1. Introduction

2. Review of Literature

3. Research Methodology

3.3. Econometric Methodology

The aims of this paper are to explore the how financial development and green technology adoption, collectively influence the carbon emissions of the BRICS countries. The paper used linear and nonlinear autoregressive distributed lag (ARDL) approaches to explore these associations. The results of the Westerlund co-integration show long-run co-integration between the load capacity factor and the independent variables. The investigation focuses on BRICS countries over the period spanning from 2001 to 2023. The research methodology involves several steps: first, assessing the homogeneity of slopes; second, examining cross-sectional dependence in panel data; and third, applying a panel co-integration test. Subsequently, based on the outcomes of these tests, the study selected the econometric model and estimation approach, leading to an analysis of the long-term causal relationships among the variables.

3.3.1. The Slope Homogeneity Test

The issue of varying slopes holds significant relevance in panel data econometrics. We examine slope heterogeneity by employing the Pesaran, & Yamagata (2008) to address this concern. This test assesses slope heterogeneity by analysing the dispersion of the weighted slope for each individual. The test statistics are determined through the following equations.

$$\Delta =\sqrt{N}\left({\displaystyle \frac{N^{-1}S\mathrm{\%}-k}{\sqrt{2k}}}\right)and\Delta adj=\sqrt{N}\left({\displaystyle \frac{N^{-1}S\mathrm{\%}-k}{\sqrt{\frac{2k(T-k-1}{T+1}}}}\right)\dots \dots .3$$

3.3.2. The Cross-Section Dependence Test

To assess cross-sectional dependence, we utilized the CD test Pesaran, (2015). The test statistics are presented as follows:

$$CSD=\sqrt{{\displaystyle \frac{2T}{N\left(N-1\right)N}}}\left({\sum }_{i=1}^{N=1}{\sum }_{K=i+1}^N{Co\mathrm{͡}rr}_{i,t}\right)$$

(4)

3.3.3. Unit Root Test

The well-known first-generation unit root tests such as the Augmented Dickey-Fuller (ADF), Phillips-Perron, Breitung, Maddala, and Hadri tests are widely utilized in econometrics. However, they are not suitable when dealing with issues like (CSD) and (SH) in the data. These problems can undermine the reliability of the results obtained from these traditional tests.

In light of these challenges, a second-generation unit root test known as the Cross-Sectional (CIPS) and the Cross-Sectional (CADF) test, as proposed by (Pesaran, 2007), come into play. These advanced tests are designed to assess the stationarity of variables in panel data, even in the presence of Cross-Sectional Dependence and Slope Heterogeneity. Equation (5) outlines a crucial step in the CIPS test, which involves calculating the cross-sectional mean of “ti.” This mean calculation is a fundamental component of the CIPS test, serving as part of the procedure to determine the stationarity of variables while accounting for the challenges posed by Cross-Sectional Dependence and Slope Heterogeneity.

$$\mathrm{CIPS}={\displaystyle \frac{1}{N}}{\sum }_{i=1}^{N}ti\left(N,T\right)$$

(5)

The Cross-Sectional Augmented Dickey-Fuller (CIPS) test has been gaining appeal in the academic sphere due to its effectiveness in addressing issues related to Cross-Sectional Dependence (CSD) and heterogeneity. In this method, the baseline hypothesis revolves around the unit-root test. If test indicates the variable exhibits stationarity at I (I), it signals the need to proceed with a cointegration test before delving into parameter estimation. To facilitate the CIPS test, the Cross-Sectional Augmented Dickey-Fuller (CADF) method is employed to calculate the necessary statistics. Conversely, Equation (6) for CADF, which stands for Cross-Augmented Dickey-Fuller, can be expressed as follows:

$${\Delta Y}_{it}={\phi }_{i{\prod }_{k=1}^n{A}_k}+{\zeta }_i{Y}_{t,t-1}+{\delta }_i{\mathrm{Ỹ}}_{t-1}+\sum _{j=0}^P{\delta }_{ij}{\mathrm{Ỹ}}_{t-1}+\sum _{j=1}^P{\lambda }_{ij}{\Delta Y}_{i,t-1}+{\epsilon }_{it}$$

(6)

This equation forms the foundation for the Cross-Sectional Augmented Dickey-Fuller Test method, enabling researchers to obtain the essential statistics used in the CIPS test, where Yt-1 and ΔYit-1 are at level (I (0)) and first difference (I (I) of each cross-sectional series.

3.3.4. Co-Integration Test

The examination of cointegration holds significant importance in econometric literature, given that many assumptions in economic theories pertain to long-run implications. Consequently, this study explores the existence of a long-run relationship among integrated series. Given the presence of cross-sectional dependency, the Westerlund, (2008) is employed due to its capability to yield robust and reliable results, as indicated by Pesaran, (2015). The Westerlund cointegration test outperforms conventional cointegration tests by effectively addressing cross-sectional dependence. One notable advantage of this test lies in its utilization of the bootstrap approach technique, which is particularly effective in accommodating cross-sectional dependence. The second-generation Pesaran, (2015), typically comprises four eqations, represented as Equations (7)–(10). These equations serve as the foundation for conducting cointegration analysis in scenarios where panel data exhibits complex characteristics such as cross-sectional dependence, heterogeneity, and non-stationarity.

$$G_a={\displaystyle \frac{1}{n}}{\sum }_{i=1}^N{\displaystyle \frac{{a\mathrm{΄}}_i}{{SE(a\mathrm{΄}}_i)}}$$

(7)

$$G_t={\displaystyle \frac{1}{n}}{\sum }_{i=1}^N{\displaystyle \frac{{Ta\mathrm{΄}}_i}{{a\mathrm{΄}}_i\left(1\right)}}$$

(8)

$$P_t={\displaystyle \frac{{a\mathrm{΄}}_i}{{SE(a\mathrm{΄}}_i)}}$$

(9)

$$P_a=Ta\mathrm{΄}$$

(10)

In the realm of statistical analysis for panel data, there are several sorts of group means statistics represented as Gt and Ga, as well as panel means statistics denoted as Pt and Pa. Each of these statistical measures serves specific purposes and is abbreviated accordingly. When we assume that the model variables are independent, often called the “null” hypothesis, and the alternative hypothesis suggests the existence of co-integration among the variables, we calculate test statistics for this purpose. These statistics help us determine whether the data provides evidence for the presence of these co-integrating relationships or if the null hypothesis of no relationship between the variables holds. Essentially, these statistics are essential for assessing the strength and significance of potential co-integration among the variables being studied.

In this research, the robustness of the estimation outcomes obtained through the ARDL method was verified by conducting FMOLS and DOLS tests. Additionally, panel causality testing was conducted to explore the causal relationships among the variables. For this purpose, the DHC test was employed, which is a variation of the Granger causality test specifically designed for heterogeneous panel datasets with fixed coefficients (Ahmed et al., 2022). The DHC test utilizes the Zbar test to assess normal distribution and the Wbar test to evaluate the mean (Dumitrescu and Hurlin, 2012). It is represented by the following equation:”

$$Z_{it}={\alpha }_i+\sum _{j=1}^p{\beta }_i^j{Z}_{it-j}+{\sum }_{j=1}^p{\gamma }_i^j{T}_{it-j\dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots .}$$

(11)

where j represents the lag length and ${\beta }_i^j$represents the autoregressive parameters.

The null hypothesis and the alternative hypothesis of this test are as follows:

$$H_0={\beta }_i^{\left(k\right)}=0fori\mathrm{n}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{u}\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}$$

$${\beta }_i^{\left(k\right)}=0,i=1,2\dots \dots ..N_{1,}$$

(12)

$$H_1\ne 0i,=N_1+1,N_1+2N_1\dots \dots \dots N\mathrm{Unidirectionally}\mathrm{causality}$$

In this analysis, we utilize the panel ARDL model to estimate the regression. The choice of employing the panel ARDL as an estimation strategy steps from preliminary statistical assessments, particularly testing of unit root, to check the stationarity of the selected series. This study conducts unit root tests including the Im, Pesaran, and Shin W-stat (Im et al., 2003), as well as Augmented Dickey-Fuller (ADF) test, which is introduced by Dickey & Fuller, (1979), and present the results in Table 5. The statistical analysis reveals a mixed trend of stationarity, with some series exhibiting stationarity at level I(0) while others show stationarity at the first difference I(1). Given this mixed trend of stationarity, we opt for the panel ARDL approach for regression analysis. The ARDL model is well-suited to handle different levels of stationarity, cointegration, and endogeneity. Additionally, (Farooq, et al. 2024) demonstrates that the panel ARDL model can provide efficient estimates even with small sample sizes. By incorporating lags, the ARDL model effectively mitigates endogeneity issues. This modelling approach has also been utilized by (Khan et al. 2022) in examining similar sets of variables.

Furthermore, to certify the robustness of the findings, this study employs the fully modified OLS and dynamic OLS models which is used in earlier studies by (Shahbaz, 2009; Priyankara, 2018; Khan et al., 2019; Olofin et. al., 2019; Olorogun, 2023; Ramirez, 2023) These models also facilitate long-run estimation of coefficients, thereby enhancing the reliability of our findings.

Figure 1. Framework of analysis.

Figure 1. Framework of analysis.

4. Results and Discussion

4.3. The Slope of Heterogeneity Test

Table 3 shows the results of the slope homogeneity test, which follows the methodology outlined.The test results reveal a problem with heterogeneity in the model, meaning that the coefficients are not consistent and vary across different countries. This variability in slopes indicates that the relationship between the variables differs from one country to another.

By rejecting the assumption that slopes are homogeneous (i.e., consistent across all countries), the findings suggest that applying a panel causality analysis under the assumption of homogeneous slopes could lead to incorrect conclusions. In other words, assuming that the effect of the independent variable on the dependent variable is the same for all countries may not be accurate and could result in misleading interpretations of the data. This highlights the importance of accounting for these differences to ensure more accurate and reliable analysis.

Table 4 displays the results of the Pesaran (2015) CD test, which checks for cross-sectional dependence in panel data. The results show that cross-sectional dependence exists, meaning that the data points across different sections (e.g., countries) are correlated and not independent of each other. Given the presence of both slope heterogeneity (as identified in Table 3) and cross-sectional dependence, it is crucial to use analytical methods that address these issues. To properly analyze the data, we will utilize second-generation panel unit root tests and cointegration methods. These advanced methods are designed to handle the complexities introduced by both varying slopes and interdependencies across different sections of the panel data, ensuring more accurate and robust results.

The next phase of the research involves ensuring the proper sequence for integrating multiple datasets. Table 5 shows the results from the CIPS, CADF, and Levin panel unit root tests. These tests reveal that some variables are stationary at their levels, indicated as I(0), while others are stationary only after first differencing, indicated as I(1). Due to the mixed integration properties of the variables, where some are I(0) and others are I(1), we use both linear and nonlinear ARDL (Autoregressive Distributed Lag) cointegration methods. These methods allow us to accurately analyze the relationships between the variables despite their different levels of integration, ensuring robust and reliable results in our analysis.

Table 5. Unit Root Test.

Table 5. Unit Root Test.

Cross Section ally Augmented IPS (CIPS)
	Level		First Difference
Variable	Statistics	Prob.	Statistics	Prob.	Decision
LCO2	1.58	0.94	-3.37***	0.00	I(0)
LBM	0.11	0.54	-8.26***	0.00	I(I)
LDCPS	-1.73**	0.04	-10.99***	0.00	I(0)
LFDI	-2.20	0.01	-6.96***	0.00	I(I)
LGTI	1.21	0.11	-3.91***	0.00	I(I)
Cross Section ally Augmented CADF (CADF)
	Level		First Difference
Variable	Statistics	Prob.	Statistics	Prob.	Decision
LCO2	3.55	0.96	31.20***	0.00	I(0)
LBM	9.20	0.90	92.51***	0.00	I(I)
LDCPS	22.93	0.01	35.11***	0.00	I(0)
LFDI	20.86	0.02	60.77***	0.00	I(I)
LGTI	15.60	0.10	37.21***	0.00	I(I)
Cross Section Levin et al. (2002)
	Level		First Difference
Variable	Statistics	Prob.	Statistics	Prob.	Decision
LCO2	0.69	0.75	-2.43***	0.00	I(I)
LBM	-1.84	0.03	-5.09***	0.00	I(I)
LDCPS	-2.95**	0.00	-4.91***	0.00	I(0)
LFDI	-1.38	0.08	-3.55***	0.00	I(I)
LGTI	-3.74	0.00	-2.85***	0.00	I(I)

The panel unit root test was performed under the null hypothesis wherein the variables are homogeneous non-stationary. ***, **, and * denote statistical signifcance level at 1%, 5%, and 10%, respectively.

After completing the unit root tests, the next step is to examine if the variables exhibit a long-term co-integration relationship. Table 6 presents the results from the co-integration assessments using the Westerlund (2007) approach.

The outcomes of the Westerlund panel co-integration test indicate that the statistics lead to rejecting the hypothesis of non-cointegration more frequently at the panel level compared to the individual level. This implies that there is a significant long-term relationship between two or more variables across the panel data. In other words, the variables move together over the long run, confirming the presence of co-integration.

4.4. Pooled Mean Group Autoregressive Distributed Lag (PMG- ARDL) Analysis

In Table 7, the analysis reveals that broad money (LBM) significantly reduces CO2 emissions in the long term, with a 2.88% decrease in emissions in BRICS countries linked to increased LBM. This reduction is due to broad money facilitating investments in green technologies, lowering financing costs, enhancing financial stability, encouraging sustainable practices, ensuring regulatory compliance, and fostering eco-friendly innovations (Batool et al., 2020; Gök, 2020; Neog & Yadava, 2020). These results align with recent studies indicating that financial development improves environmental quality and reduces CO2 emissions in BRICS economies.

Conversely, the analysis shows that LDCPS (domestic credit to the private sector) has a positive and statistically significant impact on carbon emissions, meaning a 1% increase in LDCPS leads to higher emissions. Studies by Ali et al. (2020) and Jianguo et al. (2022) have found that financial development and stock market growth can expand financing options, lower costs, reduce risks, and promote investments, which in turn increase energy consumption and emissions.

However, foreign sector development shows a negative but statistically insignificant impact on carbon emissions, indicating that a 1% increase results in a 0.74% decrease in emissions. FDI can reduce carbon emissions by introducing advanced, energy-efficient technologies and environmentally friendly practices to the host country (Zhu, et al., 2023). Foreign firms often adhere to stricter environmental regulations from their home countries, thereby improving environmental standards and lowering emissions in the host country (Pao & Tsai, 2011). Additionally, FDI can stimulate economic growth, enhancing the host country’s capacity and willingness to invest in environmental protection and sustainable practices (Cole, et al., 2021). On the other hand, FDI can have negative impacts on carbon emissions. It may be directed toward countries with lax environmental regulations, leading to higher emissions as companies exploit these lenient policies (Hoffmann et al., 2005). FDI can also lead to increased industrial production and energy consumption, particularly in carbon-intensive industries, thereby raising emissions (Shahbaz et al., 2015). Moreover, FDI can drive the exploitation of natural resources, resulting in deforestation, land degradation, and higher emissions (Tang & Tan, 2015).

Similarly, green technology innovation (GTI) benefits BRICS countries by reducing carbon emissions. A 1% increase in GTI corresponds to a 0.29% decline in emissions, indicating an adverse relationship between GTI and CO2 emissions. The negative coefficient of GTI suggests that higher levels of GTI can decrease CO2 emissions. Therefore, policies promoting innovation are crucial for minimizing emissions. This is because GTI: (i) Improves operational capabilities while reducing environmental impact, addressing the economic-environmental issue, (ii) Enhances resource use efficiency, encourages sustainable energy development and use, and lowers environmental pollution, (iii)Through advanced technology, efficient energy usage reduces consumption and improves financial development and environmental quality by decreasing CO2 emissions. To create a greener society and improve environmental quality in BRICS economies, it is essential to promote green economic growth and finance strategies, facilitate technology transfer for green investments and trade, focus on R&D, ICT, biotechnology, and nanotechnology, and implement policies that reinforce green innovation in global markets. Technological innovation is also critical in OECD economies for reducing emissions and environmental degradation, consistent with recent research by Guo et al. (2021) and Shan et al. (2021), which found that GTI positively impacts CO2 emissions. Zhao et al. (2022) revealed that GTI mitigates CO2 emissions by improving technological innovation, similar to findings by Bakhsh et al. (2021) that investing in technology innovation helps reduce CO2 emissions. To ensure the reliability of these findings, FMOLS and DOLS tests were conducted, with results presented in Table 8. Figure 2 offers a concise overview of the study’s key findings and insights, providing a clear and efficient summary. Examining Figure 2 will give a comprehensive understanding of the research outcomes. Figure 3 summarizes the model.

The study’s findings are consistent and reliable, as indicated by the results from various estimation methods. The fixed effects model and DOLS (Dynamic Ordinary Least Squares) produced results similar to those obtained through AMG (Augmented Mean Group) and FMOLS (Fully Modified Ordinary Least Squares), despite having different coefficient values. This consistency across multiple methods suggests that the study’s conclusions are robust and dependable.

Table 9. Results of Dumitrescu Hurlin (DH) panel causality tests.

Table 9. Results of Dumitrescu Hurlin (DH) panel causality tests.

Null hypothesis	W-Stat	Zbar-Stat.	Prob.	Direction of causality
LBM $\ne$LCO2	7.91	4.76	2.01	Non-directional causality between REC and LGDP
LCO2 $\ne$LBM	1.78	-0.42	0.67
LDCPS $\ne$LCO2	2.55	0.22	0.82	Non -directional causality between TI and GDP
LCO2 $\ne$LDCPS	7.74	4.62	4.E
LFDI $\ne$LCO2	2.01	-0.23	0.93	Non -directional causality between GDP and ED
LCO2 $\ne$LFDI	1.95**	-028	0.02
LGTI $\ne$LCO2	5.38	2.62	1.23	Uni-directional causality between FS and GDP
LCO2 $\ne$LGTI	2.32	0.03	0.97

Notes: 1. Asterisk(s) ***, **, * represent(s) the rejection of the null hypothesis at 1%, 5% and 10% significance levels. 2. The symbol ≠ implies does not homogeneously cause.

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