Investigating the Role of Green Innovation in Economic Growth and Carbon Emissions Nexus for China: New Evidence Based on the PSTR Model

Abstract

In the context of climate change and high-quality economic growth, the penetration of green innovation is crucial for attaining sustainable economic development. However, the economic growth and carbon emissions nexus has not been fully investigated from the green innovation perspective. Using green innovation as the transition variable, this research employs the panel smooth transition regression model to examine the influence of economic growth on carbon emissions in 30 Chinese provinces over the period 2000–2019. The empirical results indicate that economic growth and carbon emissions have a substantially nonlinear nexus. The promoting influence of economic growth on carbon emissions is offset and even transformed into an inhibiting effect as green innovation degree rises; that is, green innovation alters the economic growth and carbon emissions nexus and plays a considerable part in carbon reduction for China. Additionally, the temporal variations analysis indicates that the positive nexus economic growth effect exerted on carbon emissions decreases gradually as time goes on. In terms of spatial variations, economic growth in the eastern area with higher levels of green innovation exerts the least positive impacts on carbon emissions. The research findings indicate that it is crucial for the Chinese government to lay down effective environmental protection policies to stimulate the enthusiasm of green innovation for social entities.

1. Introduction

Since the enforcement of the market-oriented reform and the opening-up in 1978, China has witnessed high-speed economic growth for more than 40 years, creating a growth miracle with a mean annual GDP growth rate of above 10%. However, the high-speed growth driven by extensive development is achieved at the expense of enormous fossil fuel use and CO₂ emissions [1]. The high levels of carbon emissions all over the world have led to a train of environmental issues, such as global warming, sea level rise and the El Niño phenomenon, which have been constantly threatening human habitation [2]. Meanwhile, the pursuit of high economic growth has long been a vital goal for all the countries in the world, especially for developing countries such as China. Therefore, reducing carbon emissions without sacrificing economic growth has evolved into a crucial issue that China and countries all around the world are concerned about [3]. For the sake of tackling the increasingly aggravated environmental pollution issues, the Chinese authorities have committed to carbon reduction and have formulated a carbon emission target schedule and a number of initiatives. In 2015, the Chinese authorities delivered the Intended Nationally Determined Contributions (INDCs), which proposed emission reduction targets, such as peaking greenhouse gas emissions in 2030. At the 2020 Climate Ambition Summit, China reiterated that carbon emissions in 2030 would be reduced by more than 65% compared with 2005. As the largest carbon emission country and the largest emerging economy, China is at an important period of accelerating industrialization and urbanization. It is anticipated that energy use and carbon emissions will continuously increase if the previous extensive growth pattern continues, and the pressure to reduce carbon emissions will also be strengthened. China is currently facing the enormous challenge of figuring out how to balance economic development and CO₂ emission reduction.

The economic growth and carbon emission nexus has always been a hot topic in the domain of energy and environmental economics. The famous Environmental Kuznets Curve (EKC) directly reflects the income and environmental degradation nexus [4] and has now become a popular tool to describe the economic growth and environmental pollution nexus. The EKC hypothesis holds that there is an inverted U-shaped curve between income and environmental degradation; that is, environmental pollution increases along with economic development during the initial stage of income, while after income reaches a certain threshold, the environmental contamination tends to improve with the economic development [5]. Lopez believed that environmental resources are a factor of production and that the improvement of environmental quality is caused by the substitution of production factors such as technology for environmental resource factors [6]. In the long term, for the purpose of effectively addressing the issue of environmental pollution, it is essential to rely on technological progress [7], particularly green technology-oriented innovation [8].

Facing the previous vicious circle of the environment and the economy, green innovation has become a powerful means and effective linker to reconcile economic expansion with environmental preservation [9]. Green innovation is innovation consisting of new processes and management that can offer consumers and businesses outpouring value and meanwhile can greatly mitigate the adverse effects on the environment during production [10]. Chen et al., (2006) and Kemp (2010) improved the notion of green innovation and proposed that green innovation could decrease expenditures of energy and environmental externalities in the production process through process transformation and technological upgrading [11,12]. Different from the traditional innovation, green innovation has the following unique characteristics [13]. First, green innovation’s primary purpose is to lessen the harmful influences of economic activities on the environment in order to accomplish the goal of sustainability; therefore, environmental benefits are the essential difference compared with other general innovation [14,15]. The role of green innovation in achieving low-carbon economic development and enhancing resource utilization has been thoroughly documented in the economic literature [16]. Second, green innovation exerts a favorable effect on economic expansion. By promoting resource recycling, green innovation realizes the transformation of the growth path from factor dependence to technology dependence, eliminates outdated production capacity, cultivates new kinetic energy, and gradually expands the breadth and depth of the social division of labor [17], which is beneficial to fundamentally changing the traditional extensive development mode, thus to promote the quality and efficiency of economic growth [18]. However, due to the huge investment capital and long cycle of green innovation, there exists the possibility of restricting the economy’s growth rate in a short period [19], and there may exist “threshold conditions” [20]. Third, in the long haul, under the trend of resource constraints and green development, green innovation is an inevitable choice [21]. Green innovation provides the possibility of creating economic growth and improving social welfare while utilizing fewer resources and preserving the environment, which is beneficial to truly decoupling the economy, resources, and the environment [22].

Empirically, the evidence for green innovation’s effects on economic growth and carbon emissions nexus has been strong. The relevant existing studies can be classified into two groups. The first is to examine how green innovation affects carbon emissions, while a consensus has not been reached. Some studies support the beneficial influence of green innovation in reducing CO₂ emissions [23,24], while some studies argue that the influence is not significant [25]. Within the EKC framework, the second group aims to explore the simultaneous impact of innovation and economic growth on CO₂ emissions. To the best of the authors’ knowledge, very few studies have focused on this topic; only two articles could be retrieved. On the basis of regional differences, Lamini et al., discussed how innovation and economic growth affect CO₂ emissions and concluded that innovation reduced CO₂ emissions in G6 and that the BRICS were the only countries where the EKC hypothesis held true [26]. Thong et al., argued that innovation contributed to carbon reduction in G20 countries but inhibited economic expansion, which confirmed the EKC’s existence [27]. To sum up, although some studies have concentrated on the influence of green innovation on economic growth or CO₂ emissions, a unified analytical framework has not yet been formed among green innovation, economic growth, and carbon emissions, and there are also no empirical studies focusing on the topic.

This research aims to take a different standpoint from previous studies to examine the impact of economic growth on carbon emissions by using nonlinear panel smooth transition regression (PSTR), which takes into account the importance of green innovation. The traditional research techniques used in previous related studies have the following limitations. First, most studies using panel data encounter the problem of cross-sectional heterogeneity and temporal instability, which lead to biased estimates. Second, the traditional nonlinear threshold approaches cannot capture the threshold level endogenously or a transition’s smoothness from the low regime to the high regime. To overcome the above econometric issues, we use the newly introduced PSTR model, which differs from previous studies in both theoretical and empirical design. The PSTR model is a regime-switching model with smooth transitions between different regimes, which allows for several regimes connected to the value of a transition function [28]. However, the technical difficulty of implementing the model and the complexity of the testing steps prevent it from being widely used.

The previous relevant studies most employ linear models to examine the nexus among green innovation, economic growth, and carbon emissions [23,24,25,26,27], all of which are predicated on the premise that the coefficients of the concerned variables are constant and do not change with other variables. However, the influence economic growth exerts on carbon emission is likely to vary with the magnitude of green innovation changes, which is corroborated by the inconsistency of linear empirical results [23,24,25]. Therefore, it is necessary to employ the nonlinear model to examine how economic growth affects carbon emissions. To the best of our knowledge, no research has employed the nonlinear PSTR model to investigate the dynamic impact of economic growth on carbon emissions when green innovation varies in China, and the possible contributions of this work are described as follows. First, the main stream of the existing research focuses on the direct correlation between economic growth and carbon emissions under the EKC framework; however, this research highlights the underlying mechanism by which the carbon reduction effect of economic growth may be strengthened with the improving of the green innovation. Hence, from a theoretical standpoint, our study aims to fill the gap by postulating green innovation as a transition variable to explore the possible decoupling mechanism when studying how economic growth affects carbon emissions.

Second, from the empirical point of view, our research aims to explore the nonlinear influence of economic growth on carbon emissions. This study uses the PSTR model, which takes into consideration the cross-sectional dependence of estimation coefficients and solves the issue of time instability, to explore the dynamic influence of economic growth on carbon emissions with the changing of green innovation [29]. Third, this study expands the literature by including green innovation, economic growth and carbon emissions in the same analytical framework and provides a reference value for exploring the economic growth—CO₂ emissions relationship from the standpoint of green innovation. Furthermore, the temporal and spatial variations of the influence economic growth exerting on the carbon emissions are examined, all of which provide valuable policy implications for China and other similar countries in carbon emission reduction.

The remainder of this research is listed as follows. The second portion reviews EKC’s related research and the nexus among green innovation, economic growth and carbon emissions. The model and data utilized in this article are presented in the third portion. The empirical findings of the research are reported and analyzed in the fourth portion. Lastly, the conclusions and policy proposals are elaborated.

2. Literature Review and Research Hypotheses

2.1. The Environmental Kuznets Curve

A bulk of research on the economic growth and environmental contamination nexus begins around the environmental Kuznets curve [4]. Scholars have empirically examined the EKC hypothesis using a variety of environmental indicators, including air pollutants (such as PM2.5 and nitrogen oxides, etc.), industrial waste (such as wastewater and solid waste, etc.), and other pollutants [30,31]. The influence of economic development on carbon emissions has been controversial for a long while. Galeotti and Lanza (2006), Arouri et al., (2012), Hamit-Haggar (2012), and Saboori et al., (2012) etc., confirmed an inverted U-shaped carbon emissions–economic growth nexus, demonstrating the EKC theory’s validity [32,33,34,35]. However, several studies discovered an N-shaped link between economic growth and carbon emissions [36,37], or even a linear relationship [38,39].

These contradictory findings involve a single nation or a collection of nations. In studies of one country, some studies demonstrated the validity of the EKC theory [40,41,42,43], while others denied the hypothesis of the EKC [44,45,46]. In studies with a group of countries, Shahbaz et al., (2014) and Apergis (2016) provided evidence for the EKC hypothesis [47,48], while some rejected the validity of the EKC [49,50]. Controversies arising from different studies have gradually drawn attention to the econometric methods used in the test of EKC hypothesis. The existing research on the EKC test is based on the premise that different countries are homogeneous [51]; that is to say, the factors affecting the environmental quality of different countries is convergent. However, this assumption is too harsh and does not correspond to economic reality in many cases because different countries exhibit great differences in many aspects, such as the level, speed, structure, and technical and policy background of economic development [52]. Therefore, some scholars concluded that looking at the historical experience of specific countries is a more effective way to assess the link between economic development and environmental quality [53].

The empirical literature of the Chinese EKC theory has not yet reached a consensus. Two categories of the related literature can be distinguished. The first group focuses on the existence of the EKC. Some researchers have confirmed the EKC hypothesis’s validity in China. Cheng et al., employed the dynamic spatial panel model to demonstrate the validity of the EKC hypothesis [54]. Dong et al., employed the Pedroni cointegration test and a fully modified ordinary least squares (SMOLS) to confirm the valid of the EKC [55]. Gokmenoglu et al., performed the ARDL and the VECM model to verify the EKC’s validity [56]. In contrast, some other studies have come up with the opposite conclusion. Using the cointegration analysis, Pao et al., discovered that the empirical findings could not verify the EKC theory [57]. Based on the extreme bound analysis (EBA) over the period 1995–2010 in 29 provinces, Yang et al., concluded that the EKC hypothesis was not supported [58]. He et al., used the STIRPAT model and indicated that the EKC is supported in China [59]. In addition, there also exist research conclusions showing that the EKC hypothesis is partially supported. Lin used the ridge regression method from 1978 to 2010 and found that the EKC could not be confirmed when only examining the influence of economic development on CO₂ emissions, while considering the influences of economic development, industrialization, and urbanization on CO₂ emissions, the EKC theory is tenable [60]. Chen et al., (2019) deduced that the inverted U-shaped link was only verified in the eastern area [61]. The second group has investigated the specific shape of the EKC curve. He and Zhang (2012) conducted the extended STIRPAT model and concluded that the CO₂ Kuznets curve of Chinese industrial sector presented an N-shaped trend [62]. Deng et al., (2014) found that carbon emissions trend was monotonically upward with economic development, not the inverted U-shape described by traditional EKC theory [63]. Utilizing nonparametric regression and threshold regression analysis, Zou (2015) confirmed an inverted N-shaped link between CO₂ emissions and income levels [64]. Yu et al., (2016) argued that Chinese carbon emission EKC was U-shaped and the future carbon emission trend was to continue to rise with the economic growth [52].

In brief, although a bulk of studies have concentrated on how economic growth affects environmental quality, the academic circle has not formed a doubtless conclusion, and the economic growth–environmental quality nexus is still worthy to be further investigated. Firstly, the previous relevant empirical research is limited to employing restricted functional forms, such as linear, quadratic, and cubic polynomial models. The more flexible nonlinear functional models may be more suitable to figure the economic growth–environmental quality nexus, but it is rarely investigated in previous studies. Secondly, most of the empirical methods employed in previous studies did not account for issues such as endogeneity, cross-region heterogeneity and temporal variability of the income-pollution links. Lastly, the findings on Chinese EKC theory of carbon emissions are inconclusive. The majority of previous studies have studied the EKC theory, but little emphasis has been given to the importance of green innovation between economic growth and carbon emissions. This research seeks to further expand the economic growth and carbon emissions nexus in the light of conventional EKC theory from the perspective of green innovation.

2.2. Green Innovation, Economic Growth and Carbon Emissions

Green innovation is a subset of technological innovation directly relating to the environment, which has received continuous attention since 2006 due to the increasingly severe environmental problems [65]. Green innovation is thought to generate double dividends for promoting the improvement of environmental quality when achieving economic growth [66]. Different from conventional innovation, green innovation attempts to improve resource efficiency and the effective reduction of pollution by adopting new technology and new ideas and obtains corresponding economic benefits [67]. In addition, green innovation aims to produce positive environmental advantages rather than only ease environmental concerns [68]. Therefore, green innovation is frequently considered a key tactic for creating sustainable competitive advantage [69].

Green process innovation and green product innovation are two kinds of the green innovation [70]. Clean production technology innovation and end treatment technology innovation are examples of green process innovation that seek to boost energy efficiency and reduce the creation of dangerous compounds and pollutant emissions by enhancing current production processes or creating new ones [71,72]. For the purpose of minimizing the damaging environmental effects of the complete product life cycle, green product innovation stresses the incorporation of environmental protection ideas into raw material selection, product design, and other links [73,74]. Although the two kinds of green innovation work in different ways, they both contribute to decreasing carbon emissions. Green innovation assists to reduce carbon emissions through the following several mechanisms. Firstly, green innovation decreases carbon emissions by saving energy. For one thing, utilizing alternative energy sources, improving processes, and recycling resources are all excellent ways for green process innovation to increase energy efficiency [75]. For another thing, green product innovation can lower the energy consumption during the use of the product and create a more complete recycling system by adopting environmentally friendly materials, thereby decreasing the negative influences of products on the environment during their entire life cycle [11]. Secondly, with the increasing agglomeration of relevant elements, especially the spatial agglomeration of human capital and physical capital, knowledge spillovers might be achieved. In via the spillover effect, the efficiency of regional green innovation can be improved, the upgrading of the industrial structure can be further prompted, and the ratio of the tertiary industry can be raised, which helps to lower the high carbon emissions brought by industrialization. Finally, green process innovation can provide possible methods for the end-of-pipe treatment of carbon emissions and lessen the pollutants emitted at the end of production.

To sum up, green innovation is not considered as a simple exogenous determinant of carbon emissions. Oppositely, it is designed as a moderate that affects economic growth and carbon emissions nexus; that is the influence economic growth exerts on carbon emissions depends upon the magnitude of green innovation. Accordingly, the following hypothesis is put forth:

Hypothesis 1. 

Green innovation is an internal mechanism that influences economic growth and carbon emissions nexus, and this impact has dynamic characteristics of threshold and gradual changes.

3. Data and Empirical Design

3.1. Data

Considering the availability of the data, the paper adopts the 30 Chinese provincial annual data covered from 2000 to 2019 to explore the nexuses among economic growth, carbon emissions, and green innovation. The data are collected from the China Energy Statistical Yearbook, 60 Years of New China Statistical Data Compilation, China Population and Employment Statistical Yearbook, China Statistical Yearbook, and Provincial Statistical Yearbooks. The variables used in this paper are described as follows:

(1) The explained variable: carbon emissions ($C{O}_2$). In China, carbon emissions are mostly produced by energy-related activities. Considering the carbon emissions data is not available from the statistical yearbooks, this paper follows the method of Chen (2009) to calculate carbon emissions according to the quantity of fuel burned and the default emission factor [76]. The specific calculation formula is as follows:

$$C{O}_2={\displaystyle \sum _n^{18}C{O}_{2,n}}={\displaystyle \sum _n^{18}{E}_n\times NC{V}_n\times CE{F}_n\times CO{F}_n\times \frac{44}{12}}$$

(1)

where $E_n$ denotes energy sources (The 18 energy sources consist of raw coal, cleaned coal, other washed coal, briquette, coke, coke oven gas, other gas, crude oil, gasoline, kerosene, diesel, fuel oil, liquefied petroleum gas, refinery dry gas, natural gas, other petroleum products, other coking products, and other energy sources) that directly contribute to carbon emissions. $NVC$ is the average low calorific value of each energy source, $CEF$ stands for the carbon emission coefficient, $COF$ refers to the carbon oxidation factor, the molecular weights of CO₂ and C are 44 and 12, respectively. The carbon emissions calculated in this research are consistent with the CO₂ data from Carbon Emission Accounts & Datasets (CEADs).

(2) The core explanatory variable: economic growth ($GDP$). Following most of the existing relevant literature, this paper also adopts per capita $GDP$ to represent each province’s economic growth (thousand yuan).

(3) The transition variable: green innovation ($GI$). Green innovation is a kind of technological innovation directly related to environmental quality. Following Fai and Wu, our research assesses the degree of green innovation by the quantity of green invention patent applications [77,78]. We identify green invention patents from the patent database by drawing on the environmental technical indicators provided by the Organization for Economic Co-operation and Development (OECD) and the green technology classification list provided by the World Intellectual Property Organization (WIPO).

(4) Control variables. Population ($POP$). Demographic factors affect greenhouse gas (GHG) emissions in terms of both total amount and speed [79], and population has been identified as the cause of the continued rise in carbon emissions [80]. The population density, which is expressed by the ratio of the total population to the area of each province, is utilized in this research to assess the impact of population [81].

Industrialization ($IND$). Industrial development needs a lot of fossil energy and leads to environmental contamination and degradation [82]. Thus, rapid industrialization may have a detrimental influence on the urban environment [83]. The industrialization is represented by the percentage of industrial added value to regional GDP [84].

Urbanization ($URB$). As Du et al., concluded, urbanization had two aspects of impact on CO₂ emissions [85]. On one side, the relatively concentrated urban population brings scale advantage in energy utilization, which is conducive to improving energy utilization efficiency (such as central heating, etc.). Further, urban residents use more low-carbon energy which will help curb carbon emissions. On the other side, urbanization brings about large-scale urban infrastructure construction, and the energy-intensive manufacturing and construction industries in the process of urban infrastructure construction may lead to more carbon emissions to the city. So this research employs the ratio of urban residents to the overall regional population as a proxy variable for the urbanization rate [86].

All the variables are transformed into their natural logarithms when constructing the PSTR model, in which case the parameters of the explanatory variable can be interpreted as elasticities in economics.

Table 1. Descriptive statistics of variables.

Variable	Obs.	Mean	Std. Dev.	Min.	Max.
$C{O}_2$	600	7.187	6.880	0.126	45.590
$GI$	600	2219.185	4817.761	1.000	33,523
$GDP$	600	34.317	27.280	2.645	164.212
$POP$	600	4.314	6.190	0.072	38.297
$IND$	600	45.530	8.140	16.157	61.478
$URB$	600	51.115	15.198	23.200	89.600

presents descriptive statistics for each variable. As can be observed, the standard deviations of carbon emissions, green innovation, economic growth, population, industrialization. and urbanization are 6.880, 4817.761, 27.280, 6.190, 8.140, and 15.198, respectively, which shows that green innovation has the highest standard deviation, indicating its relatively high volatility throughout the investigated period. In addition,

Table 2. Coefficients of the correlation matrix.

	LCO2	LGI	LGDP	LPOP	LIND	LURB
$LC{O}_2$	1.000
$LGI$	0.283 ***	1.000
$LGDP$	0.583 ***	0.814 ***	1.000
$LPOP$	−0.149 ***	0.511 ***	0.309 ***	1.000
$LIND$	0.229 ***	−0.123 **	−0.109 ***	−0.107 ***	1.000
$LURB$	0.465 ***	0.631 ***	0.842 ***	0.433 ***	−0.152 ***	1.000

Note: **, *** indicate significance at 5%, and 10% levels, respectively.

shows the correlation matrix for all the variables. As can be observed, economic growth and carbon emissions are positively correlated in a statistically meaningful way. However, the accurate economic growth-carbon emissions nexus under the influence of green innovation would be further investigated in the subsequent modeling analysis.

3.2. Empirical Design

The panel threshold regression (PTR) model is a simple model to examine the nonlinear nexus among variables [87]. The estimated parameters of PTR model abruptly switch between the regimes and each regime differs from others depending on the measured threshold value. However, for many economic phenomena, the transition of different mechanisms is not a discrete change but a continuous and gradual process. Thus, the regression parameters change not instantly but smoothly. Therefore, we employ PSTR model to conduct our research, which allows the estimated coefficients to move smoothly between regimes [29]. Further, the PSTR model provides a more flexible nonlinear functional form to investigate the dynamic impact of economic growth on carbon emissions with the level of green innovation changes. Specifically, in contrast to the traditional econometric models, the PSTR model possesses the following advantages. First, the estimation accuracy is probably improved, because the PSTR model concerns the cross-region heterogeneity and time instability. Moreover, as Gonzalez et al., concluded that it is beneficial to use the PSTR model when endogeneity and nonlinearity exists [29]. Lastly, it permits elasticities to change over time and between geographical regions. More accurately, the PSTR model permits the coefficients to move smoothly as the transition variable green innovation changes. Accordingly, we provide a straightforward parametric technique to detect both cross-section heterogeneity and time-varying in the economic growth-carbon emissions nexus. The PSTR model with multiple regimes is expressed as follows:

$$LC{O}_{2i,t}={\mu }_i+\beta LGD{P}_{i,t}+\theta X_{i,t}+{\displaystyle \sum _{j=1}^r({\beta }_j^{\prime }LGD{P}_{i,t}+{\theta }_j^{\prime }{X}_{i,t})\ast g_j(LG{I}_{i,t};{\gamma }_j,c_j)}+{\epsilon }_{i,t}$$

(2)

where $X_{i,t}$ is the vector of the control variables; ${\epsilon }_{i,t}$ refers to the error term and ${\mu }_i$ represents the fixed-effect factor; $i=1,2,\dots ,N$ stands for the quantity of provinces; $t=1,2,\dots ,T$ denotes the time periods. The transition function $g_j(LG{I}_{i,t};{\gamma }_j,c_j)$ is smoothly converted between 0 and 1 with the transition variable $LG{I}_{i,t}$ changes. Further, ${\gamma }_j$ is the slope parameter indicating how quickly a transition function changes between regimes and $c_j$ is the location parameter. It is assumed that the transition function usually takes a logistic function and is expressed as follows:

$$g_j(LG{I}_{i,t};{\gamma }_j,c_j)={\left.\left\{1+\exp \left[-{\gamma }_j{\prod }_{j=1}^m(LG{I}_{i,t}-c_j)\right]\right.\right\}}^{-1}$$

(3)

where ${\gamma }_j>0$, $c_1\le c_2\le \dots \le c_m$. $m_j$ is the quantity of location parameters, which is usually considered to be 1 or 2. For $m=1$, it is a two-regime model. When $\underset{LG{I}_{i,t}\to -\infty }{\lim }{g}_j(LG{I}_{i,t};{\gamma }_j,c_j)=0$, it is called the low regime. Oppositely, when $\underset{LG{I}_{i,t}\to +\infty }{\lim }{g}_j(LG{I}_{i,t};{\gamma }_{\mathrm{j}},c_j)=1$, it is the high regime. The coefficient of $LGD{P}_{i,t}$ in Model (2) smoothly transform between $\beta$ and $\beta +{\beta }^{\prime }$ with the change of the transition variable. For $m=2$, it is a three-regime model, and the values of the transition function change symmetrically around the midpoint $\frac{c_1+c_2}{2}$, where it achieves the minimum value. As the smoothness parameter ${\gamma }_j$ nears infinity, the transition function approaches the indicative function. In this instance, the PSTR model is converted into a PTR model. As the smoothness parameter ${\gamma }_j$ gets closer to 0, the transition function turns out to have a constant value, and the PSTR model is degraded into a linear fixed-effects model.

The analysis of the PSTR model is implemented in three steps: testing the linearity and figuring out how many transition functions there are ($\gamma$) and how many regimes they correspond to ($m$), model estimation. Testing for linearity is analyzed under the null hypothesis of ${\gamma }_j=0$ or ${\beta }_j^{\prime }={\theta }_j^{\prime }=0$. However, under the null hypothesis, the test cannot be carried out because of the unidentified parameters nested in the model. Hence, the first-order Taylor expansion around ${\gamma }_j=0$ is employed to replace the transition function $g_j(LG{I}_{i,t};{\gamma }_j,c_j)$, and the auxiliary regression model is expressed as follows:

$$LC{O}_{2i,t}={\mu }_i+{\beta }_0^{\prime *}{x}_{i,t}LG{I}_{i,t}+\dots +{\beta }_k^{\prime *}{x}_{i,t}{(LG{I}_{i,t})}^k+\theta X_{i,t}+{\epsilon }_{i,t}^{*}$$

(4)

where $x_{i,t}=[LGD{P}_{i,t},X_{i,t}]$, the parameters ${\beta }_0^{\prime *},\dots ,{\beta }_k^{\prime *}$ are the multiples for the slope parameters ${\gamma }_1$. ${\epsilon }_{i,t}^{*}={\epsilon }_{i,t}+R_k{\beta }_1^{*}{x}_{i,t}$, $R_k$ is the remaining part of the Taylor expression. Thus, testing the nonlinear economic growth–carbon emissions nexus under the influence of green innovation is equivalent to test $H_0^{*}:{\beta }_0^{\prime *}=\dots ={\beta }_k^{\prime *}=0$. Following Gonzalez et al., we employ $LM$, $L{M}_F$, and $LRT$ statistics to test the hypothesis:

$$LM=\frac{TN(SS{R}_0-SS{R}_1)}{SS{R}_0}$$

(5)

$$L{M}_F=\frac{(SS{R}_0-SS{R}_1)/mK}{SS{R}_1/(TN-N-mK)}$$

(6)

$$LRT=-2\log \frac{SS{R}_1}{SS{R}_0}$$

(7)

where $K$, $T$, and $N$ are the quantity of explanatory variables, years, and provinces, respectively. $SS{R}_0$ is the sum of squared residuals under the null hypothesis of $H_0^{*}$, and $SS{R}_1$ is the sum of squared residuals under the corresponding alternative hypothesis. The $LM$ and $LRT$ statistics have an approximate ${\chi }^2(mK)$ distribution, while $L{M}_F$ has an $F(mK,TN-N-mK)$ distribution.

Multiple regimes may be present in the model if the linearity test is rejected. Then the remaining nonlinearity test should be conducted to confirm the amount of transition functions. The null hypothesis, which denotes no remaining nonlinearity, can be defined as ${\gamma }_2=0$. The following definition applies to the PSTR model with two transition functions:

$$LC{O}_{2i,t}={\mu }_i+{\beta }_0^{\prime }{x}_{i,t}+{\beta }_1^{\prime }{x}_{i,t}{g}_1(LG{I}_{i,t},{\gamma }_1,c_1)+{\beta }_2^{\prime }{x}_{i,t}{g}_2(LG{I}_{i,t},{\gamma }_2,c_2)+{\epsilon }_{\mathrm{i},\mathrm{t}}$$

(8)

Likewise, the first-order Taylor expansion of Equation (8) around ${\gamma }_2=0$ is conducted and the auxiliary regression model is:

$$LC{O}_{2i,t}={\mu }_i+{\beta }_0^{\prime }{x}_{i,t}{g}_1(LG{I}_{i,t},{\gamma }_1,c_1)+{\beta }_{21}^{\prime *}{x}_{i,t}LG{I}_{i,t}+\dots +{\beta }_{2k}^{\prime *}{x}_{i,t}{(LG{I}_{i,t})}^k+{\epsilon }_{i,t}^{*}$$

(9)

Consequently, examining the null hypothesis $H_0:{\gamma }_2=0$ is the same as examining $H_0^{\prime }:{\beta }_{21}^{\prime *}=\dots ={\beta }_{2k}^{\prime *}=0$. The procedure involves contrasting the null hypothesis $H_0:r=r^{*}$ with the alternative hypothesis $H_1:r=r^{*}+1$ while considering a model with $r^{*}$ transition functions. If the null hypothesis is rejected, the new null hypothesis $H_0:r=r^{*}+1$ is examined against $H_1:r=r^{*}+2$. The process repeats until the null hypothesis is accepted. In the final stage, the nonlinear least squares method based on grid search is employed to estimate the model parameters.

Equation (10) is used to compute the elasticity coefficient of economic growth to carbon emissions for province $i$ at time $t$. The coefficients can be regarded as the weighted average of elasticity coefficients ${\beta }_j^{\prime }$ obtained from $\gamma +1$ transition regimes:

$$e_{i,t}=\frac{\partial LC{O}_{2i,t}}{\partial LGD{P}_{i,t}}=\beta +{\displaystyle \sum _{j=1}^{\gamma }{g}_j(LG{I}_{i,t},{\gamma }_j,c_j)}*{\beta }_j^{\prime }$$

(10)

4. Empirical Results

4.1. Model Construction

For the purpose of capturing the dynamic characteristics of the impact of economic growth on carbon emissions under the effect of green innovation, the one-lagged term of carbon emissions is incorporated into the model, which is expressed as follows:

$$\begin{array}{l}LC{O}_{2i,t}={\mu }_i+{\theta }_{0}LC{O}_{2i,t-1}+{\beta }_{0}LGD{P}_{i,t}+{\theta }_1{X}_{i,t}+\\ \hspace{1em}\hspace{1em}\hspace{1em}{\displaystyle \sum _{j=1}^r({\theta }_{0j}^{\prime }LC{O}_{2i,t-1}+{\beta }_{0j}^{\prime }LGD{P}_{i,t}+{\theta }_{1j}^{\prime }{X}_{i,t})*g_{\mathrm{j}}(LG{I}_{i,t};{\gamma }_j,c_j)}+{\epsilon }_{i,t}\end{array}$$

(11)

where $LC{O}_{2i,t}$ stands for the carbon emissions for province $i$ and year $t$. $LGD{P}_{i,t}$ refers to economic growth, which serves as the model’s main explanatory variable. $LG{I}_{it}$ denotes the transition variable green innovation. $X_{i,t}$ is the group of control variables, including population ($LPOP$), industrialization ($LIND$), and urbanization ($LURB$).

4.2. Panel Unit Root Tests

Before conducting the PSTR model, it is essential to examine whether the variables are stationary I(0). We employ LLC, IPS, and ADF panel unit root tests to check all the variables’ stationarity.

Table 3. Panel unit root tests.

Variables	LLC		IPS		ADF
	Statistics	p-Value	Statistics	p-Value	Statistics	p-Value
$LCO{ }_2$	−4.346	0.000 ***	−1.367	0.086 *	8.300	0.000 ***
$LGI$	−4.752	0.000 ***	−1.629	0.052 *	2.292	0.011 **
$LGDP$	−4.384	0.000 ***	−3.105	0.001 **	7.122	0.000 ***
$LPOP$	−2.805	0.003 **	−3.592	0.000 ***	15.747	0.000 ***
$LIND$	−2.086	0.019 **	−1.475	0.070 *	3.949	0.000 ***
$LURB$	−9.375	0.000 ***	−9.993	0.000 ***	6.221	0.000 ***

Note: *, **, *** indicate significance at 1%, 5%, and 10% levels, respectively.

presents the test. It can be observed that all variables are stationary, which indicates that we can use the natural logarithm of the original variables to construct the PSTR model.

4.3. Results of the Linearity Tests

As mentioned above, the existence of nonlinearity is the premise of conducting PSTR analysis.

Table 4. Linearity Test.

Transition Variables: LGI	Hypothesis	LM Statistics	LMF Statistics	LRT Statistics
$m$= 1	$H_0$: r = 0 vs. $H_1$: r ≥ 1	73.346 *** (0.000)	15.737 *** (0.000)	78.231 *** (0.000)
$m$= 2	$H_0$: r = 0 vs. $H_1$: r ≥ 1	106.615 *** (0.000)	12.101 *** (0.000)	117.384 *** (0.000)

Notes: *** denote significance at 1%.

lists the outcomes of the linearity test. The $LM$, $L{M}_F$, and $LRT$ tests’ results indicate that the linear null hypothesis is rejected at the 1% level of significance, indicating that the influence of economic growth on carbon emissions is following a non-linear model and the influence is not constant because of the transition effect of green innovation. As a result, the alternative hypothesis that there is at least one transition function is not rejected. Hence, it may be inferred that using linear models to analyze how economic growth affects carbon emissions is inappropriate. Appropriately, the relationship between the two variables should be further analyzed using the PSTR model. Considering that the linearity hypothesis is rejected, the remaining nonlinearity test must be conducted to confirm the quantity of transition functions.

4.4. Results of the Remaining Nonlinearity Tests

The outcomes of the remaining nonlinearity tests are displayed in

Table 5. Tests for the remaining nonlinearity.

Transition Variables: LGI	Hypothesis	LM Statistics	LMF Statistics	LRT Statistics
$m$ = 1	$H_0$: r = 1 vs. $H_1$: r = 2	4.620 (0.464)	0.861 (0.507)	4.638 (0.462)
$m$ = 2	$H_0$: r = 1 vs. $H_1$: r = 2	14.490 (0.152)	1.361 (0.195)	14.667 (0.145)

. It can be observed that the null hypothesis $H_0:r=1$ cannot be rejected both when $m=1$ and $m=2$, which indicates that we should select the PSTR model with $r=1$. Next, we choose the ideal quantity of location parameters in the following phase. In accordance with the results of the AIC and BIC reported in

Table 6. Determination of the number of location parameters.

Number of Location Parameters	AIC	BIC
$m$ = 1	−2.990	−2.902
$m$ = 2	−2.987	−2.891

, it is clear that $m=1$, $r=1$ performs better than $m=2$, $r=1$. Therefore, the PSTR model with $m=1$, $r=1$ is selected to monitor the dynamic influence of economic growth on carbon emissions with green innovation as the transition variable. Consequently, the model we established has one transition function (two regimes) and one location parameter. $m$$m$

4.5. Estimation Results of PSTR Model

To examine how economic growth influences carbon emissions and determine whether the influence varies according to the degree of green innovation in China, we use the PSTR model estimated by non-linear least squares techniques to carry out this study. Furthermore, the estimation results of the linear individual fixed-effects model are also presented so as to demonstrate the advantages of the PSTR model.

Table 7. PSTR model estimation results.

Variables	Nonlinear PSTR Model		Linear Panel Fixed-Effect Model
	Coefficients	T-Statistic	Coefficients	T-Statistic
The linear part
$LC{O}_{2,t}{}_{-1}$	−0.757 (0.784)	−0.965	0.719 *** (0.030)	24.235
$LGDP$	3.421 *** (1.307)	2.618	0.089 * (0.049)	1.812
$LPOP$	0.695 * (0.421)	1.652	0.266 (0.232)	1.148
$LIND$	3.380 (2.174)	1.555	0.462 *** (0.095)	4.881
$LURB$	−2.670 (1.905)	−1.402	0.252 (0.182)	1.385
The nonlinear part
$LC{O}_{2,t-1}$	1.732 ** (0.815)	2.125
$LGDP$	−3.628 ** (1.408)	−2.577
$LPOP$	0.135 (0.159)	0.848
$LIND$	−3.263 (2.205)	−1.480
$LURB$	3.501 (2.232)	1.569
Slopes parameter $\gamma$	0.625
Location parameter $c$	0.783
AIC	−2.990		0.101
BIC	−2.902
RSS	28.375		34.595

Notes: The values in parentheses are standard errors. (***), (**), (*) denote significance at 1%, 5% and 10%, respectively.

shows the corresponding results, it is obvious that both AIC and RSS statistics in the nonlinear PSTR model are much smaller than in the linear model, indicating that the nonlinear PSTR model outperforms the linear model. It is intriguing to note that the economic growth coefficients are significant both in the linear and nonlinear components of the PSTR model, showing that economic growth–carbon emissions nexus is nonlinear and is suitable to be characterized by the transition variable green innovation. The location parameter ($c$) is identified to 0.783, which indicates that when $LGI$ < 0.783, the model is in the low regime, while when $LGI$ > 0.783, the model is in the high regime. The slope parameter ($\gamma$) is very small and equals to 0.625, which shows that the influence economic growth exerting on carbon emissions switches from the low regime to the high regime with the improving of green innovation is not sudden but rather smooth. Figure 1 displays the figure of the transition function, it can be seen that the presence of continuous points between the two regions strongly suggests a smooth transition process across the entire sample.

First, we concentrate on the primary explanatory variable, economic growth. It is crucial to point out that the estimated coefficients of the PSTR model cannot be interpreted as the traditional linear model because of the nonlinear transition function in the model, and the estimated sign is important than the estimated values [29]. As can be observed, when green innovation is below the threshold value, that is in the low regime, economic growth has a significant positive impact on carbon emissions. In contrast, when the green innovation outstrips the threshold, that is in the high regime, the coefficient (defined as the sum of $\beta$ and ${\beta }^{\prime }$) is negative: −0.207. The hidden implication is that economic growth deteriorates the environment quality when green innovation is trapped in a low level, while the detrimental effect of economic growth on environment quality is offset and even changed into positive as green innovation increases. All of the above illustrates that the influence of economic growth on carbon emissions is nonlinear and varies with the magnitude of green innovation. The above findings confirm the hypothesis of this research that there is a regime-switching impact in the economic growth and carbon emissions nexus that depends on the threshold level of green innovation. Once green innovation surpasses the threshold, economic growth has a carbon emission reduction effect. The possible explanation is that the magnitude of green innovation determines the impact of the technology effect, the scale effect, and the composition effect of economic growth on carbon emissions. When the green innovation trapped in the low regime, low-level technological innovation is not enough to reverse environmental pollution and enable the “greening” of the industries, resulting in an inevitable rise in carbon emissions due to the growth of economic scale. Therefore, economic growth exerts a promoting effect on carbon emissions in the low green innovation regime. However, in the high regime, the level of green innovation is sufficient to reaping environmental benefits from economic development through the above three channels, thereby improving the environment quality.

The control variables also present some meaningful results. The empirical results are in accord with expectations and common sense. Specifically, the lag coefficients of carbon emissions are significantly positive in high regimes, indicating that carbon emissions are not only related to many influencing factors in the current period but also influenced by the previous period’s carbon emissions. The reason is possibly the inertia of economic development and the resource endowment of each province. For example, there is “inertia” in people’s life and production [88]; after they form the high-consumption habit, it is difficult to return to the previous “simple” life. As for the population variable, the results demonstrate that it greatly increases carbon emissions in the low regime, which is in accordance with Li et al., and Nan et al. [89,90]. The magnitude of green innovation is low in the low regime, and the increase in population density would bring about a crowding effect. That is, with the increase in population, people’s demands for food, shelter, and transportation also increase, resulting in a demand rise in energy use, which has a favorable influence on carbon emissions. However, the green innovation is in a higher level in the high regime, and the rise of carbon emission resulted by the augment of population density is offset by the carbon emission reduction effect induced by technological innovation, showing that population density has no influence on carbon emission. The industrialization and urbanization variables are not significant in either the high or the low regime, which indicates that industrialization and urbanization have no influence on carbon emissions, which aligns with the outcomes of Li et al. and Zhang et al. [89,91].

4.6. Temporal and Spatial Variations of Economic Growth Effects

Figure 2 depicts the average year elasticity of economic growth to carbon emissions for the whole sample from 2000 to 2019. It can be easily seen that the averaged elasticity values are always positive over the entire sample period, which demonstrates that economic growth continues to positively affect carbon emissions and that economic development has not yet attained the degree of income or green innovation required by the inflection point in EKC curve. It is also noteworthy that the average positive elasticity of economic growth to carbon emissions show a significant decreasing trend as time goes on, which indicates that the positive influence of economic growth on carbon emissions is gradually decreasing as time goes on. The possible explanation may be described as follows. On one side, the degree of green innovation is always increasing over time and the importance of green innovation in reducing carbon emission is ever-increasing. On the other side, as economic development levels rise through time, so does the public’s consciousness of protection of and attention to environmental issues. The combined impact of the above two aspects leads to the decline of the positive influence of economic growth on carbon emissions year by year.

Figure 3 summarizes the influences of economic development on carbon emissions in different areas in China. On the basis of China Statistical Yearbook, all the provinces are classified into eastern, central and western areas. It is remarkable that the elasticity coefficients of the eastern, central and western areas exhibit obvious echelon characteristics. The eastern area has the smallest average elasticity (0.827), the central area surpasses the eastern area and equals 1.062, while the western area has the largest average elasticity (1.273). The dominant reason for the above differences is the different levels of green innovation in the three areas. According to the original data of this study, the average level of green innovation in eastern area is 6.870, the central area is 5.992 and the western area is 5.292. As can be observed, the average value of green innovation in the eastern area is higher than in either the central or western areas, which lead to the lowest average elasticity coefficient in the eastern area. On the one hand, the innovation mechanism in the eastern area is comparatively well-developed, and the efficiency of the allocation of innovation resources is relatively high, which effectively stimulates the vitality of innovation. On the other hand, the eastern area provides a consummate institutional environment for green innovation, the strong awareness of green development, outstanding talent advantages and a high level of innovation input all provide important support for green innovation. In contrast, the western area is constrained by geographical location, economic development, talents and capital, which make the level of green innovation significantly lower than the eastern and central area and further leads to the largest gap in the average elasticity coefficient between the eastern and western areas. Separately, the agglomeration level of innovation elements in the western region is insufficient, which also results in the elasticity coefficient of the western area the highest.

Figure 4 shows the average elasticities of economic growth on carbon emissions for 30 provinces. Evidently, the elasticities show significant regional variation, ranging from 0.464 in Beijing to 1.917 in Qinghai. Specifically, the elasticities of Beijing, Guangxi and Guangdong are far below the other provinces and equal to 0.464, 0.543 and 0.557, respectively. The possible explanation is that the adaptability of green innovation to carbon emissions in various regions determines how economic growth influences carbon emissions. The better the regional green innovation ability, the greater the adaptability of green innovation [92]. The scientific and technological strength and R&D investment of Beijing are relatively strong. It actively promotes system reform and financial support and has built a series of platforms that are conducive to innovation, including innovation industrial parks and technology innovation centers. Therefore, its green innovation ability is more prominent. As an ecological barrier in the eastern region, Guangxi undertakes the responsibility of protecting the ecological security of Guangdong, Hong Kong and Macao and has made many efforts in promoting green innovation to cope with climate change. Because of the benefits of policy reform and opening up and its geographical proximity to Hong Kong, Guangdong’s economic development is relatively fast, so it has the ability and financial resources to develop green innovation. In addition, as the national center of technological innovation, Shenzhen has made important contributions to Guangdong’s green innovation. On the contrary, Qinghai has the highest elasticity coefficient (1.917). On one side, the resource endowment dominated by fossil energy has led to the chronic extensive expansion of Qinghai’s economy, and the local authority does not attach importance to green innovation. On the other side, its economic growth is comparatively lagging, there is not sufficient funds to develop green innovation, so the spending in R&D is low, both of which lead to the lowest degree of green innovation in Qinghai, exhibiting the highest elasticity coefficient.

5. Conclusions and Policy Implications

The decision to prioritize either economic expansion or environmental preservation has always been an important issue perplexing human development. Green innovation is introduced as a powerful tool for striving to achieve economic prosperity and environmental modification in harmony. In this setting, existing research has paid scant attention to the crucial part that green innovation plays in the economic growth and carbon emissions nexus. Using green innovation as the transition variable, our research uses the PSTR model to examine the influences of economic growth on carbon emissions in 30 Chinese provinces between 2000 and 2019. The following are the main empirical conclusions: (1) The pattern of carbon emissions is in keeping with a nonlinear PSTR model with green innovation as a transition variable exerting an influence on the economic growth–carbon emissions nexus. The result validates our hypothesis in which we assume the threshold value of green innovation (0.783) drives a regime switching effect of economic growth on carbon emissions. In addition, the outcomes support that green innovation benefits low-carbon development and helps to fight global warming. (2) To limit the error brought on by omitted variables, a set of control variables is included in our research, including population, industrialization and urbanization. Population exerts a favorable influence on carbon emissions under the low regime. (3) This research also analyzes temporal and spatial variations in the influences economic growth exerts on the carbon emissions. In terms of time dynamics, the favorable influence of economic growth on carbon emissions has diminished as time goes by due to the role of green innovations and increased public awareness of environmental protection. Separately, economic growth in the eastern areas exerts less impact on carbon emissions than other areas due to its higher level of green innovation. Regarding specific provinces, economic growth exerts a minor influence on carbon emissions especially in the provinces with stronger green innovation ability, such as Beijing, Guangxi and Guangdong, while economic growth exerts the greatest influence on carbon emissions in Qinghai with the lowest level of green innovation. (4) Furthermore, it is important to compare the results above with similar studies on other countries. For instance, the empirical evidence suggests that innovation exerts a favorable long-term impact on economic growth and carbon emissions in the US, EU-15 and China [93], and the level of technology innovation has not yet assisted BRICS nations decouple economic growth from carbon emissions, but it does contribute to reducing carbon emissions [94]. Additionally, spending on innovation will decrease carbon emissions in selected G-20 countries, which will enhance the environment quality [27].

In consideration of the relevant conclusions obtained above, the following policy recommendations are proposed: First, it is essential to strengthen the supply and support of green innovation. Green innovation is crucial for striking a balance between environmental preservation and economic prosperity. On the one hand, using the market competition mechanism to encourage the growth of green innovation and improve the efficiency of green technology transfer and transformation. On the other hand, the government should facilitate green innovation through financial, policy and platform support. Encourage green product R&D by increasing green innovation investment and subsidies supported by fiscal and financial policies. Cultivate green innovative talents and improve the scientific research incentive mechanism and green innovation base platform construction. Second, publicize the concept of “low-carbon city” and carry out reasonable population distribution planning. On one side, accelerate the transformation of residents’ consumption patterns and lead low-carbon development with green consumption. On the other side, improve the urban infrastructure while ensuring that the population density is close to the optimal value to avoid resource and environmental pollution caused by the crowding effect. Finally, strengthen the regional collaborative governance of green innovation to address climate change. In order to address the issue of uncoordinated technological innovation in various areas, the eastern area should fully exploit its innovation resources and encourage the rational expansion and movement of associated technologies, capital and businesses to the central and western areas. The central and western areas should also fully utilize the enormous market advantages of environmental improvement and vigorously pursue the movement of innovation resources in the eastern. In addition, to broaden the green industry chain, strengthen the diffusion and configuration of green industries in the three areas. Moreover, the government should encourage and promote green innovation policies that address the area’s development needs because each province has diverse resource endowments and economic conditions.

Nevertheless, this study has a few limitations that need further investigations. First, from an empirical point of view, the PSTR model developed in this research does not test the EKC hypothesis, future research can further refine the model to test whether it holds true or whether the inflection point changes under different regimes. Second, the current research concentrates on the important role of green innovation in economic growth and carbon emission nexus in China, future studies should conduct the research on the global level in order to obtain more interesting findings.