Drivers of CO₂ Emissions in Brics Countries: A Comparative Analysis Using Stirpat and Ardl Models

Sanjiv Sarkar^1*, B. Mathavan²

¹Department of Economics, Faculty of Arts, Annamalai University, Annamalai Nagar, Chidambaram, Tamil Nadu, India – 608002.

²Department of Economics, Faculty of Arts, Annamalai University, Annamalai Nagar, Chidambaram, Tamil Nadu, India – 608002.

Abstract

Environmental sustainability has become a pressing challenge for BRICS nations due to rapid industrialization, rising energy demand, and accelerated economic growth. This study examines the determinants of CO₂ emissions in BRICS countries by analyzing the influence of population, affluence, technology, and industrialization. The research problem centers on understanding whether socioeconomic development patterns in these emerging economies contribute to worsening environmental degradation. The study employs the STIRPAT framework and an Autoregressive Distributed Lag (ARDL) model using annual data from internationally recognized sources. Unit root testing, panel regression, cointegration analysis, and diagnostic evaluations were conducted to ensure statistical validity and robustness. The empirical findings demonstrate that economic growth is the most significant driver of CO₂ emissions, with strong positive elasticity across models. Technology, proxied by energy intensity, also increases emissions, indicating reliance on fossil-fuel-dependent and inefficient energy systems rather than environmentally friendly innovations. Industrialization shows a consistent positive effect, confirming that manufacturing-driven growth remains carbon intensive. Population growth reveals a smaller but statistically meaningful influence. Cointegration results confirm a long-run equilibrium relationship between emissions and their determinants, while the negative and significant error correction term indicates long-run adjustment after short-run disturbances. The discussion highlights the need for green technological transition, energy efficiency reforms, and sector-specific decarbonization strategies. Policy recommendations include carbon pricing, renewable energy expansion, environmental governance strengthening, and sustainable industrial restructuring. The study concludes that BRICS countries must decouple economic growth from emissions to ensure a sustainable developmental trajectory. Future research should consider sectoral emissions, renewable energy indicators, and nonlinear modelling to deepen insights.

Keywords: BRICS, CO₂ emissions, STIRPAT, ARDL, energy intensity, economic development, industrialization, population dynamics, sustainability policy.

1.0            INTRODUCTION

The BRICS economies—Brazil, Russia, India, China, and South Africa—have emerged as major contributors to global carbon emissions due to rapid urbanization, industrial expansion, and structural economic transformation. These countries collectively account for a substantial share of global CO₂ emissions, driven primarily by accelerated economic growth, rising energy demand, and increasing industrial activity (Koilakou et al., 2024; Zakarya et al., 2015). Rapid industrialization and energy consumption in BRICS countries significantly contribute to global emissions, as these economies continue to rely heavily on fossil-fuel-based energy systems to sustain growth (Koilakou et al., 2024; Zakarya et al., 2015; Li et al., 2021).

The relationship between economic development and environmental degradation has been widely examined in environmental economics, particularly in the context of emerging economies. Studies suggest that while economic growth improves living standards, it often leads to increased energy consumption and environmental pressure, especially in the early stages of development (Li et al., 2021; Mohanty & Sethi, 2021). In BRICS nations, this challenge is more pronounced due to their dual objective of maintaining high economic growth while transitioning toward sustainable development pathways.

To analyze the determinants of environmental impact, the STIRPAT (Stochastic Impacts by Regression on Population, Affluence, and Technology) model has become a widely accepted analytical framework. Originally developed by (Dietz and Rosa, 1997) and extended by (York et al., 2003), the STIRPAT model allows for flexible empirical estimation of how demographic, economic, and technological factors influence environmental outcomes. Empirical applications of STIRPAT in BRICS contexts highlight that population growth, affluence, and energy intensity significantly affect carbon emissions (Mohanty & Sethi, 2021; Razzaq et al., 2021).

In addition to structural analysis, understanding the dynamic relationship between emissions and their determinants is equally important. The Autoregressive Distributed Lag (ARDL) model, developed by (Pesaran et al., 2001), has been extensively used to examine both short-run and long-run relationships in environmental studies. Recent studies applying ARDL techniques in BRICS countries confirm that economic growth, energy consumption, and industrialization exert significant long-term impacts on CO₂ emissions, while short-run effects vary across countries (Tukhtamurodov et al., 2024; Chishti & Sinha, 2022).

Despite the growing body of literature, existing studies reveal mixed findings regarding the role of technology and energy intensity. While technological advancement is often expected to reduce emissions, empirical evidence suggests that in many emerging economies, technology remains energy-intensive and fossil-fuel dependent, thereby increasing emissions instead of mitigating them (Mohanty & Sethi, 2021; Erkılıç et al., 2025). Furthermore, the magnitude and direction of emission drivers differ significantly across BRICS countries due to variations in economic structure, policy frameworks, and energy mix (Hamrouni, 2025; Mehta & Shah, 2024).

Given these complexities, a comprehensive and comparative analysis of CO₂ emission drivers across BRICS countries is essential. While prior studies have examined these determinants individually or within single-country frameworks, limited research has integrated both structural decomposition and dynamic modelling approaches to capture the full spectrum of emission dynamics. Therefore, combining the STIRPAT framework with ARDL modelling provides a more robust analytical approach to understanding both the structural drivers and temporal adjustments of emissions. This integrated approach enables policymakers to design targeted and country-specific strategies for achieving sustainable development and carbon reduction goals.

1.1 Scope and significance of the study

This study focuses on identifying and analyzing the key drivers of CO₂ emissions in BRICS countries using the STIRPAT framework and ARDL modelling, covering both short-run and long-run dynamics (Li et al., 2021). The scope includes demographic, economic, technological, and energy-related determinants, allowing cross-country comparative insights. The study’s significance lies in its potential to inform policymakers about country-specific and collective mitigation strategies, as BRICS nations significantly influence global carbon trajectories (Koilakou et al., 2024). Additionally, integrating structural decomposition with dynamic modelling provides a robust methodological contribution, helping to bridge gaps in existing research on environmental sustainability, economic growth, and energy policy in emerging economies (Zakarya et al., 2015).

1.2 Statements of the problem

The BRICS countries—Brazil, Russia, India, China, and South Africa—have experienced rapid industrialization, urbanization, and economic growth, resulting in significant increases in CO₂ emissions. Despite global efforts to mitigate climate change, these nations continue to contribute a substantial share of global greenhouse-gas emissions, posing challenges for sustainable development and environmental policy. While population growth, economic expansion, energy consumption, and technological factors are recognized as major drivers of emissions, the relative impact of each factor differs across countries due to structural, policy, and energy-mix variations. Existing studies often analyze these drivers independently or focus on individual countries, limiting the ability to design coordinated or country-specific interventions. Therefore, there is a critical need to systematically examine and compare the key drivers of CO₂ emissions across BRICS nations using robust analytical frameworks like STIRPAT and ARDL. This approach can identify the most influential economic, demographic, and energy-related factors shaping emission patterns and inform targeted mitigation strategies.

1.3 Objectives

To examine and compare the key drivers of CO₂ emissions across BRICS countries using the STIRPAT and ARDL models, in order to identify the most influential economic, demographic, and energy-related factors shaping emission patterns.

1.4 Novelty and Contribution of the Study

This study makes several important contributions to the existing literature on environmental economics and sustainability. First, it integrates the STIRPAT framework with ARDL modelling, thereby combining structural decomposition with dynamic time-series analysis within a single empirical framework. Second, it provides a comparative country-level analysis across BRICS economies, capturing cross-country heterogeneity that is often overlooked in panel-based studies. Third, the study reinterprets technological factors using energy intensity, offering new insights into whether technological development in emerging economies contributes to or mitigates environmental degradation. Finally, by simultaneously examining short-run and long-run relationships, the study provides a more comprehensive understanding of emission dynamics, which is essential for designing effective and targeted environmental policies.

2.0 OVERVIEW OF REVIEWED LITERATURE AND RESEARCH GAP

The drivers of CO₂ emissions in BRICS countries have been extensively examined in the environmental economics literature using both structural and dynamic modelling approaches. A substantial number of studies have applied the Autoregressive Distributed Lag (ARDL) model to analyze short-run and long-run relationships between socio-economic variables and environmental degradation. For instance, (Tukhtamurodov et al., 2024) employed a dynamic panel ARDL approach and found that GDP, energy consumption, and industrialization significantly increase CO₂ emissions across BRICS economies. Similarly, (Chishti and Sinha, 2022) investigated the impact of technological and financial innovation shocks using ARDL and reported that certain forms of technological advancement may initially exacerbate emissions before contributing to environmental improvement.

In parallel, the STIRPAT framework has been widely utilized to examine the structural determinants of environmental impact, particularly the roles of population, affluence, and technology. (Mohanty and Sethi, 2021) extended the STIRPAT model by incorporating outward foreign direct investment and identified an inverted-U relationship between economic growth and emissions, suggesting the possibility of environmental improvement at higher levels of development. (Mehta and Shah, 2024) further analyzed the asymmetric effects of energy mix, financial development, and income, highlighting that renewable energy adoption and financial deepening can contribute to reducing emissions. Additionally, governance and institutional factors have been found to play a critical role; (Hamrouni, 2025) demonstrated that trade openness and policy uncertainty tend to increase emissions, whereas environmental technologies and regulatory stringency help mitigate them.

Recent studies also emphasize the importance of green technological innovation and nonlinear dynamics in understanding emission patterns. (Razzaq et al., 2021) showed that green technology innovation has a stronger emission-reducing effect at higher emission levels, indicating scale-dependent and nonlinear relationships. Furthermore, (Cheng et al., 2023) combined Data Envelopment Analysis (DEA) with the STIRPAT model to assess sustainable development efficiency, confirming that population growth and economic expansion exert significant upward pressure on emissions in both BRICS and G7 countries. Collectively, these studies highlight the complex, multidimensional, and heterogeneous nature of CO₂ emission drivers in emerging economies.

Despite this growing body of literature, several important scientific gaps remain insufficiently addressed. First, most existing studies rely on either the STIRPAT framework or ARDL modelling independently, thereby limiting the ability to simultaneously capture both structural relationships and dynamic temporal adjustments. While STIRPAT-based studies effectively analyze the impact of population, affluence, and technology on environmental degradation (York et al., 2003; Mohanty & Sethi, 2021), they often fail to incorporate time-series dynamics and long-run equilibrium relationships. Conversely, ARDL-based studies (Pesaran et al., 2001; Chishti & Sinha, 2022) focus on short-run and long-run dynamics but lack a strong theoretical decomposition of environmental drivers.

Second, a significant portion of the literature focuses on single-country case studies or pooled panel analyses, which overlook cross-country heterogeneity within BRICS nations. Given the substantial differences in economic structure, energy consumption patterns, and policy frameworks among BRICS economies, a lack of comparative country-specific analysis limits the applicability of policy recommendations (Razzaq et al., 2021; Mehta & Shah, 2024).

Third, existing studies often treat technological factors as uniformly emission-reducing, without critically examining the role of energy intensity as a proxy for inefficient or fossil-fuel-based technological systems. This leads to an incomplete understanding of whether technological progress contributes to environmental sustainability or exacerbates emissions in emerging economies (Erkılıç et al., 2025).

Fourth, limited attention has been given to simultaneously analyzing both short-run and long-run elasticities of emission drivers within a unified framework. Understanding this distinction is crucial, as short-term economic shocks and long-term structural changes may have different implications for environmental policy and sustainability planning (Tukhtamurodov et al., 2024).

In light of these limitations, the present study addresses these gaps by integrating the STIRPAT framework with the ARDL modelling approach in a comparative BRICS context. This combined methodology enables the simultaneous estimation of structural determinants, dynamic adjustments, and country-specific heterogeneity. By doing so, the study provides a more comprehensive and policy-relevant understanding of CO₂ emission dynamics, thereby contributing to both the theoretical and empirical literature on environmental sustainability in emerging economies.

3.0 MATERIALS AND METHODS

3.1 Research Design: This study adopts a quantitative, explanatory, and comparative research design to investigate the determinants of CO₂ emissions across BRICS countries. The analysis integrates both structural and dynamic modelling approaches to capture the complex interactions between environmental and socio-economic variables. Specifically, the study combines the STIRPAT (Stochastic Impacts by Regression on Population, Affluence, and Technology) framework with the Autoregressive Distributed Lag (ARDL) model. This dual approach enables the examination of both cross-sectional structural relationships and time-series dynamic adjustments, thereby providing a comprehensive understanding of emission patterns in emerging economies.

3.2 Population and Study Period: The study focuses on five BRICS countries: Brazil, Russia, India, China, and South Africa. Annual data from 1990 to 2022 is considered to capture long-term structural changes, industrialization, and policy impacts on CO₂ emissions (UN, 2023; Global Carbon Atlas, 2023).

3.3 Data Sources

·        CO₂ emissions (metric tons per capita) – World Bank, Global Carbon Atlas

·        Economic variables (GDP, industrial output, energy consumption) – IMF, World Bank

·        Demographic variables (population, urbanization) – UN, World Bank

·        Energy/technology indicators – International Energy Agency (IEA)

3.4 Variables of the study

3.5 Conceptual Framework: STIRPAT Model

The STIRPAT model, developed by (Dietz and Rosa, 1997) and further extended by York et al. (2003), provides a stochastic reformulation of the deterministic IPAT identity (Impact = Population × Affluence × Technology). Unlike the traditional IPAT framework, which assumes proportional and deterministic relationships, the STIRPAT model allows for statistical estimation, hypothesis testing, and flexibility in capturing nonlinear and elastic relationships between environmental impact and its driving forces.

Mathematically, the STIRPAT model can be expressed as:

Where:

·        III represents environmental impact (CO₂ emissions)

·        PPP denotes population

·        AAA represents affluence (GDP per capita)

·        TTT captures technology (energy intensity)

·        aaa is a constant term

·        b,c,db, c, db,c,d are elasticity coefficients

·        eee is the error term

Taking logarithms, the model is transformed into a linear econometric specification:

This transformation allows the coefficients to be interpreted as elasticities, indicating the percentage change in CO₂ emissions resulting from a one percent change in each explanatory variable. The STIRPAT framework has been widely used in environmental economics due to its ability to incorporate additional variables such as industrialization, urbanization, and energy consumption, thereby improving model flexibility and empirical relevance (York et al., 2003; Mohanty & Sethi, 2021).

3.6 Econometric Framework: ARDL Model

To complement the structural analysis, this study employs the Autoregressive Distributed Lag (ARDL) model, developed by (Pesaran et al., 2001), to examine both short-run and long-run relationships between CO₂ emissions and its determinants. The ARDL approach is particularly advantageous in empirical studies where variables are integrated of mixed order, i.e., I(0) and I(1), but not I(2). This makes it highly suitable for macroeconomic time-series data commonly used in environmental studies.

The general ARDL model specification is expressed as:

Where:

·     Δ\DeltaΔ represents first differences (short-run dynamics)

·     ECTt−1ECT_{t-1}ECTt−1​ is the error correction term capturing long-run equilibrium

·     λ\lambdaλ indicates the speed of adjustment toward equilibrium

·     ϵt\epsilon_tϵt​ is the white-noise error term

The ARDL bounds testing approach is used to determine the existence of a long-run cointegration relationship among variables. If the computed F-statistic exceeds the upper critical bound, a long-run relationship is confirmed (Pesaran et al., 2001). Once cointegration is established, both long-run coefficients and short-run dynamics can be estimated simultaneously.

3.6.1 Error Correction Mechanism (ECM)

An important feature of the ARDL model is the Error Correction Mechanism (ECM), which captures how quickly deviations from long-run equilibrium are corrected. A negative and statistically significant error correction coefficient confirms the existence of a stable long-run relationship and indicates the speed at which the system returns to equilibrium after short-run shocks.

·     A negative and significant ECT coefficient indicates the speed at which deviations from long-run equilibrium are corrected.

3.7 Estimation Procedure

1.               Unit Root Tests: Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests to check stationarity

2.               Model Estimation:

o   STIRPAT regression to estimate elasticities

o   ARDL bounds testing for cointegration and short-run dynamics

3.               Diagnostic Tests: Serial correlation, heteroskedasticity, and stability tests (CUSUM/CUSUMSQ)

4.               Comparative Analysis: Compare elasticities and ARDL coefficients across BRICS countries to identify the most influential drivers.

3.8 Hypothesis of the Study

H1: Population, economic growth (affluence), technology, and industrialization significantly affect CO₂ emissions in BRICS countries.

H1a: Population growth has a statistically significant positive effect on CO₂ emissions in BRICS countries.
H1b: Economic growth (affluence) increases CO₂ emissions in BRICS countries.
H1c: Technology has a statistically significant effect on CO₂ emissions in BRICS countries (direction to be determined empirically).

H1d: Industrialization has a statistically significant positive effect on CO₂ emissions in BRICS countries.

H2: There exists a long-run cointegration relationship between CO₂ emissions and its determinants in BRICS countries.

H3: Population, economic growth, technology, and industrialization have statistically significant short-run effects on CO₂ emissions.

H4: The error correction term (ECT) is negative and statistically significant, indicating convergence toward long-run equilibrium.

H5: The effect of population, economic growth, technology, and industrialization on CO₂ emissions varies across individual BRICS countries.

3.9 Software Tools

·        EViews: ARDL, ECM, cointegration analysis.

·        STATA / R: STIRPAT regression, elasticity estimation.

·        Excel: Data preparation and visualization.

3.10 Ethical Considerations

·        The study uses secondary, publicly available data.

·        Proper citation and acknowledgment of all sources will be ensured.

3.11 Analytical flow chart.

  Fig.1: Analytical Workflow from Data Collection to Model Interpretation.

4.0 RESULTS AND DISCUSSIONS

Table No: 4.1 Descriptive statistics (1990–2022) — by country.

Source: Compiled from World Bank (WDI), IMF, UN Data, IEA, and Global Carbon Atlas datasets.

Table No. 4.1 presents descriptive statistics for the study variables across the five BRICS countries from 1990 to 2022. The values include mean, standard deviation, minimum, and maximum, providing an overview of the distribution and variability of CO₂ emissions, population, affluence (GDP per capita), technology (energy intensity), and industrialization. The results indicate considerable variation between countries in terms of emissions and economic structure. South Africa and Russia have the highest per capita emissions, while India records the lowest, reflecting differences in industrial energy dependence and development levels. China demonstrates significant growth, with a wide range in both GDP per capita and emissions, indicating rapid industrial expansion. Population levels vary substantially, with China and India dominating the BRICS group, reflecting their demographic scale. Energy intensity is highest in China and South Africa, suggesting higher energy consumption relative to economic output. Industrialization is most prominent in China and Russia, consistent with their resource-heavy and export-driven economies. Overall, the descriptive indicators suggest diverse development pathways among BRICS nations. The statistical differences justify the use of econometric methods such as STIRPAT and ARDL for analyzing the dynamic impact of demographic, economic, and technological factors on CO₂ emissions. This summary supports further inferential analysis and hypothesis testing.

Fig No 2: Comparative Analysis of Key Socioeconomic and Environmental Indicators across BRICS Countries (1990–2022).

Table No: 4.2 Pooled Correlation Matrix (log-levels: lnCO₂, lnP, lnA, lnT, lnI).

Source: Author’s calculation using compiled dataset from World Bank, IMF, UN Data, IEA, and Global Carbon Atlas.

Table No. 4.2 presents the pooled correlation results among the log-transformed variables used in the study: carbon emissions (lnCO₂), population (lnP), affluence (lnA), technology (lnT), and industrialization (lnI) across BRICS economies. The correlation matrix indicates varying degrees of association among variables, helping understand initial direction and strength before regression modeling. The results show that lnA (affluence) has the strongest correlation with lnCO₂ (r = 0.72), suggesting that economic growth and increased income levels are strongly associated with higher carbon emissions in BRICS countries. Technology (lnT) also displays a moderate positive correlation with CO₂ emissions (r = 0.59), implying that energy intensity contributes to pollution levels, although the effect may differ depending on efficiency improvements or energy sources. Industrialization (lnI) shows a moderate correlation with lnCO₂ (r = 0.46), indicating that countries with greater industrial activity tend to emit more CO₂. Population (lnP), however, demonstrates a relatively weak correlation with CO₂ emissions (r = 0.18), suggesting demographic size alone may not directly drive emissions without accompanying economic and industrial activities. The correlation levels are below multicollinearity thresholds, justifying the use of regression-based inferential methods. Overall, these results support the conceptual assumption that economic and structural variables are key drivers of CO₂ emissions in BRICS nations.

Table No: 4.3 Stationarity tests (ADF) — summary (levels and first differences).

Source: Author’s empirical computation using time-series data from World Bank, IMF, UN Data, IEA, and Global Carbon Atlas.

Table No. 4.3 reports the results of the Augmented Dickey-Fuller (ADF) unit root test conducted at both level and first-difference forms for the key variables used in the study. The purpose of these tests is to determine whether the data series are stationary, which is essential for selecting the appropriate econometric modeling approach. The results indicate that for most countries, the lnCO₂ variable is non-stationary at level but becomes stationary after first differencing, confirming it as an I(1) process. India represents an exception, where lnCO₂ is already stationary at level, indicating I(0) behavior. Similar mixed results appear for other explanatory variables, particularly affluence (lnA), which is non-stationary at level in countries like Brazil and Russia but becomes stationary at first difference. The presence of mixed integration orders—some variables being I(0) and others I(1)—validates the selection of the Autoregressive Distributed Lag (ARDL) model, as it can accommodate such heterogeneity. No variable is integrated beyond I(1), meaning additional transformations such as second differencing are unnecessary. Overall, the ADF results confirm the empirical suitability of ARDL and justify proceeding with cointegration testing and dynamic modeling to examine long- and short-run relationships between emissions and explanatory variables.

Fig No 3: Stationarity Test Results of Variables Using ADF (Level vs First Difference).

Table No: 4.4 Country-level STIRPAT (log-linear OLS) — Elasticities (short table showing Elasticities B,C,D,f from ln CO₂ on lnP, lnA, lnT, lnI).

Source: Author’s estimation using secondary data from World Bank, IMF, UN Data, IEA, and Global Carbon Atlas.

Table No. 4.4 presents the estimated elasticities from the country-specific STIRPAT regression model, examining the impact of population, affluence, technology, and industrialization on CO₂ emissions across BRICS countries. The results reveal heterogeneous relationships across nations, demonstrating varying developmental and environmental dynamics. Affluence (lnA) emerges as the strongest and most statistically significant predictor across all countries, with China, South Africa, and Russia displaying high elasticities (0.72, 0.92, and 0.85 respectively). This indicates that economic expansion is a key driver of emissions, consistent with growth-led industrialization patterns. Technology (lnT), measured through energy intensity, is also significant across most countries, suggesting that higher reliance on energy input per unit of GDP exacerbates emissions rather than reducing them—implying inefficient or fossil fuel–based energy structures. Population (lnP) shows mixed effects. It is statistically significant in Brazil, India, and China, indicating demographic pressure influences emissions, whereas Russia and South Africa show weak or insignificant population effects, likely due to slower demographic growth. Industrialization (lnI) shows positive but smaller coefficients, significant in Russia, China, and South Africa, highlighting industry’s role in pollution, particularly where manufacturing remains carbon-intensive. Overall, the results support the hypothesis that economic and structural factors significantly contribute to CO₂ emissions in BRICS, with notable cross-country variation.

Table No: 4.5 Panel STIRPAT — Fixed Effects (countries) pooled regression.

Source: Author’s statistical analysis based on compiled dataset from World Bank, IMF, UN Data, IEA, and Global Carbon Atlas.

Table No. 4.5 presents the results of the panel fixed-effects estimation based on the STIRPAT framework, pooling data from the five BRICS countries while accounting for country-specific heterogeneity. The coefficients indicate the direction and magnitude of the impact of population, affluence, technology, and industrialization on CO₂ emissions after controlling for unobserved structural differences across countries. All four explanatory variables are statistically significant at the 5% level or better, confirming their relevance in explaining variations in carbon emissions. Affluence (lnA) has the strongest positive influence (β = 0.61, p < 0.001), suggesting that higher income levels are consistently associated with increased emissions, reflecting the carbon-intensive nature of economic development in BRICS economies. Technology (lnT) also shows a strong positive effect (β = 0.29, p < 0.001), implying that existing technological structures are energy-intensive rather than efficiency-enhancing. Industrialization (lnI) shows a moderate yet significant positive effect (β = 0.12), reinforcing the role of manufacturing and industrial expansion in emission growth. Population (lnP), though weaker than other predictors, remains statistically significant (β = 0.11), indicating demographic contribution to environmental pressure. The model demonstrates strong explanatory power (within R² = 0.78), confirming that the STIRPAT determinants collectively explain a substantial portion of emission variation. These findings support the main hypothesis that socioeconomic and structural variables significantly drive CO₂ emissions in BRICS countries.

Fig. 4: Estimated Coefficient Effects of Population, Affluence, and Technology on CO₂ Emissions.

Table No: 4.6 Multicollinearity check — VIF (pooled STIRPAT Regressors).

Source: Author’s computation from processed regression dataset derived from World Bank, IMF, UN Data, IEA, and Global Carbon Atlas.

Table No. 6 reports the Variance Inflation Factor (VIF) values for the explanatory variables included in the panel STIRPAT model. The purpose of the VIF test is to assess whether multicollinearity exists among the independent variables, which could distort coefficient estimates and weaken statistical inference. The results show that all VIF values range between 1.25 and 2.48, with a mean VIF of 1.75, which is well below the commonly accepted threshold of 5, and significantly below the critical level of 10, which indicates severe multicollinearity. Affluence (lnA) has the highest VIF value (2.48), suggesting that it shares some correlation with other predictors, particularly industrialization and technology, which is expected in developing and emerging economies undergoing simultaneous income growth and structural transformation. However, this value remains acceptable and does not pose a threat to model stability. The lowest VIF belongs to industrialization (lnI), indicating minimal overlap with other independent variables. Overall, the low VIF values confirm that the model variables are sufficiently independent and that multicollinearity is not a concern. This supports the reliability of the estimated coefficients and validates the robustness of subsequent regression and diagnostic procedures.

Table No: 4.7 ARDL bounds test for cointegration — example per country (F-statistic vs critical bounds).

Source: Author’s econometric output using time-series data from World Bank, IMF, UN Data, IEA, and Global Carbon Atlas.

Table No. 4.7 presents the results of the ARDL bounds test conducted for each BRICS country to determine whether a long-run cointegration relationship exists between CO₂ emissions and its determinants: population, affluence, technology, and industrialization. The F-statistic for each country is compared against the critical lower and upper bounds at the 5% significance level to evaluate the presence of cointegration. The findings indicate strong evidence of long-run relationships in Brazil, Russia, and China, where the computed F-statistics (5.86, 6.42, and 8.11 respectively) exceed the upper critical bound value of 4.35. This confirms that the variables move together in the long run, supporting the assumption of structural dependency between emissions and socioeconomic factors. South Africa shows a borderline result (F = 4.02), suggesting possible cointegration but requiring cautious interpretation. In contrast, India’s F-statistic (3.05) falls below the lower bound, indicating no conclusive evidence of long-run equilibrium among the studied variables. Overall, the mixed outcomes justify using country-specific ARDL and ECM models, rather than a uniform pooled approach. The presence of cointegration in most BRICS economies supports the hypothesis that environmental degradation is structurally linked to economic and demographic forces over time.

Fig No 5: Cointegration Analysis Using ARDL Bounds Test: F-Statistic vs Critical Values.

Table No: 4.8 ARDL long-run coefficients and Error Correction Term (ECT) — selected results.

Source: Author’s model estimation using compiled dataset from World Bank, IMF, UN Data, IEA, and Global Carbon Atlas.

Table No. 4.8 presents the long-run elasticity estimates and the Error Correction Term (ECT) coefficients derived from the ARDL model for each BRICS country. These results provide insight into how population, affluence, technology, and industrialization influence CO₂ emissions over time and how quickly deviations from long-run equilibrium are corrected. Affluence (lnA) demonstrates the strongest and most statistically significant long-run effect in all countries, with coefficients ranging from 0.29 in India to 0.88 in South Africa, indicating that economic growth is a major long-term driver of emissions. Technology (lnT) also has a significant positive effect in most economies, suggesting that current technological conditions are energy intensive and emission-generating rather than efficiency oriented. Population impacts are significant in Brazil, India, and China, while industrialization shows moderate but positive long-run effects in Russia, China, and South Africa. The ECT coefficients are negative and statistically significant for all countries except India, confirming long-run stability and adjustment toward equilibrium following short-run fluctuations. Russia and China exhibit the fastest speed of adjustment (−0.53 and −0.47), indicating quicker correction mechanisms. Overall, the results validate the presence of long-run structural relationships between emissions and socioeconomic variables and support the study’s hypothesis on long-run causality.

Fig No 6: Estimated Long-Run Coefficients of Population, Affluence, Technology, and Industrialization on CO₂ Emissions.

Table No: 4.9 ARDL short-run dynamics (Error Correction Model) — example coefficients (ΔlnA and ΔlnT shown).

Source: Derived from ARDL estimation using data from World Bank, IMF, UN Data, IEA, and Global Carbon Atlas.

Table No. 4.9 presents the short-run coefficients derived from the ARDL Error Correction Model (ECM), showing how changes in affluence (ΔlnA) and technology (ΔlnT) influence CO₂ emissions in the short term across BRICS countries. Unlike long-run elasticities, these values capture immediate or transitional effects, reflecting how economic fluctuations, energy use adjustments, and industrial activity shocks impact environmental outcomes over time. The results indicate that short-run affluence effects are statistically significant in Russia, China, and South Africa, demonstrating that rapid economic expansion contributes to immediate increases in emissions. Brazil also shows a positive short-run effect of affluence, though comparatively weaker, while India’s short-run affluence coefficient is insignificant, implying that the effect of economic growth on emissions materializes only in the long run for India. Similarly, the technology variable (ΔlnT) shows mixed significance. It is statistically significant in Russia, India, China, and South Africa, suggesting that short-term changes in energy intensity directly affect emissions. In Brazil, however, the effect is insignificant, indicating slower responsiveness to technological variations. Overall, the results demonstrate that both economic and technological drivers exert short-run influence on CO₂ emissions in most BRICS countries, confirming dynamic adjustment processes and supporting hypothesis H3 regarding short-run relationships.

Fig No 7: Estimated Short-Run Coefficients of ΔlnA and ΔlnT on CO₂ Emissions.

Table No: 4.10 Diagnostic tests (selected) — for ARDL/ECM residuals and model stability.

Source: Author’s internal model validation using dataset from World Bank, IMF, UN Data, IEA, and Global Carbon Atlas.

Table No. 4.10 presents the diagnostic test results conducted to assess the reliability, stability, and statistical validity of the ARDL and Error Correction Model (ECM) estimations across BRICS countries. The diagnostic checks include the LM Serial Correlation Test, Breusch–Pagan Heteroskedasticity Test, Jarque–Bera Normality Test, and model stability tests using CUSUM and CUSUMSQ procedures. The serial correlation results indicate that Brazil, China, and South Africa do not suffer from autocorrelation, while Russia shows borderline results and India exhibits signs of serial correlation, suggesting additional lag adjustments or robust correction may be required for India’s model. The Breusch–Pagan results show no significant heteroskedasticity issues for most countries, except India and partially South Africa, where mild variance instability appears. The normality test results indicate that residuals are normally distributed in Brazil, India, and China, whereas Russia and South Africa show deviations, which are common in macroeconomic time-series data. The CUSUM and CUSUMSQ stability tests confirm that the estimated ARDL models are structurally stable for all countries except India, where borderline instability suggests parameter shifts or structural policy changes over time. Overall, the diagnostic evidence confirms the robustness and suitability of the ARDL-ECM models for most BRICS economies, ensuring reliable inference.

Table No: 4.11 Hypothesis testing.

Source: Author’s synthesis based on all econometric outputs from STIRPAT and ARDL results.