Economic Growth and Environmental Pollution; Testing the EKC Hypothesis in Brazil

Abstract

The study looks at Economic growth and environmental pollution: an assessment of the Environmental Kuznets Curve in Brazil from 1990 to 2018. The ADF-Fisher, PP-Fisher, Im Pesaran, and Chin unit root tests checked stationarity. The VAR model was used to check the influence of individual endogenous variables, and the Wald test was used to determine the variables’ combined impact. The researchers used the Pairwise Dumitrescu Hurlin panel causality (PDHPC) and Pairwise Granger causality tests to assess all of the hypotheses. At order one, the variables are integrated. The lag order used for further calculations is the Akaike Information Criterion. The Fisher cointegration test revealed the cointegration according to the individual cross-section result. According to the Pairwise Dumitrescu Hurlin panel causality (PDHPC) and Pairwise Granger causality tests, economic growth and carbon dioxide emissions are bidirectional. Both the PDHPC and the PGCT support the environmental Kuznets curve theory. Because the EKC hypothesis exists in Brazil, the study concluded that both pure and filthy productions coincide. When Brazil reaches a particular level of development, however, its population may seek a healthier environment, and governments in these countries may pass stricter environmental regulations to encourage cleaner industry. When followed, the procedures may help to improve environmental quality.

1. Introduction

Brazil is one of the five significant emerging “BRICS” economies, and its greenhouse gas (GHG) emissions are the sixth-highest globally. In the run-up to the Paris climate change summit, Brazil boosted the ambition of its climate initiatives. CO₂ poisons the brain and harms overall well-being. Increases in the gas’s concentration cause different reactions in different people. The mind may have become clouded or may have struggled to concentrate on a particular subject. A headache, a lack of focus, and exhaustion are signs of high carbon dioxide levels. Cognitive and decision-making abilities can also be affected. People exposed to CO₂ levels of 2500 ppm in the workplace are unable to perform simple tasks such as proofreading or solving simple math problems [1, 2]. CO₂ emissions can also cause slower productivity and increased absences at work or school. Acidosis occurs when someone is exposed to high levels of CO₂ for an extended period. The rate of breathing, blood pressure, and heart rate all increase. Long-term exposure to CO₂ emission is fatal [3].

On the other hand, the Environmental Kuznets Curve theorizes the relationship between environmental indices and per capita income [4, 5]. Pollution and degradation increase during the early stages of economic expansion. After per capita income reaches a specific level, which varies depending on the indicator, the trend reverses, and economic growth leads to environmental recovery [1, 6, 7, 8, 9]. This suggests that the indicator of environmental effect is a per capita income inverted u-shape function. A quadratic function of income logarithm is commonly used to define the indicators logarithm. The Environmental Kuznets Curve (EKC) is named after Kuznet [2, 3, 10, 11, 12, 13], who hypothesized that income disparity grows and declines as economies progress. The EKC concept emerged in the early 1990s as a result of Grossman and Krueger’s groundbreaking research into the possible implications of the North American Free Trade Agreement (NAFTA) in 1991 and the concept’s popularization through the 1992 World Bank Development (WBD) report [14, 15, 16]. If the EKC hypothesis is correct, rather than being a hindrance to mobility, as the environmentalist movement and related scientism have claimed in the past, i.e. [17, 18, 19], the economic expansion would improve the environment in the long run. This shift in thinking was represented in the world commission on environment and development’s [20] shining notion of sustainable economic development in our common future. Even though the Environmental Kuznets curve-EKC has been used in a wide range of situations, including endangered species and nitrogen fertilizers, and is even featured in beginning textbooks, academic debate continues [21, 22, 23, 24, 25, 26, 27]. Although EKC is primarily an empirical phenomenon, statistically, several EKC model estimations are not robust. Although some local pollutant concentrations have fallen and some pollutant emissions have reduced in industrialized countries, there is still no consensus on the causes of these changes. Brazil’s rapid economic growth is unquestionably accompanied by poor environmental quality, particularly carbon dioxide emissions from fossil fuel consumption and other energy-related activities [19, 22, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38]. The Economic research growth and environmental pollution: an examination of the Environmental Kuznets Curve in Brazil was necessitated by the background mentioned above. The research is divided into five components. The first portion introduces the study, followed by a literature review in the second section, methodology in the third section, empirical data, interpretation, discussion in the fourth section, and conclusion and policy recommendations in the last section.

2. Literature review

2.1 Theory of environmental Kuznets curve EKC

Legitimate growth globally in the scale of the economy could end in a corresponding growth in environmental pollution and divers’ environmental implications if the technology/economy’s structure remained unchanged. This effect is known as the scale impact. The scale effect underpins the conventional belief that economic expansion and environmental damage are mutually exclusive aims [39, 40, 41, 42]. According to [43], at the highest level of growth, structural variation in information-intensive industries and services, combined with increased environmental awareness, regulation enforcement, advanced technology, and increased expenditures, lead to a leveling up off and continuous reduction of pollution. As a result, the approximate components of the environmental Kuznets curve are listed below: The first is about the increase in production volume. The second focuses on different industries that produce varying pollution levels, and the output mix frequently alters over time as the economy grows.

On the other hand, the composition effect is a term used to describe this [42, 44]. The six elements are as follows: Input mix variability entails the substitution of less environmentally damaging inputs with massively negative inputs. Again, technological progress comprises improvements in production efficiency (e.g., using fewer polluting inputs per unit of output) and process dynamism (e.g., reducing the quantity of CO₂ emitted per unit of pollution input).

The methods effect is the result of combining the third and fourth elements. Variability in variables such as environmental regulation creativity policy/measures, which could be influenced by core economic variables highlighted, could affect these proximate elements. The composition effect, for example, could be affected by comparative advantage. Developing countries would likely focus on labor-intensive and natural-resource-intensive goods, whereas developed countries will concentrate on education and capital-intensive manufacturing activities. As a result of environmental legislation in developing countries, pollution activities may be redirected to emerging countries [45, 46]. In recent literature on Environmental Kuznets Curve (EKC), dual key theoretical arguments have been suggested to explain why, beyond a certain per-capita income level, the link between economic expansion and environmental pollution becomes a “virtuous” circle. When per capita income fluctuates, the theories are concerned with variations in relative demand levels.

According to the first argument, the demand structure for commodities and services changes endogenously. According to this theory, as per capita income rises, the most negligible environmental impact sectors become more critical. Demand for services increases at the expense of demand for manufacturing underpins this position. Nonetheless, much more empirical research is needed to support the premise that underpins this argument. Some service activities may have as much as or more environmental impact, either directly or indirectly, than those in the industrial sector. In any case, this logic would only reveal a reduction in environmental pressures per unit of GDP as income rises. It could not explain a drop in absolute terms unless the assumption is made that the industries that pollute the environment the most produce worse goods. In truth, this is a long shot [47, 48, 49]. In the week/relative meaning, a difference in demand structure can appear to contribute to a “delinking” of economic progress and to come to extend environmental pressures, but not in the solid or absolute sense [50]. Furthermore, the second study is based on people’s preferences and relative demand dynamism that arise as income rises. In this scenario, the differences in the intake of marketable products and services are essential, not the variation in the relative demand for various goods and services purchased in the market and, on the other hand, environmental damage.

2.1.1 Empirical literature review

From 1980 to 2010, [35] examined the relationship between economic growth and CO₂ emissions in the context of the Environmental Kuznets Curve (EKC) for emerging countries. Using Driscoll-Kraay standard errors, the study discovered that the cubic functional form has an N-shape and an inverted N-shape relationship. As a result, their data do not support the EKC hypothesis, which states that CO₂ cannot automatically solve economic growth. From 1981 through 2011, [51] investigated the environmental Kuznets curve theory in Vietnam. According to the ARDL technique, the environmental Kuznets curve does not exist in the sense that the relationship between GDP and CO₂ is positive in the long and short run. Borhan et al. [52] conducted research in eight ASEAN nations between 1965 and 2010. The Hausen test validated the EKC theory. CO₂ has a significant negative relationship with income. This is predicated on the assumptions that as pollution levels rise, so does income and that CO₂ emissions can affect output directly by lowering labor and artificial capital productivity. According to the survey, ASEAN 8 countries have lost working days due to health difficulties, and industrial equipment has deteriorated due to filthy water and air. From 1980 to 2017, [43] conducted a study on Gulf Cooperation Council countries. The validity of the EKC hypothesis in GCC countries was supported by results from the STIRPAT model and the PML-ARDL approach. From 1970 through 2020, [53] used the ARDL model to examine the EKC hypotheses. The results of the ARDL model validated the EKC hypothesis. Despite this, Algeria’s high GDP per capita value has hit a tipping point, indicating that the country’s economic progress is increasing emissions. [54] conducted a study from 1990 to 2015 on foreign financing, economic growth, and pollution linkages in 32 OECD nations. The results show an inverted U-shape relationship between foreign direct investment and pollution. GMM and FE-IV results revealed an inverted U-shape and N-shape association. The N-shape can be explained as follows: GDP causes significant CO₂ emissions growth in the first phase, but the effect becomes negative after a certain level of growth is reached. In the OECD countries, the IV-FE revealed an N-shape connection. From 1979 through 2009, [55] researched the environmental Kuznets curve in Algeria. The results of the ARDL technique revealed that the EKC hypothesis did not exist in Algeria. From 1980 to 2011, [56] looked at the factors that influenced CO₂ emissions in OECD countries. The EKC hypothesis curve between urbanization and CO₂ emission is advocated in the study. This indicates that increased urbanization harms environmental quality. [57] used the ARDL model to conduct a study in Turkey and discovered that the EKC curve exists for CO₂ measures. According to the study, increasing GDP per capita reduces CO₂ emissions. From 1980 to 2014, [58] used structural breakdowns tests to examine the influence of clean energy and non-renewable energy use, as well as real income, on CO₂ emissions in the United States. The Environmental Kuznets Curve was not well supported in the United States. The study by [18] looked into the role of environmental regulation in confirming the pollution hypothesis in two Brazil member groups, namely the fourth and fifth enlargement countries. The environmental Kuznets curve hypothesis and the PHH were valid in Brazil’s nations. According to the study, EKC evidence is confirmed in the fifth enlargement countries, but it is not supported in the first to fourth expansion countries due to differences in environmental legislation adoption timelines. [42] looks at the history of the EKC as well as potential replacements. According to the method that combines the EKC and convergence methodologies, convergence is crucial for describing pollution emissions and concentration. Economic growth has a big impact on CO₂, GHG emissions, and sulfur dioxide, but it has a smaller impact on non-industrial particle concentrations and non-industrial GHG emissions. The literature does not agree on the income level at which CO₂ emissions begin to drop whenever an EKC is empirically empirical evidence is noticed. [59] reviewed the literature on the environmental Kuznets curve and concluded that the evidence for the EKC’s actuality is inconclusive. Only a few air quality indicators, though not conclusive, exhibit clear evidence of the Environmental Kuznets Curve. Furthermore, some recent work has cast doubt on the Environmental Kuznets Curve (EKC’s) presence even for indicators that appear to match the pattern. In fact, because of the scarcity of long time series of environmental data, several studies have used a cross-country approach. Even though environmental contamination increases in developing countries while decreasing in developed countries, the method may be misleading. As a result, rather than representing the evolution of a single economy over time, the Environmental Kuznets Curve (EKC) may only illustrate the juxtaposition of two (2) opposing patterns. In truth, single-country studies that looked at the environmental-income link over time found no evidence of an Environmental Kuznets Curve (EKC). [60] survey study offered empirical evidence for the Kuznets hypothesis and its possible interpretation in the environmental context. The survey found EKC for flow and local pollutants but a steadily increasing PIR for stock and global pollutant measures, as well as aggregate pollution measures. The survey shows, among other things, that time series analysis is better appropriate than cross-country analysis, based on estimating approaches. In [26] study, the inverted u-shape curve between per-capita income and pollution for NO₂ emissions was discovered. CO₂ and income have an n-shape relationship. Furthermore, it was determined that the intensity of a country’s trade did not affect its internal pollution levels. From 1965 until 2009, [61] conducted an EKC study in Algeria. The EKC hypothesis was supported by the ARDL results, which showed an inverted u-shape nexus between carbon dioxide emissions and GDP. In the long and short run, the results favored EKC in Algeria. [62] tested the EKC theory in 24 Asian countries from 1990 to 2011. In this investigation, the GMM method was used. The study found that estimations have the expected indications and are statistically significant in terms of the presence of an inverted u-shape relationship between emissions and income per capita, proving the existence of the EKC curve hypothesis. [63] evaluated the environmental Kuznets Curve theory, a panel of twenty OECD nations. Four estimates supported the EKC. In the OECD countries, country-specific findings receive varying levels of support for EKC. Environmental Kuznets Curve (EKC) was detected in nine countries, with five (5) documenting a classic inverted U-shape link. Three countries shared an N-shape nexus, whereas one country had an inverted N-shape nexus. The classic EKC hypothesis is useless for understanding the relationship between GDP and CO₂ emissions, according to [64] empirical investigation. According to the study, there was no unanimity in the literature to provide an empirical foundation for the GED. The two competing viewpoints attempt to establish the existence of an EKC with an inverted U-shape. Empirically, an inverted N-shape global environmental Kuznets (GEKC) is demonstrated. In addition, according to [41, 56], wealthier households may produce higher car emissions due to increased vehicle ownership and driving. Because of their usage of top vintage and inadequate upkeep, poorer individuals may pollute more. The existence of a U-shape hydrocarbon emissions EKC relationship was demonstrated in this article using microdata from 1993 California automobiles. [65] investigated economic models for the EKC in a survey study. The environmental Kuznets Curve hypothesis, which states that the link between environmental pollution and per capita income is inverted U-shaped, was confirmed by empirical evidence [66]. The study indicated that, as money rises, environmental quality improves at first but ultimately deteriorates. [67] investigate the relationship between carbon dioxide emissions, income, energy use, and foreign trade in Pakistan from 1972 to 2008. Using the Johansen approach, the study revealed a quadratic long-run link between CO₂ emissions and income, confirming the existence of EKC in Pakistan. Using panel data analysis, [68] examined the environmental Kuznets curve and sustainability from 1990 to 2012. CO₂ and income were shown to have an inverted U-shape relationship. The redesigned EKC revealed an inverted U-shape link between sustainability and human development. In a study conducted in Vietnam from 1981 to 2011, [69] discovered that EKC did not exist. Because the ARDL method suggested that capital increases CO₂ emissions, this was the case. [70] investigated the potentials of renewable energy in Indonesia from 1971 to 2010, taking the environmental Kuznets curve into account. The ARDL method revealed an inverted u-shape EKC nexus between economic growth and environmental degradation. The approximate turning point was determined to be 7729 dollars per capita, which is beyond the study sample’s time period. [71] use new international data to evaluate the EKC theory of IWP-industrial water pollution. According to the study, while the sector share of output growth exhibits a Kuznets-type-trajectory-KTT, the other two indicators do not. When considered together, the findings suggest that the EKC hypothesis for industrial water contamination is incorrect; it rises rapidly until middle-income status is attained, then stays relatively stable. [72] looked at the Kuznets curve for the environment in 113 countries from 1971 to 2004. The authors’ assessment of the findings shows that the energy EKC hypothesis is not viable. The link is monotonously positive for the entire world. After 1989, there was a decrease in elasticity. The study discovered no evidence of EKC at the country level. The Environmental Kuznets Curve –EKC is depicted graphically in Figure 1.

Figure 1.

Cubic and quadratic functions for the estimation of environment income nexus. The dashed lines indicates negative pollution levels.

3. Methodology

This section of the research focuses on data selection, variable selection, and the econometrics process employed throughout the study.

3.1 Data source and variables

Panel data on two endogenous variables form makes it possible to test the validity of EKC for CO₂ in Brazil. Thus CO₂ emissions (metric tons per capita) and GDP per capita growth (annual %). Carbon dioxide by the combustion of fossil fuels and cement manufacture. Carbon dioxide is created by the consumption of solid, liquid, and gas fuels, as well as gas flaring—also, the annual percentage growth rate of GDP per capita based on constant local currency. The totals are calculated using constant 2020 U.S. dollars. Gross domestic product divided by midyear population equals GDP per capita. The sum of gross value added by all resident producers in the economy, adding any product taxes, subtracting any subsidies not included in the value of the items, is the GDP at the purchaser’s price. It is estimated without considering the depreciation of manufactured assets or natural resource depletion and degradation. The dataset for this study covered 1990 to 2018 due to data constraints—our study’s data source World Bank Development Indicators (WDI). The natural logarithms of the two endogenous variables are calculated.

3.1.1 Model specification

The study’s functional nexus form is depicted as:

$${\mathrm{CO}}_2=f\left(\mathrm{GDP},{\mathrm{GDP}}^2,\mathrm{Z}\right)$$E1

Eq. 1 forms the basic conceptual foundation for examining the link between variables [73, 74].

According to Stern [42, 52] the standard environmental Kuznets curve hypothesis model is specified as:

$${\mathrm{E}}_{\mathit{it}}={\mathrm{\alpha }}_i+{\mathrm{\gamma }}_{\mathrm{t}}+{\mathrm{\beta }}_1{\mathrm{{\rm Y}}}_{\mathrm{i}\mathrm{t}}+{\mathrm{\beta }}_2{{\mathrm{{\rm Y}}}^2}_{\mathrm{it}}+{\mathrm{\varepsilon }}_{\mathrm{it}}$$E2

Where E is the natural logarithm of carbon dioxide emissions, Y is the natural logarithm of GDP per capita, and t is the error term. I and t are nation indices and time, respectively. The use of logarithm necessitates a positive or negative prognosis for the experimental variable, which is appropriate.

The first two (2) terms on the right-hand side of the model are country and time impacts. While CO₂ per capita may vary by the county at any particular income level, the sensitivity of all pollutants to income in almost all of Brazil at that level, according to country effects. The timing implications are viewed as time-varying omitted variables and random shocks that Brazil is experiencing.

3.1.2 Lag length selection

The initial step in cointegration is to choose an appropriate lag length criteria. As a result, we conducted a joint test of lag selection, which implies that we should take the two lags of each variable (based on AIC).

3.1.3 Vector auto-regression estimates

The word Autoregressive comes from the fact that the dependents variable’s lagged values show on the right-hand side, and the term vector comes from the fact that the model includes a vector of two or more variables. By treating every variable in the model as endogenous and a function of the actual values of all endogenous variables in the system, the VAR approach avoids the necessity for structural modeling. The VAR is frequently used to anticipate systems of interconnected time series and to analyze the dynamic influence of random disturbances on the system of variables. The VAR model is specified as:

$${\text{LnCO}}_{\text{2t}}=\mathrm{a}+\sum _{i=1}^k{\mathrm{\beta }}_i{\mathit{\text{lnCO}}}_{\mathit{\text{2t}}-I}+\sum _{j=1}^k{\mathrm{\phi }}_{\mathrm{j}}{\text{lnGDP}}_{\mathrm{t}-\mathrm{j}}+\sum _{m=1}^k{\mathrm{\varphi }}_{\mathrm{m}}{{\text{lnGDP}}^2}_{\mathrm{t}-\mathrm{m}}+{\mathrm{\mu }}_{\text{1t}}$$E3

$${\text{LnGDPi}}_{\mathrm{t}}=\mathrm{b}+\sum _{i=1}^k{\mathrm{\beta }}_i{\mathit{\text{lnGDP}}}_{t-I}+\sum _{j=1}^k{\mathrm{\phi }}_{\mathrm{j}}{\text{lnCO}}_{\text{2t}-\mathrm{j}}+\sum _{m=1}^k{\mathrm{\varphi }}_{\mathrm{m}}{{\text{lnGDP}}^2}_{\mathrm{t}-\mathrm{m}}+{\mathrm{\mu }}_{\text{2t}}$$E4

$${{\text{LnGDP}}^2}_{\mathrm{it}}=\mathrm{c}+\sum _{i=1}^k{\mathrm{\beta }}_i{{\mathit{\text{lnGDP}}}^{\mathit{2}}}_{t-I}+\sum _{j=1}^k{\mathrm{\phi }}_{\mathrm{j}}{\text{lnGDP}}_{\mathrm{t}-\mathrm{j}}+\sum _{m=1}^k{\mathrm{\varphi }}_{\mathrm{m}}{\text{lnCO}}_{\text{2t}-\mathrm{m}}+{\mathrm{\mu }}_{\text{3t}}$$E5

In the model, the dependent variable is a function of its lagged values and other variables_{’ lagged values.} Where k = the optimal lag length, a,b,c, = intercept, Lngdp_t = β_i,φ_j,ϕ_m,= short run dynamic coefficients of the model’s adjustment long run equilibrium,

μ_1t μ_2t, μ_3t represent the impulses, innovation or shocks often called the stochastic error term.

3.1.4 Panel causality

In the classical sense, regression does not imply causal interaction. As a result, investigating the causal flow within the variables. This is correct, given the test’s predictive power. This study applies the widely utilized Granger causality test technique among the elements under investigation. When one variable, for example, X, Granger causes another, the implication is that variable X and its previous expression can forecast the outcome of variable Y, rather than only the historical variable of Y alone, as is generally thought in the literature. A bivariate relationship between (X, Y) can be expressed in a Granger-causality test.:

$${\mathrm{X}}_{\mathrm{t}}={\mathrm{ր}}_0+{\mathrm{ր}}_1{\mathrm{X}}_{\mathrm{t}-1}+{\mathrm{ր}}_2{\mathrm{Y}}_{\mathrm{t}-1}+{\mathrm{\epsilon }}_t$$E6

$${\mathrm{Y}}_{\mathrm{t}}={\mathrm{ր}}_0+{\mathrm{ր}}_1{\mathrm{Y}}_{\mathrm{t}-1}+{\mathrm{ր}}_2{\mathrm{X}}_{\mathrm{t}-1}+{\mathrm{\epsilon }}_t$$E7

3.2 Data analysis techniques

The data analysis techniques adopted for the study follow the following simple steps. First, prior to examining the nature of the link between carbon dioxide emissions and economic growth, the study examined the sequences in which the two variables were integrated. The ADF unit root test by [75], PP-Fisher by [76] Im Pesaran, and Chin unit root test were used to check for stationarity. VAR model was used to check the individual endogenous variables’ impact and the Wald test determined the collective impact of the variables. The model will prove to be stable through the VAR stability checks. The study made use of Pairwise Dumitrescu Hurlin panel causality (PDHPC) and Pairwise Granger causality test to test all the hypotheses. The Akaike Information Criterion is the lag order utilized for further estimations. Our study will employ the Pairwise Dumitrescu Hurlin panel causality (PDHPC) and Pairwise Granger causality test in the fourth and final phase based on the parameters stability test findings performed in the third phase.

4. Empirical result, interpretation, and discussions

The information on the unit root test is presented in Table 1. The variables are non-stationary in their level form, according to Table 1, but they become stationary after the first difference I. (1). Because all variables are integrated at order one I, we may proceed with cointegration analysis (1). In Table 2, the lag order selection criteria are used to decide which criterion best fits the study—the icteric (*) number with the lowest value is chosen as the criterion for selecting the delays. One SC reported −24.55327* under lag, according to the table. With icteric (*) in lag two, four criteria were identified: LR-36.39728, FPE-1.55e-05*, AIC-2.560914*, and HC -2.507760*. Among the criteria, the AIC with the number − 2.560914 is the lowest number with icteric (*) under lag two. As a result, the Akaike Information Criterion is chosen as the lag order for future estimations.

Variables	At level		At First Difference		Conclusion
	I	I&T	I	I&T
ADF-Fisher Chi-square
LgCO2	0.9912(no)	0.6177(no)	0.0000***	0.0000**	I(I)
LgGDP	0.0050***	0.0107**	0.0000***	0.0000***	I(I)
LgGDP^2	0.0130***	0.0262***	0.2088***	0.6752***	I(I)
PP-Fisher Chi-square
LgCO2	0.9751(no)	0.2719(no)	0.0000***	0.0000**	I(I)
LgGDP	0.0050***	0.0104**	0.0001***	0.0000***	I(I)
LgGDP^2	0.0130***	0.0368***	0.0000***	0.0000***	I(I)
Im, Pesaran and Shin W-stat
LgCO2	1.405(no)	0.027(no)	−11.806***	−10.728***	I(I)
LgGDP	−8.855***	−6.880***	−21.002***	−17.912***	I(I)
LgGDP^2	−8.873***	−6.9487***	−22.0883***	−19.135***	I(I)

Table 1.

Unit root test.

I- denote intercept, I&T- represent intercept and trend (*) Significant at the 10%(**)Significant at the 5%(***)Significant at the 1%(No)Not significant. Lag length based on SIC. Probability based on MacKinnon (1996) one sided p-value.

LAG	LOGL	LR	FPE	AIC	SC	HC
0	−573.5986	NA	0.001057	1.661668	1.681304	1.669261
1	891.2532	2912.818	1.59e-05	−2.533871	−24.55327*	−2.503497
2	909.6373	36.39728*	1.55e-05*	−2.560914*	−2.423462	−2.507760*
3	3914.1947	8.98339	1.57e-05	−2.548111	−2.351751	−2.472176

Table 2.

Lag order selection criteria.

* Indicates lag order selected by the criterion, LR: sequential modified LR test statistics (each test at 5% level), FPE: Final prediction error, AIC: Akaike information criterion, SC: Schwarz information criterion, HQ: Hannan-Quinn information criterion.

Table 3 provides Vector Auto-regression estimates-VAR estimate_s. Given that C (1) is the coefficient of the first lag of CO₂ and it is a log-log formation, the interpretation will be on elasticity form. The coefficient signs tell us the direction of the impact; negative signs indicate a decrease, and positive signs indicate an increase. Therefore, looking at CO₂, we can see that CO₂ strongly influences itself at LGGDPSQ(−1). The past realization of CO₂ is associated with a 100% increase in CO₂ emissions on average certris paribus. LGGDPSQ(−1) recorded t-statistic value of 1.96983* and its corresponding coefficient of 0.004306. Therefore, a percent increase in GDP per capita is associated with a 0.431 percent increase in carbon dioxide emissions on average. The findings from Table 4- the VAR estimates indicated that economic growth increase environmental pollution cetris paribusThe Wald test is shown in Table 4. Table 4 shows that the P-value is significant at the 1% level; as a result, we reject the null hypothesis; (5) = C (6), since the Wald test shows that the coefficient of log GDP data to the first and second lags of GPD have a statistical impact on the log of CO₂. We may conclude that GDP GDPSQ has a combined significant effect on CO₂ based on the results of the Walt test. It can also be observed in Table 5 that no root lies outside the unit circle. This indicates that VAR meets the stability requirement.

		LGCO2	LGGDP	LGGDPSQ
LGCO2(−1)	Coefficients	1.001878	1.526624	3.082094
	Standard errors	(0.03792)	(0.48075)	(1.11605)
	T-statistics	[26.4216***]	[3.17553]	[2.76162]
LGCO2(−2)	Coefficients	−0.014756	−1.685399	−3.384602
	Standard errors	(0.03793)	(0.48092)	(1.11644)
	T-statistics	[−0.38902***]	[−3.50456*]	[3.03161*]
LGGDP(−1)	Coefficients	−0.003035	−1.685399	−3.384602
	Standard errors	(0.00517)	(0.06549)	(0.15203)
	T-statistics	[−0.58753]	[4.80273***]	[1.79354***]
LGGDP(−2)	Coefficients	0.014185	0.161283	0.468169
	Standard errors	(0.00495)	(0.06275)	(0.14567)
	T-statistics	[2.86608***]	[2.57035*]	[3.21396*]
LGGDPSQ(−1)	Coefficients	0.004306	0.061816	0.285895
	Standard errors	(0.00219)	(0.02771)	(0.06434)
	T-statistics	[1.96983*]	[2.23055*]	[0.06434***]
LGGDPSQ(−2)	Coefficients	−0.004597	−0.061609	−0.133240
	Standard errors	(0.00569)	(0.07209)	(0.06187)
	T-statistics	[−2.18715**]	[−2.31176]	[−2.15363***]
C	Coefficients	0.003280	0.301598	0.584892
	Standard errors	(0.00569)	(0.07209)	(0.16736)
	T-statistics	[0.57690***]	[4.18350**]	[3.9479***]

Table 3.

Vector auto-regression estimates.

(*) depicts Significant at 10%, (**) denotes Significant at 5%, (***) represents Significant at 1% level.

Test statistics	Value	Df	Probability
Chi-square	7.470434	1	0.0063
Null hypothesis:C(5) = (6)
Null hypothesis summary:
Normalized Restriction(=0)		Value	Std.Err.
C(5)-C(6)		0.008927	0.003266

Table 4.

Wald test.

Restriction are linear in coefficients.

Root	Modulus
0.982854	0.982854
0.502592	0.502592
0.146208	0.146208
−0.035224 - 0.107841i	0.113448
−0.035224 + 0.107841i	0.113448
−0.102302	0.102302

Table 5.

VAR stability conditions checks.

The Pairwise Dumitrescu Hurlin panel causality (PDHPC) and Pairwise Granger causality tests are estimated in Table 6. Economic growth and carbon dioxide emissions are bidirectional, according to the PDHPC. The Zbar-stat and its probability values (2.21122, 0.0270; 3.41367, 0.0006) respectively verified this. This finding agrees with [77, 78, 79, 80], who believe that economic expansion leads to increased pollution. The Pairwise Granger causality test (PGCT) also revealed a bidirectional association between economic growth and pollution. The findings are in line with those of [6, 14, 15, 56, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90], who discovered a similar link between economic growth and pollution. The findings are confirmed by PGCT F-statistics and their probability values (F-stat 6.01514, p-value 0.0026; F-stat 8.31827,P-value 0.0003). Both the PDHPC and the PGCT support the environmental Kuznets curve theory.

Granger causality: Pairwise Dumitrescu Hurlin Panel Causality Test and Pairwise Granger causality test
1.Pairwise Dumitrescu Hurlin Panel Causality Test
Null Hypothesis	W-Stat	Zbar-Stat	Prob.
LGGDP→LGCO2; LGCO2→LGGDP	2.81152; 3.46328	1.30380; 2.69518	0.1923; 0.0070
LGGDP^2→LGCO2; LGCO2→LGGDP^2	3.23502; 3.79785	2.21122; 3.41367	0.0270; 0.0006
LGGDP^2→LGGDP; LGGD→LGGDP^2	2.67254; 4.19400	1.00711; 3.41367	0.3139; 0.0000
2.Pairwise Granger causality test
Null Hypothesis:	Obs	F-statistics	Prob.
LGGDP→LGCO2; LGCO2→LGGDP	723	6.23136; 6.72034	0.0021; 0.0013
LGGDP^2→LGCO2; LGCO2→LGGDP^2	723	6.01514; 8.31827	0.0026; 0.0003
LGGDP^2→LGGDP; LGGD→LGGDP^2	723	3.17036; 10.1542	0.0426; 0.00004

Table 6.

Pairwise Dumitrescu Hurlin panel causality test.

→Depicts X does not Granger cause Y and Y does not Granger cause X.

5. Conclusion and policy direction

The study looks at economic growth and CO₂ emissions: an assessment of the Environmental Kuznets Curve in Brazil. ADF-Fisher, PP-Fisher, Im Pesaran, and Chin unit root test checked stationarity. VAR model was used to check the individual endogenous variable’s impact and the Wald test determined the collective impact of the variables. The model proved to be stable through the VAR stability checks. The study used Pairwise Dumitrescu Hurlin panel causality (PDHPC) and Pairwise Granger causality test to test all the hypotheses. The variables are integrated in order one. The Akaike Information Criterion is the lag order utilized for other estimations. Pairwise Dumitrescu Hurlin panel causality (PDHPC) and Pairwise Granger causality test indicated bidirectional causality between economic growth and carbon dioxide emissions. Both the PDHPC and PGCT validate the environmental Kuznets curve hypothesis.

The following recommendation was made based on the study’s findings; the investigation supported the EKC concept. Because the EKC hypothesis exists in Brazil, both pure and filthy productions are taking place simultaneously. However, after Brazil has reached a certain level of development, its inhabitants may seek a healthier environment, and the Brazilian Government may impose stricter environmental regulations to encourage a cleaner industry. The measures listed above can help to reduce pollution in Brazil. The Brazilian Government could enhance collaboration among industry, institutions, and researchers, as well as the formation of a single alliance. Creating a safe and ecologically friendly energy usage structure will remain a goal as alternative energy sources become more widely used, could reduce the reliance on fossil fuels and other sources for economic development. As a result, it is critical to strengthen ties between tertiary research institutions and enterprises because joint tertiary and industry-based research would aid in the translation of scientific and technological advances into actual output in the Brazilian economy. The findings of this study and other existing research show that economic growth has a primarily positive impact on emissions, reaffirming an earlier dilemma that the environmental Kuznets literature would lead policymakers to overlook ecological policies in favor of developing a solution. The data imply that environmental quality may suffer significantly and that the economic impact of expansion on certain pollutants is more negligible in Brazil. The most practical application of these discoveries is to notify businesses about their emission forecasts, which can then be used as benchmarks for evaluating environmental policies.

Acknowledgements

I thank the Almighty God for granting me strength and wisdom. Inputting this chapter together, I realized how true this gift of writing is for me. You have given me the power to believe in my passion and pursue my dreams. I could never have done this without the faith I have in God. I want to express my gratitude to IntetchOpen for the opportunity granted me. Heartfelt thanks go to my family and friends for their encouragement and support in diverse ways.

Authors contributions

BAA wrote the introduction section and methodology and interpreted the data with a conclusion. The author’(s) read and approved the final manuscript.

Funding

This current study did not receive any funding from anybody or an organization.

Conflict of interest

The author(s) declare that they have no competing interest.