Examining the Correlation among Economic Development, Foreign Direct Investment, and CO 2 Emissions by Utilizing the VECM Model—Empirical Study in Vietnam

: From 1990 to 2019, Vietnam entered a period of economic growth, attracting foreign investment. However, during this period, CO 2 emissions also increased signiﬁcantly. This paper will examine the short- and long-term relations of Vietnam’s relationship among FDI, economic growth, and CO 2 emissions based on the data on CO 2 , GDP, and FDI of Vietnam in 1990–2019. This article uses the VECM model to test the effect among variables. Research results identify an impact and causal correlation among CO 2 emissions and economic growth and foreign direct investment in Vietnam. Research results show a long-term relationship between CO 2 emissions, GDP, and FDI. The authors did not ﬁnd a short-run relationship between the above variables. Assessing impacts of CO 2 emissions on economic growth and foreign direct investment will help policymakers make reasonable policies to balance the increase in foreign investment capital and economic growth and reduce CO 2 to achieve the commitment in COP26.


Introduction
Recent years have seen an increase in the number of academics interested in the relationship among economic activity and CO 2 emissions. In some developing countries, with technological progress, adaptation to climate change has increased carbon emissions. Rapid economic growth and climate change also make it difficult for many economies to comply with the recommendations of the United Nations. The primary objective of the Intergovernmental Climate Agreement (IPCC) is to constantly control the number of greenhouse gases at a concentration that prevents harmful anthropogenic effects on the climate system in the atmosphere. Reducing CO 2 emissions also needs to be done within a time that will allow habitats to adjust to climate change naturally, protect food security, and support sustainable economic growth. Anthropogenic and biogeographical variables are the main sources of climate change. The amount of greenhouse gas emissions will cause the ozone layer to thin, solar thermal radiation to rise, and the earth's surface to absorb more heat [1]. Carbon Dioxide (CO 2 ) emissions also include some form of greenhouse gas and thus the environmental consequences of human activities.
In Vietnam, rapid economic development has substantially impacted the environment over the past few decades. Vietnam still exhibits a clear lack of understanding regarding environmental sustainability. Therefore, the promotion of GDP growth and the maintenance of FDI flows must be balanced to maintain the carbon emission toward sustainable development. In the COP26, Vietnam has a strong commitment to reducing the CO 2 Emissions to zero in 2050 [2]. Vietnam's implementation of commitments at COP26, especially the commitment to bring net emissions to "zero" by the middle of the century, is an inevitable and irreversible trend. Therefore, the timely implementation of these commitments will

Literature Review
Numerous papers have examined the connection among CO 2 emissions and GDP. Bello et al. [6] suggested that the link among CO 2 and economic prosperity is U-shaped inverted. However, the positive correlation among economic growth and CO 2 emissions will diminish after the economy reaches a certain stage of development. This can reasonably assess because, when the income level increases, the standard of living increases, leading to a higher demand for environmental quality.
The linkages among countries in terms of economic activity and trade have spurred studies investigating hypotheses about pollution and economic growth as well as trade integration. The research of Grossman and Krugger was the initial investigation into how the Carbon Index affected economic growth [7]. The two authors argued that reducing trade barriers and the expansion of economic activities will affect the environment. This study also provides empirical evidence to assess the relative extent of these three effects by applying the process of trade liberalization in Mexico. Naranpanawa [8] used the ARDL model and Johansen cointegration technique to investigate the long-term relationship among economic development and the trade environment. The findings of this study indicate that commerce and CO 2 emissions only have a temporary link. Keho [9] also used the ARDL model to analyze the long-term effects of the environmental impact of global trade in 11 ECOWAS countries between 1970 and 2010 and came to the conclusion that global trade causes environmental degradation. Rahman and Kashem [10] used Toda and Yamamoto's causal model to investigate the connections carbon emissions, energy use, and economic growth in Bangladesh between the 1970s and 2010s. Most of these studies show a long-term association and a pivotal correlation among the variables. In addition, studies also show a positive correlation among GDP growth and the increase in CO 2 during the study period. Esso and Keho [11] have shown causal and long-term relationships among energy usage, CO 2 emissions, and economic development in various African nations.
Balsalobre-Lorente, lvarez-Herranz, and Shahbaz [12] employed the Kuznets curve to evaluate the association among GDP and CO 2 emissions in a set of 16 OECD member countries among 1995 and 2016. The study discovered that, as economies deal with institutional mismatches in the energy development process, environmental sustainability is hampered. The authors proved the Kuznets curve hypothesis and showed that widespread economic growth and the usage of renewable energy decreased environmental pollution between 1990 and 2012 in 17 OECD nations. Sarkodie [13] used a sample of some developing countries and showed a marked decline in energy intensity as FDI increased. The above deterioration can be attributed to the use of modern technologies accompanied by FDI, i.e., a leap forward from the outdated traditional technologies being used in other countries, thereby reducing emissions that pollute the environment.
Numerous studies have also looked into the relation among FDI, capital flows, and environmental damage in various nations or economic blocs. Frankel and Romer [14] has discovered that financial development and deregulation may draw FDI, stimulate the economy, and thus improve environmental performance dynamics. In the UAE, Shahbaz [15] applied the ARDL paradigm for integration to examine the long-term connections among FDI, renewable energy, trade in natural resources, carbon emissions, and GDP in the UAE from 1975 to 2011. The authors affirm that, over time, these variables would have a link. They discovered that trade integration and foreign direct investment both lower greenhouse gas emissions. Economic expansion has a favorable impact on energy use.
Hakimi and Hamdi [4] explored the correlation among trade openness, FDI flows, environmental quality, and GDP in Morocco and Tunisia using the VECM model and cointegration methods. This study argued that both economies have benefited from trade liberalization, which frequently affects CO 2 . Michieka [16] examined the effects of energy depletion, trade, and financial improvement on China's economic growth. The findings indicate that, while economic and commercial development has a considerable impact on pollution, it also has long-term implications on CO 2 .
Research by Ren et al. has shown that excessive trade surplus along with foreign direct investment (FDI) inflows are the basic causes for the rapid increase in CO 2 emissions in China.
Michieka, Fletcher, and Burnett [16] used a sample of about 20 developing countries and showed a marked decline in energy intensity as foreign direct investment increased. The reason for the above decline can be attributed to the use of modern technologies accompanied by foreign direct investment, i.e., a leap forward from the outdated traditional technologies being used in other countries, thereby reducing emissions that pollute the environment.
Soytas and Sari [17] used a error correction vector model (VECM) to evaluate the relationship between energy consumption and manufacturing sectors in Turkey. The research results show a positive relationship between the variables in the model. In addition, the variables in the model also show a cause-and-effect relationship. In 2009, the two authors conducted another study on the relationship between economic growth, energy consumption, and CO 2 emissions by the linear regression method. The research results also show the co-integration relationship between the parameter variables. In addition, the study also found no long-term association between CO 2 emissions and economic growth. Therefore, the study has come to the conclusion that it is possible to reduce CO 2 emissions without slowing economic growth. The study of Ozturk and Acaravcı [18] also had similar results based on the ARDL model and causality with real data in Turkey. The author used variables including energy, employment rate, and emissions. The results show the opposite of the Kunetz curve.
The study by Begum et al. [19] showed that experimental results from the limited test method ARDL showed that, during the period 1970-1980 in Malaysia, emissions per capita decreased as GDP per capita increased. However, from 1980 to 2009, the amount of CO 2 emissions per capita increased sharply, leading to an increase in GDP per capita. The study came to the conclusion that the EKD hypothesis was not valid in Malaysia during the study period. The results also show that energy consumption and GDP per capita have a long-term positive relationship with carbon emissions per capita. The study also shows that, in the long term, economic growth can have a negative impact on CO 2 emissions. Therefore, the transition to high-tech machinery and equipment with low emissions and the use of alternative energies will contribute to reducing emissions while maintaining economic growth. Table 1 summarizes the basic research findings, methods and author in relationship between the CO 2 and other variables. The correlation among foreign direct investment, economic expansion, economic integration, and CO 2 emissions has been examined in numerous empirical research. However, the research results have differences among countries regarding short-term and long-term effects, cointegration relationships, and negative and positive effects of the relationship among factors. Because of the different results among countries, the author wants to conduct an empirical study to evaluate the correlation among GDP growth rate, CO 2 emissions, and FDI in Vietnam. The empirical results can help policymakers balance reducing CO 2 emissions while increasing FDI attraction and achieving economic growth in the future.

Data
This study is constructed on statistical data from the General Statistics Office of Vietnam and the World Bank (Worldbank) from 1991 to 2019. The extracted data include GDP economic growth rate, the percentage of FDI in GDP in Vietnam, and CO 2 emissions from 1991 to 2019. This study will structure three variables including: economic growth (GDP), Foreign Direct Investment (FDI), and CO 2 emissions (CO 2 ). To correct for the skewed variance in the data and the strong data variability, the values in each of the three variables were converted to logarithmic. Figure 1 shows that the share of FDI in the period 1990-2020 has increased unevenly and peaked in two periods, in 1993 and 2008, GDP growth has less volatility and only emissions. CO 2 has a steady increase every year.
Begum et al. [19] ARDL model long term, economic growth can have a negative impact on CO2 emissions The correlation among foreign direct investment, economic expansion, economic integration, and CO2 emissions has been examined in numerous empirical research. However, the research results have differences among countries regarding short-term and long-term effects, cointegration relationships, and negative and positive effects of the relationship among factors. Because of the different results among countries, the author wants to conduct an empirical study to evaluate the correlation among GDP growth rate, CO2 emissions, and FDI in Vietnam. The empirical results can help policymakers balance reducing CO2 emissions while increasing FDI attraction and achieving economic growth in the future.

Data
This study is constructed on statistical data from the General Statistics Office of Vietnam and the World Bank (Worldbank) from 1991 to 2019. The extracted data include GDP economic growth rate, the percentage of FDI in GDP in Vietnam, and CO2 emissions from 1991 to 2019. This study will structure three variables including: economic growth (GDP), Foreign Direct Investment (FDI), and CO2 emissions (CO2). To correct for the skewed variance in the data and the strong data variability, the values in each of the three variables were converted to logarithmic. Figure 1 shows that the share of FDI in the period 1990-2020 has increased unevenly and peaked in two periods, in 1993 and 2008, GDP growth has less volatility and only emissions. CO2 has a steady increase every year.

Research Method
The article will use the VECM model using the OLS method with no constraints. Suppose we have a VAR(p) model:

Research Method
The article will use the VECM model using the OLS method with no constraints. Suppose we have a VAR(p) model: The model can be rewritten as follows: The model contains the terms ΠY t−1 , and this is the error correction part. Granger also shows that, if the rank of the matrix Π, r(Π) = r < k, then there will be two matrices of order α (level mxr và β (level r × m) so that Π = α β and β Yt is I(0); r is the number of cointegrated relations, and each column of β is a co-integration vector; α is the matrix of correction parameters [20]: The variance decomposition model to test the impact between three variables of economic growth (GDP), foreign direct investment (FDI), and CO 2 emissions (CO 2 ) is re-constituted into the following equation:  Table 2 performs some logarithimic table statistics. Skewness measures the asymmetry of the probability distribution around the mean. In the normal distribution, the skewness is equal to the two-sided probability distribution, which is equally symmetric. Kurtosis is a measure of kurtosis or a probability distribution. The kurtosis of a normal distribution is around 3.

Research Results and Discussion
The stationarity of the data must be examined when analyzing time series. The stationarity test will avoid the situation of the pseudo-regression series [21]. However, if a linear combination among nonstationary series is stationary, then the regression is an actual regression, and those nonstationary time series are cointegrated. In other words, if the residual in the model among nonstationary time series is stationary, then the regression result is accurate and represents a long-run equilibrium correlation among the variables [22]. Table 3 shows that all three variables GDP, FDI, and CO 2 are nonstationary variables. However, when taking the 1st difference, all the above variables are stationary. The variables in the model all stop at the first difference, which is a necessary condition for the VAR model and the VECM model.  The SC and HQ standards give a lag of 1, FPE and AIC give a lag of 2, and LR gives a lag of 1 (Table 4). Using the 1st lag can lead to an ordering of correlation in the residuals, and the model cannot be generalized satisfactorily. Using too many lag orders in the model can lead to many pushbacks, with strong time oscillations because it may not satisfy the stability conditions for the VAR model. Therefore, the author considers the optimal lag 2 to be appropriate according to the AIC criteria. In addition, lag two also satisfies the necessary conditions better.

Check Model Stability
The estimated model is stable since all of the root values are contained within the unit circle ( Figure 2).

Estimating the VAR Model
With lag 2, we have the following VAR model results (Table 5):

Estimating the VAR Model
With lag 2, we have the following VAR model results (Table 5):  The outcomes of the VAR model suggest that an increase in intensity in FDI capital and GDP growth rate has an impact on increasing CO 2 emissions. Conversely, an increase in CO 2 also has an impact on increasing FDI and GDP.
If FDI increases by one unit, then at a 1-year lag with other variables constant, CO 2 will increase by 2.2%. At a 2-year lag, an increase in FDI by one unit can increase CO 2 by about 1.4%. With all other variables constant, an increase in GDP by one unit will increase CO 2 by about 5%.
On the other hand, if one unit of CO 2 emissions increases at a lag of 2 years, with all other variables unchanged, the amount of FDI will increase by 27.3%, and GDP will increase by 17.4%. Thus, with a lag of 2 years, it can be concluded that there is evidence of a relationship among GDP and CO 2 emissions and FDI.
Our results are also coherent with the study by Ozturk and Acaravcı [23], reporting that increasing trade results in rising CO 2 emissions. Seker et al. [24] for Turkey reported that FDI has a long-term positive correlation with CO 2 emissions per capita, comparable to [25], who discovered the negative effect of increased FDI on Turkey's clean energy consumption. Our study demonstrates that FDI inflows have a favorable impact on CO 2 , increasing emissions by 2.2%. According to an International Energy Agency report (IEA), CO 2 emissions had a sharp increase in the period from 2017-2019, the highest growth rate since 2013, for which the electricity generation sector accounts for two-thirds of total CO 2 emissions [26]. The cause for this sharp increase is that many developing countries produce coal power. China is the largest emitter in Asia, accounting for 30% of total emissions.

Analysis of the Impulse Response Function
The push-response function tests the responses of variables to unexpected shocks. The Cholesky analytical method was used with a reaction time of 10 years. The response function results (Figure 3) are analyzed as follows: Sustainability 2022, 14, x FOR PEER REVIEW 10 of 16 Figure 3. Results of the variable-to-variable impulse response function (In graph, if two red lines touch each other at position 0 (black line), then the independent variable has no effect on the dependent variable. The black line is above the two red lines, then the independent variable has a negative influence on the dependent variable).
Firstly, the impact of CO2 emissions affects increasing FDI in the long run, with the increase starting in year 3, then decreasing gradually from years 9 and 10.
Second, regarding the impact of FDI on CO2 emissions, an increase in FDI reduces CO2 in year 2 and increases CO2 emissions from year 3 to year 10.
Third, the impact of GDP growth reduces CO2 emissions from year 1 to year 3. How- Figure 3. Results of the variable-to-variable impulse response function (In graph, if two red lines touch each other at position 0 (black line), then the independent variable has no effect on the dependent variable. The black line is above the two red lines, then the independent variable has a negative influence on the dependent variable).
Firstly, the impact of CO 2 emissions affects increasing FDI in the long run, with the increase starting in year 3, then decreasing gradually from years 9 and 10.
Second, regarding the impact of FDI on CO 2 emissions, an increase in FDI reduces CO 2 in year 2 and increases CO 2 emissions from year 3 to year 10.
Third, the impact of GDP growth reduces CO 2 emissions from year 1 to year 3. However, CO 2 emissions start to increase again from years 4 and 5 to year 3.
Attracting foreign direct investment associated with sustainable development has become one of the important goals in Vietnam's economic development strategy in recent years. However, besides positive contributions, many FDI projects also have negative impacts on the natural environment. Vietnam has emerged as a potential location for foreign investors due to political stability, an abundance of human resources, and low labor costs since the country's transformation from a centrally planned economy to a model of a market economy that is socialist-oriented, managed, and regulated by the State. However, market opening and economic development increase emissions and contribute to more severe climate change. Therefore, attracting FDI and economic growth must be carefully calculated to avoid damage to the environment and increase emissions.

Cointegration Test
The trace test shows that there is a co-integration relationship at a 5% significance level. Check with a reasonable ratio: H0: there are r co-integration relations; H1: there is r + 1 co-integration relation: For r = 2, LRmax = 1.008, the 5% critical value equals 3.84, so H1 is accepted. Both tests lead to the conclusion that there are no co-integrated relations (Tables 6 and 7). Based on the conclusion that there is not a co-integration relation, we estimate the error correction model with no co-integrated relation. The same results with the test of Max-Eigen (Table 7).
The rational function ratio test shows no cointegration relationship at the 5% level of significance. We will estimate the error correction model with two co-integrated relations after determining the number of co-integration relations r = 2 with a 5% significance level. LnGDP is indicated as the independent variable of the model, and signs suggest a long-run correlation.
In the long run, LNCO 2 has a co-integrated relationship among GDP, CO 2 , and FDI variables. Thus, the hypothesis that there is no co-integration relationship among the variables is rejected. We accept the hypothesis of at least one co-integration relationship among the variables.
The results of the causality test also show that there is a causal relationship among GDP economic growth and CO 2 emissions. Thus, economic growth has the effect of increasing emissions. This finding shows that the government needs to come up with policies to balance emissions reduction and economic growth. At the same time, it is necessary to focus on economic development for people, instead of GDP growth that at all costs can lead to environmental damage. The test results show that there are no cointegration relationships among the three variables. In the long run, for the FDI variable, one unit change in FDI will increase 8.5% of GDP. For the CO 2 variable, a one unit change in CO 2 would result in a 2.2% decrease in GDP ( Table 8).
The OLS model that evaluates the long-run effects among variables will have the following form: In addition, the OLS model evaluates the short-term impact among variables in the form of a regression equation as follows:

Testing the Long-Term Relationship
In this model, the lambda values of GDP are C1, FDI is C6, and CO 2 is C11. For the GDP variable, C(1) has a negative sign, which is a good sign, it tells us the convergence in the long run, and the T statistic is −2.6 with a p-value of 0.01, with a significance level of 0.05; then, we can reject the null hypothesis of causality, and thus there is a long-term causality at a 5% significance level. Thus, at the 5% level of significance, GDP has a long-term correlation with FDI and CO 2 . The results are similar to Jalil and Feridun [27] when they analyze the effects of CO 2 emissions on China's economic growth, energy consumption, trade, and financial development from 1953 to 2006. C(6) has a positive sign of the correction factor, which is not a good sign. However, with a T-statistic of 3.29 and a p-value of 0.0016 at the 0.05 level of significance, we can rule out the null hypothesis that FDI and the other two variables do not have any long-term causal relationships and accept the hypothesis of H1 (there was a long-term relationship among variables). There is a cause-and-effect relationship in the long run at the 5% significance level. C(11) also carries a negative adjustment; however, the p-value of 0.94 is greater than the 5% significance level. We cannot reject the hypothesis that there is no long-term causal correlation among CO 2 and the remaining variables with the above value ( Table 9).
As a result, the correlation among FDI inflows and GDP growth rate is positive and causal, suggesting that an increase in FDI capital boosts GDP growth rate and improves the environment for attracting and retaining FDI into Vietnam. The positive causal correlation between CO 2 emissions and FDI inflows shows that the shift of industrial production chains from developed countries has led to an increase in the environmental pollution in Vietnam as well as in many other developing countries in Asia.

Testing the Short-Term Cointegration Relationship
To evaluate the short-term relations among the variables in the model, the author uses the technique of extracting p-values. The table below is the result of the extraction of p-values. The short-term causality among GDP, FDI, and CO 2 is shown through two coefficients C(3) and C(4). Both coefficients have p-values greater than a 10% significance level, so that there is no short-term positive correlation between GDP and FDI and CO 2 . The short-term causality among FDI and GDP and CO 2 is shown in C(7) and C (9). C(7) has a value of 0.95, more significant than the 10% significance level. There is no short-term causal relationship among FDI and GDP. The coefficient C(9) has a value of 0.0002, which is less than the 5% significance level, so it can be seen that there is a short-term causal correlation between the variable FDI and CO 2 at the 5% significance level. The short-term causalities between CO 2 and FDI and GDP are C(13) and C(12), respectively. Both coefficients C(13) and C(12) have values of 0.7601 and 0.7207, respectively, greater than the 10% significance level, so it can be concluded that there is no causal relationship among CO 2 and FDI and GDP (Table 10). Thus, in the short run, there is no causal relationship among the variables in the model. However, according to the impulse response, from the 3rd, and 4th year onwards, i.e., in the long run, the variables FDI and GDP have a significant influence on CO 2 emissions. These findings are also consistent with the experimental results of Akbostanci [28] examining data for the period 1968-2003 and 1992-2001 in Turkey or the findings Fodha and Zaghdoud [29] in Tunisia.

Conclusions and Policy Recommendations
Many developed and developing economies, particularly developing nations like Vietnam, are still engaged in a discussion about how FDI and economic expansion affect carbon emissions. In international trade, production is heavily concentrated in developing countries, and consumption occurs in developed countries. Therefore, the increase in CO 2 emissions in developing countries can be considered as a transfer from developed countries due to strategies of outsourcing or linking production in production lines. International trade has displaced many highly polluting industries from some developed countries to developing countries. The increase in FDI can be offset by high energy consumption and polluting sectors. The process of industrialization is increasingly strong, and the demand for product consumption is increasing. Therefore, the continuous increase in product production leads to high energy consumption and contributes to an increase in CO 2 emissions. This paper uses the VAR and VECM models to evaluate the relationship between FDI, GDP, and CO 2 in Vietnam in the long term and the short term. The VAR model and VECM are built stably and with a delay that is consistent with reality. Testing the VAR model shows that CO 2 emissions impact the total amount of FDI invested in Vietnam and economic growth and vice versa. The impact of foreign direct investment on CO 2 emissions is negative, meaning that an increase in FDI and economic growth by one unit will increase CO 2 emissions by 4.2 and 4.8%, respectively. In addition, the amount of CO 2 also impacts the amount of FDI investment and GDP economic growth with an impact ratio of 27.3% and 17.4%, respectively.
The study also found a long-term causal relationship among GDP, FDI, and CO 2 variables. In the long run and at a 5% significance level, GDP has a causal relationship with FDI and CO 2 . However, no causal relationship was found among the CO 2 variable and the other two variables in the long run. In the short-term causality, only a causal relationship among FDI and CO 2 is found at a 5% significance level. As such, the factors affecting FDI inflows need to be seriously considered because its increase will affect the reduction of CO 2 emissions. This study is also consistent with the study of Ren et al. [3], which shows that excessive trade surplus along with foreign direct investment inflows are the underlying causes for the rapid increase in CO 2 emissions in China.
Based on the obtained results, the study has shown that FDI plays a considerable role in the development of Vietnam's economy. Environmental protection standards are often set lower than usual to prioritize economic development and attract foreign investment. Thus, foreign direct investment also affects the environment, so the Government of Vietnam needs strategies to change the national environment comprehensively. Governance systems are being changed continuously through the process of public administration reform. Membership in international trade organizations and signing agreements are also additional factors in the scale and dynamics of change in the Vietnamese economy. Each new law passed by the National Assembly is a substantial reform of the Government and industries to promote domestic progress, in line with international standards, such as the Law on Environmental Protection, Land, and Resource Management. This shows that the relationship between the Government, businesses, and the community has been adjusted. However, despite the Government's efforts in administrative reform, environmental pollution is still increasing.
Based on the research results, in the future, the Vietnamese Government needs to come up with appropriate policies to grow the economy, and increase trade openness, but still have to reduce CO 2 emissions according to the government's commitments to environmental protection. It is necessary to implement sustainable growth strategies closely linked with environmental protection policies to achieve both goals of reducing CO 2 emissions and economic growth as well as increasing trade openness.
With the growth strategy of attracting FDI and the combination of import and export strategies, the trade openness of the Vietnamese economy is increasing rapidly. The increased trade openness reflects the deepening international integration trend but also has negative impacts on the Vietnamese economy. Therefore, policies are necessary to strengthen environmental management to attract investment capital and FDI enterprises.
In addition, the increased pollutant emissions due to the participation of multinational corporations need to be offset by the transfer of green technology and towards sustainable development. Policymakers should implement policies that encourage the production and use of environmentally friendly energy and green technologies to reduce carbon emissions and promote balanced economic growth.
The limitation of this study is the lack of sector-specific data. Therefore, in future studies, we will try to use data from industries to examine symmetry in econometric models or use disaggregated data. In addition, we also wanted to conduct studies on other growth drivers that have not been performed in this study.