The role of government spending within the environmental Kuznets curve framework: evidence from G7 countries

Abstract

This study assesses the role of government spending on environmental sustainability based on a framework that combines the environmental Kuznets curve (EKC) hypothesis with the Armey curve hypothesis. Specifically, the inverted U-shaped relationships between carbon (CO₂) emissions and economic growth (EKC hypothesis) and between government spending and economic growth (Armey curve hypothesis) are analyzed using a composite EKC model tested for cross-sectional dependence and heterogeneity, panel unit root, panel co-integration, and the augmented mean group estimation. In so doing, this study pursues a potential transmission mechanism leading from government spending to CO₂ emissions through the growth channel and presents a novel way to develop a better understanding of how economic growth policy and energy policy can be synchronized. Empirical results show that economic growth acts as a transmitter between government spending and CO₂ emissions in the USA, UK, and Canada. However, the composite EKC hypotehesis is confirmed only for the USA and Canada, where the optimal level of government spending that maximizes CO₂ emissions is 29.87% and 29.22% of GDP, respectively. In contrast, the optimal level of government spending equivalent to 28.30% of GDP minimizes CO₂ emissions in the UK. The key policy implication is that governments can achieve sustainable economic growth by setting standards for their spending levels.

Introduction

The link between government spending and energy policy has already been recognized as a critical component of global efforts. Recent initiatives demonstrate that this link has reached the highest political level as commitments to meet the Paris Agreement goals at COP21 and to implement the 2030 Agenda for Sustainable Development have been scrutinized in the public spotlight.¹ One area of great importance in this context is making financial flows consistent with a “sustainable” pathway to achieve long-term climate and development goals. This is evident in the proposals of António Guterres, the Secretary-General of the United Nations, who suggests that public money should flow to sustainable businesses that help the climate, implying the end of fossil fuel-oriented practices (UNDGC 2020). The Glasgow COP26 summit in late 2021 also underscores this connection with its international agreement to shift global public funds for the unabated fossil fuel energy into the renewable energy transition by the end of 2022 (Ware 2021).

Since public finance is a key mechanism to align funding policies with climate goals, developed countries, particularly the G7, have focused their agenda on directing the flow of public capital toward sustainable investments, for which at least EUR 1 trillion should be mobilized over the next decade (European Commission 2020). COVID-19 has accelerated this process through global stimulus packages. Governments from all across the world have allocated almost USD 19 trillion to mitigate the impact of the pandemic (ILO 2022). The amount of authorized government spending on clean energy has surpassed USD 480 billion, and the majority of this expenditure has occurred in G7 countries. The global clean energy stimulus is anticipated to be spent by the end of 2023 (IEA 2021). However, building such capacity requires resilient policies, significant collaboration, and a high degree of commitment for prioritizing renewable energy. To this end, governments need to diversify public sources to lessen carbon entanglement, align fiscal and budgetary incentives with climate goals and leverage the influence of government spending while ensuring an inclusive transition (OECD 2018).

As is seen, governments play a major role in stimulating the economy, and their contribution to economic growth is now more focused than ever on sustainable development goals especially in response to the pandemic. Hence, evaluating the impact of the size of government spending in the economy on eco-friendly growth deserves attention. Given the importance of government spending in delivering climate solutions, it is timely to provide policymakers with a new analytical tool based on the level of government spending to optimize their economic growth policies and energy policies to achieve a more sustainable environment. Intiutively, the environmental Kuznets curve (EKC) hypothesis and the Armey curve hypothesis appear as two different but not mutually exclusive postulates that may collectively lend insight into how government spending, economic growth, and environmental concerns interact with each other. Looking more closely to these theoretical constructs, the EKC hypothesis, which elucidates the inverted U-shaped curvilinear relationship between economic growth and environmental pollution, can be analyzed in combination with the Armey curve hypothesis, which explains a similar inverted U-shaped curvilinear relationship between economic growth and government spending, The basic premise is that economic growth driven by government spending via the Armey curve may translate into an increase in carbon (CO₂) emissions through a single composite EKC model. This is plausible because economic growth, which is common to both hypotheses, is the dependent variable in the Armey curve hypothesis, while it is the independent variable in the EKC hypothesis. Moreover, the identical inverted U-shaped pattern of these two curves implies that it is possible to determine a maximum level of spending that allows policymakers to manage and allocate public resources in such a way that economic growth policies and energy policies are compatible with each other.

In this vein, this study differs from many past studies by investigating whether the impact of government spending on economic growth, i.e., GDP per capita, is transmitted to CO₂ emissions by means of a composite variant of the EKC in G7 countries. This Armey curve–induced composite EKC model can provide useful information in two different perspectives: (1) when the model is inverted U-shaped and (2) when the model is U-shaped. The first case is illustrated in Fig. 1 and suggests that it is possible to identify a maximum level of government spending that maximizes CO₂ emissions by maximizing economic growth. This implies that CO₂ emissions decline following a turning point in government spending–induced economic growth. Additional government spending after that critical point, thus reduces GDP per capita (left-hand side) and CO₂ emissions (right-hand side). This supports a more sustainable environment at the cost of economic growth, thereby creating a trade-off. In policy terms, this conjecture can be interpreted in the way that economic growth policies and energy policies would be compatible as long as they are aligned with sustainable development goals to promote sustained, inclusive, and sustainable economic growth, which may require some time.

Fig. 1

Source: Ongan et al. (2022), Isik et al. (2022)

The inverted U-shaped composite EKC model.

However, in the second case, as shown in Fig. 2, it would be possible to determine a maximum level of government spending that minimizes CO₂ emissions through a maximum level of GDP. This would imply that beyond a critical point, additional government spending is no longer necessary because it lowers GDP per capita (left-hand side) and increases CO₂ emissions (right-hand side). Hence, it is possible to argue that both economic growth and energy policies are concurrently congruent with each other and an effective level of government spending would be attained easier to achieve sustainable development goals.

Fig. 2

Source: Ongan et al. (2022), Isik et al. (2022)

The U-shaped composite EKC model.

It is worth to note that the empirical analysis based on the composite EKC model must satisfy the following conditions: (1) The Armey curve hypothesis must be verified by an inverted U-shaped curve for a G7 country. (2) The composite EKC model must be significant for that G7 country. If the composite EKC model is inverted U-shaped, then the EKC hypothesis is also verified (see Fig. 1). A U-shaped composite EKC model, on the other hand, indicates that the EKC hypothesis is not supported by the Armey curve hypothesis (see Fig. 2).

In this framework, the corresponding variables of interest are government spending, GDP per capita, and CO₂ emissions, which are inherently used in the EKC and the Armey curve literature. However, the use of renewable energy consumption as a control variable makes another difference in this study. It matters to include renewable energy consumption, since it would be reasonable to observe whether it has reached a point where it can affect economic growth and pollution levels. But, on top of that, this study does not merely opt for using “renewable energy consumption,” but rather it consciously precludes having an “energy consumption” variable in the modeling. This has conceptual and empirical grounds. As for the former, it is expected that greater use of renewables in final energy consumption will eventually lower global CO₂ emissions (Boluk and Mert 2014) and will affect the turning point of the EKC (Yao et al. 2019). As for the latter, one of the reasons behind why EKC pattern cannot be observed in many studies is attributed to the high correlation between energy consumption, economic growth and CO₂ emissions (Sugiawan and Managi 2016). Since it is well documented that higher economic growth requires higher energy consumption, leading to higher CO₂ emissions (Ang 2007; Apergis et al. 2010), CO₂ emissions are then imputed from energy consumption, which may make the relationship that is estimated by the EKC model somewhat tautological. Therefore, this study takes into account the potential of renewable energy consumption in modeling the EKC hypothesis.

Finally, the G7 countries form a natural setting for at least three reasons. First, the G7 is well known as an informal group with coordinated political, economic, and policy responses to common dynamics of growth and prosperity. Second, the G7 is leading the way in working together to fully decarbonize the global economy in line with the Paris Agreement. Third, the G7 share of global renewable energy consumption is 36.1% by 2021, with an average growth rate of 9.3% over the past decade. While the USA is the second largest consumer of renewable energy after China with a share of 18.7%, Germany, Japan, the UK, Italy, France, and Canada rank fourth, sixth, seventh, ninth, tenth, and fourteenth, respectively (BP 2022). That said, although the high economic status enables them to follow common energy policies without harming their economies, G7 countries differ in their economic growth, government spending (Gurdal et al. 2021), CO₂ emissions (Yilanci and Pata 2022), and exposure to energy security risks and their energy diversification strategies (Couharde et al. 2020).

Overall, this study adds to the body of knowledge by being one of the few studies to argue that the Armey curve hypothesis and the EKC hypothesis are complementary in that there is transmissibility between government spending and environmental concerns through the economic growth channel. Although numerous studies have addressed the confirmation of either hypothesis, previous research remains almost silent about their possible complementarity. By showing the transmission mechanism between the two hypotheses, this study makes a threefold contribution. (1) It shows the value of integrating two theories in a holistic and parsimonious manner to explain the interaction between economic growth policy and energy policy; (2) it introduces a new methodology that enables policymakers to determine certain thresholds for government spending and economic growth, which in turn would translate into an effective environmental management; and (3) renewable energy consumption is considered a key variable affecting both the growth and the environment.

The rest of the study is organized as follows. “Literature review” reviews the literature. “Data and methodology” describes the data and methodology. “Results and discussion” reports and discusses the main findings. “Conclusion and policy implications” concludes.

Literature review

The Armey curve literature

There are two main economic perspectives (classical and Keynesian) on government spending (Mitchell 2005). The first is the classical doctrine that government spending has a negative impact on economic growth (Roy 2009; Bergh and Karlsson 2010; Connolly and Li 2016; Afonso and Jalles 2016). Scholars who hold this view argue that the growth of government spending has shifted to inactive areas. Moreover, when government spending is funded by taxes or borrowings from the domestic market, factors like lower private sector investment and higher interest rates have a negative impact on growth (crowding-out effect). Consistent with arguments claiming that increasing government spending has no negative effects on economic growth, the second view originated by Keynes (1936) purports that stronger and more effective government spending will eliminate market disruptions and stimulate economic growth (Karras 1997; Wu et al. 2010; Akpan and Abang 2013; Choi and Son 2016). An increase in government spending will have a positive multiplier effect on investment and employment, and an increase in social spending will result in a rise in national welfare.

Over time, these two viewpoints were combined into a third one that considers both the positive and negative effects of government spending. Accordingly, studies following the third approach, known in the economics literature as the Armey curve hypothesis (Armey 1995), suggest that government spending positively affects growth up to a certain level, but negatively above a certain level. The Armey curve hypothesis postulates that an increase in government spending in the economy will boost economic growth up to a certain point. For any economy, there is an optimal level of government size. When that level is exceeded, the increase in government spending starts to have a negative effect on growth. Following Armey (1995), a multitude of studies has been conducted to assess this non-linear approach in examining the relationship between the government size and economic growth (Vedder and Gallaway 1998; Gwartney et al. 1998; Pevcin 2004; Chen and Lee 2005; Chobanov and Mladenova 2009; Abounoori and Nademi 2010; De Witte and Moesen 2010; Forte and Magazzino 2011; Altunc and Aydin 2013; Magazzino 2014; Hok et al. 2014; Asimakopoulos and Karavias 2016; Chen et al. 2017; Lazarus et al. 2017; Rennane 2019; Nuredin 2019; Bozma et al. 2019; Kim et al. 2020; Jain et al. 2021; Al-Abdulrazag 2021; Nouira and Kouni 2021; Isik et al 2022; Jain and Sinha 2022; Nikolova and Angelov 2022; Can and Aktas 2022). Most of these studies albeit conducted in many countries, with different methodologies, and over various sample periods share a common observation that there is a non-linear relationship between government size and economic growth.

The EKC-renewable energy consumption literature

The EKC hypothesis originally postulates an inverted U-shaped relationship between economic growth and income inequality, pointing to a certain level of development at which growth-related inequalities begin to decline (Kuznets 1955). It has been adapted to the energy literature to test the relationship between economic growth, i.e., per capita income and environmental quality. At the initiative of Grossman and Krueger (1991), numerous studies have attempted to establish the validity of the EKC hypothesis in both country-specific and cross-country contexts. The common practice in these studies is to model the relationship between economic growth and CO₂ emissions to examine whether a similar inverted U formation exists, which states that environmental degradation and pollution increase in the early stages of economic growth; however, the situation reverses when per capita income, which is an indicator of growth, reaches a certain level.

Recently, a growing amount of research has focused on the effect of renewable energy consumption in this relationship. Among many others, Farhani and Shahbaz (2014), Dogan and Seker (2016), Jebli et al. (2016), Bilgili et al. (2016), Zaghdoudi (2017), Khoshnevis Yazdi and Ghorchi Beygi (2018), Balado-Naves et al. (2018), Inglesi-Lotz and Dogan (2018), Sinha and Shahbaz (2018), Chen et al. (2019), Elshimy and El-Aasar (2020), Altintas and Kassouri (2020), Sarwat et al. (2022), Miao et al. (2022), Murshed et al. (2022), Aydin and Cetintas (2022) provide evidence for the inverted U-shaped EKC. However, there are also studies arguing against the validity of the EKC hypothesis (Boluk and Mert 2014; Al-Mulali et al. 2015; Liu et al. 2017; Zoundi 2017; El-Aasar and Hanafy 2018; Ansari et al. 2020; Dogan et al. 2020; Yilanci and Pata 2020; Altintas and Kassouri 2020; Massagony and Budiono 2022).

The reviewed literature is summarized in Table 1 as follows:

Table 1 Summary of the literature

The Armey curve EKC link and hypothesis development

The Armey curve hypothesis examines the impact of government spending on economic growth, while the EKC hypothesis looks at how economic growth affects CO₂ emissions. Although there are mixed results, the literature largely justifies the validity of both hypotheses. Therefore, it is conceivable to consider the possibility that these two seemingly unrelated hypotheses are interconnected. Such a connection would manifest itself when, according to the same inverted U-shaped mathematical theorem, a rise in government spending causes to an increase in economic growth and, consequently, an increase in CO₂ emissions. By this means, the Armey curve hypothesis and the EKC hypothesis can be merged into one pot and tested together by a single composite model combines the relationships between economic growth, government spending, and CO₂ emissions.

This approach is first introduced by Ongan et al. (2022) and Isik et al. (2022) to the literature. Ongan et al. (2022) scrutinize the validity of the composite EKC hypothesis for NAFTA countries (i.e., the US, Canada, and Mexico). The authors find that the Armey curve hypothesis per se is verified only for the USA, while the EKC hypothesis per se is not supported in any country. The results also suggest that the composite EKC model does not have the empirical properties required to test for the transmission mechanism of the Armey curve hypothesis for any NAFTA country. Isik et al. (2022) follow the same path for 50 US states from 1990 to 2017. This state-level study reveals that the Armey curve hypothesis per se is validated for 15 states. However, only 7 of these states, namely Colorado, Georgia, Indiana, Kentucky, Maine, South Dakota, and Tennessee, provide evidence for the composite EKC model. The authors conclude that state policymakers can determine the maximum spending levels that will maximize their economic growth and maximize (minimize) CO₂ emissions.

In both studies, which are currently the only ones available in the extant literature, academics and policymakers are encouraged for future attempts to consider the composite EKC model as a different viewpoint in analyzing the environmental stewardship of economic and energy policies at once. This paper, therefore, intends to answer whether a transmission mechanism of the Armey curve hypothesis exists in the context of the EKC hypothesis, which results in a single maximum level of government spending that maximizes or minimizes CO₂ emissions. It also takes this novel approach one step further and proposes an innovative framework based on the controlling capability of renewable energy consumption in the Armey curve and EKC models. The reasoning is that renewable energy consumption will eventually affect the turning point of the EKC (Yao et al. 2019) by lowering global CO₂ emissions (Boluk and Mert 2014). Moreover, possible high correlations between energy consumption, economic growth, and CO₂ emissions (Ang 2007; Apergis et al. 2010; Sugiawan and Managi 2016) have the potential to distort the validity of the empirical analysis results.

As previously noted, since inverted U-shaped curves must be obtained to mathematically verify both the Armey curve hypothesis and the composite EKC hypothesis, this study jointly proposes the following hypotheses:

• H_1a: There is an inverted U-shaped relationship between government spending and economic growth for a G7 country under the control of renewable energy consumption (the Armey curve hypothesis).

• H_1b: There is an inverted U-shaped relationship between CO₂ emissions and government spending–induced economic growth for a G7 country under the control of renewable energy consumption (the composite EKC hypothesis).

Data and methodology

This study strictly follows the methodology of Ongan et al. (2022) and Isik et al. (2022), but slightly modifies their model to include renewable energy consumption as a control variable and test whether there is a transmission mechanism running from the Armey curve to the EKC.

In this context, the following Armey curve and EKC models are used in order to derive the composite EKC model:

$$\mathrm{Armey}\;\mathrm{curve}\;\mathrm{model}:\;\ln{\mathrm{GDP}}_{\mathrm{it}}=\alpha+\beta_1{\mathrm{lnGS}}_{\mathrm{it}}+\beta_2\mathrm{lnGS}_{\mathrm{it}}^2+\beta_3{\mathrm{REN}}_{\mathrm{it}}+\varepsilon_{\mathrm{it}}$$

(1)

$$\mathrm{EKC}\;\mathrm{model}:\;\ln{\mathrm{CO}2}_{\mathrm{it}}=a+{\mathrm b}_1{\mathrm{lnGDP}}_{\mathrm{it}}+{\mathrm b}_2\mathrm{lnGDP}_{\mathrm{it}}^2+{\mathrm b}_3{\mathrm{REN}}_{\mathrm{it}}+u_{\mathrm{it}}$$

(2)

In Eq. (1) and Eq. (2), GDP and GS represent GDP per capita and government spending, respectively, in current prices in US dollars; REN denotes renewable energy consumption (% of total final energy consumption); CO₂ stands for carbon emissions (million tonnes); ε and $u$ are the error terms. A positive sign for β₁ (${b}_{1}$) is expected since an increase in government spending (GDP per capita) will yield the same for GDP per capita (CO₂ emissions). However, the sign for β₂ (${b}_{2}$) should be negative as additional government spending (GDP per capita) will decrease GDP per capita (CO₂ emissions) beyond a critical point. The Armey curve (the EKC) model in Eq. (1) [Eq. (2)] is verified when the signs for β₁ (${b}_{1}$) and β₂ (${b}_{2}$) are positive and negative, respectively, for a G7 country. It is anticipated that the sign for β₃ (b₃) would be positive (negative) because an increase in renewable energy consumption will lead to an increase (a decrease) in GDP per capita (CO₂ emissions). Data for GDP, GS, and REN variables are from the World Development Indicators, while CO₂ emissions data are from BP (2022). The sample period is set as 1971–2020 based on the availability of data.

After replacing the lnGDP variable in Eq. (2) with its equivalent in Eq. (1), the following composite EKC model is derived in Eq. (3):

$$\mathrm{Composite}\;\mathrm{EKC}\;\mathrm{model}:\;\ln{\mathrm{CO}2}_{\mathrm{it}}=a+b_1\left(\alpha+\beta_1{\mathrm{lnGS}}_{\mathrm{it}}+\beta_2\mathrm{lnGS}_{\mathrm{it}}^2+\beta_3{\mathrm{REN}}_{\mathrm{it}}\right)+b_2{(\alpha+\beta_1{\mathrm{lnGS}}_{\mathrm{it}}+\beta_2\mathrm{lnGS}_{\mathrm{it}}^2+\beta_3{\mathrm{REN}}_{\mathrm{it}})}^2+b_3{\mathrm{REN}}_{\mathrm{it}}+u_{\mathrm{it}}$$

(3)

The EKC hypothesis in Eq. (3) is tested by the Armey curve hypothesis using the signs of the coefficients ${b}_{1}$ and ${b}_{2}$. In other words, an inverted U-shaped curve is confirmed if b₁ has a positive and b₂ has a negative sign.

The methodology for conducting the empirical analysis in this study is fourfold. First, cross-sectional dependence is tested to determine whether common shocks have heterogeneous impact or spillover effects exist, and for slope heterogeneity to show that slope coefficients are identical across cross-sectional units. The Lagrange multiplier (LM) test (Breusch and Pagan 1980), CD and CD_LM tests (Pesaran 2021), and the LM_adj test (Pesaran et al. 2008) are used to test for cross-sectional dependence, while the $\widetilde{\Delta }$ and $\widetilde{\Delta }$ _adj tests (Pesaran and Yamagata 2008) are used to test for slope heterogeneity. Second, the cross-sectional augmented Dickey-Fuller second generation panel unit root tests of Pesaran (2007), as known as CADF and CIPS tests, which take into account the cross-sectional dependence in the variables, are employed to check for the stationarity of the data. Third, error correction–based panel co-integration tests (Westerlund 2007) are performed to test for the presence of long-run relationships among integrated variables in the panel. As a final test, the augmented mean group (AMG) estimator (Eberhardt and Bond 2009), which accounts for cross-sectional dependence, is robust to non-stationary variables, and allows for heterogeneous slope coefficients across panel members, is used. The AMG estimator includes a common dynamic effect which indicates unobservable common factors in the main model. The augmented model includes the co-integration relationship that differs across countries when the unobservable common factors are part of the country-specific co-integrating relationship. This method provides the long-run parameters for the aggregate panel as well as the underlying country-specific regression results.

This study also determines the optimal level of government spending that maximizes (see Fig. 1) or minimizes (see Fig. 2) CO₂ emissions as follows. First, the level of government spending of a G7 country is obtained from the first-order optimization condition dlnGDP/dlnGS, which is applied to Eq. (1):

$$\mathrm{lnGS}=-\frac{{\beta }_{1}}{2{\beta }_{2}}$$

(4)

The sufficient condition for maximization is d²lnGDP/dlnGS² = 2 ${\beta }_{2}$ < 0, so ${\beta }_{2}$ should be negative. Since lnGS is positive by definition, ${\beta }_{1}$ should also be positive. Then, the optimal point for the composite EKC model is obtained in Eq. (3), from the first-order condition dCO2/dGS:

$${\mathrm{lnGS}}_{1}=-\frac{{\beta }_{1}}{2{\beta }_{2}}$$

(5)

$${\mathrm{lnGS}}_{\mathrm{2,3}}=\frac{{\beta }_{1}+\sqrt{{{\beta }_{1}}^{2}-2\left(\frac{{b}_{1}}{{b}_{2}}\right){\beta }_{2}-4\alpha {\beta }_{2}}}{2{\beta }_{2}}$$

(6)

The value in Eq. (5) will be the optimal CO₂ emissions level for Eq. (3). When Eq. (5) is inserted into d²CO2/dlnGS² = 2b₁ ${\beta }_{2}$+2b₂(β₁ + 2 ${\beta }_{2}$ lnGS)² + 4b₂ ${\beta }_{2}$ (α + β₁lnGS + ${\beta }_{2}$ lnGS²), the following formula is derived:

$$\frac{{d}^{2}\mathrm{CO}2}{d{l\mathrm{nGS}}^{2}}\left({\mathrm{lnGS}}_{1}\right)=-{b}_{2}{{\beta }_{1}}^{2}+2{b}_{1}{\beta }_{2}+4{b}_{2}\alpha {\beta }_{2}$$

(7)

If ${\beta }_{2}$ is negative and the value of Eq. (7) is positive, then the Armey curve is inverted U-shaped, while the composite EKC is U-shaped. However, if both ${\beta }_{2}$ and the value of Eq. (7) are negative, then the Armey curve and the composite EKC both have the form of an inverted U.

Results and discussion

The findings of the tests for cross-sectional dependence and slope heterogeneity regarding the Armey curve, the EKC, and the composite EKC models are reported in Table 2.

Table 2 Cross-sectional dependence and slope heterogeneity tests

As Table 2 suggests, the null hypothesis of no cross-sectional dependence is strongly rejected, indicating that a shock in one G7 country can affect other G7 members. This is not surprising because shocks can be easily spilled over to other countries due to the high level of integration between them. In addition, the null hypothesis of slope homogeneity is rejected, which reveals that each G7 country has its own dynamics. This is also expected since slope coefficients often differ across territorial units, i.e. countries, and they cannot be treated as a single entity, particularly in the case of large time-series (Pesaran and Smith 1995).

These findings imply that dependencies among the cross-sections and heterogeneous slope coefficients require using panel econometric models that are robust to such considerations. Accordingly, the order of integration between the variables is next checked using second generation of panel unit root tests.

Test results of the CADF and CIPS panel unit root tests are demonstrated in Table 3.

Table 3 Panel unit root test results

According to the results in Table 3, all series include unit root at their levels, but are stationary at first differences under the presence of cross-sectional dependence. This is due to the fact that both the CADS test and CIPS test statistics of the first differences of each panel variable are lower than the corresponding critical values.

Since, the variables of interest are integrated of order one (i.e., I(1)), this study examines whether a structural long-run equilibrium relationship exists between the variables of interest in the models. Table 4 provides the results:

Table 4 Panel co-integration test results

In Table 4, panel statistics are represented by the columns (P_a, P_t), whereas group mean statistics for overall co-integration are represented by the columns (G_a, G_t). The results indicate that the statistics of the co-integration test broadly support co-integration. For instance, G_t test statistic suggests that a co-integration relationship exists in the Armey curve model. P_t and G_t test statistics are significant for the EKC model to imply co-integration. Moreover, G_t test statistic shows that there is co-integration in the composite EKC model. All these findings confirm a stable long-run relationship among the variables in the models and warrant the estimation of the models by using the AMG estimator. On the other hand, it should be noted that the AMG estimator performs similarly well in terms of bias or root mean squared error in panels with non-stationary variables (co-integrated or not) (Eberhardt 2012). The final results are demonstrated in Table 5.

Table 5 Augmented mean group estimator test results

The results in panel A of Table 5 suggest that H_1a, i.e., the Armey curve hypothesis, is confirmed for the USA, UK, and Canada with an inverted U-shaped curve. These results are consistent with Vedder and Gallaway (1998) and Bozma et al. (2019) for the USA and Di Matteo and Barbiero (2018) and Bozma et al. (2019) for Canada. The results also reveal that the optimal level of government spending, which maximizes growth, is 29.87% and 29.22% of GDP for the USA and Canada, respectively. However, in the case of the USA, the turning point of the Armey curve is calculated as 17.45% over the 1947–1997 period by Vedder and Gallaway (1998), while it is 12.46% over the 1980–2014 period according to Bozma et al. (2019). These differences may be due to various definitions of the Armey curve in relating government spending to economic growth as well as due to the choice of the sample period. Regardless of these technical concerns, recent actual data show that the US government spending is 14.7% as of 2020 (World Bank 2022). The case of Canada exhibits a similar pattern. Di Matteo and Barbiero (2018) find the optimal level of government spending as 22% between 1870 and 2013, whereas Bozma et al. (2019) indicate a level of 18.93% between 1980 and 2014. The corresponding World Bank data, however, show 22.7% for 2020. Thus, the USA and Canada both appear to be still in the positively sloped portion of the Armey curve—higher government spending is associated with higher level of growth.

Interestingly, the literature generally does not support the Armey curve hypothesis for the UK (Pevcin 2004; Bozma et al. 2019). For instance, De Witte and Moesen (2010) have shown that the UK is one of the few countries that should optimally increase its government spending, implying that the country has not yet reached the peak of the Armey curve. However, government spending increased so much in the sample period, particularly between 2019 and 2020 (HM Treasury 2022), that the relationship between government spending and GDP may have formed an inverted U in the UK. The model results also suggest that the optimal level of government spending that maximizes the economic growth in the UK is 28.30% of GDP. The most recent UK data show that the ratio of government spending to GDP is 22.2% (World Bank 2022). When viewed from this aspect, the results are consistent with De Witte and Moesen (2010) in the sense that the UK is still on its way to the peak of the Armey curve. This is because, the country, likewise in the USA and Canada cases, stands on the curve’s positively sloped portion.

On the other hand, the result regarding the U-shaped relationship for France seems to contradict prior literature that has provided strong evidence for an inverted U-shape (Facchini and Melki 2013; Bozma et al. 2019). This may be attributed to the legal environment in France. In a very interesting study, Facchini and Seghezza (2021) showed that there was a positive and significant relationship between the production of legislation and the government spending-to-GDP ratio during the period 1905–2015. The authors pointed out that an increasing number of laws and regulations leads to an expansion of government spending as well as to an inefficient allocation of resources that hinders economic growth, which echoes the inverted U-shaped Armey curve. Given the sample period, however, this legislative process may have improved, so that economic growth has been driven by increased government spending. Indeed, it has been recently reported that the French government has made significant progress in the transparency and accessibility of its regulatory system over the past decade (US Department of State 2022).

According to panel B of Table 5, the EKC hypothesis is verified only for the USA (Atasoy 2017; Shahbaz et al. 2017) and Canada (Ajmi et al. 2015; Olale et al. 2018). It is found that a U-shaped form of EKC exists for the UK, which is not in line with many studies such as Fosten et al. (2012) and Sephton and Mann (2016). However, there are others that confirm the findings as well (De Bruyn et al. 1998; Figueroa and Pastén, 2009; Bese and Kalayci 2021).

These results imply that the potential candidate countries to confirm the appropriateness of the composite EKC model would be the USA, the UK, and Canada, because the empirical properties of the composite EKC model are only satisfied when both the Armey curve hypothesis is validated and the composite EKC model is significant. The test results of the composite model in;panel C of Table 5, therefore, are important to deliver the information regarding the latter condition, i.e., the significance of the composite EKC model. Indeed, the results show that the USA, the UK, and Canada are the G7 countries where there is a transmission mechanism running from the Armey curve model to the EKC model. The composite EKC model for the USA and Canada validates the existence of the EKC hypothesis, indicating two inverted U-shaped curves (the Armey curve and the composite EKC). In other words, H_1b cannot be rejected for these two countries. Considering the Armey curve results discussed immediately above, the optimal levels of government spending, which are found to be 29.87% and 29.22%, also maximize CO₂ emissions for the USA and Canada, respectively (see Fig. 1). Both countries currently have some room to keep growing by spending at the cost of increasing pollution until their optimal levels where the CO₂ emissions are maximized. When the optimal levels are once attained, further spending would evidently reduce GDP and CO₂ emissions, which would confront policymakers with an inevitable choice between a higher growth and a cleaner environment. However, it would then be valuable to know at what point it is possible to avoid environmental degradation in lieu of economic growth, so that policymakers would have to give appropriate priority to “sustainable” growth policies. A similar path is unfolded for several US states in the literature. Isik et al. (2022) determine optimal levels of government spending that maximize both growth and CO₂ emissions for Kentucky, Maine, South Dakota, and Tennessee and observe an analogous dilemma for the state policymakers in choosing between economic growth and sustainability. These empirical evidences prove the ability of the composite EKC model to serve policymakers in drafting aligned economic and energy policies at lower costs.

Although the Armey curve for the UK is inverted U-shaped, the EKC hypothesis is not verified by the composite EKC model because of its U-shaped form. Thus, H_1b is rejected for the case of the UK. The optimal level of government spending in the country, already calculated as 28.30%, also indicates the point that minimizes CO₂ emissions (see Fig. 2). Thus, there is no need for further government spending beyond this point, as it would both reduce growth and harm the environment. Isik et al. (2022) corroborate these findings in that some US states, namely Colorado, Georgia, and Indiana, have their optimal levels of spending that maximize economic growth and minimize CO₂ emissions. These results imply that the composite EKC model once again is able to provide policymakers an important decision-making tool in evaluating the consequences of additional spending.

Finally, the model results demonstrate that an increase in renewable energy consumption leads to a significant reduction in CO₂ emissions in almost all G7 countries. This is in parallel to previous studies suggesting a significant negative relationship between renewable energy consumption and CO₂ emissions in G7 countries (Raza and Shah 2018; Isik et al. 2020; Zhao et al. 2022). However, the impact of renewable energy consumption on economic growth is not consistent. For instance, renewable energy consumption appears to increase economic growth in Italy, the USA, and the UK, while it has a negative impact in France and Canada. While the literature also offers inconclusive results, the negativity, or at least weakness, in the relationship between renewable energy consumption and economic growth is G7 countries is more prominent (Behera and Mishra 2020; Okumus et al. 2021; Khan et al. 2022; Wang et al. 2022; Ghosh et al. 2022). This can be taken as evidence that renewable energy consumption, while clearly reducing environmental degradation, has not yet reached a point where it boosts economic growth in these countries. Moreover, certain limitations of renewable energy investments such as high upfront costs, geographical issues, and high storage capacity requirements may be leading to hesitancy for the economic agents in the industry (Khan et al. 2022).

Table 6 displays the shapes of the Armey curve, the EKC, and the composite EKC models in a nutshell.

Table 6 Summary of the findings regarding the empirical models

Before concluding, a robustness check is performed as a last resort by replacing CO₂ emissions with greenhouse gas emissions and ecological footprint as alternative indicators for environmental degradation. Greenhouse gas emissions are conceptually defined as the sum of emissions of various gases including CO₂ (EPA 2022). Ecological footprint, however, is a measure of the pressure that humans exert on the planet as a whole (FootprintNetwork 2022). Since these two indicators are more comprehensive than CO₂ emissions (Dada et al. 2022a, 2022b), they would give an idea about the applicability of the composite EKC model for G7 countries in broader settings. According to the results portrayed in Appendix, the significant relationships in the composite EKC model appear to gradually get lost. For instance, the USA remains the only country for the validation of the composite EKC model with greenhouse gas emissions, while none of the countries provide significant evidence when ecological footprint is considered though the majority of countries have expected coefficient signs. These findings indicate that government spending–induced EKC hypothesis cannot be verified with the current composite model for most of the G7 countries. However, the literature contains conflicting results for the traditional EKC hypothesis as well in the context of broadscale measures (i.e., greenhouse gas emissions or ecological footprint) of pollution. For instance, Wang et al. (2020), Nathaniel (2021) and Ghosh et al. (2022) argue that a standard EKC is empirically valid, while Yilanci and Ozgur (2019) and Pata and Yilanci (2020) fail to confirm the EKC hypothesis for the G7 countries. This is probably by virtue of the fact that the EKC hypothesis is very sensitive to the environmental degradation indicators under concern (Altintas and Kassouri 2020). Another explanation would be that it would take more time for the G7 governments to spend to have influence on various aspects of pollution through the growth channel. Consequently, having a focus on the CO₂ emissions would represent a good starting point for developing sound policies to mitigate environmental degradation.

Conclusion and policy implications

G7 countries have recently taken serious initiatives in support of long-term environmental goals, including their commitment to net-zero emissions of greenhouse gases by 2050 and emission reduction targets by 2030. However, all of these commitments require significant financial resources, especially from the government. In this context, it is extremely important to explore the role of government spending in achieving a more sustainable environment.

In this study, the EKC hypothesis for G7 countries is tested between 1971 and 2020, taking into account a possible transmission mechanism extending from the Armey curve hypothesis. The empirical methodology is based on the construction of a composite EKC model that allows determining the optimal level of government spending that minimizes or maximizes CO₂ emissions and provides information for policymakers to make appropriate economic and environmental policy decisions.

Various analyses on cross-sectional dependence and heterogeneity, panel unit root, panel co-integration, and augmented mean group estimation are performed. The results show that the government spending-economic growth (the Armey curve model) nexus can be used to explain the relationship between CO₂ emissions and economic growth (the composite EKC model) for the USA, the UK, and Canada. The EKC hypothesis, which is derived based on the Armey curve hypothesis, is valid for the USA and Canada. The optimal level of government spending that maximizes CO₂ emissions is calculated to be 29.87% and 29.22% of GDP per capita for the USA and Canada, respectively. On the other hand, despite the composite EKC hypothesis is not verified, this study finds the optimal level of government spending that minimizes CO₂ emissions in the UK as 28.30% of GDP per capita. On the other hand, the US consistently satisfies the empirical properties of the composite EKC model when the regressand is greenhouse gas emissions. However, the model seems not to provide statistically significant results for the estimation of maximum or minimum levels of ecological footprint among the G7 countries.

This being the case, the composite EKC model approach would offer important policy implications. First and foremost, it can help policymakers to take precautionary measures when setting harmonized growth and energy policies. The novel policy method introduced in this study has two facets: (1) it determines the threshold at which government spending maximizes economic growth; (2) a compatible energy policy can be formed based on that certain threshold. This integrated perspective provides an important clue for achieving the targets for reducing the pollution levels that countries must comply with within the framework of the Paris Agreement. By using the optimal government sizes as an auxiliary indicator for reducing CO₂ emissions, it would be possible to maximize economic growth through government spending and to pursue a corollary environmental policy. For this reason, the composite model enables policymakers to calculate the optimal level of government spending as a more environmentally friendly growth strategy proposal for countries. Another policy implication concerns model results, which show that the increase in renewable energy consumption leads to a significant reduction in CO₂ emissions in almost all G7 countries. It is inevitable for decision-makers to replace traditional energy with renewable energy for a sustainable environment. However, the relationship of this shift with other economic indicators (such as economic growth) at the beginning of the process can be investigated better with an overarching framework as the composite model suggests. Furthermore, the model sheds light on the relationship between renewable energy and growth. Although the literature is controversial, there are signs that this relationship is negative or weak in the G7 countries. Increasing the use of renewable energy at the expense of growth is far from the policy sets that countries will actually implement. However, understanding the nature of the process will guide policymakers. When countries are dedicated to replace the use of conventional energy with renewable energy, they may face high production costs and a decrease in energy efficiency in the short term, which may cause a slowdown in growth. Therefore, with a new agenda through the lens of government spending, the costs and production constraints in renewable energy can be mitigated in a way that supports growth from a holistic perspective. Last but not least, creating sub-categories for optimal government size would provide clearer results in the examination of the relationship between environmental sustainability and government spending. There are many classifications of government spending. The composite model can be adapted to other studies which investigate the relationship between any sub-classification of government spending and the EKC hypothesis. It is however important to note that not all government spending is equally efficient and their impacts on the economic environment can be very different.

One limitation of this study is that it uses the general level of government spending in the transmission between the Armey curve hypothesis and the EKC hypothesis. It would be more appropriate to consider a direct measure for government spending that is devoted specifically to environment protection. However, although the data for government spending to protect the environment are available for some countries, they are relatively new and only extend for a few years.²A second limitation is owing to the composite model itself at the center of this study. The mathematical reasoning inherent in the model may not be generalized to other occasions such as different countries or even other variables just as was the case for different pollutants in this study. Hence, it is highly recommended that the composite approach that this study argues should be kept under scrutiny and be augmented when necessary—if not required—in order to allow researchers annotate new information about the relationships among the variables of interest. A final limitation is that the relationships prevailing in both hypotheses may be time-varying. Particularly COVID-19 will lead to a severe structural break within the data so that the models should be revisited to handle the possible effects of the pandemic. These would be considered as topics for future research.

Appendix

Table 7 Augmented mean group estimator test results (greenhouse gas emissions)

7,

Table 8 Augmented mean group estimator test results (ecological footprint)

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Table 9 Summary of the findings regarding the empirical models

9.