Sustainable Development in Focus: CO₂ Emissions and Capital Accumulation

Abstract

In the modern era, CO₂ emissions is a popular and significant study topic. Environmental sustainability is adversely affected by CO₂ emissions, which have become the main cause of climate change. Using panel data analysis, this study investigated the connections between CO₂ emissions and economic development, capital accumulation, and the use of renewable energy. Long-term connections between variables were examined using the Augmented Mean Group (AMG) and Common Correlated Effects Mean Group (CCEMG) estimators, taking into account heterogeneity and cross-sectional dependence. Additionally, the Dumitrescu–Hurlin Panel Granger Causality Test was used to assess dynamic interactions between variables. Although CH₄ emissions increase CO₂ emissions, the effects of economic growth and capital accumulation are not statistically significant, as determined using the AMG and CCEMG. Although the use of renewable energy was shown to have the potential to lower CO₂ emissions, this impact was not statistically significant. The results of the dynamic panel demonstrate that CO₂ emissions increase with capital accumulation. Although methane (CH₄) emissions significantly impact CO₂ emissions, economic growth, capital accumulation, and renewable energy use do not show statistically significant effects, highlighting the varying influences of these factors across nations. The findings of this study emphasize the need to integrate environmental regulations into capital investment strategies and adopt country-specific policies to effectively reduce CO₂ emissions. They also underscore the need to customize green legislation to the specific conditions of each nation while simultaneously advocating for further expenditures in clean energy and the formulation of policies to supplant fossil fuels.

1. Introduction

The main causes of carbon dioxide (CO₂) emissions into the Earth’s atmosphere are the burning of fuels that contain carbon and the deterioration of wood and other plant materials [1]. Carbon dioxide, a naturally occurring gas on Earth, is both invisible and odorless. Although other gases also contribute to global warming, carbon dioxide has the most significant impact. From 1970 to 2004, carbon dioxide emissions rose by 70%, with the transportation sector contributing 13.1% of these emissions. In addition, GHG emissions from this sector increased the most rapidly among greenhouse gases [2]. The rise in carbon emissions, regarded as a primary contributor to global warming, persists globally and is the focus of several studies [3]. Narayan and Narayan [4] highlighted the escalating impact of environmental deterioration on healthcare costs. Pollution in the atmosphere is recognized as the fundamental source of natural deterioration, and its influence on individual health is being emphasized [5].

Addressing global environmental issues that endanger human health is one of society’s top priorities. When CO₂ emissions that contribute to global warming are balanced, net zero CO₂ emissions are attained. This is known as carbon neutrality. As a result of climate accords, 124 nations have pledged to become carbon neutral by 2050 or 2060. The Paris Climate Agreement and Kyoto Protocol were developed in response to the increasing global severity of environmental issues [6]. Regarding the environmental considerations included in the Kyoto (1997) and Bonn (2001) accords, the final outcomes represent a noteworthy advancement [7]. Following the Bali (2007) and Paris (2015) accords, countries have begun to make more specific, legally enforceable pledges to reduce emissions [8]. Reducing global emissions and ensuring sustainable economic growth are the primary goals [9]. This study aims to answer the following research questions: How do capital accumulation, economic growth, and renewable energy use influence CO₂ emissions, and what are the implications of these relationships for sustainable development policies across countries with varying levels of development?

This study contributes to the literature by applying robust econometric methods that capture heterogeneity and cross-sectional dependence, offering both short- and long-term insights.

The rest of this manuscript is organized as follows: Section 2 provides a review of the relevant literature, Section 3 outlines the data and methodology, Section 4 presents the empirical results, Section 5 discusses the findings and their implications, and Section 6 concludes with policy recommendations.

2. Literature Review

A multitude of factors related to carbon dioxide emissions have been the subject of recent studies examining a variety of factors. This study used data collected from earlier studies that examined the connections underlying carbon dioxide emissions, economic size, capital accumulation, and renewable energy. This study provides an analysis of the studies that focus on this complex relationship.

Recent research has highlighted the complex interplay between economic development, the use of renewable energy sources, and CO₂ emissions in diverse economic settings. This discourse is frequently contextualized within the Environmental Kuznets Curve (EKC) theory, which posits an inverted U-shaped correlation between economic expansion and environmental deterioration. The EKC posits that pollution and carbon emissions often escalate in the initial phases of economic growth, attributable to industrialization and heightened energy use. As nations attain an elevated GDP per capita, emissions begin to decrease due to fundamental economic transformations, technical innovations, and more robust environmental regulations [10]. Analyzing the connection between the Environmental Kuznets Curve (EKC) and gross capital formation is crucial for comprehending the interplay between economic growth and environmental sustainability. Given that gross capital formation includes investments in areas such as infrastructure, manufacturing, and energy, the environmental repercussions of these investments are essential in influencing the EKC curve. Channeling resources toward sustainable investments fosters long-term development strategies by equilibrating economic advancement and environmental conservation. This study enhances the literature by experimentally determining the link between these variables. Additionally, according to Mirziyoyeva and Salahodjaev [11], the link between GDP per capita and emissions is structured like an upside-down U. This pattern corresponds with observations from transitional economies, indicating that economic growth significantly influences emissions, with a 1% increase in GDP resulting in a 0.35% rise in CO₂ emissions. Kwakwa [12] substantiates the inverted U-shaped relationship between economic growth and CO₂ emissions, indicating that elevated economic activity initially results in higher emissions, especially within the frameworks of trade openness and urbanization. Notwithstanding this, the significance of renewable energy cannot be overstated when it comes to reducing emissions and promoting economic growth. The exploitation of renewable energy sources in the BRICS nations has a dual purpose; that is, it helps promote economic growth while simultaneously reducing carbon dioxide emissions. According to Fu et al. [13], this link is bi-directional, which indicates that the development of GDP and the use of renewable energy impact one another.

Numerous studies on the connections between CO₂ emissions, economic issues, and energy use have been carried out in various jurisdictions. These studies have particularly focused on how economic dynamics, globalization, and renewable energy affect environmental outcomes. According to Dong et al. [14], the increased use of natural gas and renewable energy sources by BRICS nations results in lower carbon dioxide emissions. More precisely, regarding natural gas and renewable energy, a one percent increase in consumption corresponds to a one percent reduction in emissions, respectively. In a similar vein, Cheng et al. [15] showed that the use of renewable energy sources significantly contributes to lowering the quantity of carbon dioxide emissions generated per person in the BRICS nations. Despite this, results also show that exports accelerate the increase in emissions, and environmental patents and GDP per capita are associated with growing emissions. One element that contributes to decreasing emissions within these economies is foreign direct investment (FDI). The Environmental Kuznets Curve concept is supported by Dogan and Seker’s [16] research in the European Union, which demonstrates that using non-renewable energy increases emissions. Conversely, trade openness and the use of renewable energy are linked to decreased carbon dioxide emissions. The effect of globalization on long-term environmental sustainability has been the subject of several debates. According to Aziz et al. [17], globalization—particularly via foreign direct investment (FDI)—increases the use of nonrenewable energy, which has a negative impact on the environment. Sun et al. [18] also provide evidence supporting this position, showing that increasing carbon emissions are linked to globalization. Meanwhile, Gyimah and Yao [19] provide a different perspective, arguing that by promoting the use of renewable energy sources, globalization could help lower carbon emissions. The results show that while globalization and economic factors do affect environmental outcomes, their impact varies depending on the percentage of energy coming from renewable versus nonrenewable sources and the implementation of policies that support sustainable development.

The connection between capital formation and CO₂ emissions has been thoroughly examined in various economic settings. Between 2002 and 2012, there was a significant increase in CO₂ emissions associated with fixed capital formation in China, which doubled from 2007 to 2012. The construction sector emerged as the primary contributor, and northern provinces served as key inter-regional net exporters of emissions [20,21]. Although emissions remained stable from 2012 to 2017, the scale of investment posed challenges to decoupling efforts, whereas embodied energy intensity played a supportive role in this process [21]. Similar trends have been observed in a number of countries where the process of capital development plays a significant role in determining the impact of emissions. According to Rahman and Ahmad [22], the consumption of coal and oil is the primary factor driving the asymmetric influence of gross capital formation on CO₂ emissions in Pakistan. In a similar vein, it has been discovered that economic expansion, urbanization, and capital creation all have a beneficial impact on emissions in Malaysia. Furthermore, unidirectional causality between these factors and CO₂ emissions has been identified [23]. Notably, the role of capital creation differs according to the economic context under consideration. The implementation of renewable energy sources and the increased capital development in nations along the currently forming Silk Road Economic Belt (SREB) have shown substantial potential to reduce emissions. This phenomenon reinforces the Environmental Kuznets Curve hypothesis, which aligns with the inverted U-shaped connection between CO₂ emissions and economic growth [24]. Emissions in G7 countries have decreased as a result of capital creation, environmental regulations, green innovation, and the use of renewable energy. Reductions in emissions have also been aided by capital creation. However, it is crucial to remember that expanding economies still have an adverse effect on environmental quality [25]. Additionally, the connection between capital spending and carbon emissions in the UK has been emphasized. In this nation, a 39 percent drop in CO₂ emissions was linked to a 53 percent decrease in capital spending during a six-year period. This result is an example of the possible impact that governance and financial tactics might have on lowering emissions [26]. The results of these investigations provide insight into the intricate connection between capital creation and CO₂ emissions. They also point out that whether capital investment worsens or lessens environmental effects depends largely on the features of economic development, the types of energy used, and the means of implementing regulatory measures.

3. Data and Method

The selection of countries for the panel data analysis in this study was based on an assessment of their economic development levels and emission densities. In this context, nations were categorized into two primary groups: those that are developed and those that are developing. The analysis encompassed countries from both groups that exhibit varying emission densities. An assessment of economic growth, capital accumulation, and the environmental impacts associated with the use of renewable energy was conducted by examining various country profiles.

The group of developed nations comprised the USA, Canada, Australia, Germany, France, England, and Denmark. These countries have a variety of distinct features in terms of their degrees of economic growth and the composition of their industrial systems. Developed nations were differentiated by high and low emission densities.

The countries characterized by elevated emission densities were the USA, Canada, and Australia. In these countries, industrial production, fossil fuel consumption, and energy demand are currently elevated. The United States and Canada stand out as prominent oil and natural gas producers, with significant carbon emissions originating from industrial and transportation activities. Australia, conversely, generates significant emissions as a result of its mining operations, fossil fuel exports, and energy-demanding production methods.

Countries with low emission intensity include France, England, and Denmark. In these countries, investments in renewable energy and the implementation of environmental policies are leading the way, significantly decreasing reliance on fossil fuels. France maintains low carbon emissions primarily because its energy system is predominantly reliant on nuclear power. England has achieved a reduction in carbon emissions through its process of deindustrialization and the implementation of renewable energy transition policies. Denmark stands out as a leader in reducing emissions, achieving remarkable progress through significant investments in renewable resources, particularly in wind energy. Conversely, although Germany is regarded as a developed nation, it has a medium level of emission intensity, which is attributed to its industrial output and energy usage.

The group of developing nations comprises China, India, Russia, Brazil, Turkey, Mexico, and Indonesia. Industrialization processes, energy consumption habits, and the pace of transition to renewable energy vary significantly among these countries. When considering emission intensity, developing nations can be categorized into two distinct groups: those exhibiting high emission intensity and those demonstrating low emission intensity. The classification of countries into high- and low-emission intensity groups was based on their average per capita CO₂ emissions and energy use patterns between 1990 and 2021, using data from the World Bank and International Energy Agency (IEA). Although there is no universally accepted threshold, relative positioning within the sample and comparative emission densities served as the basis for categorization.

Countries with high emission intensity include China, India, Russia, Brazil, and Indonesia. China and India rank among the top nations for CO₂ emissions globally, playing a substantial role in overall carbon output as a result of their industrial activities and reliance on coal for energy. Russia has a significant role in the production and export of fossil fuels, and it is regarded as a nation with high emissions due largely to the substantial carbon output from its industrial and energy sectors. Brazil and Indonesia both exhibit high emission intensity, stemming primarily from agriculture and forestry rather than the industrial and energy sectors.

Turkey stands out as a developing nation characterized by its low emission intensity. Investments in renewable energy and the application of energy efficiency regulations successfully keep emissions at control levels, even though Turkey’s industrial and energy consumption has increased recently. The current phase of industrialization, coupled with a reliance on fossil fuels, has resulted in the maintenance of a moderate level of emission intensity.

In this context, determining the differences in emissions between industrialized nations and developing countries would make it possible to conduct a more accurate analysis of the ecological consequences linked to the accumulation of capital, the exploitation of renewable energy, and the expansion of the international economy. Simultaneously, the effectiveness of environmental policies enacted in nations with varying levels of economic development, as well as their success in reaching sustainable development goals, could be assessed.

The CO₂ and CH₄ emission values, GDP per capita, capital stock, and renewable energy use rates for the specified countries from 1990 to 2021 were gathered in the form of annual data from the WB. In this study, data were analyzed using the Stata 18 software package. Tests for cross-sectional dependency and slope homogeneity were conducted. Based on the results obtained, the Peseran [27,28] test, which is categorized as a second-generation unit root test, was executed. A stationarity analysis revealed that the dependent variable, the CO₂ emission value, exhibited stationarity at the I(I) level, while the independent variables demonstrated stationarity at both the I(0) and I(I) levels. These results are crucial for identifying a suitable approach to the panel assessment of data. The observation that the variables exhibit varying levels of stationarity indicates that the Panel ARDL (Autoregressive Distributed Lag) test is suitable for exploring long-term relationships. In this context, the AMG (Augmented Mean Group) method, which was designed for estimating long-term relationships, particularly in heterogeneous panel data sets, was chosen.

The interdependence present in the data set utilized for the analysis, in addition to the variability in the slope coefficients, necessitated the application of more sophisticated and resilient techniques that surpass conventional panel ARDL methods. In this context, the AMG (Augmented Mean Group) method, which was designed for estimating long-term relationships, particularly in heterogeneous panel data sets, was chosen. The AMG method enhances the conventional Mean Group (MG) estimator by incorporating a joint dynamic process that considers cross-sectional dependence. This approach yields more stable and dependable estimates by considering the influence of shared factors while maintaining the diversity among panels.

Table 1. Variables.

Variables	Symbol	Unit	Source
CO2 (Carbon Dioxide) Emissions	CO2	Mt CO2e	WB
CH4 (Methane) Emissions	CH4	Mt CO2e	WB
Gross Capital Formation	GCF	USD	WB
GDP per Capita	ln GDPpCa *	USD	WB
Use of Renewable Energy	RenEnergy	% of total energy used	WB

* symbols of data for which the natural logarithm is taken start with “ln”.

provides information about the variables.

4. Results

The outcomes of the tests conducted on the variables specified in the Section 3 are shown below. In this study, we first performed the cross-section dependence (CD) test to determine whether the panel data exhibited cross-sectional dependence, which is crucial for selecting the appropriate estimation technique. Next, we performed the slope homogeneity (heterogeneity) test to assess whether the relationships between variables differed across countries, guiding our choice of models that account for heterogeneity. Finally, we applied unit root tests to examine the stationarity of variables, ensuring the validity of further econometric analyses such as long-term relationship estimations and causality tests.

4.1. Cross-Sectional Dependence (CD) Test

The cross-sectional dependency tests established by Pesaran [27] and further explored by Pesaran and Xie [28] represent robust methodologies for identifying cross-sectional dependency in panel data analyses. Alongside the conventional CD test established by Pesaran [29], these methods offer enhanced accuracy in identifying dependencies within extensive collections of panel data.

The Pesaran [27] test was designed for scenarios in which the conventional CD test may be less effective, offering a more appropriate approach to assessing cross-sectional dependency, particularly for heterogeneous panels and non-stationary series. Pesaran and Xie [28] advanced this methodology and introduced a test framework that yields more robust and equitable outcomes.

The main aim of these tests is to determine if there is a dependence between the cross-sections in the panel data set. The test facilitates an understanding of the relationships among the individual components in the panel data set by assessing the correlation between the individual series.

The formula for the test is as follows:

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

(1)

P is the estimated correlation coefficient between panel members I and J, T is the length of the time series, and N is the number of panel members.

A test value near zero suggests that a lack of dependency exists among the panel members, whereas substantial values, whether positive or negative, signify the existence of cross-sectional dependency. This test exhibits an asymptotically normal distribution, particularly when N (the number of panel members) and T (the length of the time series) are large [29].

Pesaran’s test effectively addresses cross-dependency issues that arise in econometric modeling, particularly in the context of macroeconomic and financial data analyses. These dependencies can emerge from a variety of influences, including global economic conditions, shifts in policy, or advancements within particular sectors.

Table 2. Pesaran (2015, 2021) [27,29] xtcd2 test results.

Variable	CD-Test	p-Value	CDw (Juodis, Reese 2021)	p-Value	Result
CO2	1.31	0.191	5.69	0.000 ***	Dependency exists.
ln_GCF	47.70	0.000	−2.88	0.004 ***	Dependency exists.
CH4	−1.58	0.115	4.58	0.000 ***	Dependency exists.
ln_GDPpCa	48.97	0.000	−2.60	0.009 ***	Dependency exists.
RenEnergy	4.47	0.000	4.65	0.000 ***	Dependency exists.

*** under the null hypothesis for cross-sectional independence, CD ~ N(0,1). The significance level is less than 1% (p < 0.01).

presents the CD test results from Pesaran [27] and Pesaran and Xie [28] for the specified data set.

4.2. Slope Homogeneity (Heterogeneity) Test

The slope homogeneity test introduced by Pesaran and Yamagata [30] assesses the homogeneity of slope coefficients in panel data sets. This assessment is frequently referred to as the “Delta test” and evaluates the uniformity of the slope coefficients. The test formula is designed to assess variations in individual slope coefficients from the mean of the panel data. The Delta test can be represented using the following formulas:

• Standard Delta Test:

$$\Delta =\sqrt{{\displaystyle \frac{N}{2}}}\left({\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{\widehat{\beta }}_i-\beta \right)$$

(2)

2.

Adjusted Delta Test (Delta_tilde):

$$\tilde{\Delta }=\sqrt{N}\left({\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{\displaystyle \frac{{\widehat{\beta }}_i-\beta }{{\sigma }_i}}\right)$$

(3)

N denotes the number of panel members, ${\widehat{\beta }}_i$ indicates the estimated slope coefficient for the ith panel member, β signifies the average slope coefficient, and σ_i represents the standard error of the estimated slope coefficient for the ith panel member.

Whether the null hypothesis—which holds that the slope coefficients are homogeneous—is rejected is determined by the outcomes of these tests. Elevated values imply that there is variability in the slope coefficients, indicating variations among the panel members.

By investigating the slope homogeneity hypothesis in panel data studies, Pesaran and Yamagata [30] created tests that consider the different reactions and behaviors of individual units. When analyzing financial and macroeconomic data, these tests are crucial for assessing the homogeneity of slope coefficients. The slope homogeneity test results for the data set are shown in

Table 3. Slope homogeneity test.

Test	Delta	p-Value	Result
Pesaran–Yamagata (2008) [30] Delta Test	12.100	0.000 ***	Slopes are heterogeneous
Adj. Delta Test	13.423	0.000 ***	Slopes are heterogeneous

*** under the null hypothesis for slope homogeneity, Delta and adj. Delta tests have an asymptotic normal distribution. The significance level is less than 1% (p < 0.01).

.

Assuming that the slope coefficients are constant across all cross-sections is the null hypothesis (H0).

Heterogeneity, or variation across cross-sections, is suggested by the slope coefficients, according to the alternative hypothesis (H1).

Both types of p-values are much lower than 0.05 and even lower than 0.01, according to the findings. This points to trend coefficient heterogeneity and implies that the null hypothesis (H0) should be rejected.

4.3. Unit Root Test

According to Pesaran [31], The Cross-Sectional Dependency Sensitive Augmented Dickey–Fuller (CADF) test evaluates the presence of unit roots in panel data sets. This test accounts for cross-sectional dependencies neglected by conventional unit root testing, resulting in more dependable outcomes. The conventional Augmented Dickey–Fuller (ADF) test for panel data is articulated as follows:

$$\Delta y_{it}={\alpha }_i+{\beta }_i{y}_{it}+{\sum }_{k=1}^{p_i}{\gamma }_{ik}\Delta y_{it-k}+{ϵ}_{it}$$

(4)

In this context, Yit represents the observation of panel member i at time t, α_i is the constant term, β_i is the lagged adjustment coefficient, γ_ik are the coefficients of the lagged differences, and ϵ_it is the error term. Pesaran’s CADF test is designed to address cross-sectional dependency and is formulated as follows:

$$\Delta y_{it}={\alpha }_i+{\beta }_i{y}_{it}+{\sum }_{k=1}^{p_i}{\gamma }_{ik}\Delta y_{it-k}+{ϵ}_{it}+\delta y¯t-1+ϵit$$

(5)

The observed stationarity levels in

Table 4. Unit root test (Pesaran’s CADF).

Variables	T-Bar	%10 CV	%5 CV	%1 CV	Z[t-bar]	p-Value	Result
D.CO2	−2.707	−2.140	−2.250	−2.440	−3.729	0.000 ***	Stationary at level I(I)
D.CH4	−2.916	−2.140	−2.250	−2.440	−4.561	0.000 ***	Stationary at level I(I)
ln_GCF	−2.460	−2.140	−2.250	−2.440	−2.746	0.003 ***	Stationary at level I(0)
ln_GDPpCa	−2.567	−2.140	−2.250	−2.440	−3.171	0.001 ***	Stationary at level I(0)
D.RenEnergy	−3.829	−2.140	−2.250	−2.440	−8.197	0.000 ***	Stationary at level I(0)

significance levels are denoted by ***, which stand for 1, 5, and 10%, respectively.

—with some variables stationary at I(0) and others at I(1)—justify the use of panel ARDL-based models. This mixed integration order would render techniques like panel cointegration or FMOLS unsuitable. Moreover, the presence of cross-sectional dependence and slope heterogeneity further supports the choice of AMG and CCEMG estimators, which are specifically designed to address such issues while exploring long-term dynamics.

4.4. AMG (Augmented Mean Group) and CCMG (Common Correlated Effects Mean Group) Estimators

Based on the presence of both cross-sectional dependence and slope heterogeneity among the panel units, along with mixed stationarity levels (I(0) and I(1)), this study applies second-generation panel data estimation techniques capable of handling these characteristics. Specifically, AMG and CCEMG estimators were employed to model long-term equilibrium relationships as these methods incorporate both heterogeneity and cross-sectional dependence by design. Additionally, to capture short-term dynamics and address potential endogeneity issues, the System GMM approach was applied. These methods were chosen over alternatives such as PMG and FMOLS due to their superior performance in preliminary robustness checks and their methodological suitability for heterogeneous macro panels.

The Augmented Mean Group (MG) estimator is a technique designed to estimate long-term associations in heterogeneous panel data sets. This approach enhances the conventional Mean Group (MG) estimator by incorporating a shared dynamic process that considers cross-sectional dependency [32].

In the panel data model, where yit represents the dependent variable and x_it denotes a k × 1 vector of the independent variables, the overall model may be articulated as follows:

$$y_{it}={\alpha }_i+{\beta }_i^{\prime }{x}_{it}+u_{it}$$

(6)

where i = 1, …, N denotes nations, t = 1, …, T signifies time periods, α_i indicates country-specific fixed effects, β_i is a k × 1 vector of coefficients for each country, and u_it is the error term. To account for cross-sectional dependency, u_it is modeled as follows:

$$u_{it}={\lambda }_i{f}_t+{\epsilon }_{it}$$

(7)

where λ_i denotes country-specific factor loadings, ft signifies common factors (common dynamic process), and ϵit represents the idiosyncratic error term. The AMG estimator augments the uit term to incorporate common variables and integrates a shared dynamic process (Rc) into the model:

$$y_{it}={\alpha }_i+{\beta }_i^{\prime }{x}_{it}+{\gamma }_i{R}_c+{\epsilon }_{it}$$

(8)

Here, Rc denotes the shared dynamic process, which is associated with ftf. The AMG estimator is a technique that concurrently tackles heterogeneity and cross-sectional dependency in the study of panel data. The conventional MG (Mean Group) estimate considers the heterogeneity among nations while disregarding cross-sectional dependency. Conversely, the AMG estimator incorporates a shared dynamic process into the model to rectify this shortcoming and also considers cross-sectional dependency. The AMG estimate outcomes are presented in the table below.

The Common Correlated Effects Mean Group (CCEMG) estimator is a sophisticated panel data estimating technique introduced by Pesaran [32] that considers cross-sectional dependency.

The CCEMG estimator retains the heterogeneity consideration characteristic of the Mean Group (MG) and Augmented Mean Group (AMG) estimators while enhancing the model’s estimation performance by addressing cross-sectional dependency (CSB) from a broader perspective.

In the panel data model, where yit represents the dependent variable and xit denotes the independent variable vector of size β for each nation with a dimension of k × 1, the general model is articulated as follows:

$$yit=\alpha i+\beta i\prime xit+uit$$

(9)

To address cross-sectional dependency (CSB), the error term is formulated as follows:

$$uit=\lambda ift+ϵit$$

(10)

where λi denotes country-specific factor loadings, ft signifies common variables within the panel data set (such as global economic shocks and policy changes), and ϵit indicates the idiosyncratic error term. This structure may lead to correlations among individual countries in the panel data model, and conventional MG or AMG estimators are unable to fully account for this dependency. The estimation results for AMG and CCEMG are presented below.

The findings presented in

Table 5. Panel ARDL estimation (AMG and CCEMG).

Variable	AMG	p-Value (AMG)	CCEMG	p-Value (CCEMG)	Result
CH4	1.0259	0.008 ***	1.2749	0.000 ***	Statistically Significant and Positive
ln_GCF	96.7884	0.187	−0.3837	0.984	Insignificant
ln_GDPpCa	−23.3100	0.711	18.7952	0.381	Insignificant
RenEnergy	−15.4232	0.536	−2.7808	0.165	Insignificant

significance levels are denoted by ***, which stand for 1, 5, and 10%, respectively.

indicate that CH₄ emissions lead to a notable increase in CO₂ emissions. The relationship between capital accumulation (ln_GCF) and economic growth (ln_GDPpCa) shows no significant impact on CO₂ levels. The utilization of renewable energy contributes to a decrease in CO₂ emissions; however, the results are not statistically significant.

Although the AMG and CCEMG estimators revealed no statistically significant relationship between capital accumulation or renewable energy and CO₂ emissions, the dynamic System GMM model indicated a significant positive effect of capital stock. This divergence can be attributed to methodological differences: the AMG and CCEMG methods capture long-run average effects across heterogeneous panels, while the System GMM approach focuses on short- to medium-term dynamics and addresses endogeneity through internal instruments. The dynamic specification in the GMM may better capture the delayed environmental effects of capital formation, particularly in developing countries with lagging policy implementation.

4.5. System GMM (Blundell and Bond) Estimate

Various estimation methods are employed in panel data analysis to assess the dynamic connections among variables. Conventional fixed and random effects models are inadequate in addressing the issue of endogeneity between lagged dependent variables and independent variables [33]. This circumstance may result in skewed and inconsistent estimate outcomes.

To address this issue, the “First-Difference GMM” estimator proposed by Arellano and Bond [34] is employed to mitigate the endogeneity problem in panel data models. This approach is associated with challenges in generating effective estimators, particularly in tiny time-dimensional panels (small T, big N). Blundell and Bond [35] devised the “System GMM” estimator to address this problem. System GMM enhances the First-Difference GMM approach by employing lagged variables as endogenous instruments, yielding more robust and trustworthy estimations.

A panel data model may be articulated as follows, where yit represents the dependent variable and xit denotes the vector of the independent variables.

$$yit=\alpha yi,t-1+\beta xit+\mu i+ϵit$$

(11)

In this context, i denotes N panel units (such as countries or firms), t signifies T time periods, α and β are the coefficients to be estimated, μi indicates individual fixed effects, and ϵit represents the error term.

The System GMM technique, established by Blundell and Bond in 1998, seeks to achieve more reliable estimates by integrating the “First-Difference GMM” and “Level GMM” methodologies. This model has two phases:

(a)

First-Difference GMM Approach

The model is reformulated by applying first differences to eliminate fixed effects and potential temporal correlation.

$$\left(yit-yi,t-1\right)=\alpha \left(yi,t-1-yi,t-2\right)+\beta \left(xit-xi,t-1\right)+\left(ϵit-ϵi,t-1\right)$$

(12)

This transformation eliminates the fixed effects μi. In the first difference model, the lagged dependent variable (yi,t-1–yi,t-2) may induce an endogeneity issue. Consequently, the First-Difference GMM technique employs lagged data as instrumental variables.

(b)

Level GMM Approach

Alongside the aforementioned model, System GMM estimates a supplementary equation incorporating the variable levels as follows: λi denotes country-specific factor loadings, ft signifies common factors within the panel data set (such as global economic shocks and policy changes), and ϵit represents the idiosyncratic error term.

$$yit=\alpha yi,t-1+\beta xit+\mu i+ϵit$$

(13)

Nonetheless, individual effects μi in this model may induce an endogeneity issue. System GMM employs lagged levels as instrumental variables for estimating difference equations and utilizes lagged differences as instrumental variables for the levels’ equations. The coefficients derived from the Arellano–Bond GMM model are displayed in

Table 6. System GMM model (Blundell and Bond).

Variable	Coefficient	Std. Error	Z-Stat	p-Value	Result
L.CO2 (Lagged)	0.7212	0.1723	4.19	0.000 ***	Statistically Significant and Positive
CH4	0.2745	0.1512	1.82	0.069 *	Statistically Significant and Positive
ln_GCF	119.8477	50.9913	2.35	0.019 **	Statistically Significant and Positive
ln_GDPpCa	0.0982	27.7317	0.00	0.997	Insignificant
RenEnergy	−1.5386	1.9792	−0.78	0.437	Insignificant
Constant	−3012.445	1160.641	−2.60	0.009 **	Statistically Significant and Negative

significance levels are denoted by ***, **, and *, which stand for 1, 5, and 10%, respectively.

.

Table 6 indicates that elevated CO₂ emissions in the preceding era led to increased CO₂ emissions in the present period. Methane emissions (CH₄) exert an escalating influence on CO₂ emissions, yet their statistical significance is constrained. Capital stock (ln_GCF) elevates CO₂ emissions, and this impact is statistically significant. GDP (ln_GDPpCa) and renewable energy use (RenEnergy) do not significantly influence CO₂ emissions.

The GMM model’s error factors’ autocorrelation is evaluated using the Arellano and Bond [34] test. This assessment evaluates the model’s validity by examining the autocorrelation levels, particularly AR(1) and AR(2).

AR(1) Test: Assesses the presence of first-order autocorrelation. Autocorrelation is anticipated to be present.

AR(2) Test: Assesses the presence of second-order autocorrelation. AR(2) autocorrelation may indicate an erroneous model specification.

The results of the AR(1) and AR(2) tests are presented in

Table 7. Arellano–Bond autocorrelation tests.

Test	Z-Value	p-Value	Result
AR(1) Autocorrelation	−1.56	0.119	No Autocorrelation
AR(2) Autocorrelation	−1.34	0.179	No Autocorrelation

.

This not only proves that the model is consistent with time but also implies that the estimator does not lack reliability. Based on the outcomes of the tests, the GMM model produces a reliable estimate.

In GMM models, it is essential to ascertain whether the instrumental variables are over-identified. The Hansen and Sargan tests are utilized for this purpose. The Hansen test (Robust Test) assesses the validity of the instrumental variables. If the p-value exceeds 0.05, the instrumental variables are deemed valid. This power may diminish if an excessive number of instrumental variables are included. The Sargan test (Non-Robust Test) resembles the Hansen test, although it is susceptible to heteroskedasticity. If the p-value is less than 0.05, the instrumental factors may be over-identified. These experiments confirm that the System GMM model yields credible estimates. The Hansen and Sargan tests were employed to assess the validity of the instrumental variables utilized in the System GMM model.

The Hansen test results (p = 0.428) indicate that the instrumental variables are legitimate in

Table 8. Hansen and Sargan tests.

Test	Chi² Value	p-Value	Result
Sargan Test	22.77	0.000	There may be too many instrumental variables.
Hansen Test	3.84	0.428	Instrumental variables are valid.

. The Sargan test (p = 0.000) suggests an excessive number of instrumental variables. Nevertheless, given that the Hansen test result is satisfactory, the model may be deemed credible. This outcome corroborates the legitimacy of the instrumental factors employed.

4.6. Panel Granger Causality Test

One of the main goals of econometric analysis is to determine the causal relationship between variables. A method of determining if one variable predicts the future values of another is the Granger causality test, which was developed by Granger in 1969 [36].

The Granger causality test was originally developed for time series data, and there can be some difficulties when applying it directly to panel data sets. A Granger causality test was created especially for panel data sets by Dumitrescu and Hurlin [37].

Taking into account the heterogeneity included in the panel data format, the Panel Granger Causality test evaluates whether an average causal relationship exists across all panel units.

The Panel Granger Causality Test evaluates the hypothesis that the variable xit Granger causally influences the variable yit.

H0: 

γi, k = 0, ∀k, ∀i

H1: 

At least one for i γi, k ≠ 0.

By taking into account panel data heterogeneity and recognizing the possibility of different correlations between cross-sections, this test produces reliable results. Instead of concentrating on a specific nation, business, or other comparable entity, it assesses average causation over all panel units.

Capital accumulation (ln_GCF), economic growth (ln_GDPpCa), and renewable energy use (RenEnergy) all have a causal influence on CO₂ emissions in the Granger sense, according to the findings of the Panel Granger Causality Test, which are shown in

Table 9. Panel Granger Causality Test.

Variables	Z-Bar	p-Value	Result
ln_GCF → CO2	5.0347	0.0000 ***	Causality exists.
ln_GDPpCa → CO2	4.4876	0.0000 ***	Causality exists.
RenEnergy → CO2	9.5103	0.0000 ***	Causality exists.

significance levels are denoted by ***, which stand for 1, 5, and 10%, respectively.

. These findings demonstrate that CO₂ emissions are influenced by both economic and environmental factors.

The environmental effects of industrialization, infrastructural investments, and economic growth processes are specifically reflected in the causal effect of capital accumulation (ln_GCF) on CO₂ emissions. An economy’s increased capital accumulation raises energy consumption, which, in turn, drives up the use of fossil fuels and, consequently, CO₂ emissions. This finding indicates that in order to control the environmental effects of industrial production and infrastructural growth, more funds should be allocated to renewable energy sources and sustainable production methods.

The Granger causal link that exists between economic growth (ln_GDPpCa) and CO₂ emissions aligns with the data corroborating the growth–emissions nexus [10]. Environmental deterioration may worsen as a result of the increase in industrial activity and energy consumption during the early phases of economic expansion. However, by increasing expenditure on renewable energy, growth may ultimately reduce emissions. More in-depth research is required since this relationship is nonlinear and differs by country. The Environmental Kuznets Curve (EKC) is another means of explaining this result. Lastly, the Granger causal link between CO₂ emissions and the use of renewable energy suggests that increasing the use of renewable energy sources might help lower emissions. This indicates that nations must invest in renewable energy. Some studies claim that investments in renewable energy have little immediate impact on CO₂ emissions and that energy transformation processes require time [38]. Therefore, policymakers need to develop long-term strategies that encourage the use of renewable energy. More broadly, the findings of our study show that environmental and economic factors significantly impact the quantity of carbon dioxide emissions. Because of this, it is crucial to consider aspects like energy consumption and economic growth while creating environmental legislation. In particular, to achieve sustainable development objectives, investments in renewable energy should be promoted, and the environmental effects of economic growth should be controlled.

The Granger causality test revealed a statistically significant causal relationship between renewable energy usage and CO₂ emissions, whereas the AMG and CCEMG results indicated no significant long-term effect. This discrepancy may reflect the time-lagged effects of renewable energy policies or measurement limitations. Although renewable energy investments have increased in many countries, their overall proportion may still be insufficient to result in measurable emission reductions in the long term. The causality results, however, indicate that renewable energy policies are directionally effective, suggesting the need for persistent and integrated energy transitions to observe stronger impacts.

5. Discussion

This study seeks to examine the interconnections between carbon dioxide (CO₂) emissions, capital accumulation, economic growth, and the utilization of renewable energy sources. The examination of long-term correlations and the directions of causation across variables was made possible by the use of sophisticated panel data estimate methods that account for heterogeneity and cross-sectional dependence. When considering the impact of common variables on CO₂ emissions, estimates derived using the CCEMG technique demonstrate that the outcomes are comparable to those derived using the AMG model. This model indicates that emissions of CH₄ significantly and favorably affect the emissions of CO₂. The interaction between methane (CH₄) and carbon dioxide (CO₂) emissions is intricate, as both are significant greenhouse gases that exacerbate climate change. Although they originate from similar sources, like fossil fuel extraction and agriculture, they do not directly contribute to each other’s emissions. The increase in global temperatures caused by CO₂-driven climate change results in the thawing of permafrost in Arctic regions; this releases previously sequestered organic matter that decomposes, producing CH₄ and CO₂. Methane, which is a more powerful greenhouse gas than carbon dioxide, intensifies heat, establishing a feedback loop [39]. Nevertheless, certain procedures can affect the emissions of both gases [40].

Studies have shown that carbon dioxide emissions are greatly impacted by economic development, capital accumulation, or renewable energy [41,42]. This situation illustrates how the variables affecting CO₂ emissions may vary from nation to nation and how models that account for heterogeneity are crucial when choosing a panel data analysis technique.

The findings of the Granger Causality Test of the panel data demonstrate that the variables of economic growth (ln_GDPpCa), capital accumulation (ln_GCF), and the use of renewable energy (ln_RenEnergy) have a Granger causal effect on CO₂ emissions. This study’s conclusions show that environmental factors and economic processes both significantly affect the quantity of carbon dioxide emissions. To be more precise, understanding the causal link between capital accumulation and carbon dioxide emissions requires taking into account the environmental impacts of industrialization and large-scale investments. In a comparable approach, Vakil [43] emphasizes the influence of economic processes on environmental results by demonstrating that economic expansion Granger causes CO₂ emissions among various groups with differing levels of economic development.

The causal link between economic development and CO₂ emissions can be associated with the Environmental Kuznets Curve (EKC) theory. This hypothesis posits that investments in sustainable energy and environmental awareness lead to a reduction in emissions above a certain income threshold, notwithstanding an initial rise during the early phases of economic growth. However, a regression analysis failed to find a statistically significant relationship between economic growth and carbon dioxide emissions. A regression analysis identifies correlations rather than establishing causality, indicating that other underlying factors may affect the observed patterns. The lack of statistical significance in this study may stem from the selection of countries that are at different stages of the EKC trajectory. While some countries may still be experiencing rising emissions due to industrialization, others may have reached the turning point at which environmental policies and clean energy investments drive emissions downward. This heterogeneity suggests that the EKC theory may not be applicable across all nations and time periods, as the environmental effects of economic growth are shaped by country-specific factors such as policy frameworks, technological advancements, and levels of globalization. Wang et al. [44] conducted a supporting study on the N-shaped Environmental Kuznets Curve (EKC) using a panel of 214 nations, incorporating 12 classic and developing factors, including institutions and hazards. The findings indicate that the Environmental Kuznets Curve (EKC) theory cannot be applied universally across countries and temporal contexts, revealing a more intricate link between economic expansion and environmental deterioration than the conventional EKC posits.

The identification of a causal link between the utilization of renewable energy sources and CO₂ emissions is a crucial result in the examination of renewable energy legislation and its effects on environmental conservation. Nevertheless, the percentage of energy that comes from renewable sources must be increased because there is no statistically significant link between utilizing renewable energy and reducing CO₂ emissions. Without a doubt, the development of alternatives is necessary to swiftly replace the usage of fossil fuels. Merely increasing investments in renewable energy sources is inadequate. Similarly, Szetela et al. [45] discovered that a one percentage point rise in renewable energy consumption results in a 1.25% decrease in per capita CO₂ emissions. The efficacy of renewable energy in mitigating emissions is influenced by factors including the rule of law and governance quality. The evaluation indicated that trade openness and energy intensity might mitigate the advantages of renewable energy and that augmenting investments in renewable energy only without considering these supplementary aspects may be inadequate.

These findings underline the importance of incorporating environmental regulations into capital investment strategies. In developing countries, infrastructure and industrial investments often lack sufficient environmental oversight, leading to increased emissions. The positive association between capital accumulation and CO₂ emissions in the GMM model suggests that without strict environmental governance, economic expansion may counteract sustainability goals. Therefore, countries must adopt tailored policy frameworks that enforce emission standards alongside development planning, especially in high-emission sectors.

6. Conclusions

The results of this study underscore the intricacy of the interplay among economic growth, capital accumulation, renewable energy utilization, and CO₂ emissions. Although these factors often affect emissions, their impacts are not consistent across all countries. Divergences in industrial composition, energy reliance, technological progress, and policy frameworks result in substantial discrepancies in the interaction of these variables. For example, while certain industrialized nations may achieve decreased emissions through a shift to cleaner energy and more efficiency, emerging economies may continue to depend significantly on fossil fuels despite their investments in renewable sources. This indicates that a universal approach to environmental policy may be ineffective, underscoring the need for tailored policies that consider economic and structural disparities within countries.

This analysis highlights the necessity of long-term energy planning and continuous investments in renewable energy sources to facilitate a gradual yet successful transition from fossil fuels. Policymakers must concentrate on customizing solutions that correspond to their own economic and industrial contexts, using both regulatory and market-oriented strategies to promote sustainable growth. Moreover, subsequent studies should employ strategies that more effectively reflect structural disparities among nations, such as panel data analyses utilizing heterogeneous modeling techniques. This would provide a more sophisticated understanding of the interplay between economic growth, capital accumulation, and renewable energy adoption concerning CO₂ emissions, ultimately resulting in a more efficient and focused climate policy. This study clarifies the intricate interplay of economic growth, capital accumulation, renewable energy use, and CO₂ emissions, demonstrating that their effects vary between nations due to differences in industrial structure, energy reliance, technical advancement, and policy frameworks. Although many developed nations mitigate emissions via efficiency enhancements and transitions to clean energy, emerging economies frequently continue to depend on fossil fuels despite investments in renewable sources, suggesting that a universal environmental strategy may be ineffectual. These findings underscore the need for comprehensive energy planning and customized policies that correspond to each nation’s economic and industrial framework, employing both regulatory and market-oriented strategies to foster sustainable growth. Future research should integrate heterogeneous modeling tools in panel data analysis to more accurately reflect structural inequities, resulting in more effective and targeted climate policies.