Introduction

Simon Kuznets (1955), as a Nobel prize winner economist–statistician, empirically detected an inverted-U-shaped relationship between the level of economic development and the degree of income inequality in this study. In this relationship, income inequality first rises and after a certain level of average income initially falls when the economic development proceeds. He believes that during the economic development, transformation of the physical capital accrual to the human capital accrual, rising democratization, and welfare state approach and others may increase per-capita income. Kuznets’ seminal work became the source of inspiration for the environmental economists, and they hypothesized a similar relationship between the economic growth/development and environmental degradation. The early-stage industrialization requiring massive use of fossil energy resources first rises environmental degradation and after a certain level of per-capita income (turning point) degradation falls. Because economy transforms from industrial-based economy to service sector–based economy, educational level increases and thereby environmental awareness arises. Accordingly, this relationship, shown in Fig. 1, between per-capita income (economic development) and environmental degradation has an inverted-U-shaped function.

Fig. 1
figure 1

Environmental Kuznets curve (EKC)

Full size image

In this figure, the pattern of this inverted-U-shaped function is so called environmental Kuznets curve (EKC) in the dedication of Simon Kuznets’ similar pattern. The EKC’s paradoxal and contested relationship between economic growth/development and environmental degradation attracted many economists since the issue deals an environment problem of today and human health directly. After Grossman and Krueger’s (1991) first study, Hettige et al. (1992), Panayotou (1993, 1995), Selden and Song (1994), Grossman and Krueger (1995), Vincent (1996), Stern et al. (1996), and others found this inverted-U-shaped relationship between usually used per-capita GDP and several environmental degradation indicators.

Literature review

Following above pioneering studies, there have been growing empirical studies testing the EKC hypothesis by applying different methodologies for different single and group of countries. However, the results of these studies do not give a clear picture about the validity of the EKC hypothesis between GDP-per-capita GDP and CO2-per-capita CO2 emissions which is the most used response variable (Isik et al. 2018; Isik and Radulescu, 2017; Isik et al. 2017); Işik and Shahbaz, 2015; Işik, 2010). Although there should be many potential different explanatory variables affecting the CO2 emissions, the most used and direct acting explanatory variables are as follows: fossil fuel energy consumption (FFEC), renewable energy consumption (REC), non-renewable energy consumption (NREC), energy consumption (EC), per-capita-energy use (PCEU), electricity production from renewable sources (EPRS), trade openness (TO), ratio of exports to imports (REI), Gini coefficient (GC), foreign direct investment (FDI), public budget in energy research (PBER), energy prices (EP), population growth (PG), population density (PD), land (L), globalization (G), financial development (FD), urbanization (U), and number of international tourist arrivals (TRA). For instance, Roca et al. (2001) applied the ordinary least squares (OLS) analysis for Spain and found no evidence of the validity of the EKC hypothesis. Lindmark (2002) used the Kalman filter and structural time-series approach for Sweden and found no evidence of EKC (also used FFEC). Friedl and Getzner (2003) used standard time-series estimation methods for Austria and found no evidence of the validity of the EKC (TO). Acaravci and Ozturk (2010) applied the autoregressive distributed lag (ARDL) bounds testing for Turkey and 19 European countries and found no evidence of the EKC for most of them except Denmark and Italy (TO and FFEC). He and Richard (2010) applied the semiparametric and flexible nonlinear parametric modeling methods for Canada and found little evidence for the EKC (TO and FFEC). Similarly, Esteve and Tamarit (2012) applied the cointegration with structural for Spain and found no evidence of the EKC. Ozokcu and Ozdemir (2017) used the panel data analysis for 26 OECD and 52 emerging countries and found no evidence of the validity of the EKC hypothesis (PCEU). Dogan and Turkekul (2016) applied the bounds testing for cointegration for the USA and found no evidence of the EKC (EC, TO, U, FD). Dogan et al. (2017) applied second-generation unit root tests, cointegration test, and causality test for the OECD countries and found no evidence of the EKC (TO, EC, TRA). However, Halicioglu (2009) applied the ARDL bounds testing for Turkey and found the evidence of the EKC (TO and FFEC). Narayan and Narayan (2010) applied the panel cointegration for 43 developing countries and found evidence of the validity of the EKC hypothesis in Middle Eastern and South Asian countries. Jobert et al. (2014) used Bayesian shrinkage estimators for 55 countries and found the evidence of the EKC for some countries, not all (EC). Franklin and Ruth (2012) used the Prais–Winsten AR (1) regression model for the USA and found evidence of the EKC (GC, RI and EP). Farhani et al. (2014) used the panel vector error correction model (VECM) technique for Tunisia and found evidence of the EKC (EC and TO). Boluk and Mert (2015) applied the ARDL model for Turkey and found evidence of the EKC (EPRS). Apergis and Ozturk (2015) applied the generalized method of moments (GMM) methodology for 14 Asian countries and concluded that the EKC is valid (PD and L). Similarly, Heidari et al. (2015) applied panel smooth threshold regression (PSTR) model for 5 Asian countries and concluded that the EKC hypothesis is valid (EC). Chen et al. (2016) applied the panel cointegration and vector for 188 countries and concluded that the EKC hypothesis is valid (EC). Dogan and Seker (2016a) applied panel estimation techniques robust to cross-sectional dependence (CD) for the EU and found the validity of the EKC (TO, REC, NREC). The same authors applied heterogeneous panel estimation techniques with CD for the top 23 renewable energy countries and found the existence of the EKC (TO, REC, NREC). Destek et al. (2018) applied second-generation panel data methodologies which take into account the CD for the EU countries and found the evidence of the EKC only for Portugal (TO, REC, NREC). These authors used ecological footprint as a dependent variable instead of CO2 emissions. Nasreen et al. (2017) applied the ARDL bounds testing for 5 Asian countries and concluded that the EKC is valid (EC and FS).

This study, differently from the above country-level empirical studies, investigates the EKC hypothesis at a state-level for the USA. This investigation includes 50 US states and a Federal District (Washington, D.C.) between 1980 and 2015. Therefore, the results of this study will fully represent the whole USA with total 51 samples. Big diversities in levels of GDP-per capita income, socio-cultural-geographic differences, and the forms of used energy among the US states necessitate the studies for this country to be investigated this hypothesis at state-level rather than a country-level. Hence, it is believed that this empirical study will fill the gap for the need of state-level studies for the USA. Furthermore, the expected empirical findings of this study will also contribute to a few US state-level studies (Aldy 2005 (48 states, 1960–1999); Dogan and Seker, 2016b (top renevable energy countries) Apergis et al. 2017 (48 states, 1960–2010); Atasoy 2017 (50 states, 1960–2010); Isik et al. 2019 (10 states, 1980–2015)) by increasing the sample number of US states and updating (expanding) the time horizon to the latest available year 2015. Unlike Aldy (2005), Apergis et al. (2017), and Atasoy (2017), the analyzed sample period of this study begins from 1980 (later than these studies). It is quite clear that more accurate statistical results require longer time period. However, the main reason of choosing quite late beginning is to eliminate the structural breaks and cover the effects of renewable energy consumption more since the forms of energy production thereby consumption have changed in last decades from fossil to alternative energy resources. Therefore, the results of this study will enable us to compare the results of abovementioned empirical studies. In the following sections of the study, the empirical model–methodology and data set, empirical findings, and concluding remarks will be presented respectively.

Empirical model and data set

In order to investigate the US state-level EKC hypothesis, we use the following natural logarithmic form of regression model:

$$ lnCO{2}_{it}={\alpha}_0+{\alpha}_1{lnPCGDP}_{it}+{\alpha}_2{\left({lnPCGDP}_{it}\right)}^2+{\alpha}_3{lnREC}_{it}+{\alpha}_4{lnFEC}_{it}+{\alpha}_5{lnPOP}_{it}+{\varepsilon}_{it} $$
(1)

In Eq. 1, CO2 represents carbon dioxide emissions, the PCGDP and PCGDP2 represent the real per-capita gross domestic product and real squared per-capita gross domestic product respectively, the REC and FEC represent renewable and fossil energy consumptions respectively, and the POP and εt represent population and error term respectively. In this function, we expect the signs of α1 and α2 are to be positive and negative respectively, because environmental degradation (rise in CO2) initially rises with an increase in PCGDP and then after a turning point it starts to fall with an increase in PCGDP2. The sign of α3 and α4 are expected to be negative and positive respectively, because increases in renewable and fossil energy consumptions decrease and increase the CO2 emissions respectively. Lastly, the sign of α5 is to be positive since increases in population (POP) increase the CO2 emissions. In order to verify the EKC hypothesis, the signs of the PCGDP and PCGDP2 must be significantly positive and negative respectively for a US state.

The variables in different units of measurement are as follow: the CO2 (per-capita metric tons), the REC (per-capita kilowatt-hour), the FEC (per-capita kg of oil equivalent (koe)), the PCGDP and squared PCGDP2 (the USD (thousand)), the POP (person in per-square mile). The data of the CO2, REC, FEC were obtained from the U.S. Energy Information Administration (EIA, 2019). The data of the GDP and the POP were obtained from Federal Reserve Bank of St. Louis (FED, 2019) and the US Census Bureau (Census 2019) respectively.

Empirical methodology

In the methodology of the study, we will follow the next steps. First, we apply the CD tests to understand whether the variables are correlated in entire panel which includes 51 US states. Second, we apply the Delta test to check whether the coefficients of the US states in the long-run are homogeneous and heterogeneous. In the next step, the covariate augmented Dickey–Fuller (CADF) test considering the CD is applied for the presence of a unit root in the variables. Lastly, the common correlated effects (CCE) and the augmented mean group (AMG) estimation procedures considering both heterogeneity and CD are applied for the estimated results of each state. All these steps are explained in detail in the next section of the study.

Before estimating the coefficients of both procedures, first we must detect the presence of the CD among the US states in the panel. To this aim, we apply Pesaran (2004) CD and Breusch and Pagan (1980) LM tests. In the examination of CD, time dimensions (T) and cross-sectional dimensions (N) are compared. If T > N, CDLM1 is used; if N > T, CDLM is used; if both T and N are large, CDLM2 is used. The deviation corrected the bias-adjusted CD test is used in both cases. The results of CD and LM tests are reported in Table 1.

Table 1 Cross-sectional dependence (CD) test results
Full size table

Empirical results

The test results in Table 1 indicate that there is a dependence between cross sections since we reject the null hypothesis of “no CD.” We take the bias-adjusted CD into consideration in our case since N > T. However, other tests also support this CD. Before the unit root test, we must determine whether the coefficients of the US states in the long-run are homogeneous and heterogeneous. To this aim, we apply the Delta test, developed by Pesaran and Yamagata (2008). The test results of this test are reported in Table 2. When (N, T)→∞, and the error terms are normally distributed, the \( \overset{\sim }{\Delta } \) test has a asymptotic standard normal distribution under the null hypothesis of “homogeneity.” The small sample properties of the \( \overset{\sim }{\Delta } \) test can be improved when there are normally distributed errors by using the following mean and variance bias-adjusted version:

$$ {\overset{\sim }{\Delta }}_{adj}=\sqrt{N}\left(\frac{N^{-1}\overset{\sim }{S}-E\left({\overset{\sim }{Z}}_{it}\right)}{\sqrt{\mathit{\operatorname{var}}\left({\overset{\sim }{Z}}_{it}\right)}}\right) $$
(2)

where

$$ E\left({\overset{\sim }{Z}}_{it}\right)=k,\sqrt{\mathit{\operatorname{var}}\left({\overset{\sim }{Z}}_{it}\right)}=2k\left(T-k-1\right)/\left(T+1\right) $$
(3)
Table 2 Delta homogeneity tests for models
Full size table

The ∆̃ adj statistics are used if the number of US states in panel are low, and if the panel is big, ∆̃ statistics are used.

The test results in Table 2 indicate that the panel group is heterogeneous since we reject the null hypothesis, that is, the slope coefficients are homogeneous. In the next step, we should make sure whether the series are stationary. To this aim, second-generation panel unit root test considering cross-sectional dependence, namely the CIPS test (Pesaran 2007), is employed. The CIPS test uses the standard ADF regression with the cross-section averages of the lagged levels and first-differences of the individual series. The test procedure includes estimation of the separate cross-sectionally augmented Dickey–Fuller (CADF) regressions for each country, hence allowing for different autoregressive parameters for each member of the panel. The CADF regression is given by:

$$ {\Delta x}_{it}={z}_{it}{\gamma}_i+{\rho}_i{x}_{i,t-1}+{\sum}_{j=1}^{k_i}{\varphi}_{ij}{\Delta x}_{it-j}+{\alpha}_i{\overline{x}}_{t-1}+{\sum}_{j=0}^{k_i}{n}_{ij}\Delta {\overline{x}}_{t-j}+{v}_{it} $$
(4)

where \( {\overline{x}}_t \) is the cross-section mean of \( {\overline{x}}_{it} \), i.e.,\( {\overline{x}}_t={N}^{-1}{\sum}_{i=1}^N{x}_{it} \). The null hypothesis is tahat each series contains a unit root, H0 = ρi = 0 for all i, while the alternative hypothesis is that at least one of the individual series in the panel is (trend) stationary, H1 = ρi < 0 for at least one i. To test the null hypothesis, the CIPS statistic is calculated as the average of the individual CADF statistics:

$$ CIPS={N}^{-1}{\sum}_{i=1}^{N_i}{t}_i $$
(5)

where ti is the OLS t ratio of ρi in the above CADF regression (Herzer and Vollmer 2012, p. 496). The results of unit root test are reported in Table 3.

Table 3 Results from CADF panel unit root tests
Full size table

The test results of panel unit root test indicate that all variables are I(0) since the calculated the CIPS statistics are lower than the critical values. In order to obtain cointegration coefficients of whole heterogeneous panel, we apply the common correlated effects (CCE) of Pesaran (2006) and the augmented mean group (AMG) of Eberhardt and Bond (2009) estimation procedures. They both serve to check robustness of the results. The test results of the CCE and AMG estimations are reported in Table 4.

Table 4 Result from CCE vs AMG estimations
Full size table

The test results in Table 4 indicate that the CCE estimation procedure does not support EKC hypothesis since the estimates of the PCGDP (positive) and PCGDP2 (negative) are statistically insignificant. On the other hand, the AMG estimation procedure supports the EKC hypothesis. Hence, the AMG estimation will be used in the state-level estimations. According to the AMG, rises in the PCGDP lead to increases in the carbon dioxide emissions (CO2) and rises in the PCGDP2 lead to decreases in the CO2. This verifies the validity of the EKC hypothesis for the entire panel. Furthermore, the signs and significant estimates of the FEC and REC in the AMG estimation are positive and negative as expected. This means that rises in fossil energy consumption (FEC) considerably increase the CO2 emissions. Similarly, rises in renewable energy consumption (REC) decrease the CO2 emissions. However, the negative impact of fossil energy consumption (FEC) on the CO2 emissions is much higher than the positive impacts of renewable energy consumption (REC) on it since the REC’s estimated coefficient is far lower than the coefficient of the FEC. Rises in population (POP) have big impacts in the increases on the CO2 emissions. The test results of the EKC (inverted-U-shaped) hypothesis for the individual US states by the AMG estimation are reported in Table 5.

Table 5 The results of the state-level EKC (inverted-U-shaped) hypothesis by the AMG estimation
Full size table

The test results in Table 5 indicate that the AMG estimation procedure for the individual states has mixed results in the EKC hypothesis. The AMG significantly (S) and highly significantly (HS) validates the EKC hypothesis for 14 states (Alabama (S), Arizona (HS), Florida (HS), Maine (HS), Montana (HS), Nebraska (HS), Nevada (HS), New H. (S), New Mexico (S), North Dakota (HS), Oklahoma (HS), Utah (HS), West Virginia (S), and Wisconsin (S)). However, it can be concluded that the AMG estimation provides weak evidence of the validity of the EKC hypothesis since it detects this hypothesis only in 14 out of 50 states. It should be noted that Atasoy (2017) applied the same method and found strong evidence of the EKC hypothesis for 30 out of 50 states. The same author in the same study applied the common correlated effects mean group estimator (CCEMG) estimation and found weak evidence of the EKC for only 10 states. On the other hand, Apergis et al. (2017) applied the CCE estimation and found evidence of the EKC only for 10 out of 48 US states. Isik et al. (2019) applied the panel estimation method with cross-sectional dependence and found the EKC hypothesis for 5 out of 10 states. Aldy (2005) applied the ordinary least squares (OLS) and feasible generalized least squares (FGLS) methods and found the evidence of the EKC for 40–44 out of 48 states. The same author applied also the dynamic OLS method and found the evidence of this hypothesis only for 9 states. Accordingly, it can be concluded that all these few US state-level empirical studies provide mix results for the validity of the EKC hypothesis for US states. These mix results are also valid on the names of the states which support the EKC hypothesis. This can be stemmed from that all these studies use different number of sample states, different time horizons, different variables, and different methods or the same methods but different time horizons. In regard to other variables in the model, rises in fossil energy consumptions (FEC) increase the CO2 emissions in all states except Texas since its coefficient is not significantly positive. Interestingly, the negative impact of increasing fossil energy consumption (FEC) on the level of the CO2 emissions has not been detected in this US state which produces oil the most in the USA ironically. This finding is consistent with result of the study of Isik et al. (2019). Furthermore, rises in renewable energy consumptions (REC) decrease the CO2 emissions only in Alaska, Connecticut, Georgia, Iowa, Massachusetts, Mississippi, Montana, New H., New York, Oregon, South C., Utah, and Wyoming. Rises in population (POP) increase the CO2 emissions in all states except Connecticut, Iowa, Massachusetts, New York, Ohio, South D., and Texas although the 25% of the all US population reside in these 7 states. Additionally, the rises in the DP, PCGDP2, REC, FEC, and POP have different size impacts on the CO2 emissions. While the most significantly strongest EKC impacts have been detected in Nevada (2.888–0.144), Oklahoma (2.583–0.129), and Arizona (2.337–0.124), the weakest impacts have been detected in North D. and Nebraska. Similarly, while the biggest negative impacts of fossil energy consumptions (FEC) on the CO2 emissions have been detected in Montana, Nevada, and Georgia, the smallest impacts have been detected in Alabama and Ohio. On the other hand, while the biggest positive impacts of renewable energy consumptions (REC) on the the CO2 emissions have been detected in Wyoming and New York, the smallest positive impacts have been detected in Utah. While the biggest negative impacts of population (POP) on the CO2 emissions have been detected in Alabama and Rhode Island, the smallest impacts have been detected in Louisiana and Washington.

Concluding remarks

If the question is asked like “does the economic growth pollute or support the environment?,” the world examples from some underdeveloped and developed countries show us that the answer is both, because the early stage of industrialization (thereby economic growth/development) requiring massive use of fossil energy resources first increases environmental degradation and after a certain level of per-capita income (turning point) degradation falls. Many scholars test this potential inverted-U-shaped relationship by environmental Kuznets curve (EKC) hypothesis for different countries.

This study, differently from these country-level empirical studies, investigates the EKC hypothesis at a state-level for the USA, because the big diversities in levels of GDP, per capita income, and the forms of used energy among the US states necessitate the studies for this country to investigate this hypothesis at state-level rather than a country-level. This investigation includes 50 US states and a Federal District (Washington, D.C.). In this manner, the empirical findings of this study fully represent the whole USA with 51 samples. Hence, this study, with its the largest state samples + district, decomposed forms of energy consumptions such as fossil and renewable energies and latest available data makes contribution to very little the US state-level studies. The empirical findings of this study are consistent with the results of these studies. Like them we also verify the EKC hypothesis for some US states reported in the previous section. However, there is no clarity about both the numbers and the names of the US states verifying the EKC hypothesis in all these studies including ours. While some studies verify this hypothesis for more US states, some do it for less states. Similarly, the US states verifying this hypothesis vary from one study to another. Therefore, the findings of this study show the need for more and further empirical studies using different methodologies to investigate this hypothesis. These further studies will help the state-level US policy makers to understand whether their economic growths are sustainable (eco-friendly). A verified EKC hypothesis may give them the answer of this question to some degree. Furthermore, these studies will also help them to see how their fossil and renewable energy consumptions affect their environments and to review their energy policies whether they are also sustainable.