G20 Countries and Sustainable Development: Do They Live up to Their Promises on CO₂ Emissions?

Abstract

The aim of this study was to analyze and measure idiosyncratic differences in CO₂ emission trends over time and between the different geographical contexts of the G20 signatory countries and to assess whether these countries are fulfilling their carbon emission reduction commitments, as stipulated in the G20 sustainable development agendas. To this end, a multilevel mixed-effects model was used, considering CO₂ emissions data from 1950 to 2021 sourced from the World Bank. The research model captured approximately 93.05% of the joint variance in the data and showed (i) a positive relationship between the increase in CO₂ emissions and the creation of the G20 [CI90: +0.0080; + 0.1317]; (ii) that every year, CO₂ emissions into the atmosphere are increased by an average of 0.0165 [CI95: +0.0009; +0.0321] billion tons by the G20 countries; (iii) that only Germany, France, and the United Kingdom have demonstrated a commitment to CO₂ emissions reduction, showing a decreasing rate of CO₂ emissions into the atmosphere; and (iv) that there seems to be a mismatch between the speed at which the G20 proposes climate policies and the speed at which these countries emit CO₂.

1. Introduction

The aim of this work was to highlight and measure idiosyncratic differences over time and between different geographical contexts in the trends of CO₂ emissions into the atmosphere by the G20 signatory countries, whose agenda involves a global commitment to sustainable development [1].

This type of research usually uses the Environmental Kuznets Curve (EKC) as a theoretical framework, which aims to describe the relationship between economic development and environmental quality. From this perspective, it is theorized that when an economy is in its early stages of development, there is an increase in the levels of environmental degradation, justified by the acceleration of industrialization, which leads to higher CO₂ emissions and greater consumption of natural resources [2]. After this stage, there should be an inflection point; that is, as a given economy develops and reaches higher income levels, there should be an association with more advanced technologies, higher levels of environmental awareness, and greater capacity to invest in infrastructure and regulations aimed at sustainability [3]. The final phase of the EKC theory proposes that environmental quality tends to improve with continued economic growth, given the possibility of intensified investment in clean technologies and sustainable public policies, thereby generating a stage of true environmental management and a drop in CO₂ emissions [4].

However, the EKC theory has some limitations. One is that it fails to capture the complexity of the inequalities between the geographical units observed [5,6]. Another possible limitation is that the EKC does not guarantee that all types of pollution will inevitably be reduced as economies grow and that long-term environmental sustainability requires active policies and interventions to mitigate environmental impacts [7].

The G20 is a group of countries with high levels of economic, social, political, and demographic heterogeneity [8]. Furthermore, as there seems to be no theoretical evidence of the EKC’s adherence to different types of pollution emitted in different geographical contexts, the approach of this research was based on the premises and assumptions of Multilevel Theory to model the behavior of the total annual CO₂ emissions of the G20 countries.

Multilevel Theory is both a theoretical and methodological field that seeks to examine and explain the behavior of structured data when arranged in hierarchical levels (contexts) [9,10,11]. In this sense, this theoretical and methodological approach attempts to understand how different variables, observed under different contexts, influence the phenomenon studied and how this influence varies at the levels of analysis considered [12,13].

In this way, this study proposes a theoretical and methodological complement to the case of CO₂ emissions, when considered concurrently in different contexts, primarily to provide a new perspective for understanding the factors that influence CO₂ emissions worldwide and to better adjust interventions and policies accordingly.

Therefore, this study aims to fill theoretical and methodological gaps regarding the proposition of other functional forms that capture CO₂ emissions more accurately when data from several countries are used simultaneously. Beyond the current proposed study, we believe that there is room for new theoretical and methodological approaches capable of accommodating new, more precise functional forms, seeking to refine information for the stakeholders of the phenomenon addressed, namely, all of us.

That said, rather than studying the EKC, our work is interested in the long-term relational behavior between CO₂ emissions and the creation of the G20, which has brought with it the assumption of various environmental agendas.

From this perspective, it was possible to simultaneously model the fixed and random effects of the observed phenomenon at the same time. By modeling the fixed effects, we captured the estimators of the phenomenon in general. However, by considering random effects together with fixed effects, we were able to measure the idiosyncratic differences between countries. In this way, as well as being able to observe and compare the individual behaviors of each country at the time of the analysis, it was possible to achieve the same for each moment in the dataset. Therefore, by capturing the heterogeneities between countries, the approach has made it possible to expand the individual analysis to consider and compare the different journeys of different countries, each with its own intercept and different slope rates, over a long period of time.

The remainder of this article is organized as follows. After Section 1, a literature review addresses the joint behavior of the G20 in terms of CO₂ emissions over time and discusses some heterogeneities between the climate policies of the countries studied (Section 2). Section 3 presents the structure of the database, and the inferential model developed, organized in a multilevel panel with repeated measures. Section 4 presents the results, robustness, and goodness-of-fit of the estimations. Section 5 presents the results of this study. Finally, Section 6 presents the final considerations of this study.

2. The G20 and Its Environmental Agenda

2.1. The G20 and the Behavior of Its CO₂ Emissions over Time

The G20 emerged in 1999 and is a group of countries made up of the eight richest and most influential countries in the world, plus 11 emerging countries, as well as two economic blocs: the African Union and the European Union. This forum emerged as a response to the financial crises of the 1990s, specifically the Asian financial crisis of 1997–1998 and other global economic turbulences [14].

The idea of creating the G20 came about through an attempt to divide the leading role of the G7 in terms of economic and financial agendas by including emerging countries in these discussions [15]. Thus, in the face of financial crises, the G20 should facilitate global economic coordination, uniting developed and developing countries in search of answers and solutions [16].

The emergence of the G20 is also based on the idea of broadening global agendas, considering, in addition to economic and financial agendas, agendas on climate change, sustainable development, global health, and international trade [17,18]. As such, the reduction in CO₂ emissions into the atmosphere has become a commitment to world society by the G20 signatory countries [19].

The problem is that CO₂ emissions are umbilically linked to economic development because they are generally connected to issues related to energy production [20,21], food production [22,23], deforestation and forest degradation [24,25], treatment of water and waste [26,27], and industrial production [28,29].

Therefore, given that CO₂ emissions and economic development still seem to go hand in hand, the main assumption made by this research was that the countries that make up the G20 should, as a rule, be among those that emit the most CO₂ per year [30]. Figure 1 suggests that the first research assumption seems reasonable.

Figure 1 shows the global time series of the total emissions of billions of tons of CO₂, considering the sum of these emissions per year for countries that are or are not part of the G20, disregarding economic blocs. Figure 1 considers data from 1999 onwards because that was the year that the G20 was created.

From Figure 1, an analogy can be made with the laws of physics, which state that the average speed of a body can be measured by its displacement in space over a given period. Based on this reasoning, it would also be possible to conclude that the acceleration of the same body could be determined by the rate of change of the object’s velocity in relation to time. Figure 1 suggests that the average speed of the reduction in CO₂ emissions into the atmosphere is given by different spaces (countries/governments/economic blocs) divided by a possible future time lapse. It is uncertain whether we will ever know, since the rate of acceleration (the slope coefficients of the linear trends in Figure 1) for the world’s top 20 economies is, on average, 4.65 [CI95: +4.52; +4.75] times higher than for the other countries.

The problem (and the contradiction) is that the emergence of the G20, in addition to the idea of sharing the lead with the G7 on economic and financial agendas, including emerging countries in these discussions [15], is also based on climate change agendas, sustainable development, and global health [17,18]. Therefore, Figure 1 seems to suggest that, in general, these countries’ CO₂ emissions commitments are not being met.

Hypothesis 1 (H1).

The creation of the G20 is also linked to an increase in CO₂ emissions through its signatories.

In an attempt to clarify the analysis in Figure 1, we could look at the movement of countries that have emitted the most CO₂ since the creation of the G20 in 1999. Figure 2 shows this information.

Figure 2 clearly shows that not every country that makes up the G20 is among the top 20 CO₂ emitters. The case in point is France, which in 1999 ranked 10th among the countries emitting the most CO₂ and in 2021 was no longer among the largest CO₂ emitters. Other countries also fell sharply in this ranking, such as the United Kingdom and Italy. These considerations have led to the idea of different temporal and regional arrangements, leading to the idea that each G20 country has its own inclination rates regarding annual CO₂ emission trends, as shown in Figure 1. In view of this, the authors adjusted their initial premise, considering that there are probably G20 countries that have adopted a higher rate of CO₂ emissions than others, just as there should be countries in this stratum that could show a negative slope in the rate of emissions discussed (see [31]).

Hypothesis 2 (H2).

Some G20 countries have a negative slope in their annual CO₂ emissions.

2.2. Climate Policies in the G20 Countries

The Paris Agreement represented a historic milestone in the fight against climate change induced by human behavior, and all G20 countries are signatories to it [32]. This treaty provides for a series of long-term targets, called Nationally Determined Contributions (NDCs), regarding the commitment to reduce the temperature of the planet by 2 °C by 2030.

However, according to the forecasts of Roelfsema et al. [33] and Rogelj et al. [34], there is no way for this target to be completely met, and after the Paris Agreement, there was an acceleration in the proposal and implementation of new climate policies, whether internal to each country or jointly.

As expected, most of these climate policies are heterogeneous because they try to approach the reduction in global temperatures (and, consequently, CO₂ emissions) from different perspectives due to different legal, cultural, and social arrangements.

For example, consider the three main CO₂ emitters in the Paris Agreement, which belong to the G20: China, the USA, and India.

China, the world’s largest CO₂ emitter since 2006, usually blames the USA, Europe, Japan, and other countries and is considered rich in its historical CO₂ emissions. For years, China has resisted global calls to regulate CO₂ emissions [35].

Since the Paris Agreement, China has changed its mind and made an international commitment to reduce its CO₂ emissions by 2030. Between 2010 and 2015, China proposed the highest number of climate policies. However, as Schreurs [35] argues, this change in China’s rhetoric is not directly linked to international pressure but rather to domestic factors, such as the high levels of dissatisfaction of its population with air pollution, the severe increase in rainfall and droughts in its territory, and extreme temperatures.

Internally, China has proposed blue carbon management policies, and Yu and Wang [36] have achieved satisfactory results in terms of climate change and sustainable development. Another relevant action by the Chinese government is reported in the studies by Zhou et al. [37], considering the case of carbon pricing and green investments, which, according to the authors, still suffer from mismatches regarding how the central government views its implementation vis-à-vis how local governments consider it. Finally, it is worth mentioning the Chinese low-carbon city pilot initiative [38,39] which, according to Pan et al. [40], promotes low-carbon innovation.

The USA, on the other hand, has a controversial history of adopting positions on the climate agenda vis-à-vis its international peers. In 1997, it signed its participation in the Kyoto Protocol, which its Senate never ratified, and later, in 2001, it abandoned the treaty. In 2015, it became a signatory to the Paris Agreement; in 2018, it began threatening to withdraw from the agreement [41]; in 2020, it submitted its withdrawal; and in 2021, it decided to return [42]. All these movements have a political background, based on their internal environment and a two-party political system that, in short, is oriented according to the agenda of its voters, which is often polarized in this regard [43,44]. In this scenario, Cory et al. [45] argued that Democratic Party voters tend to advocate for the expansion of climate policy proposals and implementation, while the Republican Party tends to expose its skepticism about current climate effects, advocating for mild changes to the status quo of climate policies.

Internally, the USA is oriented towards a tripartite division of the possibility of creating and implementing climate policies, considering the federal, state, and municipal levels of government, and each level has considerable influence on the matter. Consequently, states and municipalities can have different regulations and climate policies.

The USA’s main current actions regarding climate policies are the Infrastructure Investment and Jobs Act (IJA) and Inflation Reduction Act (IRA). The IJA came into force in 2021 and proposed a significant expansion in the transport and energy generation sectors, considering the existence of carbon capture and storage projects, hydrogen economy projects, factory decarbonization projects, and solar farms [46]. The IRA, in force from 2022, is the largest investment of all time with regard to climate change, proposing to increase renewable energy and electrifying areas of the US economy, considering tax credits for consumers and private businesses [47].

Despite being the third-largest emitter of CO₂, India has the largest number of climate policy proposals in the world. It is also interesting to note that when the metric of CO₂ emissions per capita is considered, India is one of the smallest emitters [48]. The country launched five-year plans at the national level called the National Action Plan on Climate Change (NAPCC) and Intended Nationally Determined Commitments (INDCs) [49], focusing on energy conservation, energy efficiency, and mitigation measures [50].

As pointed out by Townshend [51], the NAPCC was instituted by the Indian government in 2008 and acts as a kind of framework for climate change mitigation. The INDCs, on the other hand, according to Saran [52], present audacious targets for climate change mitigation.

What mainly emerges from the dynamics of the climate policies of the globe’s three largest emitters is the heterogeneity that exists between these countries in terms of their interests, legislation, and government behavior.

Returning to the G20 as a whole, despite the growing proposal of climate policies, all the countries in the group expect CO₂ emissions to increase [53,54]. In fact, data from the World Bank (WB) seem to reinforce an upward trend in CO₂ emissions for most of the G20 countries, when observed until 2021, as shown in Figure 3.

Also, according to WB data, the countries that make up the G20 (excluding economic blocs) were responsible for 78.5% of the more than 23.5 billion tons of CO₂ emitted worldwide in 1999. In 2021, the same group of countries accounted for 79.6% of more than 35.5 billion tons of CO₂ dumped into the atmosphere.

It follows from this behavior that it is true to say that the number of climate policies has been increasing over time [32,55,56] and that the adoption of more climate policies seems to have a negative relationship with CO₂ emissions [57]. There is therefore a mismatch; the capacity to organize and propose policies aimed (directly or indirectly) at mitigating CO₂ emissions does not seem to be keeping pace with the speed with which the G20 countries are developing and increasing their CO₂ emissions [58,59].

Hypothesis 3 (H3).

There is a mismatch between CO₂ emissions and the G20’s climate policy proposals.

2.3. Literature Review on the Modeling Approaches to CO₂ Emissions in the G20

As presented in the introductory part of this research, the intention was not to model the EKC but rather to present a distinct, long-term functional form from a multilevel perspective regarding the CO₂ emissions of the G20 countries in a comparative way.

Table 1. Extant studies on CO₂ emissions by the G20 that have not used EKC theory in the last five years.

Reference	Sample Characteristics	Modeling Strategy	Main Findings
Tripathy et al. [8]	Annual data.	Panel data regression	The authors suggest that bilateral foreign direct investment reduces the intensity of CO2 emissions and strengthens institutional quality in the G20.
Nansai et al. [19]	Annual data.	Panel data regression	CO2 emissions appear to have an impact on 1.983 million premature deaths, at an average of 67 years, including 78.6 thousand deaths of newborns.
Churchill et al. [30]	Annual data.	Panel data regression	The growth in CO2 emissions negatively affects international tourist arrivals, and this effect seems to be greater in the more-developed G20 economies.
Yao and Tang [31]	Annual data.	STIRPAT modeling	The ratio between direct and indirect financing has a negative relationship with per capita carbon emissions in developed countries but is positive in developing economies. Furthermore, the interaction between financial structure and productivity has a positive relationship with carbon emissions in developing countries.
Gao and Wang [38]	Cross-sectional data from G20 countries.	Spatial difference-in-differences model	The authors suggest positive spatial relationships between emissions between regions and that the opening of high-speed railroads seems to have a positive spillover effect.
Gao et al. [39]	Cross-sectional data from G20 countries.	Data envelopment nnalysis and spatial difference-in-differences model	The study indicates that the innovative cities policy improves the efficiency of CO2 emissions and has positive spatial spillover effects on the surrounding regions. The spillover effect of the innovative cities policy is more intense in developed, coastal regions and/or those with advanced industrial structures.
Chen et al. [60]	Annual data.	Quantile regression analysis	A more equal distribution of income favors the reduction in CO2 emissions per capita in developing countries, while in most developed countries, income inequality has little effect on CO2 emissions.
Habib et al. [61]	Cross-sectional data from G20 countries.	Regression analysis	There seems to be a positive relationship between the intensity of road transport, road passenger transport, and road freight transport in CO2 emissions. Economic growth and urbanization are positively related to CO2 emissions from road transport, while openness to trade and the price of crude oil are negatively related to CO2 emissions.
Uddin et al. [62]	Annual data.	Panel data regression	Positive relationships between military spending, energy consumption, and information and communication technologies on CO2 emissions.
Kong et al. [63]	Annual data.	STIRPAT modeling and PLS regression	Looking at shared socioeconomic pathways, there was a suggestion that 13 countries, such as China, the United States, and the United Kingdom, could peak their CO2 emissions by 2050, while six countries, such as Argentina, India, and Saudi Arabia, could not.
Alotaibi and Alajlan [64]	Annual data.	Panel data regression	Fossil fuel consumption is positively related to CO2 emissions, while urbanization and openness to trade are negatively related.
Hussain et al. [65]	Annual data.	Classical regression model; quantile regression; panel data regression and multilevel model	Negative relations between renewable energies and CO2 emissions; urbanization has negative relations with CO2 emissions.
Deng et al. [66]	Annual data.	Linear regression, ensemble modeling, support vector machines, and neural network	The authors suggest that post-pandemic CO2 emissions will be lower than projections prior to the COVID-19 pandemic. However, this reduction is still below the 1.5 °C climate target of the Paris Agreement.
Wen et al. [67]	Annual data.	Panel data regression	The results suggest a positive relationship between the governance quality indicators and carbon emissions. However, there were negative relationships between financial development accompanied by good governance and carbon emissions.
Liza et al. [68]	Annual data.	Panel data regression	The result identifies that non-renewable energy, financial development, and the workforce are significant contributors to CO2 emissions.
Sheraz et al. [69]	Annual data.	Panel data regression	The results indicated a negative relationship between carbon emissions, financial development, and human capital and a positive relationship between carbon emissions, GDP, and energy consumption in the G20.
Demirtaş et al. [70]	Annual data.	Panel data regression and multilevel model	Institutional quality is positively related to green investments, while military spending is negatively related.
Viglioni et al. [71]	Annual data.	Multilevel model	Foreign direct investment increases CO2 emissions in G20 countries.
This study	Annual data.	Multilevel model with time trend	Some G20 countries already have negative inclination rates regarding their CO2 emissions; since the emergence of the G20, the CO2 emissions of the signatory countries have generally continued to rise; as a rule, the speed at which climate policies are proposed does not match the speed at which these countries emit CO2.

presents a review of recent studies on CO₂ emissions in the G20, considering various contexts concurrently, in addition to the relationship between Gross Domestic Product (GDP) and the phenomenon studied, typical of the EKC theory.

The intention of the review proposed in Table 1 is not to be exhaustive but to present the myriad empirical methods and results that contribute to proposing public policies and observing the behavior of the G20 with regard to their CO₂ emissions.

According to Table 1, to the best of our knowledge, in recent years, only Hussain et al. [65], Demirtaş et al. [70], and Viglioni et al. [71] have considered mixed-effects modeling (fixed and random effects simultaneously) for the phenomenon studied within the G20. However, in the case of Hussain et al. [65], the authors were primarily interested in comparing models in light of issues relating to nonrenewable energy, renewable energy, GDP, and urbanization, from 1971 to 2021. On the other hand, Demirtaş et al. [70] examined the effect of institutional quality and the components of this institutional quality on green investments for G20 countries. Finally, Viglioni et al. [71] focused on issues related to intellectual property and foreign direct investment.

Our research differs in that (i) in addition to covering a longer period of time, we seek (ii) to understand which G20 countries are decreasing their inclinations regarding CO₂ emissions and (iii) whether or not a country’s membership of the G20 is related to a slowdown in its annual carbon emissions.

3. Methods

3.1. The Multilevel Perspective

Assuming heterogeneous behavior in relation to CO₂ emissions by the G20 countries [8], we opted for hierarchical multilevel modeling approach (generalized linear mixed models (GLMMs)) to understand and measure not only the different regional behaviors of the variables of interest but also the idiosyncratic differences in CO₂ emissions by countries over time.

Following Rabe-Hesketh and Skrondal [72], GLMM estimations, also known as linear mixed-effects models, mixed models, mixed-effects models, or mixed error-component models, are natural extensions of generalized linear models (GLMs).

The traditional GLM approach estimates the fixed effects of a given phenomenon, that is, it is assumed that the heterogeneity of the individuals in the sample is constant, either as a function of time or as a function of the natural nesting of the observations [9,73]. However, in most real-world situations, data are nested/grouped [74], and, as discussed by Mathieu and Chen [10], the levels of data analysis, that is, their contexts—also called nestings, either latent or non-latent—are not taken into account by GLM estimations.

In other words, considering the real case of CO₂ emissions by the G20 countries, it is reasonable to say that these nations live in different contexts. Such contexts can involve different designs and approaches to public policy [75,76], their respective regulatory peculiarities [77,78], their different governmental efforts to invest in technologies aimed at mitigating CO₂ emissions [79,80,81], different levels of public awareness and education on the subject [82,83,84], and different levels of commitment and engagement by market sectors in reducing CO₂ emissions [85,86], among many others. Furthermore, all of these myriad contexts change over time [87]. Therefore, from all of the above, it is also possible to see that each country experiences a different level of maturity in relation to CO₂ emissions [88,89,90,91].

Therefore, mathematically speaking, it would be unfair to use the same ruler to compare different countries, with different levels of maturity, inserted in different social, economic, geographical, political, and demographic arrangements (to say the least).

A fixed-effects model for this specific case would propose exactly what the previous paragraph condemned. Thus, for didactic purposes and to make it easier to explain the reasoning we disapprove of, Figure 4 proposes that we imagine the behavior of CO₂ emissions from the perspective of a model that only considers fixed effects.

Figure 4A shows the predicted CO₂ emissions from the GLM model without considering dummies representing the countries in the sample. In contrast, Figure 4B shows another GLM estimation of CO₂ emissions but with dummy variables that identify individuals in the sample.

Figure 4 unequivocally shows that a model that considers the heterogeneity of the individuals in the sample to be constant would attempt to measure the phenomenon studied by placing all the countries under the same umbrella, as it does not consider that they belong to different realities, which impact their CO₂ emissions differently. Even if the countries in the sample are controlled for by using dummy variables, as shown in Figure 4B, the resulting fits are perfectly parallel curves, without considering any different slope rates depending on the country.

In other words, according to Courgeau [9], by adopting a GLM model for the problem in question, the results do not appear to demonstrate a connection between the observations and the environment in which these individuals are inserted.

Figure 5, on the other hand, demonstrates the same empirical attempt to forecast CO₂ emissions as in Figure 4 but with considering the nesting (the so-called levels of analysis) present in the data.

Figure 5 shows the visual results of using a GLMM-type multiple equation estimation with different intercepts and slope rates for each sampling country. Thus, by considering a model that considers both the fixed and random effects of the dataset, the heterogeneities of each context were highlighted and captured.

In the case of this research, these contexts are concerned with the time span of the dataset nested within the countries in the sample. In other words, every day in every country was considered. This approach made it possible to compare the individual temporal evolution of each country in the database regarding the phenomenon studied as well as to compare the different countries over different time periods.

That said, following Headley and Clark [92], in matrix form, a two-level multilevel linear estimation can be described by Equation (1).

$$\mathbf{Y}=\mathbf{X}\mathsf{\beta }+\mathbf{W}\mathsf{\nu }+\mathsf{\epsilon }$$

(1)

where $\mathbf{Y}$ represents the vector of dimension $n\times 1$ of the observed values for the phenomenon studied; $\mathbf{X}$ is a matrix of covariates, of dimension $n\times k$, used to calculate the fixed-effects parameters $\mathsf{\beta }$; $\mathbf{W}$ is a matrix of second-level covariates, of dimension $n\times p$, used to measure the random effects $\mathsf{\nu }$; and $\mathsf{\epsilon }$ is a vector of dimension $n\times 1$ that represents the idiosyncratic error terms, assuming $\epsilon ~N(0,{\sigma }_{\epsilon }^2)$.

In Equation (1), the fixed-effects portion $\mathbf{X}\mathsf{\beta }$ of the multilevel linear estimation is calculated in a similar way to a classical regression model, estimated using the ordinary least squares criterion [93]. On the other hand, to calculate the random-effects portion of the model $\mathbf{W}\mathsf{\nu }+\mathsf{\epsilon }$, it must be assumed that $\mathsf{\nu }$ has a variance–covariance matrix $\mathbf{G}$, in addition to the assumption of orthogonality between $\mathsf{\nu }$ and $\mathsf{\epsilon }$ [72], as shown in Equation (2).

$$\mathrm{v}\mathrm{a}\mathrm{r}\left[\begin{array}{c}\mathsf{\nu }\\ \mathsf{\epsilon }\end{array}\right]=\left[\begin{array}{cc}\mathbf{G}& 0\\ 0& {\sigma }_{\epsilon }^2\mathbf{R}\end{array}\right]$$

(2)

where random effects $\mathsf{\nu }$ are characterized as elements of G, which, in turn, are estimated jointly with the overall residual variance ${\sigma }_{\epsilon }^2$ and the residual-variance parameters contained in $\mathbf{R}$.

Assuming the $j$ nesting of the data (the temporal journey of each country’s CO₂ emissions, nested in each country), it is interesting to organize the $n$ observations as a series of $C$ independent groups. Thus, as proposed by Goldstein [94], we could revisit Equation (1) and rewrite it in terms of Equation (3).

$${\mathbf{Y}}_j={\mathbf{X}}_j\mathsf{\beta }+{\mathbf{W}}_j{\mathsf{\nu }}_j+{\mathsf{\epsilon }}_j$$

(3)

where $j=1,\dots ,C$ and where the group $j$ consists of $n_j$ observations.

From Equation (3), ${\mathsf{\nu }}_j$ can be approached as $C$ realizations of a vector of dimension $p\times 1$, which adheres to a multivariate Gaussian distribution, with a mean of 0 and a variance matrix $\mathsf{\Sigma }$, whose dimension is $p\times p$ [95]. Thus, $\mathbf{G}$ and $\mathbf{R}$ are obtained by Equations (4) and (5), respectively [96].

$$\mathbf{G}={\mathbf{I}}_C⨂\mathsf{\Sigma }$$

(4)

$$\mathbf{R}={\mathbf{I}}_C⨂\mathsf{\Lambda }$$

(5)

where $\mathsf{\Lambda }$ is a variance matrix of level 1 errors; and the operator $⨂$ indicates the Kronecker product.

Following Gelman and Hill [97], it is assumed that the random effects ${\mathsf{\nu }}_j$ are adherent to a multivariate Gaussian distribution, with a mean of 0 and a variance of $\mathsf{\Sigma }$. That said, the values of can be calculated by maximizing the log-likelihood function $\mathcal{L}$ presented by Equation (6) [98].

$${\mathcal{L}}_j\left(\mathsf{\beta },\mathsf{\Sigma }\right)={\left(2\pi \right)}^{{\displaystyle \frac{-p}{2}}}{\left|\mathsf{\Sigma }\right|}^{{\displaystyle \frac{-1}{2}}}{\int }_{{\mathfrak{R}}^p}\mathrm{e}\mathrm{x}\mathrm{p}\left[\log f\left({\mathbf{Y}}_{\mathrm{j}}|{\mathsf{\eta }}_{\mathrm{j}}\right)-{\displaystyle \frac{1}{2}}{\mathsf{\nu }}_j^{-1}{\mathsf{\Sigma }}^{-1}{\mathsf{\nu }}_{\mathrm{j}}\right]d{\mathsf{\nu }}_j$$

(6)

where ${\mathsf{\eta }}_j$ represents the linear predictor ${\mathbf{X}}_j\mathsf{\beta }+{\mathbf{W}}_j{\mathsf{\nu }}_j$; $f\left({\mathbf{Y}}_j|{\mathsf{\eta }}_j\right)$ represents the conditional density function of the response vector $\mathbf{Y}$, for each of the $i$ observations, where $i=\mathrm{1,2},\dots ,n$; $\mathfrak{R}$ represents a series of values belonging to the set of real numbers; and ${\mathfrak{R}}^p$ is analogous to $\mathfrak{R}$ when considered in a p-dimensional space.

For didactic purposes, if we assume a theoretical two-level GLMM estimation, which considers random intercepts and slopes, with a phenomenon described by a continuous metric variable, we will have the combination of Equations (7)–(10).

Level 1:

$$Y_{ij}={\beta }_{0j}+{\beta }_{1j}.X_{ij}+{\epsilon }_{ij}$$

(7)

Level 2:

$${\beta }_{0j}={\gamma }_{00}+{\nu }_{0j}$$

(8)

$${\beta }_{1j}={\gamma }_{10}+{\nu }_{1j}$$

(9)

$${\beta }_{2j}={\gamma }_{20}$$

(10)

where $Y$ represents the phenomenon to be studied; $i$ is the level 1 subscript, i.e., the time lapse; j is the level 2 subscript, i.e., the nesting of the time course of the individuals considered; ${\beta }_{0j}$ and ${\beta }_{1j}$ refer to the coefficients of the first level; ${\gamma }_{00}$ and ${\gamma }_{10}$ point to the coefficients of the second level; ${\epsilon }_{ij}$ refers to the level 1 error terms, where $\epsilon ~N(0,{\sigma }_{\epsilon }^2)$; and ${\nu }_{0j}$ and ${\nu }_{1j}$ represent the random effects of level 2, assuming for these parameters, for each unit $j$, multivariate normality with a mean equal to 0 and a variance of ${\sigma }_{\nu }^2$ (it was decided at this point to abandon the notation $\mathsf{\Sigma }$ so that the reader could better grasp the calculation of the intraclass correlations that will be presented below and which depend on the separation of the variances of the error terms of the random intercepts and the error terms of the random slopes).

Equations (8)–(10) provide access to the second level of analysis in a multilevel structure. Equation (7) gives access to the model’s fixed effects, i.e., its first level, offering insights into the current status and behavior of the individuals in the sample.

Therefore, the general model assumed when considering Equations (7)–(10) is shown in Equation (11):

$$Y_{ij}={\gamma }_{00}+{\gamma }_{10}.X_{ij}+{{\nu }_{0j}+{\nu }_{1j}.X_{ij}+\epsilon }_{ij}$$

(11)

Equation (11) shows that ${\nu }_{0j}$, in fact, works as an adjustment of the term ${\gamma }_{00}$. In other words, ${\gamma }_{00}$ represents the general intercept considering the fixed effects and, when considered together with the term ${\nu }_{0j}$, we have the adjusted intercept for a given individual $j$ of the sample.

Similarly, the term ${\nu }_{1j}$ works in relation to ${\gamma }_{10}$ in Equation (11). If ${\gamma }_{10}$ represents the rate of inclination with respect to the variable $X$, when considering fixed effects, ${\nu }_{1j}$ proposes an adjustment to its value, depending on the heterogeneous catches of a given individual $j$.

That said, the variances of the random effects ${\sigma }_{\nu }^2$ of the intercepts and slopes of the second level are considered (see Equations (8)–(10) as well as the variances of the idiosyncratic error terms ${\sigma }_{\epsilon }^2$ (see Equations (7) and (11)), the possibility arises of measuring the intraclass correlations (ICCs) of the model, as proposed by Equation (12).

$$ICC={\displaystyle \frac{{\sigma }_{{\nu }_{0j}}^2+{\sigma }_{{\nu }_{1j}}^2}{{\sigma }_{{\nu }_{0j}}^2+{\sigma }_{{\nu }_{1j}}^2+{\sigma }_{\epsilon }^2}}$$

(12)

where ${\sigma }_{{\nu }_{0j}}^2$ represents the variance in the error terms of the random intercepts of the estimation; and ${\sigma }_{{\nu }_{1j}}^2$ indicates the variance in the error terms of the random slopes of the model.

According to Bliese [99], the ICC results vary between 0 and 1, and its calculation makes it possible to check how much of the variation at a lower level can be attributed to a higher level of analysis. In other words, we could measure how much of the total variability in the data was due to differences between the G20 signatory countries.

In fact, demonstrating the relevance of the assumption of contexts (levels of analysis) is of paramount importance, and as discussed by Gelman and Hill [97], this situation can be overcome by means of a likelihood ratio (LR) test between the proposed GLMM estimation and an analogous model (e.g., a GLM estimation) that considers fixed effects only. Equation (13) presents a possible form for the LR test:

$${\chi }_{LRtest}^2=-2\times \left({\mathcal{L}}_{Model1}-{\mathcal{L}}_{Model2}\right)$$

(13)

In Equation (13), multiplication by the term mathematically guarantees that the result of the LR test asymptotically converges to a distribution ${\chi }^2$, by means of the Wilks’ theorem, for a number of degrees of freedom equal to the difference in the degrees of freedom of the compared models [100]. In the LR test, it is indicated whether there are no differences between the compared estimates at a given significance level [100]. Therefore, the non-rejection of the LR test, for a given significance level, when comparing a GLMM estimation with an analogous GLM model, would suggest that the contexts adopted might not make sense, that is, that the random effects calculated have no relevance to the analysis of the phenomenon studied.

Finally, as discussed by Nakagawa and Schielzeth [101], the approximation of a goodness-of-fit measure for the GLMM estimates (i.e., the traditional R² statistic) has difficulties owing to the complexity of obtaining a precise calculation between the different levels of analysis and can be biased depending on the criterion used to estimate the model parameters (e.g., maximum likelihood or restricted maximum likelihood).

In relevant studies, Johnson [102] and Nakagawa et al. [103] proposed two ways of calculating a goodness-of-fit measure for GLMM models: the statistics Marginal $R_{GLMM}^2$ and Conditional $R_{GLMM}^2$, as shown, respectively, by Equations (14) and (15).

$$Marginal{R}_{GLMM}^2={\displaystyle \frac{{\sigma }_{fixed}^2}{{\sigma }_{fixed}^2+{\sigma }_{random}^2+{\sigma }_{\epsilon }^2}}$$

(14)

$$Conditional{R}_{GLMM}^2={\displaystyle \frac{{\sigma }_{fixed}^2+{\sigma }_{random}^2}{{\sigma }_{fixed}^2+{\sigma }_{random}^2+{\sigma }_{\epsilon }^2}}$$

(15)

where ${\sigma }_{fixed}^2$ measures the variance in the fixed-effects portion of the model; and ${\sigma }_{random}^2$ represents the variance in the random-effects portion of the estimation.

Following Johnson [102] and Nakagawa et al. [103], Equation (13), which is the Marginal $R_{GLMM}^2$, measures the variance explained by the fixed effects of the estimation alone. Equation (14), on the other hand, measures the variance in the data in the entire model, considering both fixed and random effects.

3.2. Dataset Design

The research data were found in WB repositories regarding total CO₂ emissions, measured in billions of tons per year. Data from 1950 to 2021 were taken from all countries that make up the G20, with the exception of economic blocs. Therefore, data from South Africa, Germany, Saudi Arabia, Argentina, Australia, Brazil, Canada, China, South Korea, the United States, France, India, Indonesia, Italy, Japan, Mexico, the United Kingdom, Russia, and Turkey were considered.

The researchers’ main motivation for considering data from the G20 countries from 1950 onwards and not from the creation of the aforementioned economic bloc (1999, in this case) was an attempt to capture as much of the behavioral heterogeneity of the countries under analysis before and after their entry into the G20. Therefore, in theory, one idea was to check, on an individual basis, whether or not a country being part of the G20 has made it review its CO₂ emissions into the atmosphere, taking into account the behavioral patterns of a large previous period of time. This is in addition to identifying, on a global level, whether the G20 complies with its sustainability agenda with regard to CO₂ emissions.

Thus, in view of the research objective, which is aligned with the multilevel perspective, the database was structured in a balanced longitudinal panel format, considering its repeated measures [95,104], hierarchically nested with their respective geographical units [9], as shown in Figure 6.

To reduce the computational demand in the calculations and enhance the interpretability, this study’s dependent variable (emission), which refers to the total annual CO₂ emissions per country at a given point in time, was multiplied by ${10}^{-9}$. In other words, the unit of measurement of the emission variable is represented in billions of tons.

Table 2. Univariate descriptive statistics for the variable of interest.

Variable	Min	1st Q	Median	3rd Q	Max	Mean	SD
$emission$	0.0000	0.1590	0.3860	0.6603	11.4000	0.8263	1.451

Note: 1st Q stands for first quartile, 3rd Q stands for third quartile, and SD stands for standard deviation.

shows the univariate descriptive statistics of the phenomenon studied.

Table 3. Univariate descriptive statistics for the variable of interest, stratified by G20 member country.

Country	Min	1st Q	Median	3rd Q	Max	Mean	SD
ARG	0.0298	0.0677	0.1090	0.1490	0.1910	0.1120	0.0499
AUS	0.0544	0.1320	0.2390	0.3710	0.4140	0.2440	0.1230
BRA	0.0196	0.0738	0.1910	0.3490	0.5550	0.2270	0.1600
CAN	0.1530	0.2970	0.4340	0.5540	0.5900	0.4110	0.1450
CHN	0.0784	0.6880	2.0400	4.9000	11.4000	3.4100	3.4900
DEU	0.5080	0.7950	0.9150	1.0100	1.1100	0.8930	0.1400
FRA	0.2010	0.3310	0.3880	0.4130	0.5360	0.3790	0.0810
GBR	0.3240	0.5420	0.5670	0.5920	0.6570	0.5500	0.0724
IDN	0.0093	0.0270	0.1210	0.3400	0.6560	0.1980	0.1930
IND	0.0608	0.1700	0.4100	1.0700	2.6900	0.7620	0.7770
ITA	0.0412	0.2440	0.3600	0.4300	0.5000	0.3230	0.1370
JPN	0.1020	0.5410	0.9360	1.2200	1.3100	0.8660	0.4040
KOR	0.0022	0.0365	0.1720	0.4850	0.6670	0.2610	0.2340
MEX	0.0303	0.0924	0.2970	0.4090	0.4990	0.2680	0.1630
RUS	0.4130	1.3000	1.6100	1.8300	2.5200	1.5400	0.5190
SAU	0.0000	0.0280	0.1820	0.3500	0.6750	0.2290	0.2140
TUR	0.0094	0.0354	0.1100	0.2370	0.4440	0.1540	0.1340
USA	2.4800	3.7900	4.8300	5.4100	6.100	4.5900	1.1100
ZAF	0.0607	0.1360	0.3120	0.4050	0.4920	0.2770	0.1410

Note: 1st Q stands for first quartile, 3rd Q stands for third quartile, and SD stands for standard deviation.

presents the univariate descriptive statistics for the emission variables grouped according to G20 member countries.

Table 3 shows that the highest mean, median, interquartile range, and SD values belonged to China, the USA, India, Russia, and Japan, indicating, preliminarily, constant (and large) temporal increases in CO₂ emissions over the study period. These countries, as shown in Figure 2, were among the top five CO₂ emitters in 2021.

Definitions of the explanatory variables are listed in

Table 4. Description of this study’s explanatory variables.

Explanatory Variables	Description
t	Discrete metric variable that measures the time span from 1950 to 1971 for all G20 countries. It was rescaled between 0 and 71.
g20_creation	$\mathrm{Dichotomous}\mathrm{variable}\mathrm{indicating}\mathrm{the}\mathrm{year}\mathrm{in}\mathrm{which}\mathrm{the}\mathrm{G}20\mathrm{was}\mathrm{created},\mathrm{assuming}\mathrm{a}\mathrm{value}\mathrm{of}0\mathrm{when}t<1999$ and 1 otherwise.

.

In this way, the authors sought to capture the CO₂ emission trends of the G20 countries since 1950 and, from 1999 onwards, to verify whether CO₂ emissions in the G20 have increased.

3.3. Empirical Modeling

In light of the variables assumed by this research, Equation (1) was rewritten in order to highlight its connections between levels 1 and 2 of the study, as shown in Equations (16)–(19).

Level 1:

$${emission}_{ij}={\beta }_{0j}+{\beta }_{1j}.t_{ij}+{\beta }_{2j}.{g20\_creation}_{ij}+{\epsilon }_{ij}$$

(16)

Level 2:

$${\beta }_{0j}={\gamma }_{00}+{\nu }_{0j}$$

(17)

$${\beta }_{1j}={\gamma }_{10}+{\nu }_{1j}$$

(18)

$${\beta }_{2j}={\gamma }_{20}$$

(19)

where $emission$ represents the phenomenon to be studied and is the level 1 subscript, i.e., the time elapsed; j is the level 2 subscript, i.e., the nesting of time in the geographical units considered; ${\beta }_{0j}$, ${\beta }_{1j}$, and ${\beta }_{2j}$ refer to the coefficients of the first level; ${\gamma }_{00}$, ${\gamma }_{10}$, and ${\gamma }_{20}$ point to the coefficients of the second level; ${\epsilon }_{ij}$ refers to the level 1 error terms, where $\epsilon ~N(0,{\sigma }_{\epsilon }^2)$; and ${\nu }_{0j}$ and ${\nu }_{1j}$ represent the random effects of level 2, assuming for these parameters, for each unit $j$, multivariate normality with a mean equal to 0 and a variance of ${\sigma }_{\nu }^2$.

Therefore, the general model assumed when considering Equations (16)–(19) is shown in Equation (20):

$$Y_{ij}={\gamma }_{00}+{\gamma }_{10}.t_{ij}+{\gamma }_{20}.{g20\_creation}_{ij}+{{\nu }_{0j}+{\nu }_{1j}.t_{ij}+\epsilon }_{ij}$$

(20)

Therefore, by estimating a multilevel regression model, as described in Equation (20), it was possible to: i) identify the average CO₂ emission patterns in the G20; ii) identify and compare, individually, different moments in each country with regard to CO₂ emissions; iii) compare different times in different countries in terms of CO₂ emissions; iv) use Equation (11) to identify the proportion of heterogeneity of the G20 countries in terms of CO₂ emissions, conditional on the study variables; and v) use Equations (14) and (15) to measure the capture of data variability when considering only the fixed-effects portion, as well as when considering the fixed effects and random effects of the estimation at the same time.

4. Results

The results of the research estimation are shown in

Table 5. Main results of this study’s modeling.

Parameters	Coefficients
${\gamma }_{00}$ (intercept)	0.2169 (0.2069)
${\gamma }_{10}$ ($t$)	0.0165 ** (0.0079)
${\gamma }_{20}$ ($g20\_creation$)	0.0703 * (0.0375)
${\sigma }_{{\nu }_{0j}}^2$	0.8029 (0.2705)
${\sigma }_{{\nu }_{1j}}^2$	0.0012 (0.0004)
${\sigma }_{\epsilon }^2$	0.1453 (0.0056)
$ICC$	0.8468
Marginal $R_{GLMM}^2$	0.0622
Conditional $R_{GLMM}^2$	0.9305
$\mathcal{L}$	−735.2983 d.f. = 7
$n$	1368

Note: $\mathcal{L}$ stands for log-likelihood, and $df$ stands for degrees of freedom; ** represents significance at the 5% level; * represents significance at the 10% level.

.

Table 6. Validation of the use of a mixed-effects model.

Estimation	$\mathcal{L}$	d.f.	${\mathit{\chi }}_{\mathit{L}\mathit{R}\mathit{t}\mathit{e}\mathit{s}\mathit{t}}^2$	sig. LR Test
GLMM	−735.2983	7	1773.498 d.f. 15	0.000
GLM	−1622.0474	22

shows a comparison between the research model (see Table 3) and an analogous GLM estimation, which considered the countries in the dataset as dummy variables.

The results shown in Table 6 suggest that using countries as a context, that is, taking random effects into account, seems to make sense at the 1% significance level for the phenomenon studied, ceteris paribus.

Figure 7 and Figure 8 complete the information in Table 5 by illustrating, respectively, the calculated values of ${\nu }_{0j}$ and ${\nu }_{1j}$, or in other words, the adjustments to the intercepts and slopes of the research modeling for each geographical unit analyzed.

Finally, regarding the goodness-of-fit of the research estimation, according to Table 5, approximately 93.05% of the variance in the data was captured (Conditional $R_{GLMM}^2$) when fixed and random effects were considered simultaneously. On the other hand, if the random effects present in the database were disregarded, the explanatory capacity of the data’s variability dropped to approximately 6.22% (Marginal $R_{GLMM}^2$).

The interpretation of this study’s modeling and its subsequent discussion are presented below.

5. Discussion

A preliminary interpretation of the coefficients shown in Table 5 can be made in a manner similar to the parameters of a classic regression model. In this sense, ${\gamma }_{00}$ represents the global intercept of the model, i.e., the expected average CO₂ emissions for the G20 countries at time $t_0$ in the analysis, namely, 0.2169 billion tons per year, ceteris paribus.

According to the results presented in Table 5, it is also interesting to note that the parameter ${\gamma }_{20}$, associated with the variable $g20\_creation$, showed a positive relationship and was statistically different from zero at the 10% significance level when all the other conditions remained constant. Therefore, the research model confirms H1, that is, at 90% confidence, since the entry of the countries studied into the G20, there has been an average increase in CO₂ emissions into the Earth’s atmosphere of 0.0703 billion tons per year [CI90: +0.0080; +0.1317], ceteris paribus.

While the results suggest that global CO₂ emissions from G20 countries have continued to rise since the group’s creation, the authors set out to understand whether any G20 countries have already shown a decrease in their CO₂ emission rates.

However, in an absolute preliminary way, it was possible to state that, at 5% significance, the model’s slope coefficient ${\gamma }_{10}$, associated with the time span between 1950 and 2021, indicates that for every year that passed, CO₂ emissions into the atmosphere increased, on average, by 0.0165 billion tons [CI95: +0.0009; +0.0321] by the G20 member countries, with the other conditions remaining unchanged.

In addition to the random effects of the intercept, the research estimate also considered the random effects of the slope in relation to the time course of the G20 member countries ($t$). Therefore, from a multilevel perspective, it is necessary to consider the values of ${\nu }_{0j}$ and ${\nu }_{1j}$, as shown in Figure 7 and Figure 8, respectively.

For example, if we assume the desire to estimate Argentina’s CO₂ emissions at moment $t_0$ of the analysis, that is, the conditional mean of the phenomenon when the other variables are equal to zero, it would not be enough to assume the calculated value of ${\gamma }_{00}$. Given the mixed effects of the intercept, the value of ${\gamma }_{00}$ should be adjusted by the result of ${\nu }_{0j}$ (see Figure 7) for the observed country, resulting in approximately 0.053 billion tons per year (${\gamma }_{00}+{\nu }_{0j})$, ceteris paribus. In other words, Figure 7 shows the average outlook expected from the G20 countries at the time the database was first created.

Similarly, to gauge how the trends (slopes) in Argentina’s CO₂ emissions have manifested over time, it would not be enough to assume the coefficient ${\gamma }_{10}$ in isolation. Furthermore, ${\gamma }_{10}$ must be adjusted by the coefficient ${\nu }_{1j}$ (see Figure 8), taking into account the random effects of the slope over the time period studied. Therefore, it would be necessary to calculate ${\gamma }_{10}+{\nu }_{1j}$, indicating an average annual positive rate of 0.0010. In other words, Argentina has increased its CO₂ emissions by an average of 0.0010 billion tons every year, all other things being equal.

Following the proposed reasoning, it can be seen that Germany, France, the UK, Japan, Russia, and the USA have already exceeded the average CO₂ emissions of the stratum of countries studied since 1950. On the other hand, at time $t_0$ of the analysis, China emitted the least CO₂ of all those studied.

When considering the random slope effects for all the G20 countries, that is, when calculating ${\gamma }_{10}+{\nu }_{1j}$, for each country $j$ in the database, we have access to the measurement of the different rates of inclination with regard to CO₂ emissions by the G20 countries, as shown in

Table 7. Adjustments to the slope rates of CO₂ emissions over time.

Country (1)	${\mathit{\nu }}_{1\mathit{j}}$ (2)	${\mathit{\gamma }}_{10}+{\mathit{\nu }}_{1\mathit{j}}$ (3)	Current Situation (4)
ARG	−0.01545986	0.00107223
AUS	−0.01198788	0.00454421
BRA	−0.01033377	0.00619832
CAN	−0.01113646	0.00539563
CHN	0.13325953	0.14979162
DEU	−0.01774802	−0.00121593
FRA	−0.01707696	−0.00054487
GBR	−0.01980272	−0.00327063
IDN	−0.00922262	0.00730947
IND	0.01568263	0.03221472
ITA	−0.01262307	0.00390902
JPN	−0.00033306	0.01619903
KOR	−0.00700209	0.00953000
MEX	−0.01024704	0.00628505
RUS	−0.00411994	0.01241215
SAU	−0.00811614	0.00841595
TUR	−0.01169314	0.00483895
USA	0.02918669	0.04571878
ZAF	−0.01122607	0.00530602

.

Table 7 presents the calculated values of ${\nu }_{1j}$ (Column (2)) for each country (Column (1)). Table 7 also shows the adjusted slope rates of CO₂ emissions over time (Column (3)) and then (Column (4)) indicates whether or not the country has the values of ${\gamma }_{10}+{\nu }_{1j}\le 0$. The idea behind ${\gamma }_{10}+{\nu }_{1j}\le 0$ is the reversal of the upward temporal trend in CO₂ emissions for each country analyzed.

According to Table 7, this study’s modeling suggests that only three G20 countries have reversed their CO₂ emission growth trends over time: Germany, France, and the United Kingdom. All the other countries presented ${\mathsf{\gamma }}_{10}+{\mathsf{\nu }}_{1\mathrm{j}}>0$, according to this study’s estimation. These results support this study’s H2 that some G20 countries already have negative slope rates for their CO₂ emissions. Figure 9 shows the trend in the G20 countries’ CO₂ emissions over time.

Figure 9A shows the trends in CO₂ emissions in the G20 in absolute forecast values; in Figure 9B, these trends are shown on a log10 scale. In both images, the negative inclinations of France, Germany, and the United Kingdom stand out.

It is true that if you look at Figure 2, you could say that, for example, the USA and Japan seem to show a downward trend in CO₂ emissions. However, the actions taken by these countries to reduce CO₂ emissions into the atmosphere have not yet reversed the trend captured in the 71 years of this study’s database. Figure 5 supports the assertion of the authors.

The results shown in Figure 8 reinforce this. In the image, it can be seen that the adjustments of ${\mathsf{\gamma }}_{10}$, for the USA, remain positive and visibly discrepant from the majority of G20 countries, it being ${\nu }_{1j}\approx 0.02919$. In the case of Japan, although ${\nu }_{1j}$ already shows a negative value, it is still lower than the expected average value of ${\gamma }_{10}$. Figure 8 clarifies how the values of ${\nu }_{1j}$ for China, the USA, and India are considerably higher than those for the other G20 countries.

However, this research did not aim to understand how the different climate policies of the G20 countries relate to their success in mitigating CO₂ emissions, and it did not aim to understand how the different climate policies of the G20 countries relate to their success. In mitigating CO₂ emissions, there are some similarities between the climate policies of the three countries (Germany, France, and the United Kingdom) that appear to have negative rates in relation to the phenomenon studied.

Perhaps the best answer to understand Germany’s and France’s success is to look at some of the European Union’s (EU) macro policies. Even if it is argued that Italy and Turkey do not yet have negative inclination rates regarding CO₂ emissions, it is possible to say that these countries are not far from achieving this goal.

The European Union Emissions Trading System (EU ETS I) covers approximately 40% of the bloc’s total CO₂ emissions, including those derived from power generation, energy-intensive industries, and civil aviation [105,106]. The main approach of the EU ETS I is “cap-and-trade”, i.e., the aforementioned economic bloc sets a limit for annual CO₂ emissions, and companies operating in EU countries must be allowed to emit each ton of CO₂ [105,106]. These companies are allowed to negotiate permits [105].

There are also plans to implement an additional emissions trading system (EU ETS II) with the aim of covering the distribution of fuels for the road transit system, construction sector, and other industrial sectors [106].

The EU also regulates approximately 60% of domestic CO₂ emissions through a regulation called the Effort Sharing Regulation (ESR) [106,107]. The ESR covers the regulation of CO₂ emissions from the transport, construction, and waste sectors, as well as some smaller industries and agriculture that are not considered in ETS I [107].

Another interesting point about the ESR that may help explain the success of Germany and France is that although the aforementioned regulation imposes an average reduction in CO₂ emissions by 40% by 2030, the countries concerned contribute according to their relative wealth [106,107]. In this way, the two richest EU countries will end up having to contribute to a reduction of approximately 50% in CO₂ emissions by 2030 [106,107]. If this does not occur, the ESR provides for penalties, such as forcing these countries to buy emission allocations from other member states at high prices [107].

After leaving the EU in 2020, the UK followed its own regulations. However, it is difficult to dissociate part of its success from the period when it was part of the EU.

Similar to Germany and France, the United Kingdom plans to zero its CO₂ emissions by 2050, and one of the main pillars of its climate policies is the Climate Change Act [108]. This law requires the government to establish “carbon budgets,” considering intermediate stages up to 2050 [108]. These “carbon budgets” represent limits for CO₂ emissions over a five-year period and must be defined 12 years in advance [108].

The Climate Change Act also obliges the UK to implement a Climate Change Risk Assessment, considering the opportunities and dangers of climate change. Unlike in the case of the EU, the Climate Change Act does not provide penalties for non-compliance, positioning itself as a robust legal and governance framework for climate action that, according to the results of our study, seems to work well [108].

Table 5 presents $ICC\approx 0.847$, which concerns the effect caused by the nesting of the time journeys of each country within itself. In other words, approximately 84.7% of the variations in the phenomenon can be explained by differences between countries. Moreover, the fact that the ICC value is considerably close to 1 suggests a general similarity between the G20 countries in terms of CO₂ emissions into the atmosphere. This information is reinforced when we recall the positive relationship between the variable $g20\_creation$ and the phenomenon studied. Combining all this information, which shows that CO₂ emissions are continuing to grow at a generally positive rate, as well as a general similarity in the behavior of the G20 countries in relation to the phenomenon studied, added to the continuous expansion of climate policies over time [32,55,56], it can be inferred that there is, in fact, a mismatch between the level of development and the CO₂ emissions of the G20 countries and the speed with which these policies are designed and implemented. Thus, H3 of this research is confirmed.

6. Final Considerations

The aim of this research was to highlight and measure idiosyncratic differences over time and between different geographical contexts in the trends of CO₂ emissions into the atmosphere by the G20 signatory countries. A GLMM estimation was used, which considered, in addition to the fixed effects, the random effects of the intercept and slope. The results presented in Table 5 suggest that the study model captured approximately 93.05% of the variability in the data.

When considering data from 1950 to 2021, the moment a given country joined G20 (1999) seems to be related to an average increase in CO₂ emissions of approximately 0.0703 [CI90: +0.0080; + 0.1317] billion tons per year (see Table 5), considering a 10% significance level and keeping all other conditions constant.

The results of the research also indicate that globally, CO₂ emissions into the atmosphere by the G20 are growing by 0.0165 [CI95: +0.0009; +0.0321] billion tons per year.

The research modeling also suggests that the aforementioned behavior is generally shared by the G20 countries ($ICC\approx 0.847$), and it seems to be smoothed out in the case of Germany, France, and the United Kingdom, as their rates of decline over time in CO₂ emissions seem to be negative on average (see Table 7).

These results suggest that the speed at which these countries position themselves in the fight to mitigate annual CO₂ emissions does not match the speed of their development [32,55,56], which is related to the increase in the phenomenon studied [20,21,22,23,24,25,26,27,28,29].

With the calculations presented in Figure 7 and Figure 8, as well as the results presented in Table 6, the researchers also reinforced the points made by Tripathy et al. [8] regarding the profound heterogeneity between the G20 countries. According to Table 7, if these heterogeneities had been disregarded, the accuracy of the study model would have dropped from 93.05% to 6.22%.

That said, this research has attempted to help demonstrate the importance of taking random effects into account when modeling CO₂ emissions when there is a mixture of profoundly heterogeneous contexts. It is important to mention that this study does not go against the EKC. In contrast, the authors see this as a complementary perspective.

Mar’I et al. [6], Chen et al. [60], and Wen et al. [67], using the EKC theory, suggested an inverted U shape for some developed G20 countries, which may be related to our findings regarding the presence of negative slopes for CO₂ emissions in three countries in the group. Mar’I et al. [6], Alotaibi et al. [64], and Hussain et al. [65] agree that policymakers must have a clear understanding of the different variables related to CO₂ emissions, and our research, in addition to the various studies presented in Table 1, provides a new perspective to the situation by proposing this kind of contribution.

It is also possible that the way in which France and Germany’s climate policies are mostly governed by the EU may have provided clues as to why these countries have been successful in reversing the sign of their CO₂ emissions over time. These findings are in line with the suggestions of Chen et al. [60], de Kong et al. [63], and Liza et al. [68], who advocated the need for international cooperation to mitigate the phenomenon. The UK has also stopped supporting the use of fossil fuels and coal mining since 2021 [108], remembering that the UK is a combination of countries, and perhaps this joint alignment is in fact one of the routes to the promising results in terms of reducing CO₂ emissions.

In the words of Kong et al. ([63], p. 16), “mitigating climate change requires long-term global efforts,” as well as joint international alignment, given that no country is immune to climate change induced by human behavior.

Furthermore, France, Germany, and the United Kingdom have the similarity of constantly refining their domestic laws on CO₂ emissions—the three countries presented amendments to the regulations mentioned in the research during the years 2023 and 2024 [105,106,107,108]. These points seem to have an effect on mitigating CO₂ emissions, in the view of Kong et al. [63] and Deng et al. [66].

Although our study makes marginal contributions to the underlying literature, it has some limitations. First, our study only considered G20 countries, which are largely made up of countries still in the development phase. Therefore, the suggestions made herein may not be suitable for different contexts.

This research also did not consider the economic blocs that make up the G20, nor did it consider the majority of the countries that make up these blocs. Another limitation was the consideration of variables that only indicate the passage of time, although the research model captured 93.05% of the variability in the data.

The use of data from the WB alone is also a limitation, as there may be variations in the data collection methods across countries.

This study was also limited by the fact that it did not delve into the reasons for the success or the dynamics of climate policies in Germany, France, or the United Kingdom. As such, we suggest that future studies compare the climate policies of the countries mentioned to highlight their general frameworks and their dynamics of operation and integration with the stakeholders in the process.

Given that the proposal and effectiveness of climate policies still do not seem to keep pace with CO₂ emissions, the authors also suggest and encourage the proposition of new functional forms, as well as new theoretical frameworks, so that the scientific community and policymakers have clarity about the phenomenon studied, as well as new perspectives on the subject that are of global relevance.

Another suggested future study is to delve deeper into the determinants of CO₂ emissions for each G20 country and conduct a comprehensive and unified analysis. The use of longitudinal research on this phenomenon, considering longer timeframes, would be an interesting contribution.