Theoretical Framework for the Carbon Emissions Effects of Technological Progress and Renewable Energy Consumption

This study develops a theoretical framework to quantify the impacts of technological progress, renewable energy consumption and international trade on carbon emissions (CO 2 ), unlike many other studies that consider variables of interest in an ad hoc manner. The developed framework is then applied to the data from the BRICS countries for 1990 – 2017 period. The study also takes into consideration the integration, cointegration, as well as cross-country interdependence and heterogeneity properties of the panel data, and hence, the obtained results are robust and policy insights are well-grounded. We estimate that technological progress, renewable energy consumption, and export size contribute to the reduction of the CO 2 emissions, while gross domestic product (GDP) and import size increase the pollution both in the long- and short-run. Our main policy recommendations would be the implementations of the measures, regulations, and establishment of the legislative frameworks that foster the technological enhancements and transition toward sustainable energy.


| INTRODUCTION
Environmental pollution is one of the very urgent issues of humanity. Although there are several types of pollution, air pollution is the central one causing global warming. The core of air pollution is the greenhouse gas emission, and it is mainly driven by carbon dioxide (CO 2 ). Since CO 2 is considered as the greatest threat to the ecosystem, at the global level, nations set up commitments (e.g., in Kyoto protocol and Paris agreement) and goals (e.g., UN sustainable development goals for 2030) to reduce it. Also, several studies have investigated CO 2 to understand the driving forces behind it. The majority of these studies have considered income and population using either so-called Environmental Kuznets Curve or STIRPAT frameworks and concluded that they are the main reasons for CO 2 emissions. Given that the ultimate purpose of any research is to inform policymaking about the implementation of appropriate measures, these studies were not entirely effective. Simply because, it would not be a useful policy recommendation to suggest that GDP and/or population cause CO 2 emission, and therefore, they should be reduced to mitigate the emission. In this regard, one of the key challenges for the implementation of the measures and policies based on these studies is how to implement them and reduce CO 2 emission without deteriorating the quality of life across nations.
There are also many studies in CO 2 literature that have considered other social-economic, demographic, energy indicators alongside GDP and population in their research. However, it is fairly difficult to argue that all of these studies considered the other indicators for the sake of being useful for policymaking to reduce CO 2 emission. Additionally, many of these studies have considered a set of indicators without providing a theoretical foundation for such considerations. These two points are among the reasons that motivated us in conducting this research here.
To contribute to this discourse, we consider renewable energy consumption and technological innovation in our CO 2 analysis. They have three main advantages: they both theoretically are expected to reduce the CO 2 emission; they also can support the well-being of the nations. The major sources of renewable energy are solar, hydropower, and solar energy (Zeng, Liu, Liu, & Nan, 2017). Additionally, the expansion of renewable energy consumption, that is, energy transition (ET) toward renewables is one of the key items on the agendas of nations across the world. International Renewable Energy Agency (IRENA) defines ET as a pathway toward the transformation of the global energy sector from fossil-based to zero-carbon by the second half of this century. One of the unique features of ET, which makes it more important for nations is that it can improve three key areas, namely pollution reduction, energy security, and sustainable economic growth. Among them, pollution reduction draws a lot of attention due to the urgency of the issue for the globe. For instance, the International Energy Agency (IEA) puts the environment in the heart of ET. Also, respected energy organizations such as IEA and IRENA consider technological innovations as one of the key drivers for mitigating environmental pollutions (Boshell, 2018). Lastly, recognized institutions including IEA, UN Industrial Development Organization, IRENA, and UN environmental programs affirm that technological innovations can play a considerable role in achieving other SDGs such as poverty reduction, economic growth, food, water and energy security, and health, alongside environmental protection (IEA G20, 2019). Moreover, it is common sense that technological innovations are important for the development of the social-economic and energy systems and pollution mitigation of the nations ( Negro & Hekkert, 2008;Suurs & Hekkert, 2009). Innovations, which is the core of technological progress, is considered as the key indicator in the Sustainable Development Goal (SDG) by the United Nations.
The objective of this study is to investigate the consumptionbased CO 2 effects of the renewable energy consumption and technological innovation, alongside income and international trade in the theoretically grounded framework and propose policy insights that would be useful for the reduction of carbon emissions.
As a case of this study, we considered the BRICS countries.
There are many reasons for considering these economies. First, the BRICS countries are home to 42% of the global population, which is almost over 3 billion people as per the United Nations world population report (United Nation, 2017). With such a large population, there is a huge potential for economic growth and international trade. The economic growth of BRICS countries is growing fast with 51.3% contribution to the global economy merely from 2008 to 2018 (He et al., 2020). Besides economic growth, their contribution to total world trade reached 16.4% from 11.8% during 2008-2018 (He et al., 2020).
Second, the BRICS countries consumed 40% of the total global primary energy consumption in 2018. Moreover, the BRICS countries consumed 66. 8%, 30.8%, 25.2%, 24.4%, and 19.5% of global coal, wind energy, oil, solar energy, and natural gas, respectively. In terms of energy production, there is also a huge contribution from BRICS countries. As a percentage of total global, BRICS hold 38.3% of electricity generations, 63.7% of coal production, 21.7% of natural gas production, and 21.2% of oil production in 2016. Similarly, greenhouse gas emissions also reached to 41.3% of the world in 2016 (He et al., 2020). Renewable energy, which is considered a key factor for controlling carbon emissions, is developing at a high rate in BRICS countries. In terms of renewable energy, BRICS countries have a major contribution of 36% to the total global renewable energy to reduce carbon emissions with a continuous rise in renewable energy projects (Sebri & Ben-Salha, 2014 We believe that this study contributes to the existing CO 2 literature in several ways. First, it develops a theoretical framework to analyze the consumption-based CO 2 effects of technological progress and renewable energy consumption alongside income and international trade. To the best of our knowledge, this is the first study that develops such a framework rather than including the mentioned factors in analyses in an ad hoc manner such as done by many studies in the literature. Second, there are limited studies for the BRICS countries that investigate the role of technological progress and renewable energy consumption in the reduction of the consumption-based CO 2 .
Third, with an expansion of international trade especially from the BRICS countries' standpoint, it is imperative to analyze the effect of international trade on CO 2 . In doing so, earlier studies and those for the BRICS economies considered trade openness in their analyses.
However, openness does not allow us to pinpoint the separate impacts of exports and imports on CO 2 as it is a composite indicator.
Hence, following Hasanov, Liddle, and Mikayilov (2018) and Liddle (2018a), we consider exports and imports as separate variables in the analysis to reveal their individual effects. Fourth, the expansion in international trade, as one of the main streamlines of globalization, makes itself important to be accounted for environmental pollution.
Therefore, it is important to consider the consumption-based carbon emission, which is the international trade-adjusted pollution measure.
However, literature has focused mainly only on the territory-based CO 2 emissions. Recent studies argue that it is better to consider consumption-based CO 2 than using territorial-based CO 2 (see, for example, Hasanov et al., 2018;Liddle, 2018a). Fifth, this study, unlike many studies in the literature, addresses integration-cointegration as well as cross-country interdependence and heterogeneity features of the panel data. Moreover, cutting edge econometric method, such as Pesaran (2015) cross-sectional test, Pesaran and Yamagata (2008) cross-section slope heterogeneity test, Bai and Carrion-i-Silvestre (2009) unit root test, Westerlund and Edgerton's (2008) cointegration test, cross-sectional augmented Autoregressive Distributed Lags (CS-ARDL) methods, are employed.
The rest of the sections of this paper are given as Section 2 surveys the existing studies for the BRICS economies along with the studies that used the consumption-based CO 2 emissions. Section 3 develops a theoretical framework to ground empirical analysis. Section 4 presents the data, and the panel econometric methods. The empirical findings of the study and their discussion are documented in Section 5. Section 6 concludes the research with some policy insights.

| REVIEW OF LITERATURE
In this section, we focus on two kinds of studies: papers investigated the carbon emissions in BRICS countries and papers considered the consumption-based carbon emissions as the dependent variable.
Regarding the first strand of studies, the following studies are worth surveying.
In a study by Azevedo, Sartori, and Campos (2018), the quantitative analysis of carbon emissions and GDP is conducted for the period 1990-2011.The study showed many limitations that including the use of traditional OLS methods for the analysis and mere GDP and lag of CO 2 emissions to check the territory-based carbon emissions. In another study on BRICS by Zakarya, Mostefa, Abbes, and Seghir (2015), the effect of FDI, energy consumption, and economic growth is tested by using co-integration and causality analysis. Findings reported the cointegration and one-way causality from CO 2 emissions to FDI, GDP, and energy consumption. After careful inspection of this study, it can be inferred that the study showed deficiency in terms of model justification, as no theoretical background is given for model construction.
After controlling EC & GDP, mere FDI is not enough to determine CO 2 emissions without theoretical support. Moreover, traditional territorybased CO 2 measure is used which do not take into consideration the international trade effect and thereby may bring ambiguous results.
Additionally, an analysis of BRICS showed that renewable energy consumption, trade openness, and CO 2 emissions have a long-run equilibrium relationship with feedback hypothesis confirmation by bidirectional causality analysis. However, with the use of traditional territory-based CO 2 emissions, it is not easy to see the true picture of actual CO 2 emissions; moreover, analysis of exports and imports did not take into account separately (Sebri & Ben-Salha, 2014). Wang et al. (2018) explored the moderating role of corruption in the relationship of economic growth, trade, urbanization, and CO 2 emissions from 1996 to 2015 by using partial least square (PLS) with fixed and random effects. They found the significant moderating role of corruption in determining the CO 2 emissions in BRICS. However, this study also can be enhanced if the trade-adjusted CO 2 measure, as well as the individual effect of exports and imports, were considered. Additionally, the study does not provide any theoretical framework for considering corruption as a determinant of CO 2 emissions. Michieka et al. fixed-effect method. The study found that environment-related technological innovation has a positive effect on both productionbased CO 2 emissions and production-based energy productivity. In a recent study by Adedoyin, Gumede, Bekun, Etokakpan, and Balsalobre-lorente (2020), the role of coal rents is observed in BRICS economies, finding reported the supportive role of coal rents in reducing CO 2 emissions, this study suggests examining the role of technological innovation for sustainable development.
Furthermore, in a recent study of 11 cities of Hubei province of China by Mi et al. (2019), the consumption-based CO 2 emissions are analyzed, and findings disclose that the six modern cities are importdependent consumers of carbon emissions and remaining five are the opposite. This study used cross-sectional data for the year 2012 only, which may be inadequate to generalize these findings for other provinces and countries. So, a more detailed study is needed to overcome such limitations. Additionally, Wen and Wang (2020), analyzed provincial data of China to calculate carbon leakage by considering production-and consumption-based CO 2 emissions and found the carbon leakage for the provinces. However, this study was also limited to compute only the carbon leakage and did not provide the desired outcome. The common missing point for the BRICS studies above is that their CO 2 measures do not account for the international trade as they used the territory-based CO 2 . Also, they did not consider the role of technological innovation in their analyses.

| THEORETICAL FRAMEWORK
This section describes the theoretical foundation of the framework that relates the consumption-based CO 2 to renewable energy consumption and technological innovation alongside income and trade variables. The expanding international trade, as one of the main streamlines of the globalization, makes itself important to be accounted for environmental pollution. Therefore, we considered the consumption-based carbon emission in this study.
There is a Cobb-Douglas production function that links output (Q) to the production factors of labor (L), capital (K), and energy (E) through the technology (A) as given below: where, α, β, and γ are the elasticities of Q concerning L, K, and E, respectively. A usually is called total factor productivity (TFP).
The natural logarithmic (ln) transformation of Equation (1) can be expressed as follows: It is quite reasonable to consider/assume that TFP is not constant over time (e.g., see Solow, 1957). This is because of the technological developments, innovation, and know-how related activities mainly stemmed from openness, globalization, international competitiveness, catch-up efforts, and convergences among the economies over the world.
Following a standard set of assumption as it was done by Nordhaus (1975) and Beenstock and Dalziel (1986)  (v) assumptions: where, p k , p l , p e are the prices of K, L, E; Y is income.
For brevity, we do not describe details of the derivation of Equation (3) here as it is not our aim in this research.
Step-by-step derivation of an energy demand equation such as Equation (3)  As Mikayilov (2020) discuss, following Nordhaus (1975) and Beenstock and Dalziel (1986) among others, Equation (3) can be reduced to Equation (4), where prices of other inputs than energy are dropped based on some assumptions discussed below.
For example, seminal studies such as Nordhaus (1975) and Beenstock and Dalziel (1986) assume that the price of capital is linearly dependent on GDP deflator and price of labor is proportional to income, Considering that energy is the sum of fossil fuels energy (EF) and renewable energy (ER), then equation (4) can be written as: If we apply Taylor expansion to the left hand side of equation (5) and ignore the high-order terms and constant term, the following expression will be obtained 1: ln EF + ER ð Þ ≈EF + ER Now, equation (5) can be written as below: CO 2 is produced in a given territory when fossil fuels are burned, and there are conversion scalars called emission factors for each fuel type (e.g., see https://www.eia.gov/tools/faqs/faq.php?id=73&t=11). Based on this relationship, it can be expressed that total territory-based CO 2 emissions is proportional to total fossil fuels energy: CO2T = k * EF.
Using this relationship, equation (6) can be re-expressed as follows: where, (8) below expresses the relationship between territorybased CO 2 and consumption-based CO 2 : The equation just simply states that consumption-based CO 2 can be calculated by subtracting CO 2 embedded in exports (CO2X) from territory-based CO 2 and adding CO 2 embedded in imports (CO2M).
Following Liddle (2018b), we can make the following reexpression: M and Y are imports and GDP, respectively. The same identity is true for CO2X CO2T . That is, CO2X Both identities can be expressed as the share of imports (exports) in GDP multiplied by the imports' carbon intensity (exports' carbon intensity) divided by the GDP's carbon intensity: Accounting the above identities in equation (9) yields the following relationship: Since BRICS counties do not price/tax carbon in their exports and imports (He at al., 2020) to the best of our knowledge, CO2X X = CO2T Y = 1 and CO2M M = CO2T Y = 1 can be written. 2 Then, equation (10) can be expressed as: Equation (11) can be written for territory-based CO 2 as follows: Substituting CO2T in equation (7) with its expression in equation (12) and writing the resulting expression for CO2C would yield the following equation: Taking the natural logarithmic expression of equation (13) yields equation (14) as written below: Lastly, applying Taylor expansion to the right-hand side components of equation (14) and ignoring high-order terms, multiplication of the variables and constant terms, which lead to a complicated nonlinear relationship will produce the following relationship 3 : For the purposes of empirical analyses, one can homogenize and simplify equation (15) as follows: In this section, our main purpose is to theoretically derive signs for the explanatory variables impacting carbon emissions. In this regard, equation (15) gives us an idea about the sign of the impacts of the right-hand side variables on the consumption-based CO 2 . Regardless of whether we take exports and imports percentage shares in GDP and renewable energy or natural logarithmic transformations of them, their signs do not change because none of these variables will likely take values being smaller than unity. Therefore, as Liddle (2018b) did, we can also take the natural logarithmic transformations of the shares of exports, imports, as well as renewable energy to have a homogenized relationship, that is, log-log specification in (15). The log-log specification is straightforwardly interpretable. Another advantage of the logarithmic transformation of variables is that it can significantly reduce issues such as heteroscedasticity and nonnormality in the econometric estimations. Also, if a variable is expressed in the natural logarithm, then its coefficient can be directly interpreted as an elasticity. Log-log version of equation (15) will be as: where, b 4= χ 1 , b 5= χ 2 , b 6= χ 3 for simplicity.
It is quite reasonable to expect a high positive correlation between the price of fossil fuels energy, p e , and renewable energy, ER. This is simply because when the prices of fossil fuels energy carries are high, then people will increase the share of renewables in their energy consumption mix. The opposite is also true: low prices of fossil fuels energy carries can result in less share of renewables in the energy mix. To this end, one may wish to drop either the price of fossil fuels energy or renewable energy from equation (16). Considering that carbon emission is linearly dependent on the fossil fuel energy as explained above and obviously, the latter has a negative relationship with its price while the impact of renewable energy on carbon emission provides policymaking with more useful information regarding energy transition, one may drop the price. Thus, equation (16) reduces as written below: To make equation (17) an econometric specification, we add an intercept (b 0 ) and error term (e) to it. We also denote the logarithmic expressions with small letters, i.e., lnCO2C = cco2, lnð M Y Ã 100Þ = m, lnð X Y Ã 100Þ = x, lnER = er, lnY = y, lnTFP = tfp. Thus equation (17) becomes: Theoretically, we expect that consumption-based CO 2 will be negatively affected by an export share in GDP, renewable energy, and TFP while GDP and import share in GDP will exert positive impacts.

| DATA AND ECONOMETRIC METHODOLOGY
The data set used in this study is a balanced panel of the BRICS countries, which includes China, Brazil, India, South Africa, and Russia. The period for this study is annual and covers 1990-2017. One of the advantages of considering consumption-based CO 2 as a measure of carbon emissions is that it accounts for emissions of not only the final consumption but also the purchases from abroad (Wiebe & Yamano, 2016). It is adjusted for international trade and, hence, provides an easy means for identifying carbon emissions produced in one country and consumed in the other (Peters et al., 2012).
Our theoretical framework here allows us to analyze the CO 2 effects of international trade separately through exports and imports rather than combining them as other studies did. The effect of exports, which measures goods and services produced in the home country but are consumed in other countries, on consumption-based CO 2 is expected to be negative. Imports, which measures goods and services produced in other countries but consumed in the home country, are expected to have a positive effect on consumption-based CO 2 (Hasanov et al., 2018;Knight & Schor, 2014;Liddle, 2018a). Renewable energy consumption obtaining from nonfossil fuel sources is expected to harm consumption-based CO 2 . GDP as a measure of the production of goods and services is considered one of the main sources of CO 2 emissions especially in the developing economies including the BRICS ones. Lastly, TFP as a measure of technological progress and innovations is one of the key sources to reduce CO 2 through improved methods of production and less energy-intensive technologies. In the empirical estimations, we use the specification given in (18), and hence, all the variables above are expressed in the natural logarithm.
Based on the behavior of data, the following econometric approaches are employed to achieve the designed objectives of this study.

T A B L E 1 Nomenclature of variables and sources
Variable Definition Measurement Sources

CCO 2it
It is equal to territory-based consumption subtracting carbon emissions embodied in exports plus carbon emissions embodied in imports.

| Cross-section dependence and slope heterogeneity tests
In the modern era, with increasing economic integration, lowering trade barriers, or in the era of globalization, cross-section dependence in the panel data econometrics is most likely to occur. Ignoring the issue of cross-section dependence and assuming independence between crosssection may lead to misleading information, inconsistent, and biased results from the estimators (Grossman & Krueger, 1995;Westerlund, 2007

| Panel unit root tests
In the presence of heterogeneous cross-sectional slopes for coeffi-

| Panel co-integration tests
The use of first-generation tests, McCoskey and Kao (1998), Westerlund (2005), and Pedroni (2004) in the presence of structural breaks, cross-sectional heterogeneous slope coefficient is invalid. This study uses two-panel cointegration approaches, that is, Westerlund (2007) and Westerlund & Edgerton's (2008). Westerlund (2007) approach uses four statistics, two for group mean statistics and two for panel statistics. Group means statistics are denoted by Gt and Gα, while Pt and Pα for cointegration. Westerlund (2007) cointegration is also robust to slope homogeneity and cross-section dependence.
Besides Westerlund (2007), this study also uses Westerlund and Edgerton's (2008) with the power of dealing with cross-section dependence and is robust to the heterogeneous slope, the serial correlation for the cross-section as well as structural breaks in each cross-section at different locations. This approach is used for the long-run or co-integration relationship among the sampled variables.

| Cross-sectional augmented ARDL
The issue of cross-section dependence is dealt with using a newly proposed approach by Chudik et al. (2017) and Chudik and Pesaran (2015). This approach augments the conventional autoregressive distributed lags model (ARDL) by including cross-sectional averages of regressors and the dependent variable. The baseline regression model for cross-sectionally augmented ARDL (CS-ARDL) is given below as: In equation (19), , Y t and Z t are for the averages of cross-sections. The averages of both dependent and independent variables are denoted by X t −1 in Equation (19). The long-run and mean group coefficients are calculated as given below: where equation (20) provides long-run coefficients and equation (21) is for mean group estimator. This study uses CS-ARDL over crosssection augment distributed lags (CS-DL) due to various reasons. CS-DL is not robust as CS-ARDL, although it is superior to the conventional ARDL Also, the CS-DL does not allow for feedback effects on regressors from dependent variables, but CS-ARDL does (Chudik et al., 2013). Since CS-ARDL is robust to endogeneity issue, it perfectly fits our case here as we may potentially have endogeneity between the consumption-based CO 2 and regressors such as GDP or renewable energy consumption.

| RESULTS
This section provides the results of the econometric estimations and testing. The first section covers the results of cross-section dependence, slope heterogeneity, and unit root tests, while the second part discusses the cointegration test as well as long-and short-run estimations results. Table 2 shows results obtained from the Pesaran (2015) test for cross-section dependence (Panel A) and the results of the Swamy's (1970) slope heterogeneity test standardized by Pesaran and Yamagata (2008) The results for cross-section dependence reject the null hypothesis of no cross-section dependence in units meaning that our variables are not independent of each other across the sections, that is, countries. The sample values of Swamy's (1970) test and adjusted version of it both reject the null hypothesis of homogenous suggesting that the slope coefficients for each cross-section are heterogeneous.   (2007) test although they show level stationarity for few variables. However, the evidence of the level stationarity for these variables is very weak as only one out of three test statistics (i.e., P statistic for cco 2it , x it and tfp it , and the Z statistic for y it ) suggest so and only at the 10% significance level. Overall, the results of the tests indicate that all the variables are nonstationary, that is, they are the unit root processes at their level, and the first differences of them are stationary. Table 4 reports the outcomes of the Westerlund and Edgerton (2008) and the Westerlund (2007) tests for panel co-integration.
The sample values of the Z φ (N) and Z τ (N) statistics reject the null hypothesis of no co-integration at the 1 and 5% significant levels, respectively, which favor that the variables, that is, cco2 it , x it , m it , y it , er it , and tfp it are cointegrated. As for the results of the Westerlund (2007) test, one panel and one group mean test statistics, that is, Pt and Gt suggest co-integration among the variables while the other two cannot reject the null hypothesis of no co-integration. Being unable to reject the null hypothesis is quite common for these test statistics, as it is well known that Westerlund (2007)  Given that the variables are co-integrated, the following two things should be valid: (a) estimation of the level relationship is not spurious and the estimated coefficients can be used for analysis and forecasting; (b) there should be equilibrium error correction representation of the co-integration relationship among the variables. To this end, we estimate the long-run/level relationship as well as short-run dynamics for our dependent variables using the CS-ARDL method. Apparently, from the table, both the long-and short-run estimation results are reasonable, as the signs of the obtained coefficients are consistent with the theoretical expectations as discussed in Section 3. Moreover, the estimated coefficients of the explanatory variables are statistically significant at the conventional levels.
T A B L E 2 Cross-section dependence and slope heterogeneity tests *Indicates the rejection of the null hypotheses at the 10% significance level. **Indicates the rejection of the null hypotheses at the 5%, significance level. ***Indicates the rejection of the null hypotheses at the 1% significance level.
Furthermore, the sizes of the estimate coefficients are in the acceptable ranges. In particular, the ECT term is highly statistically significant and its coefficient, that is, speed of adjustment (SoA) parameter is in the acceptable range. This indicates that the co-integration relationship found among the variables is stable. It also shows that deviations of the dependent variable in the short-run are temporary and can be corrected back to the long-run equilibrium path that it establishes with its explanatory variables.

| Discussion
According to Table 2, GDP in China is correlated with that in other countries in our sample. Such kind of interdependences among the variables across Brazil, China, South Africa, Russia, and India are expected due to some reasons including but not limited to globalization, regional connectivity, and spillover effect through international relations including trade, local, and global economic shocks that are common for all of them (see discussions in Liddle and Hasanov, 2020;Pesaran, 2015).
Nonstationarity of having unit root implies that the variables drifting over time, and hence, they do not return to their previous mean as the mean changes over time. Any shock to such kind of drifting series can create a permanent effect. It would be difficult to predict future values of the (log) levels of the variables due to the changing mean and permanent effects of shocks. One should use the stationary transformation of the variables for prediction purposes as mean, variance, and covariance of the stationary series do not change over time, and they "dance" around their mean values. In other words, the stationary series revert to their mean, and hence, they are called mean-reverting process.
Consumption-based CO 2 establishes a long-run relationship with export shares in GDP, imports share in GDP, renewable energy consumption, GDP, and TFP. Put differently, consumption-based CO 2 shares a common trend with these variables, and they move together and establish an equilibrium relationship in the long-run. Another interpretation of the co-integration is that the relationship between the (log) levels of the variables is not spurious, they are consistent with economic or environmental theory and thereby one can use the long-run coefficients to make analysis and projections. To this end, we estimated the long-run impacts of the mentioned variables on consumption-based CO 2 and reported the results Panel A of Table 5.
According to the results, in ceteris paribus, a 1% increase in the export share in GDP results in a 0.22% decrease in the consumptionbased CO 2 in the long run. Theoretically, as we discussed in Section 3, the more export from a country, the fewer goods and services are billion USD from the rest of the world (Simoes et al. 2011).
The long-run estimation results show that, in ceteris paribus, a 1% increase in GDP leads to a 0.42% rise in the consumption-based CO 2 . This finding is in line with the theoretical framework of Section 3.
Additionally, the environmental theories such as the STIRPAT and the EKC predict that GDP can result in more CO 2 emissions: a rise in the economic activity or income level is associated with more consumption of intermediate and final goods and services, which will bring more CO 2 emissions.
Panel A further document that a 1% expansion in renewable energy consumption reduces the consumption-based CO 2 by 0.66% holding other factors unchanged in the long-run. As we discussed in Section 3, considering total energy consumption as a sum of the consumption of fossil fuels and renewable energy sources, an increase in the latter source will reduce the share of the former source, and hence CO 2 emissions will be reduced. According to the International Renew- Lastly, a 1% increase in TFP can reduce the consumption-based CO 2 by 0.09% in the long-run according to the estimation results.
Negative emissions effects of TFP are theoretically expected as the technological progress, innovations, efficiency, and economies of scale should lead to fewer resources to be consumed in the production of goods and services. Such progress expands the application of efficient production technologies, machines, and equipment as well as efficient home appliances. These result in the rational usage of the resources and less environmental pollution. Our findings for TFP and renewable energy consumption are similar to the outcomes of Khan, Ali, Jinyu, et al. (2020) and Khan, Ali, Umar, et al. (2020). Hasanov et al. (2018) interpreted that 11 oil-exporting developing countries will produce more emissions over time as the long-run GDP elasticity of the consumption-based CO 2 was found to be larger than that of the short-run elasticity. We can extract some useful information by doing the same fashion comparison of the long-and short-run elasticities in Table 5. The estimated long-run the consumption-based CO 2 elasticities concerning GDP is slightly smaller than that for the short-run. This finding can be interpreted that in the long-run, the BRICS countries can manage to reduce emissions, or at least to keep it at the same level as today. This also implies that these countries will advance their environmental policies and take efficient measures to reduce CO 2 . Among other measures to be implemented, from our theoretical framework standpoint, such an achievement can be obtained through technological progress, using more renewable energy in total energy consumption as well as exporting more and importing less CO 2 embedded goods and services over the long term. Indeed, the obtained elasticities documented in Table 5 support this interpretation in the sense that that the long-term emission reduction effects of the technological innovations, renewable energy consumption, and exports are larger than those in the short-run. It also appears that these countries will import more CO 2 contained goods and services over a long time horizon.

| CONCLUSION AND POLICY INSIGHTS
This study explores the consumption-based CO 2 effects of the technological progress and renewable energy consumption alongside GDP and trade variables for the BRICS countries over the period 1990-2017. Unlike, other existing studies that include variables in their CO 2 analysis in ad-hoc manner, we developed a theoretical framework for such an analysis. Also, we accounted for the integration, cointegration, as well as cross-country interdependence and heterogeneity properties of the panel data in the estimations. Therefore, our results are robust and policy insights are well-grounded. We found that the above-mentioned variables can be considered the main determinants of the consumption-based CO 2 both in the long-and short-run in the BRICS countries. We estimated that technological progress, renewable energy consumption, and export size contribute to the reduction of CO 2 emissions, while GDP and import size increase the pollution. Obviously, Taylor expansion of ln(EF+ER) will produce EF+ER+a 0 . Where, a 0 is a constant term. We ignored the constant term for simplicity to avoid complications because it does not change the signs of the explanatory variables and their functional forms in equation (6).