Unveiling the dynamic nexuses between foreign investment,trade openness,energy consumption,and CO 2 emissions in South Africa: A vector error correction model approach

Theoretical frameworks

The EKC hypothesis proposes a relationship between economic development and environmental degradation, characterized by an inverted U-shape. ²² In the initial stages of a country’s development, environmental degradation tends to increase, but beyond a certain income threshold, it starts to decline. This suggests that economic growth may have both positive and negative impacts on CO₂ emissions. ²² As South Africa experiences economic growth driven by foreign investment and trade openness, the question arises: does the trajectory of CO₂ emissions align with the expected inverted U-shape?. ²³ The pollution haven hypothesis asserts that FDI might flow to countries with lenient environmental regulations, potentially leading to increased pollution. This hypothesis implies that foreign investment could influence CO₂ emissions, contributing either to environmental improvement or degradation. ²⁴ The trade–environment nexus suggests that international trade, by affecting production and consumption patterns, has implications for the environment. ²⁵ The Porter Hypothesis suggests that trade can drive environmental improvements through innovation. ²⁶ Trade openness may impact CO₂ emissions by changing production efficiency and composition. This study investigates how South Africa’s trade openness influences CO₂ emissions, considering the nature of traded goods, their environmental impact, and whether trade encourages sustainable production practices.^27,28 The relationship between foreign investment, trade, and energy consumption in South Africa holds significance for the country’s progress toward sustainable and low-carbon development, aligning with the United Nations SDGs, particularly Goal 13 (Climate Action). The study’s findings can offer insights for policies and actions aimed at achieving SDGs related to climate change mitigation, considering the broader implications for South Africa’s sustainable development agenda. ²⁹

Empirical review

This section examines the connections among foreign investment, trade openness, energy consumption, and CO₂ output. The association between these pivotal factors encapsulates the complex dynamics that emerge as nations strive to meet the dual objectives of economic prosperity and environmental sustainability. This review navigates the extensive body of literature that has explored these relationships, a concise synthesis of key findings and insights are presented while also identifying gaps that motivate the need for further empirical examination in South Africa.

Literature gaps and contributions

A comprehensive review of the empirical literature highlights a well-established exploration of the linkages between foreign investment, trade openness, energy consumption, and CO₂ emissions. However, there remains a dearth of research focusing on the comprehensive combination of these factors concerning environmental pollution, particularly in the realm of time series analyses, leading to conflicting findings. Consequently, there is a pressing need for further research to enrich the limited discourse on foreign investment, trade openness, energy consumption, and environmental pollution, especially within emerging economies. A noticeable gap exists regarding the absence of studies scrutinizing and contrasting outcomes in South Africa. In light of these identified gaps, this study endeavors to provide valuable policy recommendations. The contributions of this research are outlined across three dimensions. This study marks the pioneering attempt in South Africa to amalgamate foreign investment, trade openness, energy consumption, and environmental pollution into a comprehensive analysis. The study also explores the impact of trade openness on the relationship between foreign investment and environmental pollution. The insights garnered from this investigation hold substantial potential for informing policy formulation aimed at mitigating environmental pollution. Should trade openness demonstrate a favorable influence on both foreign investment and environmental pollution, South Africa stands to gain both economically and environmentally. It is pertinent to note that this study differs from the works of Udeagha and Ngepah ²¹ and Rafindadi and Usman, ⁷ which solely focuses on assessing the direct effects of these variables on environmental degradation.

Data

The data presented in the research covers the entire period from 1990 to 2020. The study period was selected based on the availability of data for both dependent and independent variables and also allows for an exploration of significant political, economic, industrial, and policy changes that have occurred in South Africa over the past three decades, providing context for the analysis. The selected variables in this study align with established academic practice and are chosen based on prior literature and theoretical considerations. The dependent variable, carbon dioxide (CO₂) emissions, measured as per capita metric tons, is utilized in a manner consistent with Li et al., ⁶⁵ reflecting its relevance as a key indicator of environmental pollution. FDI is included as an independent variable, measured as net inflows percent of GDP, following the rationale outlined by Apergis et al. ⁴⁶ and Ekwueme et al. ⁷¹ It is expected that FDI will interact with CO₂ emissions, potentially influencing environmental outcomes through technology transfer, investment in cleaner production processes, and economic development. Trade openness (TRADE), expressed as a proportion of GDP, is another independent variable considered, drawing from the works of Chhabra et al. ⁶⁰ and Haseeb et al.. ⁵² It is anticipated that TRADE may affect CO₂ emissions by influencing the volume and nature of trade activities, thereby impacting energy consumption and environmental pollution levels. EU, quantified as kilograms of oil equivalent per capita, is included based on insights from Adeleye et al. ⁶⁴ and Li et al.. ⁶⁵ EU is expected to have a direct relationship with CO₂ emissions, as higher energy consumption tends to result in increased carbon emissions. Control variables encompass economic growth (GDPG), inflation (INFL), and population (POPG). GDPG, measured as an annual percentage, is included following Ying et al. ⁷² and Zhang et al., ⁷³ reflecting its potential influence on both economic activity and environmental outcomes. INFL, determined by the annual percentage change in consumer prices, is incorporated based on the works of Sadiq et al. ⁷⁴ and Zhang et al., ⁷⁵ considering its impact on economic stability and investment decisions. POPG, measured as an annual percentage of the total population, is included following insights from Cropper and Griffiths, ⁷⁶ Karim et al., ⁷⁷ and Shadman et al., ⁷⁸ recognizing its relevance in demographic dynamics and resource utilization and its impact on the environment. All of the data sources for these variables are derived from the extensive and reputable World Bank’s World Development Indicators (WDI). ⁷⁹ Table 1 succinctly summarizes these variables and presents their units of measurement for clear reference.

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Table 1.

Variables description and abbreviations.

Symbol	Indicator	Unit measurement	Source
CO2	CO2 emissions	Metric tons per capita	WDI
FDI	Foreign investment	Proportion of net inflows to GDP	WDI
TRADE	Trade openness	Proportion of GDP	WDI
EU	Energy consumption	Per capita kilogram of oil equivalent	WDI
GDPG	Economic growth	Annual percentage	WDI
INFL	Inflation	Consumer prices (annual percentage)	WDI
POPG	Population	Annual percentage	WDI

Model

This study aims to examine the connection between foreign investment, trade openness, EU, and CO₂ emissions in South Africa. Specifically, CO₂ is considered the dependent variable, while foreign investment, trade openness, and EU are considered independent variables. Economic growth, inflation, and population growth constitute the study’s control factors. Based on the theories, increased foreign investment may lead to the adoption of cleaner technologies and environmental standards by firms, reducing CO₂ output. Trade openness can affect CO₂ output through changes in production methods, transportation, and consumption patterns. Higher energy consumption is typically associated with higher emissions, but improvements in energy efficiency could mitigate this impact. Economic growth can lead to increased industrial activities, potentially raising CO₂ outflow. Nevertheless, the environmental Kuznets curve theory suggests that emissions may decrease after a certain level of economic development. Inflation may influence emissions through its impact on economic activities and production, and a higher population may lead to increased demand for resources and energy, potentially impacting CO₂ output. It is noteworthy to mention that comparable variable selections can be observed in the research conducted by Li et al.. ⁶⁵ An econometric model for the relationship is expressed as:

CO 2 = f ( FDI , TRADE , EU , Z )

(1)

CO 2 t = β 0 + β 1 FDI t + β 2 TRADE t + β 3 EU t + β 4 GDPG t + β 5 INFL t + β 6 POPG t + ε t

(2)

CO 2 t = β 0 + β 1 F D I t + β 2 TRADE t + β 3 EU t + β 4 GDPG t + β 5 INFL t + β 6 POPG t + β 7 ( FDI × TRADE ) t + ε t

(3)

Methodology

Establishing long-term equilibrium relationships between variables is a common study goal in the modeling field. Nevertheless, it is imperative to acknowledge that in the immediate period, exogenous disturbances have the potential to displace variables from their long-term equilibrium states. ⁸⁰ The vector error correction model (VECM) differs from models that only consider long-term equilibrium, as it examines both long-run connections and short-run variances through the use of a correction mechanism. To address concerns related to endogeneity, all variables are treated as endogenous.

Unit root test

To determine if a variable is stable, a unit root test must be conducted. In econometrics, there are several commonly used tests, such as the Dickey-Fuller (DF) test, the augmented Dickey-Fuller (ADF) test, and the Phillips-Perron (PP) test.^81,82 Foreign investment, trade openness, energy use, and CO₂ outflow are some of the time-varying variables analyzed in this study using the trend-accounting ADF and PP unit root tests. The following regression model forms the basis for the ADF and PP tests:

Δ X t = δ 1 + α 1 T + α X t − 1 + ∑ j = 1 k δ 2 Δ X t − 1 + ε t

(4)

In this model, X t determines whether the variable has a unit root, T indicates a linear pattern, Δ represents the operator of the first difference, and t is the time, ε t symbolizes the term for Gaussian white noise, and k selected to guarantee residuals of white noise. To determine the optimal lag, the research employs the Akaike information criterion (AIC). The study further utilizes advanced unit root techniques including Dickey-Fuller Generalized Least Squares (DF-GLS) as well as Zivot and Andrews ⁸³ unit root test which takes into account structural breaks.

Lag order determination and cointegration test

Subsequently, a suitable criterion is employed to establish an optimal lag order, after which the number of cointegrations is determined by a cointegration test. Cointegration is a statistical concept that suggests the possibility of achieving stationarity in a time series by combining nonstationary time series linearly. Two commonly used methods for cointegration testing are the Johansen maximum likelihood method and the Engle-Granger cointegration method. ⁸⁴ This research employs the Johansen cointegration test, a statistical method that not only detects the presence of a cointegration connection but also estimates the precise quantity of cointegration vectors. Engle and Granger ⁸⁴ have presented a regression formula for cointegration evaluation, which is mathematically written as:

Y t = α + β 0 X t + β 1 X t − 1 + λ Y t − 1 + μ t

(5)

In this equation Y t stands for the variable that is being measured, α represents the intercept, β 0 and β 1 , are the parameters requiring estimation; t − 1 indicates the variable lag.

VECM

VECM are created based on previous testing. The Error Correction Model (ECM) was first introduced by Engle and Granger ⁸⁴ as a complementary approach to the cointegration regression model. The VECM is utilized for two primary reasons: Firstly, the time series data are nonstationary in their original levels but exhibit stationarity in their first-order differences. Secondly, the variables included in the model are found to be cointegrated. ⁶⁵ VECM is suitable for analyzing nonstationary time series data, allowing for the modeling of long-term relationships among variables that exhibit trends or unit roots. ⁸⁵ By incorporating cointegration, VECM captures the long-term equilibrium relationships among variables, providing a more comprehensive understanding of the underlying economic dynamics. The inclusion of ECTs ensures that the model accounts for deviations from equilibrium and captures the adjustment process back to long-run equilibrium, enhancing its predictive accuracy. ⁸⁶ The generic regression equation utilized for estimating the VECM encompasses the following components:

Δ Y t = α 0 + ∑ j = 1 k α i Δ Y t − 1 + ∑ j = 1 k β j Δ Y t − j + φ V E C M t − 1 + μ i

(6)

Here, Δ Y t represents the first difference of Y t , with k denoting the lag order and μ i as the error term. E C T t − 1 , the ECT represents the stable equilibrium connection among the variables. The adjustment coefficient φ indicates the velocity and orientation of the correction toward the equilibrium position when it strays from the long-run equilibrium status. To illustrate how short-run changes in each explanatory variable affect instantaneous changes in the outcome variable, consider the coefficients of variance of the difference terms of these variables. Using the VECM, this study analyses the long run equilibrium and short run corrective connections between FDI, TRADE, EU, and CO₂. The VECM is represented using the formula that follows:

Δ CO 2 i t = α 1 + ∑ j = 1 k β 1 Δ CO 2 i ( t − j ) + ∑ j = 1 k β 2 Δ FDI i ( t − j ) + ∑ j = 1 k β 3 Δ TRADE i ( t − j ) + ∑ j = 1 k β 4 Δ EU i ( t − j ) + ∑ j = 1 k β 5 Δ GDPG i ( t − j ) + ∑ j = 1 k β 6 Δ INFL i ( t − j ) + ∑ j = 1 k β 7 Δ POPG i ( t − j ) + φ 1 ECT i ( t − j ) + μ i

(7)

In the models presented above, Δ CO 2 i t , Δ FDI i t , Δ TRADE i t , Δ EU i t , Δ GDPG i t , Δ INFL i t , and Δ POPG i t denote the first differences, capturing short run fluctuations in the variables. ECT i ( t − j ) signifies the ECT, representing the residual derived from the cointegrating estimation. Here, j signifies the quantity of lag orders, β stands for the estimation coefficient of the independent variables, illustrating their immediate impact on the dependent variable, and φ represents the correction coefficient, referring to the speed at which the system transitions from an unbalanced condition to a stable state in the long run. The study also evaluates the interactive effect of foreign investment and trade openness on CO₂ emissions. The interactive model is represented in the equation below:

Δ CO 2 i t = α 1 + ∑ j = 1 k β 1 Δ CO 2 i ( t − j ) + ∑ j = 1 k β 2 Δ FDI i ( t − j ) + ∑ j = 1 k β 3 Δ TRADE i ( t − j ) + ∑ j = 1 k β 4 Δ EU i ( t − j ) + ∑ j = 1 k β 5 Δ GDPG i ( t − j ) + ∑ j = 1 k β 6 Δ INFL i ( t − j ) + ∑ j = 1 k β 7 Δ POPG i ( t − j ) + ∑ j = 1 k β 8 ( Δ FDI × Δ TRADE ) i ( t − j ) + φ 1 ECT i ( t − j ) + μ i

(8)

In the model above, Δ FDI × Δ TRADE represents the first difference of the interactive term, β 8 denotes the coefficient of the interactive term to be estimated, and all the other variables remain the same.

Causality test

This research proceeded to examine causation between the factors, specifically focusing on the relationship between FDI, TRADE, EU, GDPG, INFL, POPG, and CO₂. According to Engle and Granger, ⁸⁴ cointegration occurs when two or more series are integrated of order one (1), signifying the presence of a minimum of one causal connection. To determine causation, both the VEC Granger and the block exogeneity Granger causality tests. One way to use the VECM to find causality is with the Engle-Granger test, which compares the residuals to the variations off the equilibrium parameters. This research used the following formulae to conduct time series Granger causality tests:

Δ Y t = α 0 + β 1 ∑ p = 1 r Δ Y t − 1 + ψ ∑ p = 1 r Δ X t − 1 + ECT + ϵ t

(9)

Here, Δ represents the operator for the first difference, t represents time, and ECT constitutes the term that corrects errors produced by the short-run cointegration model. The most optimal lag was chosen using the AIC.

Descriptive statistics and correlation analysis

Table 2 provides an overview of the summary statistics and correlation analysis for the variables examined in this study. For a more comprehensive view of these indicators in South Africa from 1990 to 2020, Figure 1 illustrates their development and statistical characteristics over time. In Table 2, the mean values for CO₂, FDI, TRADE, and EU are 7.11, 1.12, 48.68, and 2586.82. Notably, FDI displays the lowest average among these variables, implying that, on average, South Africa’s FDI is relatively modest compared to other African nations over the study period. The highest and lowest values for FDI, TRADE, and EU are 5.37 and −0.06, 65.98 and 34.32, and 3241.62 and 2121.28. In terms of standard deviation (SD), the figures for CO₂, FDI, TRADE, and EU are 0.89, 1.13, 8.17, and 289.07. The correlation matrix in Table 2 elucidates the relationships between these variables. It's evident that some variables exhibit positive correlations while others demonstrate negative ones. Specifically, the dependent variable, CO₂, is positively correlated with all variables except INFL and POPG. Contrary, INFL and POPG exhibit negative correlations with all the variables. Figure 1 visually represents these trends over time. CO₂ demonstrates fluctuations but generally decreases from 6.25 in 1990 to 6.62 in 2020. FDI also fluctuates but experiences a gradual decline from 0.01 in 1990 to 0.98 in 2020. TRADE shows a gradual increase from 39 in 1990 to 65 in 2008, after which it fluctuates before experiencing a gradual decrease from 2014 to 2020. In contrast, EU depicts a substantial and consistent increase, rising from 2100 in 1992 to 3300 in 2020.

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Figure 1.

Time-series evolution of variables (1990–2020).

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Table 2.

Summary statistics and correlation analysis.

Variables	CO2	TRADE	FDI	EU	GDPG	INFL	POPG
Mean	7.11	48.68	1.12	2586.82	1.97	6.71	1.35
Median	7.55	49.59	0.89	2593.84	2.49	5.79	1.23
Maximum	8.45	65.98	5.37	3241.62	5.60	15.34	3.08
Minimum	5.72	34.32	−0.06	2121.28	−6.34	−0.69	0.39
SD	0.89	8.17	1.13	289.07	2.49	3.48	0.54
Skewness	−0.24	−0.12	1.95	0.52	−1.22	0.72	1.38
Kurtosis	1.51	2.20	7.68	2.40	5.25	3.72	5.31
Jarque-Bera	3.20	0.91	47.87	1.85	14.18	3.36	16.73
Observations	31	31	31	31	31	31	31
Correlations analysis
CO2	1
TRADE	0.87***	1
FDI	0.35	0.43*	1
EU	0.70***	0.71***	0.20	1
GDPG	0.23	0.18	0.15	−0.26	1
INFL	−0.55**	−0.48**	−0.16	−0.54**	−0.32	1
POPG	−0.46**	−0.50**	−0.37*	−0.39*	−0.37*	0.70***	1

Note: ***, **, and * signifies 1%, 5%, and 10% significance level.

Unit root tests

To ensure that all variables were stationary, unit root tests were conducted. Table 3 displays the outcomes of this analysis. Consistent results were found in both the ADF and PP tests, which took into account the intercept and time trend factors. The vast majority of time series variables, in particular, did not pass the tests at the 10% significance level for level (I [0]). The results demonstrate that, after the first differentiation (I [1]), all variables were stationary. As a result, the first differences of these variables will be used in the study. Subsequently, a cointegration test can be conducted to validate the presence of a long-run connection between the variables. The time series data undergoes further examination utilizing an advanced unit root test, specifically the DF-GLS method, as shown in Table 3. This approach offers distinct advantages as it concurrently addresses autocorrelation and heteroscedasticity, demonstrating superior performance in terms of small-sample size and statistical power compared to the conventional DF test. ⁸⁷ The findings from this analysis reveal that forest rents, economic growth, natural gas rents, and R&D expenditures exhibit stationarity at the first difference. CO₂, FDI, and EU stand out as the sole variables displaying stationarity at the level. The null hypothesis positing stationarity at level (0) for these variables is rejected, prompting acceptance of the alternative hypothesis.

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Table 3.

Unit root test results.

Variables			CO2	TRADE	FDI	EU	GDPG	INFL	POPG
ADF	Level	Constant	−1.268	−1.8	−4.882***	0.396	−1.521	−2.566	−3.936***
		Constant and trend	−0.43	−2.553	−4.899***	−1.885	−1.464	−2.798	−3.368**
	First difference	Constant	−4.739***	−6.152***	−8.343***	−4.586***	−4.449***	−5.046***	−5.028***
		Constant and trend	−4.970***	−6.196***	−8.218***	−4.780***	−4.867***	−5.061***	−5.166***
PP	Level	Constant	−1.257	−1.748	−4.877***	0.299	−1.624	−2.585	−3.923***
		Constant and trend	−0.348	−2.614	−4.896***	−2.062	−1.459	−2.863	−3.365
	First difference	Constant and trend	−4.722***	−6.169***	−8.559***	−4.597***	−4.438***	−5.050***	−5.026***
		Constant and trend	−4.936***	−6.231***	−8.434***	−4.797**	−4.828***	−5.063***	−5.164***
DF-GLS	Level	Trend	−1.998	−2.304	−3.278	−3.159**	−1.343	−2.686	−2.339
		No trend	−2.003	−1.066	−2.745***	0.694	−1.016	−1.271	−0.958
	First difference	Trend	−2.836	−3.899***	−4.009***	−3.869***	−3.316	−4.711***	−5.343***
		No trend	−3.017***	−3.415***	−6.101***	−3.712***	−2.981***	−4.726***	−3.501***

Note: *** and ** mean that the null hypothesis was rejected under the statistical significance at 1% and 5% levels.

These unit root tests, however, fail to account for potential structural breaks in the time series, potentially leading to incorrect conclusions when the data exhibit trend stationarity with a structural break. ⁸⁸ The Zivot and Andrews ⁸³ unit root test is employed in the empirical methodology, as it mitigates unit root bias in the presence of structural breaks. The Zivot and Andrews ⁸³ unit root test results indicate that only foreign investment is stable at the level, i.e., I (0) as shown in Table 4. However, all the other regressors achieve stability after first differencing. The integration order thus necessitates applying cointegration techniques to ascertain the long-term relationships among the regressors.

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Table 4.

Zivot-Andrews unit root test results.

	Level		First difference
Variables	Intercept and trend	Break year	Intercept and trend	Break year
CO2	−3.469455	2010	−6.457373***	2001
TRADE	−4.582557	2007	−6.052565***	2007
FDI	−6.093424***	2003	−7.526713***	2002
EU	−4.480356	2009	−5.086942**	2011
GDPG	−3.294263	2008	−5.988986***	2015
INFL	−3.408314	2008	−6.881616***	2007
POPG	−2.657822	2000	−7.155535***	2015

Note: *** and ** mean that the null hypothesis was rejected under the statistical significance at 1% and 5% levels.

Johansen cointegration test

The fundamental concept behind the cointegration test lies in establishing a stable, long-term relationship between nonstationary sequences. ⁸⁹ Before conducting the cointegration test, the lagged differences were calculated. Table 5 displays the outcomes. Except for the AIC criterion, all other criteria (LL, LR, FPE, SC, and HQC) suggested that the variables showed the highest level of significance at the first-order lag. All the variables were assumed to have a first-order lag. After determining the best lag sequence, the data were subjected to cointegration tests to confirm the number of cointegration relations. The findings are summarized in Table 6. The table demonstrates the rejection of the null hypothesis proposing “no cointegration relationship” and the acceptance of the alternative hypothesis. This indicates the existence of at least one cointegration relationship. Both the Trace test and the Max Eigenvalue test indicate the presence of four cointegrating equations with a significance level of 5%. This indicates that a maximum of four variables have a persistent relationship or balance with one another. The null hypothesis suggesting “a maximum of three cointegration relationships” was tested using the Trace statistic, which yielded a value of 44.06439. This number is significantly lower than the critical value of 47.85613 at a 5% significance level. The Max Eigenvalue value was 35.03041, which is noticeably below the 5% critical value of 40.07757 at a 95% confidence level, and the null hypothesis was upheld. To summarize, the outcomes of the Johansen cointegration test conclusively indicate the presence of a stable cointegration relationship among the variables. The equation for long-term cointegration can be formulated as:

CO 2 = − 30.98264 + 6.878633 FDI − 0.455957 TRADE + 0.012818 EU − 0.707395 GDPG − 1.172852 INFL + 11.18012 POPG

(10)

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Table 5.

Results on VAR lag order selection criteria.

Lag	LL	LR	FPE	AIC	SC	HQ
0	−479.1003	NA	855301.7	33.52416	33.85419	33.62752
1	−354.8520	179.9458a	5282.637a	28.33462	30.97492a	29.16153a
2	−301.2610	51.74305	7535.697	28.01800a	32.96855	29.56845

Notes: The endogenous variables are CO_2, FDI, TRADE, EU, GDPG, INFL, and POPG; VAR = vector autoregressive; LL = Levin Lin; LR = likelihood ratio; FPE = final prediction error; AIC = Akaike information criterion; SC = Schwarz criterion; HQ = Hannan–Quinn criterion.

a

Lag order selected by the criterion.

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Table 6.

Results on Johansen cointegration test (Lag 1).

Hypothesized number of cointegration equations	Eigenvalue	Trace statistic	0.05 Critical value	Probability**
Unrestricted cointegration rank test (trace)
None*	0.857335	165.1698	125.6154	0.0000
At most 1*	0.701189	108.6994	95.75366	0.0048
At most 2*	0.639711	73.66898	69.81889	0.0238
At most 3	0.529979	44.06439	47.85613	0.1086
At most 4	0.351962	22.17005	29.79707	0.2892
At most 5	0.255627	9.589670	15.49471	0.3136
At most 6	0.034844	1.028491	3.841465	0.3105
Trace test indicates 3 cointegrating equation(s) at the 0.05 level

Hypothesized number of cointegration equations	Eigenvalue	Max-Eigen statistic	0.05 Critical value	Probability**
Unrestricted cointegration rank test (max-eigenvalue)
None*	0.857335	56.47044	46.23142	0.0030
At most 1	0.701189	35.03041	40.07757	0.1661
At most 2	0.639711	29.60459	33.87687	0.1488
At most 3	0.529979	21.89434	27.58434	0.2258
At most 4	0.351962	12.58038	21.13162	0.4915
At most 5	0.255627	8.561179	14.26460	0.3245
At most 6	0.034844	1.028491	3.841465	0.3105
Max-eigenvalue test indicates 1 cointegrating equation(s) at the 0.05 level

Note: * denotes rejection of the null hypothesis at the 0.05 level; ** denotes MacKinnon et al. ⁹⁰ p-values.

In this equation, FDI, TRADE, EU, INFL, and POPG all exhibit a 1% significance. In equation (8), in the long run, a 1% rise in foreign investment results in a 6.878633% reduction in CO₂ output per unit of GDP. Conversely, a 1% rise in TRADE and a 1% increase in EU contribute to 0.455957% and 0.012818% growth in CO₂. In essence, these findings reveal a long-run negative equilibrium relationship between CO₂ and FDI. This empirical evidence underscores the potential for reducing CO₂ output through the infusion of foreign investment, offering valuable support for sustainable environmental practices.

To validate the Johansen cointegration test, the study also utilized the Augmented Engle-Granger test for cointegration to evaluate the long-term cointegration of the variables. ⁸⁴ The findings indicate that all variables exhibit cointegration and maintain a long-run relationship as shown in Table 7.

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Table 7.

Augmented Engle-Granger cointegration test.

Variables	Test statistic	1% Critical value	5% Critical value	10% Critical value
TRADE	−4.346**	−4.925	−4.136	−3.758
FDI	−3.943*	−4.925	−4.136	−3.758
EU	−4.071*	−4.925	−4.136	−3.758
GDPG	−4.462**	−4.925	−4.136	−3.758
INFL	−4.590**	−4.925	−4.136	−3.758
POPG	−4.511**	−4.925	−4.136	−3.758

Note: ** and * mean that the null hypothesis was rejected under the statistical significance at 5% and 10% levels; Critical values are from MacKinnon. ⁹¹

VECM estimates

The VECM estimates presented in both Table 8 are instrumental in assessing the relationships among the variables, both in the long and short term. Based on the insights gained from the VECM estimations, several key observations can be made. The upper section of Table 8 demonstrates that FDI, TRADE, EU, GDPG, INFL, and POPG together explain approximately 57.27% of the variations in CO₂ output in the short run. An R² value of 0.572662 represents this. It is worth mentioning that the statistical tests show a negative and statistically significant ECT (−0.055653) and a significance level of 0.01%. This signifies that deviations from South Africa’s CO₂ emission equilibrium will naturally adjust over time, and any disruptions to the system will gradually return to equilibrium, albeit at a relatively low pace of 5%. This relatively slow adjustment rate is of particular significance considering South Africa's substantial reliance on fossil fuel energy. The results illustrate that TRADE and EU both exhibit a significant negative correlation with CO₂ in the short run. A 1% rise in EU leads to a 0.001216% reduction in CO₂, while a 1% increase in TRADE equates to a 0.057655% CO₂ reduction. The negative correlation between trade openness and CO₂ may result from South Africa importing cleaner and more energy-efficient technologies and machinery, which can replace older and more carbon-intensive production processes. ⁹² Participation in international trade often entails compliance with global environmental standards. This can motivate businesses to switch to greener and less carbon-intensive production processes to meet the requirements of export markets. ⁹³ Increased trade openness may encourage industries to adopt more energy-efficient technologies and practices to remain competitive in international markets. Cost reduction is a common goal for businesses, including energy expenses, which can result in lower CO₂ output per unit of production.^94,95These findings conform with Wang et al., ⁹⁶ who concluded that importing eco-friendly technologies and utilizing inputs for production that are less energy-intensive is a major way in which trading internationally helps improve the quality of the environment in BRICS countries. Udeagha and Ngepah ²¹ also found that trade openness decreases CO₂ outflow in the short run. Conversely, FDI demonstrates a positive statistical relationship with CO₂ output in the short run, indicating that a 1% increase in FDI leads to a 0.220012% rise in CO₂ output in the short run. The outcome aligns with the study investigated by Chidiebere-Mark et al., ⁹⁷ which showed that FDI promotes CO₂ output in the short run. Notably, there exists a significant positive relationship between INFL and POPG.

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Table 8.

VECM results.

	Linear model		Interactive model
Variables	Coefficient	t-Statistic	Coefficient	t-Statistic
Short run
ECT (−1)	−0.055653***	−4.53645	−0.1685374*	−1.80899
D (CO2 [−1])	0.143858	0.65646	0.0497094	0.16299
D (FDI [−1])	0.220012***	3.81734	1.246441*	1.75713
D (TRADE [−1])	−0.057655***	−2.82909	0.0362527*	1.75400
D (EU [−1])	−0.001216*	−1.86725	0.0001248	0.12511
D (GDPG [−1])	0.029201	0.72516	0.0772452	1.42742
D (INFL [−1])	0.053927	1.63258	0.0461255	1.04105
D (POPG [−1])	0.519587**	2.59433	0.3304352	1.08903
D (FDI × TRADE [−1])			−0.0228539***	−2.66850
Constant	0.126785*	2.12677	−0.1124075	−0.90
Long run
CO2 (−1)	1.000000		1.000000
FDI (−1)	6.878633***	7.95879	−1.246953***	−3.33360
TRADE (−1)	−0.455957***	−3.86146	−0.0294793**	−2.50334
EU (−1)	0.012818***	3.50804	0.0042973***	15.98334
GDPG (−1)	−0.707395	−1.32273	−0.5358415***	−12.7939
INFL (−1)	−1.172852***	−3.61472	0.3333086***	10.8556
POPG (−1)	11.18012***	6.36063	3.821107***	29.5288
FDI × TRADE (−1)			−0.0027398***	−3.39307
R 2	0.572662		0.426548
Adjusted R2	0.401727		0.357039
F-statistic	3.350175		6.136569
Probability (F-statistic)	0.013421		0.000832
Log likelihood	1.395240		−6.194289
Akaike information criterion	0.524466		1.116848
Schwarz criterion	0.948799		1.5888329
Hannan–Quinn criterion	0.657362		1.264510
Durbin-Watson statistics	2.104865		2.020706
Diagnostics tests	Statistics	Probability
Portmanteau autocorrelation	71.23201	0.9378
White heteroscedasticity	464.0000	0.2910
Jarque-Bera normality	16.29964	0.2954

Note: ***, **, and * denote significance levels of 1%, 5%, and 10%.

Looking at the middle section of Table 8, it's apparent that foreign investment (FDI) demonstrates a negative relationship with CO₂ emissions, while trade openness and energy consumption exhibit a long-run positive relationship with CO₂ output. To be precise, a 1% increase in FDI leads to a 6.878633% decrease in CO₂ outflow. Foreign investment may introduce cutting-edge technologies and optimal methodologies that lead to more efficient and cleaner production processes. Multinational corporations, often major sources of FDI, may implement technologies that reduce emissions as part of their global sustainability initiatives. ⁹⁸ Foreign investment in the energy sector, particularly in renewable energy projects, can contribute to a reduction in CO₂ emissions. Investments in wind, solar, and other clean energy sources can help South Africa transition to a lower-carbon energy mix, thereby reducing its overall emissions. Host countries often impose stringent environmental regulations on foreign investors, which can encourage them to adopt cleaner technologies and processes. Complying with these regulations can lead to lower emissions intensity in the long term. ⁹⁹ If FDI leads to energy efficiency improvements, the carbon intensity of the energy source can offset these gains. The result conforms with a study by Lin et al., ³⁶ which identified FDI's contribution to emission reduction in China. Mahmood ¹⁰⁰ also revealed that FDI has negative direct and spillover effects on CO₂ outflow.

Conversely, a 1% rise in TRADE is linked to a 0.455957% CO₂ reduction, and a 1% rise in EU is connected to a 0.012818% rise in CO₂ output. This confirms what Li and Haneklaus ¹⁰¹ found: that G7 nations’ CO₂ output rises as trade opens up. Also, Kongkuah et al. ¹⁰² discovered a considerable increase in China’s CO₂ output due to trade. Ozatac et al. ¹⁰³ also found that trade and energy consumption increase carbon emissions in Turkey. Boateng et al. ¹⁰⁴ revealed in their study that FDI reduces carbon emissions among 182 countries globally, however, institutions must regulate the activities of foreign investors in both low- and high-income nations. Trade openness can lead to an expansion of industries that are energy-intensive or reliant on fossil fuels. Increased trade may result in more production, transportation, and overall energy consumption, leading to higher emissions. ²¹ Exporting goods or commodities that are energy-intensive or carbon-intensive can drive up CO₂ outflow. ¹⁰⁵ South Africa's significant dependence on coal for energy production is likely to contribute to elevated levels of CO₂ output. Higher emissions can result from a coal-dominated energy mix.^49,106

It is worth noting that economic growth exhibits a significant negative relationship, at a 1% significance level, with CO₂ emissions. This finding is in agreement with Li et al. ⁶⁵ and goes against the conclusions drawn by Sikder et al., ¹⁰⁷ who concluded that emerging nations’ GDP growth is the primary factor affecting CO₂ outflow. GDP increases environmental pollution in the short run and reduces environmental pollution in the long run which confirms the existence EKC theory. Gokmenoglu and Sadeghieh ¹⁰⁸ concluded in their study that economic growth significantly reduces environmental degradation in Turkey in the long run. Ozatac et al. ¹⁰³ confirmed the EKC hypothesis for Turkey from 1960 to 2013, taking into account variables such as energy consumption, trade, urbanization, and financial development. Aydin et al. ¹⁰⁹ investigated the validity of the EKC hypothesis for the G7 countries. The findings revealed that while the EKC hypothesis holds for Canada, France, the USA, and the overall panel of G7 nations, it does not hold for Germany, Italy, Japan, and the UK. These outcomes collectively highlight the complex relationship between foreign investment, trade, EU, and CO₂ outflow in South Africa. The long-run negative connection between FDI and CO₂ implies that proactive environmental regulations, sustainable energy investments, and technological advancements within the FDI sector can lead to environmental benefits. The positive associations between TRADE, EU, and emissions underscore the need for strategies to balance economic growth with sustainability, particularly in trade and energy sectors.

In the second model, the study examines how the relationship between FDI and CO₂ emissions is influenced by trade openness, considering that increased trade boosts foreign investment in South Africa. The research investigates whether greater trade amplifies or diminishes the impact of FDI on CO₂ emissions, as described in Equation (3). The results are presented in an interactive model. The regression shows positive coefficients for both foreign investment and trade openness, though their impacts vary in magnitude. Holding all other factors constant, a 1% increase in FDI and trade leads to a short-term rise in CO₂ emissions by 1.25% and 0.04% at a 10% significance level. Interestingly, an increase in the FDI and trade coefficients predicts a decrease in CO₂ emissions in the long run at a 1% significance level. Increased FDI typically brings more industrial activities, which often result in higher energy consumption and emissions. ¹¹⁰ Greater trade openness can boost economic activity and industrial output, leading to higher CO₂ emissions. ²¹ This short-term increase is consistent with the idea that economic growth and industrial expansion initially lead to higher environmental degradation. In the long term, FDI might introduce more advanced and cleaner technologies, improve energy efficiency, and enhance environmental regulations and practices. This technological spillover can mitigate the initial negative environmental impacts, leading to reduced CO₂ emissions over time. The study finds negative significant coefficients (−0.0228539 and −0.0027398) for the interaction terms when assessing the moderating effect of trade openness on the FDI-CO₂ emissions relationship in the short and long run. The analysis concludes that while increased trade raises CO₂ emissions, higher FDI combined with trade openness has a mitigating effect on CO₂ emissions, given the negative impact of FDI and the negative coefficient of the interaction term. The interaction term suggests that while trade alone may increase CO₂ emissions, its combination with FDI results in a mitigating effect. This can be understood as trade openness facilitating the transfer and adoption of environmentally friendly technologies and practices associated with FDI. When foreign investors bring in advanced technologies and practices, and these are complemented by an open trade environment, the overall impact on CO₂ emissions can be reduced.

The research incorporates various diagnostic tests at the bottom part of Table 8, and the test outcomes unequivocally demonstrate the absence of serial correlation within the model. There is no indication of heteroscedasticity, affirming the model's soundness. Figure 2 verifies that the VECM model's stability criterion is met. The eigenvalues of the adjoint matrix are all located within the unit circle, except for one unit root assigned by the VECM. This indicates the model's stability, allowing the study to advance to an impulse response analysis. Figure 3 summarizes the outcomes derived from the long-run linear and interactive VECM results.

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Figure 2.

Stability diagram of the VECM.

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Figure 3.

Summary of the VECM results.

IRF analysis

To ensure the reliability of the results, the study reordered the four main variables, enhancing the robustness of both the IRF and VD analyses. The analysis was conducted over ten phases, which, considering that the variable was measured annually, equates to a decade. The IRF was explored within the variable sequence: CO₂, FDI, TRADE, and EU. According to Figure 4, the first row illustrates the impact of FDI, TRADE, and EU on CO₂. Notably, FDI exerts a negative effect on CO₂, peaking at Phase 3. This finding emphasizes the substantial role FDI played in the long-term reduction of CO₂ output. This finding aligns with the notion that FDI may bring in cleaner technologies, promote energy efficiency, and enhance environmental regulations, leading to lower carbon emissions in the host country. ¹¹¹ The fact that CO₂ has a positive effect on itself suggests that inertia, to some extent, influences CO₂ levels primarily through historical values. The positive effect of CO₂ on itself indicates inertia in CO₂ levels, implying that historical CO₂ emissions influence current emissions to some extent. As for the impact of the EU on CO₂, it appears to be relatively small.

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Figure 4.

Impulse response relationships between CO₂ FDI, TRADE, and EU.

The second row delves into the influence of a one-unit deviation in FDI, CO₂, TRADE, and EU on FDI. Here, the study continues to observe a negative effect of FDI. This effect is positive in the first year but turns negative from the second year onwards, suggesting that CO₂ emissions influence foreign investment in South Africa. This suggests that CO₂ emissions may initially attract foreign investment due to lower environmental standards or cheaper energy sources but could deter investment in the long run due to concerns about environmental sustainability. Interestingly, TRADE exerts a significant influence on the pulse of FDI. In contrast, the EU's effect on FDI is rather minor. This points to persistent energy production and consumption insufficiency in South Africa, necessitating accelerated changes in the energy structure. The self-effect of FDI remains positive. The significant influence of trade openness on FDI suggests the importance of market access and economic integration in attracting foreign investment, while the minor effect of EU highlights the need for South Africa to address energy inefficiency and transition to cleaner sources.

Moving on to the third row, the study explores the effect of a one-unit SD of FDI, CO₂, TRADE, and EU on TRADE. The results reveal that fluctuations in CO₂ and FDI have both positive and negative effects on TRADE, while the EU negatively influences TRADE. It is worth noting that TRADE exhibits a positive self-effect, although this effect is notably weaker than that of the other variables. The negative influence of the EU on TRADE underscores the challenges posed by energy inefficiency and the need for structural reforms in the energy sector to support sustainable trade growth.

In the fourth row, the study investigates the influence of a one-unit SD of FDI, CO₂, TRADE, and EU on the EU. Here, it becomes evident that CO₂ and TRADE both have a positive impulse influence on the EU, rising from the first year and declining from the third year onwards. Conversely, FDI negatively affects the EU, with a consistent effect from year two until year ten. The self-effect of the EU remains positive. The effect of CO₂ emissions and TRADE on EU highlights the feedback loop between environmental pollution, economic activities, and energy consumption patterns. While CO₂ emissions and TRADE positively influence EU in the short term, the negative effect of FDI on EU suggests the importance of promoting energy efficiency and transitioning to cleaner energy sources to mitigate environmental impacts and enhance energy security. ¹¹² This analysis sheds light on the complex relationship of these variables and their effects over time.

VD

The VD process aligns with the order and lag used in the impulse response analysis. In Figure 5, the study presents the VD results for CO₂, FDI, EU, and TRADE. These findings provide valuable insights into how these variables contribute to their variances and those of others. Table 9, on the other hand, offers a comprehensive view of the contribution of each variable to the total variance over the first to tenth years of the analysis. Notably, it can be observed that all four variables have a considerable impact on their variance. To assess the relative significance of each variable, the study employs a method that dissects the predicted error variance for every variable into parts that are associated with every part of the system. The study's focus is primarily on the variables of interest: CO₂, FDI, EU, and TRADE. The outcomes reveal the extent to which these variables contribute to the overall variance at the tenth period. For CO₂, the variance is primarily explained by the variable itself, accounting for approximately 52.95% of the total variance. The dominance of CO₂ in explaining its variance, suggests that internal factors, such as local policies, industrial activities, and energy consumption patterns, primarily drive carbon emissions in South Africa.

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Figure 5.

Variance decomposition of CO_2, FDI, EU, and TRADE.

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Table 9.

Variance decomposition of CO_2, FDI, EU, and TRADE.

Period	SE	CO2	FDI	EU	TRADE	GDPG	INFL	POPG
Variance decomposition of CO2
1	0.277685	100.0000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
2	0.570343	71.25545	8.489395	11.87962	1.335173	2.637966	4.100847	0.301548
3	0.820042	59.83889	12.42798	13.90487	3.607153	2.890289	2.916450	4.414367
4	0.978705	54.59589	11.46707	18.10210	3.158333	3.478656	2.265060	6.932896
5	1.065819	51.97550	11.58300	19.36878	2.856344	3.240445	1.912007	9.063916
6	1.131721	51.89122	11.20924	19.72289	2.576487	3.084901	1.707582	9.807690
7	1.191300	52.60732	10.99234	19.47926	2.458497	2.959363	1.591632	9.911586
8	1.261424	53.23331	10.87279	19.27589	2.408242	2.933980	1.535202	9.740581
9	1.337562	53.24281	10.91843	19.33272	2.391397	2.935122	1.469084	9.710439
10	1.411026	52.95312	10.94019	19.55435	2.350878	2.934651	1.388113	9.878701
Variance decomposition of FDI
1	1.194241	1.713422	98.28658	0.000000	0.000000	0.000000	0.000000	0.000000
2	1.338158	2.133295	79.71092	0.739955	12.10239	0.081374	0.703558	4.528510
3	1.534560	2.347551	61.76934	4.748894	11.85763	1.765371	0.953811	16.55741
4	1.734248	3.056931	51.85877	4.856513	10.36216	1.408814	2.828788	25.62802
5	1.913982	4.571787	48.86403	3.990570	8.819837	1.176232	4.445877	28.13167
6	2.053898	5.629936	48.46094	3.685562	7.892913	1.073115	5.288807	27.96872
7	2.151943	5.707074	48.28348	3.489208	7.686994	0.983485	5.580470	28.26929
8	2.238394	5.479602	47.65888	3.226065	7.851684	0.922472	5.670647	29.19065
9	2.329524	5.292084	46.52201	3.004526	7.985440	0.877688	5.814294	30.50396
10	2.425383	5.251962	45.40855	2.802600	7.901773	0.821669	6.052178	31.76126
Variance decomposition of EU
1	90.86299	0.870233	0.753318	98.37645	0.000000	0.000000	0.000000	0.000000
2	148.4067	2.948346	16.99386	77.40571	1.304132	0.205455	1.114522	0.027979
3	189.6949	8.542098	21.36053	64.28931	2.300625	0.975755	2.380645	0.151030
4	219.4329	9.896687	23.67284	58.78311	3.065089	1.485776	2.665227	0.431268
5	243.9139	9.953450	25.50014	56.27989	3.250985	1.673070	2.534975	0.807494
6	265.0257	9.774403	26.30533	55.63028	3.164421	1.691649	2.415529	1.018383
7	285.2147	9.554004	26.40310	55.91766	3.091230	1.641506	2.336406	1.056103
8	304.6427	9.502016	26.37838	56.08296	3.067253	1.624593	2.325657	1.019148
9	323.2727	9.571551	26.56066	55.80176	3.093664	1.636788	2.341873	0.993707
10	340.8230	9.687060	26.84603	55.30316	3.133225	1.667436	2.359653	1.003430
Variance decomposition of TRADE
1	3.589949	5.247103	5.522273	7.682385	81.54824	0.000000	0.000000	0.000000
2	5.368528	7.473496	3.877424	13.08531	65.44147	9.939847	0.175730	0.006723
3	6.942010	4.703273	4.943694	20.42351	55.35234	8.128804	1.246077	5.202297
4	8.038085	3.627470	3.723942	25.24204	48.18599	7.449897	1.851980	9.918682
5	8.665062	3.727312	3.839102	24.18328	46.85214	6.655752	3.298655	11.44376
6	9.083133	3.763421	4.302242	23.20815	46.94556	6.289712	4.147790	11.34313
7	9.470358	3.484218	4.193324	22.69842	48.06334	6.087405	4.407766	11.06553
8	9.935701	3.205543	3.872135	22.61350	49.02762	6.052232	4.338772	10.89019
9	10.44375	2.920077	3.535901	22.81042	49.40782	6.038812	4.309610	10.97737
10	10.92671	2.668078	3.272257	23.06429	49.34844	5.968159	4.424366	11.25441
Cholesky one SD (d.f. adjusted) innovations
Cholesky ordering: CO2 FDI EU TRADE GDPG INFL POPG

As for FDI, it contributes to roughly 10.94% of its variance, while EU and TRADE explain approximately 19.55% and 2.35% of their respective variances in CO₂. Foreign investment, while contributing to its variance by approximately also influences CO₂ emissions to some extent, reflecting the potential impact of international capital flows on environmental outcomes. This suggests that FDI may play a role in shaping South Africa's environmental policies, technological advancements, and industrial structure, thereby affecting CO₂ emissions. EU and trade openness also exhibit significant contributions to their variances, reflecting their importance in the South African context. EU, accounting for approximately 19.55% of its variance in CO₂, highlights the critical role of energy consumption patterns in driving environmental pollution. Meanwhile, TRADE's impact on CO₂ emissions, albeit relatively smaller at around 2.35%, underscores the linkages between international trade dynamics and environmental outcomes, suggesting the potential influence of trade policies and market integration on CO₂ emissions.

When attention is turned to FDI, it can be found that CO₂, FDI, EU, and TRADE elucidate approximately 14.7%, 5.25%, 45.41%, 2.80%, and 7.90% of the variance in the tenth period. Similarly, the study found that EU, CO₂, FDI, EU, and TRADE account for approximately 9.50%, 26.38%, 56.08%, and 3.07% of the variation in the EU during the tenth period. Lastly, focusing on TRADE, it was noted that CO₂, FDI, EU, and TRADE are responsible for explaining about 2.67%, 3.27%, 23.06%, and 49.35% of the total variance in TRADE at the tenth period. The cross-variable impacts revealed through the VD further emphasize the interconnectedness of these factors. For instance, FDI, EU, and TRADE collectively account for a considerable portion of CO₂ variance, indicating the complex interactions among foreign investment, energy consumption, and trade activities in shaping environmental outcomes. These results underscore the dynamic relationship among these variables and their contributions to the changes observed over time.

Granger causality analysis

An effective method for investigating potential causal correlations between economic variables is the Granger causality test. Table 10 clearly summarizes the results of the block exogeneity Granger causality test. There was a resounding rejection of the null hypothesis, which states that the variables are not causally related, in this analysis. This outcome underscores the presence of causal associations, with the influence generally flowing from independent variables to dependent ones. Of particular note, the study identified bidirectional causality between D(CO₂) and D(POPG) at levels of significance of 1% and 5%. This could be attributed to population growth driving increased energy consumption and industrial activities, thereby contributing to higher carbon emissions, while environmental degradation, in turn, may affect public health and demographic patterns. A unidirectional causal link is detected from D(FDI), D(TRADE), D(EU), D(INFL), and D(POPG) to D(CO₂) (D(FDI), D(TRADE), D(EU), D(INFL), D(POPG) → D(CO₂). Similarly, a unidirectional causal influence runs from D(FDI) and D(EU) to D(TRADE) (D(FDI), D(EU) → D(TRADE). Causality is observed from D(EU) and D(INFL) to D(GDPG) (D(EU), D(INFL) → D(GDPG), and from D(TRADE) to D(INFL) (D(TRADE) → D(INFL). This implies that these factors play a role in shaping environmental pollution levels in South Africa. For instance, higher levels of FDI and trade openness may lead to increased industrialization and economic activities, resulting in higher carbon emissions. ¹¹³ Similarly, changes in EU and population growth can impact carbon emissions through their influence on energy demand and economic activity. In summary, the Granger causality analysis reveals an intriguing network of causal relationships, marked by bidirectional causality from CO₂ to POPG, while other associations remain unidirectional. These findings conform to outcomes of previous research studies. For instance, Wang et al. ¹¹⁴ found that CO₂ emissions affected FDI in western and central China, but that there was only a one-way causal relationship between CO₂ emissions and trade in eastern China. Similarly, Mitić et al. ¹¹⁵ reported a one-way causality between energy and GDP, suggesting that energy availability affects economic performance. Khobai and Le Roux ¹¹⁶ unveiled unidirectional causal connections within a multifaceted network. Specifically, these researchers found that carbon dioxide emissions, economic growth, and TRADE influenced energy use. Simultaneously, EU, CO₂ output, and TRADE exerted their influence on GDP.

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Table 10.

VEC granger causality/block exogeneity Wald tests results.

Variables	D(CO2)	D(FDI)	D(TRADE)	D(EU)	D(GDPG)	D(INFL)	D(POPG)
D(CO2)	—	1.419854 (0.2334)	0.009295 (0.9232)	0.311765 (0.5766)	0.005739 (0.9396)	1.353966 (0.2446)	4.769838** (0.0290)
D(FDI)	14.57205*** (0.0001)	—	11.74120*** (0.0006)	0.039085 (0.8433)	2.191732 (0.1388)	0.537210 (0.4636)	0.428572 (0.5127)
D(TRADE)	8.003757*** (0.0047)	1.180523 (0.2772)	—	0.311765 (0.4955)	2.046907 (0.1525)	2.998742* (0.0833)	0.519318 (0.4711)
D(EU)	3.486618* (0.0619)	0.425100 (0.5144)	5.793887** (0.0161)	—	6.866318*** (0.0088)	0.103331 (0.7479)	0.774978 (0.3787)
D(GDPG)	0.525853 (0.4684)	0.066616 (0.7963)	4.892611 (0.0270)	0.013150 (0.9087)	—	2.028363 (0.1544)	0.005034 (0.9434)
D(INFL)	2.665310* (0.1026)	2.443418 (0.1180)	0.044333 (0.8332)	0.248846 (0.6179)	3.338284* (0.0677)	—	0.124177 (0.7245)
D(POPG)	6.730539*** (0.0095)	0.712302 (0.3987)	1.342114 (0.2467)	2.192939 (0.1386)	0.003133 (0.9554)	0.000168 (0.9897)	—
All	20.04789*** (0.0027)	5.901302 (0.4343)	23.38987*** (0.0007)	2.759044 (0.8384)	25.01807*** (0.0003)	14.42623** (0.0252)	6.074935 (0.4148)

Note: ***, **, and * represent null hypothesis was rejected at 1%, 5%, and 10%; chi-square statistics (p-value).

Robustness analysis

To enhance the robustness of the study's findings, as presented in Table 8, we employed a supplementary estimation method. To be precise, given that the variables are cointegrated, we used a FMOLS technique, and Table 11 shows the results. FMOLS introduced by Phillips, ¹¹⁷ stands out for its resilience against diverse forms of nonstationarity and autocorrelation within the dataset. By addressing serial correlation and heteroscedasticity, it offers precise parameter estimates, rendering it applicable across a broad spectrum of time series analyses. Notably, FMOLS possesses the capability to accommodate both I (0) (stationary) and I (1) (integrated of order 1) variables within the regression model, thereby making it well-suited for the examination of different categories of time series data. ¹¹⁸ It is noteworthy that the FMOLS results closely align with the long-run results shown by the VECM estimation detailed in Table 8. The FMOLS results reaffirm the study’s key assertions, underscoring the substantial negative effect of foreign investment on CO₂ outflow in the long run. Simultaneously, they confirm the substantial positive effect of TRADE and the EU on CO₂ output in the long term. The interaction between foreign investment and trade also has a reducing effect on environmental pollution, confirming the main VECM regression outcomes. This congruence between the long-run VECM and FMOLS results reinforces the reliability and robustness of the study’s conclusions.

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Table 11.

FMOLS—robustness checks results.

	Linear model		Interactive model
Variables	Coefficient	t-Statistic	Coefficient	t-Statistic
FDI	−0.113557*	−1.736930	−0.142797**	−2.263039
TRADE	0.099693***	7.194181	0.069859***	2.786455
EU	0.000454*	1.692685	0.001167**	2.531112
GDPG	0.136285***	4.776381	−0.124206*	−1.927067
INFL	−0.012586	−0.478860	0.017514	0.478986
POPG	0.808203***	4.058724	0.442294	1.598860
FDI × TRADE			−0.003265***	−3.301321
R 2	0.650889		0.775471
Adjusted R2	0.578158		0.716898

Note: ***, **, and * denote significance levels of 1%, 5%, and 10%.

Conclusion

This research contributes to the existing body of knowledge by providing comprehensive insights into the impacts of foreign investment, trade openness, energy consumption, and the interactive effects of FDI and trade openness on environmental pollution within the context of South Africa. The study employed data spanning from 1990 to 2020, and its objectives were accomplished by employing cointegration, VECM, and causality test analyses. The results showed a statistically significant long-term relationship among the variables being examined, as shown by the outcomes of the cointegration tests. The results obtained from the cointegration analyses confirm that foreign investment, trade openness, EU, and CO₂ outflow are inherently interconnected in the long term. It was also shown that any deviations from the balance of CO₂ emissions in South Africa will automatically self-correct, although at a rather slow rate, due to South Africa's significant dependence on fossil fuel energy use. The analysis revealed a significant short-term correlation, indicating that trade openness and energy use harm CO₂ output. There was a negative correlation between foreign investment and carbon dioxide emissions, which remained consistent over the long run. The prospective consequences for South Africa are encouraging, as increased foreign investment can result in a decrease in CO₂ outflow. The interactive analysis revealed that trade interacts with foreign investment to reduce environmental pollution in the short and long run. The Granger causality test results provide a full depiction of causation within the analyzed series. Significantly, they revealed a reciprocal cause-and-effect relationship, notably linking population growth with CO₂ emissions. There was a noticeable unidirectional causal connection among the remaining variables (FDI, TRADE, EU, INFL, POPG → CO₂), (FDI, EU → TRADE), (EU, INFL → GDPG), and (TRADE → INFL).

Policy implications

Drawing from empirical findings, a set of policy recommendations emerges, grounded in the complex dynamics among foreign investment, trade, energy, and CO₂ emissions within the context of South Africa.

The first policy consideration entails promoting sustainable FDI. Encourage environmentally responsible FDI by providing incentives for investments in green technology and sustainable energy. Offer financial rewards and tax benefits to attract FDI that contributes to reducing carbon emissions. Emphasize the long-term benefits of FDI in fostering sustainable development and mitigating CO₂ emissions.

Limitations and future research directions

There are several promising areas for future research. (1) Expanding the study to include regional or continental levels would offer significant insights into the broader influence of these four variables on the African continent. Regional divisions can be fascinating, as they have the potential to unveil variances and subtleties in the interactions between these variables throughout different regions of the continent. (2) To further explore the dynamic interaction of these variables, it is recommended to utilize advanced analytical techniques and tools including machine learning algorithms. Implementing threshold models can assist in identifying crucial turning points or thresholds within these interactions. Implementing this technique might improve the comprehension of the underlying mechanisms and their consequences. (3) Broadening the scope to include cross-country comparisons, particularly with developed economies, offers a compelling opportunity for investigation. Through conducting such analyses, it becomes feasible to distinguish the benefits and experiences of various countries in effectively managing these variables. By employing a comparative perspective, we may extract useful insights and exemplary methods that can guide policy choices and tactics for achieving both environmental and economic sustainability. (4) Future research direction could involve investigating the role of renewable energy, technological innovations, and government policies as moderators in the relationship between foreign investment and CO₂ emissions within the context of South Africa. This exploration could shed light on how increased foreign investment influences CO₂ emissions through its impact on renewable energy development and adoption.