Introduction

Over the past few decades, applied econometric patterns have been the instigator in determining the relationship among CO2 emission, economic growth, and energy consumption. Accordingly, many authors review and classify the existence literature (e.g., Ozturk 2010; Payne 2010a, b; Smyth and Narayan 2015). Notably, one vital and intriguing perspective puts forward the inherent uncertainty of the process, and that is, authors using the prevalent patterns with the common covariates, by changing only the estimated time period, have no more potential to contribute to the existing literature (Karanfil 2009). Furthermore, most of the studies across the literature examine the relationship between energy consumption and economic growth (and CO2 emission) at a national level (Akhmat et al. 2014; Ali et al. 2016; Amri 2017; Attiaoui et al. 2017; Bildirici 2017; Dogan and Turkekul 2016; Dogan and Ozturk 2017; Farhani and Ozturk 2015; Rafindadi et al. 2014; Wolde-Rufael 2012). There is an abundance of empirical papers which examine not only the relationship of causalities for the trivariates, but also they test the validity of the environmental Kuznets curve (EKC) hypothesis (inter alia Ang 2007; Apergis and Payne 2009; Halicioglu 2009; Lean and Smyth 2010; Soytas et al. 2007). However, there are only a few authors who used data at a state level (Apergis et al. 2010; Apergis and Payne 2010; Aslan 2011; Narayan et al. 2010). Subsequent research has hardly filled this void. Hence, this is a gap which this study seeks to address. This study contributes to the relevant literature by offering valuable insights about the interrelation among CO2 emission, economic growth, and energy consumption in the 50 US states by using the time-varying causality for the first time in the relative literature.

In light of the pre-mentioned research, this study further contributes by examining the existence of a time-varying relationship via the application of a time-varying causality for the case of 50 US states over the periods 1960–2010.Footnote 1 Regarding the Granger non-causality test in time varying, we apply the method proposed by Sato et al. (2007) and the extension of time-varying causality proposed by Ajmi et al. (2015), which allow the test to be implemented in a simple framework. We investigate the causality from the perspective of the time-varying trivariate relationship among economic growth, energy consumption growth, and CO2 emission. This pattern allows the researcher to capture the time-varying relationship and, also to perceive the interrelationship between the covariates during the period, which could not be discerned via a time-constant framework. Additionally, as already stressed above, many studies investigated the validity of the EKC hypothesis without taking into the account the time-varying parameters (such as natural disasters, economic crises, new technologies) between the three variables. As time progresses, all of these conclusions could lead to inefficient environment policy implications. The time-varying approach encompasses all these parameters in order to tackle ex ante uncertainty (Ajmi et al. 2015). We can conclude that compared to the conventional time-constant approach, including its offspring, the time-varying method has a better functionality.

We draw evidence from a comprehensive sample of 50 US states, which reveals pronounced time-varying causalities of the examined relationship. The contribution of this paper is fourfold. To begin with, this is the first time to our knowledge that the causality between CO2 emission, energy consumption, and economic growth is evaluated at the US state level. Secondly, this paper contributes to the existing thin body of time-varying causality literature. Thirdly, it is the first time that time-varying causality is evaluated at a state level. Fourthly, the validity of the EKC hypothesis is evaluated at the US state level.

The rest of the paper is structured as follows. Section 2 succinctly reviews the related literature. Section 3 introduces our sample and outlines our proposed methodology, which is used in the subsequent analysis. We report our empirical results in Section 4. Finally, Section 5 concludes our work reporting some relevant policy implications.

Literature review

Zhang and Cheng (2009) identify three aspects in the literature which adjudicate the relationship among energy consumption, economic growth, and CO2 emission. The first aspect is related to CO2 emission and economic growth nexus. The second aspect focuses on the relationship between economic growth and energy consumption. The third aspect based on the relationship between energy consumption, economic growth, and CO2 emission. Our study contributes to the third aspect, by investigating the trivariate nexus.

The first aspect is about the CO2 emission—economic growth nexus. Moreover, the research reflects the de facto validity of the EKC hypothesis between the two variables. The EKC hypothesis presumes that CO2 emission—economic growth nexus implies an inverter U-curve (videlicet, CO2 emission will increase up to certain level as economic growth increases, and then declines). Grossman and Krueger (1991) first propounded the EKC hypothesis.Footnote 2 A vast body of literature has emerged on the impact of EKC. For instance, implementing Johansen cointegration techniques for a group of 88 countries over the periods 1960–1990, Coondoo and Dinda (2008) pointed out that EKC does not exist. Likewise, Robalino-López et al. (2015) applied a cointegration technique for Venezuela over the periods 1980–2025 and they found no credence to this hypothesis. On the other hand, many studies have identified the existence of EKC. Padilla and Serrano (2006) applied a non-parametric estimation and underlined that EKC exists among a group of countries from 1971 to 1999. Similarly, Narayan and Narayan (2010) confirmed the existence of EKC for 35% of 43 developing countries. Along these lines, Esteve and Tamarit (2012a) employed threshold cointegration and Esteve and Tamarit (2012b) employed EKC analysis for the case of Spain and their results support the EKC. The same result is also confirmed for Spain by Sephton and Mann (2013) who used multivariate adaptive regression splines. Fosten et al. (2012) applied non-linear threshold cointegration and error correction method at the case of UK over the periods 1830–2003 and confirmed the EKC hypothesis. Lastly, Baek (2015) investigated the EKC for Korea over the periods 1978–2007, by employing bound testing cointegration. His core finding is similar to the aforementioned research.

The second aspect of causal ordering between energy consumption and growth is the plethora of empirical studies. They either focus on country-specific case studies or use multi-country samples. As summarized by Payne (2010a, b) and Ozturk (2010), a number of different hypotheses have been proposed and tested. The reported findings are mixed and significantly vary across countries and studies as pointed out by Payne (2010b). In broad terms, no unequivocal consensus seems to have emerged from the empirical scrutiny of the nexus that governs growth and energy consumption. For instance, Karanfil (2008) note that the nexus between energy consumption and growth could be affected by a number of factors. They encompass climate conditions, income level, development level, the structure of the economy, the concomitant national gross output, and the degree of urbanization that significantly differs especially between developed and developing countries. Regime type, institutional arrangements, and national energy policies may also be contributing factors that explain the absence of any clear consensus in the reported findings for this relationship (Adams et al. 2016). Finally, but by no means of lesser importance in explaining the diversity of findings, the variety of alternative econometric methodologies employed in the empirical examination as well as the different time horizons add to the contradicting findings reported (Payne 2010b).

Succinctly, the testable hypotheses that have been proposed are as follows. The growth hypothesis postulates that energy consumption spurs economic growth since increasing energy production and consumption positively affects GDP. An implication that stems from this hypothesis is that policies aimed at energy conservation may adversely impact growth. The conservation hypothesis points to a reverse causal ordering, i.e., increasing real GDP brings about an increase in the consumption of energy. But it may very well bring about a reduction in energy consumption as the production paradigm shifts towards less energy-intensive sectors and production processes. The absence of any causal ordering is proposed by the neutrality hypothesis. Energy consumption accounts for a small share in total GDP; hence, there is no significant and traceable effect from energy consumption to GDP and vice versa. In such case, supported by the absence of a Granger causality finding in empirical studies, energy conservation policies do not adversely affect growth. Finally, the fourth hypothesis that has been proposed is that of a bidirectional nexus between them. The feedback hypothesis postulates bidirectional Granger causality, and hence, an increase (decrease) in the one variable will Granger cause a corresponding increase (decrease) in the other.

Since the seminal study of Kraft and Kraft (1978), the majority of the empirical studies apply Granger causality tests (Granger 1969, 1980) in order to examine the causal ordering between the covariates. As already mentioned above and summarized by Ozturk (2010) and Payne (2010a, b), even though the general perception is that the two variables in question are causally linked, no strong and unequivocal empirical consensus emerges from the reported empirical findings. For instance, evidence of unidirectional causality from economic growth to energy consumption has been reported by several studies using different methodological approaches (inter alia: Stern 1993, 2000; Soytas et al. 2001; Bowden and Payne 2009; Hossain 2011). On the other hand, a large number of studies have reported findings in favor of a reverse causal ordering from energy consumption to economic growth that renders substantial support the growth hypothesis (inter alia: Kraft and Kraft 1978; Aqeel and Butt 2001; Al-Iriani 2006; Zhang and Cheng 2009; Alkhathlan and Javid 2013). Bidirectional causality and the absence of any nexus have also been found by other studies (inter alia Ghali and El-Sakka 2004; Zhang and Xu 2012; Shahiduzzaman and Alam 2012; Yu and Jin 1992). The important policy implication associated with the empirical investigation of this nexus is the driving motive for such studies that probes into this issue.

The third aspect of causal ordering between energy consumption, economic growth, and CO2 emission is the voluminous of the empirical investigations. They either cynosure on the causality case studies and/or examine the validity of the EKC hypothesis. Indisputably, sharp information of causalities exists among covariate nexus. Acaravci and Ozturk (2010), using ARDL bounds and VECM framework for 19 European countries for the periods 1960 to 2005 found two-way causality between income, income square, and energy use solely for Switzerland. More crucial is the fact that disclosed the validity of EKC hypothesis only for Denmark and Italy. Ajmi et al. (2015) employed time-varying causality in order to determine the causality between the G7 countries. Their core finding depicts bidirectional causality for income and energy (Japan) and for energy and CO2 emissions (USA). Moreover, he argued that U-shaped does not exist. Employing the same pattern as Ajmi et al. (2015), Shahbaz et al. (2016) investigated the relationship between 11 countries from 1972 to 2013. The results show two-way causality between income, income square, and energy use only for South Korea. Furthermore, EKC is verified for Pakistan and Turkey. According to Ozturk and Acaravci (2010), EKC hypothesis does not attest for Turkey. Moreover, the authors reveal miscellaneous causality between the variables, employing ARDL bounds and VECM from 1968 to 2005. Ozturk and Acaravci (2013) applied the same framework for the time periods 1960–2007 and their results indicate long-run unidirectional causality running from income, income square, and energy use to CO2 emission. In an interesting view, Ozcan (2013) provides evidence of 12 Middle East countries, by evaluating panel cointegration over the periods 1990–2008. The findings probe that long-run energy and income causes CO2 emission but short-run only income causes energy. Notably, the evidence from EKC bears out U-shaped for five counties (Bahrain, Syria, Turkey, Oman, and Yemen) and inverted U-shaped for three countries (UAE, Egypt, and Lebanon). Intriguingly, studies from Pao and Tsai (2011a, b) substantiate the underlying EKC hypothesis for Brazil and BRIC countries, respectively. In addition, evaluating gray prediction model (Brazil) and panel cointegration (BRIC) finds bidirectional causality between energy and income, and income and CO2 emission, respectively. Another substantial research from Soytas et al. (2007) uses Toda–Yamamoto procedure to analyze the relationship for USA over the periods 1960–2004. The results probe one-way causality running from energy to CO2 emission and unexpected results for EKC validity, which does not exist. In a much similar vein, Dogan and Turkekul (2016) do not endorse the validity of EKC regarding the case of USA. The authors assessed ARDL bounds and VECM methodology over the periods 1960–2010 and the results revealed bidirectional causalities for the pairs CO2 emission, income and CO2 emission, energy consumption. Although, they used the same patterns with Dogan and Turkekul (2016), Farhani and Ozturk (2015) found identical outcomes regarding the EKC hypothesis but different causality results for the case of Tunisia. In a different vein, Jayanthakumaran et al. (2012), Tang and Tan (2015), and Wang et al. (2011) confirm the EKC hypothesis. As we stressed out above, there are authors who investigate only the relationship between the tri-dimension nexus. Not surprisingly, the majority of the empirical studies employ Granger causality tests. For instance, Chang (2010) examines the case of China and finds miscellaneous causalities among the covariates using Johansen cointegration VECM. In a similar research area but with different results and pattern, Zhang and Cheng (2009) evaluated Toda–Yamamoto procedure and found (i) one-way causality from income to energy and (ii) that energy causes CO2 emissions. In a similar framework, Soytas and Sari (2009) found a unidirectional causality running from energy to CO2 emission. Halicioglu (2009) signified four pairs of two-way causalities, energy—CO2 emission, CO2 emission—income, CO2 emission—square of income, and income—square of income for the case of Turkey. Omri (2013), using simultaneous equation models for 14 MENA countries, found a bidirectional causality for energy and CO2 emission from 1990 to 2011. No trace of two-way causality from Ang (2007) and Menyah and Wolde-Rufael (2010) for France and South Africa, respectively. Ang (2008) supported the bidirectional interrelationship for income and energy for Malaysia over the periods 1971–1999. Lastly, Alam et al. (2012), employed ARDL bounds and dynamic causality for the case of Bangladesh. He endorsed long-run bidirectional relationship for energy and CO2 emission, and dynamic two-way causality for energy consumption and income. Table 1 summarizes existing studies between energy consumption, economic growth, and CO2 nexus.

Table 1 Summary of the existing studies between energy consumption, economic growth, and CO2 nexus
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Data and methodology

Data and pretests

For the purpose of our analysis, we use yearly data for the 50 US states,Footnote 3 over the periods 1960–2010 (50 observations). The data regarding the energy consumption has been extracted from Energy Information Agency (EIA),Footnote 4 whereas, the data for the CO2 emissions comes from Carbon Dioxide Information Analysis Center (CDIAC).Footnote 5 Finally, the data for GDP have been extracted from the Bureau of Economic Analysis.Footnote 6 All the variables have been logged as has been suggested from the relevant literature.Footnote 7

Initially, we investigate the level of the integration among our variables by applying several unit root tests (i.e., Elliott et al.— Dickey–Fuller generalized least squares (DF-GLS) 1996; Phillips and Perron—PP 1988; Kwiatkowski et al.—KPSS, 1992). The AIC statistic has been applied to indicate the proper time length, whereas the tests have been applied both on the trend and the drift of the data (Table 2). Accordingly, as a robustness check, we implement the Zivot and Andrews (1992) test (ZA) for possible structural breaks (Table 3). As a result, the tests endorsed that the covariates are integrated of order one I(1).

Table 2 Unit root test results
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Table 3 Results from the ZA unit root tests with a structural break
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Time-varying vector autoregressive model

The principal concept of Granger (1969) has an unprecedented impact on the research field. Given a bivariate (x, y) vector autoregressive (VAR) model, Granger (1969) defined the following specification:

$$ {Y}_t={e}_0+\sum \limits_{i=1}^n{e}_i{Y}_{t-i}+\sum \limits_{i=1}^n{f}_i{X}_{t-i}+{w}_i, $$
(3.1)

and

$$ {X}_t={g}_0+\sum \limits_{i=1}^n{g}_i{X}_{t-i}+\sum \limits_{i=1}^n{h}_i{Y}_{t-i}+{z}_i, $$
(3.2)

in the equations (3.1) and (3.2), X t and Y t denote stationary time series and w i , z i are assumed to be white-noise errors.

By focusing on the different VAR patterns, Sato et al. (2007) extended the Granger causality test based on the theoretical framework of locally stationary processes (Dahlhaus et al. 1999). Introducing a time-smooth variation in the framework, Sato et al. (2007) constructed a time-varying vector autoregressive model. This dynamic VAR (as called) approach includes a multivariate time series (x t, T ) with dimension (s) and a number of observations(T), x t, T  = (x 1t, T , x 2t, T , x 3t, T , …, x st, T )′. The computational representation of the function is as follows:

$$ {x}_{t,T}=u\left(\raisebox{1ex}{$t$}\!\left/ \!\raisebox{-1ex}{$T$}\right.\right)+\sum \limits_{l=1}^p{A}_l\left(\raisebox{1ex}{$t$}\!\left/ \!\raisebox{-1ex}{$T$}\right.\right){x}_{t-l,T}+{\varepsilon}_{t,T}, $$
(3.3)

in the expression (3.3), u(t/T) denotes the vector of intercepts, A l (t/T) represents the autoregressive coefficients, and ε t, T denotes the error vector. Moreover, Ajmi et al. (2015), reconstructed Eq. (3.3) by using the M- and B-spline functions (Eilers and Marx 1996). These M- and B-spline functions are applied in order to estimate the dynamic VAR using a multiple linear regression model. The time-varying vector autoregressive equation obtains the following form:

$$ {x}_t=\sum \limits_{n=0}^M{u}_n{y}_n(t)+\sum \limits_{l=1}^p{A}_n^l{y}_n(t){x}_{t-l}+{\varepsilon}_t $$
(3.4)

in the expression (3.4), u n denotes the vectors and \( {A}_n^l \) represents the B-spline coefficients. Notably, we can test the time-varying Granger causality by employing the Wald tests on the coefficients. To elaborate, by testing if the coefficients are tantamount to zero or not, we test for time-varying Granger causality between two variables. Additionally, by testing the significance of coefficients for every B-spline, we are able to check whether the Granger causality is constant or time-varying. By employing a pairwise pattern, we follow Ajmi et al. (2015) and set a dynamic VAR of order l = 1, M = 3, and lag = 1 for a bivariate VAR model (for more details see Ajmi et al. 2015; Sato et al. 2007).

Empirical study

Table 4 delineates the results of classical (conventional) causality test (Eq. 3.1 and 3.2). The results probe two bidirectional causalities between energy consumption and CO2 emissions in the case of IL and TX, nine (AR, MI, MS, MT, ND, NH, PA, UT, and WY) unidirectional causality running from energy consumption to CO2 emissions, and seven (CA, CT, GA, MO, NC, RI, and WA) unidirectional causality for the opposite side. Furthermore, our empirical results also disclose 32 neutrality hypotheses for the rest of the states. Regarding the relationship between economic growth and energy consumption, the results reveal seven (AK, DE, HI, IL, MA, MS, and OH) unidirectional causalities running from economic growth to energy consumption, six (CT, MN, MO, OK, PA, and TX) unidirectional causalities running from energy consumption to economic growth, and the rest support the neutrality hypothesis. Moreover, there is no bidirectional causality for these pair of variables. Lastly, the results probe one (WI) bidirectional causalities between economic growth and CO2 emissions, eight (AK, AZ, HI, IL, ME, OH, RI, and WV) unidirectional causalities running from economic growth to CO2 emissions, and five (AR, MO, MS, PA, and TX) for the opposite side.

Table 4 Classical Granger causality test results
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Table 5 depicts the results for the dynamic Granger causality test (Eq. 3.3). The results probe six (AR, CO, GA, LA, MN, and PA) bidirectional causalities between energy consumption and CO2 emissions, five (ME, NY, OK, PA, and TX) unidirectional causality running from energy consumption to CO2 emissions, and four (KY, NM, NV, and UT) unidirectional causality for the opposite side. Furthermore, our empirical results also disclose 35 neutrality hypotheses for the rest of the states. Regarding the relationship between economic growth and energy consumption, the results reveal five (GI, HI, ID, MS, and PA) bidirectional causalities between economic growth and energy consumption, 15 (IN, MD, MI, MN, MO, NC, NM, NY, OH, OR, SD, VT, WA, WV, and WY) unidirectional causality running from economic growth to energy consumption, and 14 (AK, AR, AZ, CO, FL, LA, MT, ND, OK, TN, TX, UT, and WI) unidirectional causality for the opposite side. Moreover, our empirical results also reveal 16 cases of neutrality hypothesis for the rest of the states. Accordingly, when we analyze the relationship between economic growth and CO2 emission, the results show five (CO, DE, ID, MO, and UT) bidirectional causalities between economic growth and CO2 emission, 11 (IL, IN, MD, NC, NM, NV, OH, PA, SD, VT, WV, and WY) unidirectional causalities running from economic growth to CO2 emission, and 12 (AK, FL, IA, KS, LA, ME, MS, MT, OK, SC, TN, VA, and WI) cases for the opposite side.

Table 5 Results of the dynamic Granger causality tests
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The results of the time-varying Granger causality tests (Eq. 3.4) are tabulated in Table 6. The results disclose eight (AR, CO, GA, LA, MN, NH, PA, TX, and UT) bidirectional time-varying causalities between energy consumption and CO2 emission, six (CA, DE, KY, RI, and WA) unidirectional time-varying causality running from CO2 emissions to energy consumption, and four (CT, ME, NY, and OK) unidirectional time-varying causality for the opposite side. Additionally, our empirical results also disclose 32 neutrality hypotheses for the rest of the states. Regarding the relationship between economic growth and energy consumption, the results reveal six cases (GA, ID, MO, MS, NJ, and PA) of two-way time-varying causalities between economic growth and energy consumption, 14 cases (HI, IN, MD, MI, NC, NM, NY, OH, OR, SD, VT, WA, WV, and WY) of unidirectional time-varying causality running from economic growth to energy consumption, and 11 (AK, AR, AZ, CO, FL, LA, ND, SC, TN, TX, and WI) one-way causalities for the opposite side. Moreover, our empirical results show 19 cases of neutrality hypothesis for the rest of the states. Likewise, when we analyze the relationship between economic growth and CO2 emissions, the results show five (CO, HI, MO, MS, and UT) two-way time-varying causalities between economic growth and CO2 emission, 12 cases (ID, IL, IN, MD, NC, NM, NV, OH, PA, SD, VT, WV, and WY) of unidirectional time-varying causalities running from economic growth to CO2 emission, and 14 (AK, AR, DE, FL, MI, OK, RI, SC, TN, TX, VA, and WI) cases for the opposite side. These different findings for each state are justified by the state differences such as, among others, the composition of GDP for each state over the years, the fuel mix, and the rate of technical progress (Judson et al. 1999).

Table 6 Results of the time-varying Granger causality tests
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In order to capture the validity of the traditional EKC hypothesis, we will follow the strand from Ajmi et al. (2015). Ajmi et al. (2015) were the first who proposed the “curve causality” graphs in order to determine the validity of EKC hypothesis. Illustrating the significant time-varying causality running from GDP to CO2 emissions, they attested the shape of an inverted-U curve between the two variables. In our case, Fig. 1 describes the causality curves for 18 significant states (Table 6). It should be highly stressed that our results reject the EKC hypothesis, albeit, the majority of states verify an inverted N-shape curve. This insinuates that as time goes by, an increasing of income range would fundamentally improve environmental performance.

Fig. 1
figure 1

Pseudo-EKC curve causality

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Concluding remarks

There are a large number of researchers who have studied the relationship between the energy consumption, economic growth, and CO2 emission. From a methodological point of view, the contribution lies on the fact that for the first time at a state level, this relationship has been examined with time-varying causality for the case of 50 US states over the periods 1960–2010. Our study broadens the understanding of the determinants of the relationship between energy consumption, economic growth, and CO2 emissions, and deepens the investigation of the validity of the EKC hypothesis at a state level.

The results of the causality test indicate (in the case of classical causality) that there is two bidirectional causalities between energy consumption and CO2 emissions, nine unidirectional causality running from energy consumption to CO2 emissions, and seven unidirectional causality for the opposite side. Regarding the relationship between economic growth and energy consumption, the results reveal seven unidirectional causalities running from economic growth to energy consumption, six cases unidirectional causalities running from energy consumption to economic growth. Lastly, the results probe one-bidirectional causality between economic growth and CO2 emission, eight unidirectional causalities running from economic growth to CO2 emission, and five for the opposite side. On the side from dynamic Granger causality test, the results show six bidirectional causalities between energy consumption and CO2 emission, five unidirectional causalities running from energy consumption to CO2 emissions, and four unidirectional causalities for the opposite side. Similarly, the relationship between economic growth and energy consumption, the results reveals five two-way causalities between economic growth and energy consumption, 15 unidirectional causalities running from economic growth to energy consumption, and 14 unidirectional causalities for the opposite side. Accordingly, when we analyze the relationship between economic growth and CO2 emissions, the results show five bidirectional causalities between economic growth and CO2 emission, 11 unidirectional causalities running from economic growth to CO2 emission, and 12 cases for the opposite side.

Lastly, the results of the time-varying Granger causality tests probe eight bidirectional time-varying causalities between energy consumption and CO2 emission, six unidirectional time-varying causalities running from CO2 emissions to energy consumption, and four unidirectional time-varying causalities for the opposite side. Regarding the relationship between economic growth and energy consumption, the results reveals six cases of two-way time-varying causalities between economic growth and energy consumption, 14 cases of unidirectional time-varying causalities running from economic growth to energy consumption, and 11 unidirectional causalities for the opposite side. Finally, when we evaluate the relationship between economic growth and CO2 emission, the results show five bidirectional time-varying causalities between economic growth and CO2 emission, 12 cases of unidirectional time-varying causalities running from economic growth to CO2 emission, and 14 cases for the opposite side. Interestingly enough, regarding the investigation of the existence of EKC hypothesis, our results reject the EKC hypothesis, albeit, the majority of states verify an inverted N-shape curve.

As far as policy implications, our discoveries suggest that these states are in general exceptionally energy-dependent economies but with distinctive significance level. Plausibly, these states necessary will look for an adjusted harmony between energy and economic growth. Nonetheless, those states could be change first: reorganization of energy efficiency buildings; second, enhancement of energy conservation policies in order to have better waste-processing industry; and third, the utilization of alternative energy sources (such as solar panels, wind power, and geothermal power). All these perspectives suggest the reduction of greenhouse gases. Moreover, our outcomes in respect of time-varying framework exhibit different policy implications between the covariates. To elaborate, our results support that USA should pass legislation to mitigate GHGs and moderate environmental degradation. Such policies should aim to decrease energy intensity, increase energy efficiency, and alter the fuel mix towards renewable energy sources. Furthermore, we signify the importance for the decision makers to take into account the time-varying causality between energy consumption, GDP growth, and CO2 emission.

As next step in our research, we will concentrate on the time-varying field. Presumably, future study should determine the time-varying relationship between these covariates at a state level instead of a national level which is most commonly used. This will be pursued in our future study.