other factors held constant, economic growth diminishes by 0.27% for each 1% rise in hydropower usage. This suggests that hydropower has not contributed positively to economic growth in these countries. Moreover, with all else being equal, a 1% increase in wind power is associated with a 0.30% reduction in economic growth. This implies that wind power, over the studied timeframe, has not driven economic growth in the BRICS countries. Additionally, the study highlights a negative relationship between economic growth and other renewable resources. Under the assumption of all else being equal, there is a 1.09% decrease in economic growth for every 1% increase in the use of other renewable energies. These results indicate that alternative renewable energy sources have not successfully stimulated economic growth in the BRICS countries. These conclusions are at odds with the findings of the PNARDL model, which suggested that both positive and negative shocks to alternative renewables had a negligible impact on the economic progression of the BRICS countries.

There is a positive correlation between nuclear energy and economic growth in the BRICS nations. Specifically, economic growth sees a 0.63% increase for each 1% rise in nuclear energy generation, with the assumption that other factors remain constant. This suggests that nuclear energy significantly contributes to economic growth in these countries and ought to be encouraged. Meanwhile, a 1% uptick in capital stock notably leads to a 0.05% increase in economic growth, also with other variables held constant. This indicates that capital is key to the economic progress of BRICS countries and should be prioritized. In contrast, trade openness does not show a significant influence on economic growth in BRICS nations. These findings align with the long-term results from the PNARDL model mentioned earlier.

5. Discussion

This study primarily aimed to examine how the shift to renewable energy affects economic growth in BRICS nations from 1990 to 2023, focusing on individual renewable energy sources. To fulfill this aim, the study poses several research questions: Is there a long-term, persistent link between renewable energy and economic growth? Are there symmetrical or asymmetrical associations between renewable energy and economic growth in both the short and long runs? Do the effects of renewable energy on economic growth in BRICS countries differ between short-term and long-term perspectives? Which specific disaggregated renewable energy source best enhances economic growth within the BRICS nations? What are the potential policy implications of transitioning to renewable energy on the economic development of BRICS countries? To analyze the connections between the renewable energy transition and economic growth in the BRICS countries, the study utilizes the PNARDL model, alongside the panel DOLS and FMOLS for robustness verification.

The key findings from the study are provided below for the short-run results; long-run results, panel DOLS, and FMOLS models are presented in this section. The short-run results of the PNARDL model are as follows: Firstly, with hydropower under consideration, positive shocks increase economic growth in Brazil (0.04%) but decrease it in Russia (−0.18%), India (−0.04%), and China (−0.03%). These results are consistent with refs. [20,26,29,37], which found that renewable energy boosts economic growth. Nonetheless, negative shocks decrease economic growth in Russia (−0.11%), India (−0.11%), and China (−0.01%). These results are inconsistent. Refs. [29,32] found that negative shocks to renewable energy boost economic growth. Secondly, when it comes to nuclear power, positive shocks increase economic growth in Brazil (0.14%), Russia (−0.38%), and South Africa (0.41%). These results are consistent with the study by [32] that positive shocks to nuclear power boost economic growth. On the other hand, negative shocks decrease economic growth in Brazil (−0.09%) and China (−0.11%). These results are inconsistent with the study by [32], which found that negative shocks to nuclear power boost economic growth.

Third, regarding wind power, positive shocks have been observed to enhance economic growth by 0.86% in India, 0.04% in China, and 1.54% in South Africa. These findings align with the conclusions of ref. [29] that positive shocks in renewable energy stimulate economic growth. Conversely, negative shocks are associated with a reduction in economic growth in Brazil, showing a decline of 1.01% and contradicting the findings of ref. [29] that negative shocks in renewable energy boost economic growth. Fourth, when other renewable sources like biomass, are under examination, positive shocks lead to growth in Brazil (0.62%) and India (0.35%) while causing a decline in China (−0.13%). These observations support the conclusions of studies [7,8,43,46], which found that renewable energy contributes to economic growth. However, negative shocks result in decreased growth in India (−0.66%) and China (−0.21%) but cause an increase in Brazil (0.42%), which contrasts with the findings of studies [7,8,43,46] suggesting that renewable energy fosters economic growth.

Moreover, analyzing the homogeneous long-term impacts of the PNARDL model reveals that positive disturbances in nuclear power lead to economic growth in BRICS nations by 0.08%. These findings align with the study conducted by [32], which concluded that positive changes in nuclear energy enhance economic development. Regarding wind energy, positive impacts result in a 0.09% increase in economic growth in these countries. This finding matches the conclusions of studies [7,8,20,26], which indicated that renewable energy promotes economic growth. Additionally, while positive changes in capital lead to economic growth, negative disturbances cause a decline, in line with studies [36,45,46] that reported capital’s positive influence on economic progress.

When the robust results from both DOLS for the short term and FMOLS for the long term are analyzed, it becomes evident that hydropower exhibits a negative correlation with economic growth during both short-run and long-run periods in the BRICS nations. This aligns with the findings of [6,21], which also indicated that transitioning to renewable energy can negatively affect economic growth. On the contrary, nuclear power shows a positive correlation with economic growth over both timeframes in the BRICS countries, echoing the PNARDL long-run findings and supporting the conclusions of [32] that nuclear energy enhances economic growth. Furthermore, capital investment positively influences economic growth in both short-run and long-run periods within the BRICS nations, consistent with the findings of [36,45,46], which suggested that capital investment boosts economic growth. However, wind power is found to have a negative correlation with long-term economic growth, whereas other renewable energy sources do not significantly correlate with economic growth in these countries. These findings are in disagreement with the PNARDL long-run analysis, which reported that wind power positively impacts economic growth in the long term. Overall, the conclusions suggest that the impacts of various renewable energy types on economic growth in BRICS countries differ, with variations evident between short-run and long-run effects. Based on these observations, the research questions are addressed as follows:

Research Question 1: Is there a sustained correlation between renewable energy and economic growth in the long run?

Indeed, there is an enduring connection between renewable energy and long-term economic growth. The PNARDL model indicates that favorable changes in nuclear and wind energy have a positive impact on the economic expansion of BRICS nations over the long term. Furthermore, the findings from panel DOLS and FMOLS reveal notable associations between nuclear energy, capital, and economic growth in BRICS countries.

Research Question 2: Do symmetrical or asymmetrical relationships exist between renewable energy and economic growth in both the short and long runs?

In both the short and long terms, renewable energy and economic growth share asymmetrical relationships. The results indicate that positive and negative shocks from various forms of renewable energy influence economic growth differently in the short term. Over the long term, the PNARDL model reveals that positive shocks to nuclear and wind power positively affect economic growth.

Research Question 3: Do renewable energy’s impacts on economic growth in BRICS nations remain the same between short- and long-term periods?

Rather than remaining consistent over time, the effects of renewable energy on economic growth in BRICS countries fluctuate between short- and long-term periods. Findings indicate that various forms of renewable energy impact economic growth differently, depending on the time frame and models used. For instance, according to the PNARDL model, hydropower negatively affects economic growth in the short term but shows no significant influence in the long term. Meanwhile, analyses using the DOLS and FMOLS models reveal that different renewable energy sources exert varying impacts during both short- and long-term periods.

Research Question 4: Which source of disaggregated energy contributes the most to economic growth in BRICS countries?

In BRICS countries, nuclear and wind power are leading contributors to economic development. The findings indicate that positive changes in these energy sources favorably affect long-term economic growth. Additionally, the results from the panel DOLS and FMOLS analyses reveal that nuclear power exerts a substantial positive impact on economic growth. Research Question 5 examines the potential policy impacts of transitioning to renewable energy on the economic growth of BRICS countries, which will be discussed in the policy recommendation section.

6. Conclusions

This research has explored how different renewable energy sources affect economic growth in BRICS countries, utilizing a panel nonlinear autoregressive distributed lag (PNARDL) model, as well as panel dynamic ordinary least squares (DOLS) and fully modified ordinary least squares (FMOLS) estimators, spanning the time period from 1990 to 2023. The results offer important insights into the intricate relationships between renewable energy sources and economic growth in these rapidly developing economies. The analysis concludes that the impact of renewable energy on economic growth varies by source and country. In the long run, Brazil’s economic growth benefits from positive shocks in hydropower, while China, India, and Russia see negative effects. Conversely, positive shocks in nuclear power enhance economic growth in South Africa, Russia, and Brazil. Wind power is positively linked with economic growth in South Africa, China, and India; however, it exhibits a negative impact. Other renewables negatively affect economic growth in China but show a positive correlation with economic growth in Brazil and India.

Over the long term, the research concludes that nuclear and wind energy significantly bolster economic growth within BRICS nations. These insights indicate that both nuclear and wind power are vital for driving economic expansion in BRICS and warrant encouragement. Additionally, the research identifies capital as a critical component of BRICS economic progress, underlining the necessity of capital stock investment for fostering growth. However, the research notes that trade openness appears to have a negligible effect on economic growth in BRICS nations and may not substantially enhance economic development within the scope of this study.

The panel analyses conducted with DOLS and FMOLS provide an additional understanding of the link between renewable energy sources and economic growth in BRICS countries. These analyses demonstrate a short-term negative association between hydropower and economic growth, while nuclear power shows a positive association. These results suggest that, within the BRICS framework, nuclear power serves as a more effective driver of economic growth than hydropower. Based on the findings, the policy recommendations are as follows: For renewable energy policy, it is advised that policymakers diversify the energy mix by incorporating a variety of sources such as wind, renewables, and hydropower, to reduce over-dependence on any single source and cater to the specific needs of each nation. Meanwhile, considering the favorable impact of nuclear energy on economic growth, policymakers should consider expanding nuclear power infrastructure, given its status as a low-carbon energy option. In terms of economic policy, an emphasis on capital investment should be prioritized by BRICS countries, as capital is crucial for economic development. Additionally, the effect of trade openness on economic growth varies across these countries, requiring tailored trade policies that align with each nation’s unique conditions. By implementing these policy suggestions, BRICS nations can promote sustainable economic growth, reduce dependency on fossil fuels, and mitigate climate change effects to achieve sustainability.

This study offers several key contributions: It conducted a disaggregated analysis of renewable energy to assess how various renewable sources affect economic growth in BRICS nations, revealing the distinct contributions of each energy type. It examined the differential impacts of positive and negative renewable energy shocks on economic growth, shedding light on potential nonlinear relationships. Additionally, the research included a country-specific examination of renewable energy’s economic effects, identifying the unique contributions of each source in individual countries. The study used a variety of estimation methods—namely PNARDL, DOLS, and FMOLS—to verify the robustness of the results, thereby enhancing confidence in the study’s conclusions.

The results of the study add to the existing body of literature concerning renewable energy and economic development by presenting fresh evidence regarding the effects of distinct renewable energy sources on economic growth within BRICS nations. This information can guide policymaking. Additionally, the study underscores the significance of acknowledging the non-uniform impact of renewable energy sources on economic growth, aiding policymakers in crafting more effective policies. The research offers insights specific to each country, illuminating the influence of renewable energy sources on economic growth, which can help shape individual nations’ policies. The study’s findings that nuclear power and capital positively affect economic growth align with endogenous growth theory, which highlights the importance of internal elements such as technology and investment in human capital for spurring economic advancement. Furthermore, the study reinforces the renewable energy-led growth hypothesis by demonstrating that renewable energy, through the positive effects of nuclear and wind power, can propel economic growth.

The authors of this study acknowledge the following limitations when interpreting its results. The study relied on panel data from 1990 to 2023, using the PNARDL, DOLS, and FMOLS, which may involve their limitations and assumptions; as such, different models might yield different results. Furthermore, the study focused on specific renewable energy sources due to the availability of data, which might not capture the full range of renewable energy sources. To overcome these limitations, subsequent research should explore alternative models, examine causal relationships between variables, and include a wider array of renewable energy sources. Moreover, future studies might expand this research by integrating more macroeconomic variables like inflation and unemployment to delve deeper into the intricate connections between the transition to renewable energy and economic growth.

Overall, this study offers significant insights into the link between renewable energy sources and economic expansion in the BRICS nations. The findings indicate that both nuclear and wind power are key contributors to economic growth, with capital being essential for fostering this growth. These conclusions highlight that the shift to renewable energy sources is beneficial for attaining sustainable economic development, aligning with efforts to combat climate change and global warming. Furthermore, these efforts contribute to meeting the targets of the Paris Agreement and the Sustainable Development Goals, specifically Goal 13 on climate action, Goal 7 on Affordable and Clean Energy, and Goal 8 on Decent Work and Economic Growth. These results can assist policymakers in shaping strategies that support economic progression and sustainable development within these burgeoning economies.