Low-Carbon Innovation, Economic Growth and CO2 Emissions: Evidence From a Dynamic Spatial Panel Approach in China

5 Low-carbon innovation plays an essential role in carbon reduction worldwide. This study investigates how low-carbon 6 innovation affects carbon emissions by the Dynamic Spatial Durbin Model based on 30 Chinese provinces from 2007 to 7 2017. The empirical results show that: First, there exists provincial agglomeration of carbon emissions. High emission 8 provinces concentrate in major economic zones and energy extraction areas. Second, low-carbon innovation decreases 9 carbon emissions in general. The spillover effects are higher than the direct effects in the short run, but the spillover effects 10 are not significant in the long run. Third, the environmental Kuznets curve (EKC) hypothesis is valid both in the short- 11 run and long-run. Ninety percent of the provinces' GDP is above the inflection point by 2017. The summary of policy 12 implications is as follows. First, targeted incentives for R&D in low-carbon technologies are needed; Second, the 13 externalities of low-carbon innovation require attention; Third, energy transition need to be promoted as soon as possible.


Introduction 18
Since the Industrial Revolution, the concentration of atmospheric greenhouse gas (GHG) produced by fossil fuels and 19 biomass burning has caused global warming, widely recognized, leading to climate change (Atasoy, 2017). Therefore, it 20 became a consensus to slow down the carbon emission process. Several agreements had been signed (to slow down the 21 process), such as the Kyoto Protocol and the Paris Climate Agreement (PCA) 1 . Furthermore, carbon-neutral goals have 22 been proposed in countries worldwide. As the developing country with the most carbon emissions, China proposed the 23 30-60 target in 2020, suggesting peaking carbon emissions by 2030 and realizing carbon neutrality by 2060. The Chinese 24 government has advocated the circular economy and environmental regulations to achieve this milestone (Zhang et al., 25 2020). Technology innovations, such as knowledge externality, human capital, and Research and Development (R&D), 26 play an essential role in achieving carbon dioxide neutrality (Arrow, 1962;Lucas, 1988; Romer, 1990Romer, , 1986. 27 The nexus between innovations and carbon emissions got widespread attention ( carbon productivity more than general innovation does (Liu and Zhang, 2021). It is because low carbon innovation 43 provides a more direct measure than general innovation. However, the mechanism of how low-carbon innovation impacts 44 carbon emissions may be heterogeneous in different regions. 45 Environmental Kuznets Curve (EKC) suggested an inverted U-shaped relationship between environmental pollutions 46 and affluence (Bhattarai and Hammig, 2001;Grossman and Krueger, 1995;Stern, 2004 The contributions of this paper can be summarized into the following two aspects. First, we discussed the dynamic 61 relationship between low-carbon innovation and carbon emissions through DSDM. On the one hand, DSDM eliminates 62 the time inertia of carbon emissions, solving the problem of SDM overestimating the impact of low-carbon innovation.

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On the other hand, we measure the direct and spillover effect of explanatory variables both in the short and long term. 64 Second, we verified the EKC hypothesis under a dynamic framework. The results of this paper construct a new 65 understanding of the relationship between low-carbon innovations, economic growth, and carbon emissions for 66 policymakers, which has a positive meaning for carbon peaking and carbon neutral. 67 The rest of this paper is organized as follows. In the following section, we present the theoretical framework and data 68 used in this paper. Section 3 illustrates the empirical results and discussions. Section 4 summarizes and discusses the 69 empirical findings, then concludes with policy implications. 70 (2) Where is a constant term, , , and are the parameters to be estimated. is the logarithm of , the resid of the 80 estimation. 81

Spatial panel model 82
Moran Index 83 It is necessary to verify the spatial dependence before using spatial econometrics in our analysis (Anselin, 2013). 84 Moran Index (also called Moran's I) is widely used to measure global spatial autocorrelation (Anselin, 1995 (3) Where is the spatial weight matrix after row standardization, and is the residual of the OLS estimation. The value 88 of Moran`s is between -1 to 1; when the value of is higher than zero, there is a positive spatial correlation, showing a 89 "High-High" or "Low-Low" distribution state; the higher the Moran index, the stronger the positive autocorrelation. 90 However, a negative value of reflects a negative spatial correlation, showing a distribution of "High-Low" or "Low-91 High." When = 0, it indicates that there is no spatial correlation. 92 By decomposing the global Moran's I into the units of each province in China, the local spatial autocorrelation can be 93 obtained, as shown in equation (4), for province i: 94 Among them, the observation value is the weight matrix obtained after the standardized transformation = ( − 95 )/ , and the sum of each row of equals to one and is asymmetric. The Moran scatter plot is widely used to show the 96 local Moran index in order to determine the spatial agglomeration characteristics of specific provinces. 97 Spatial weight matrix 98 According to the previous econometric literature, the spatial weight matrix is used to capture the spillover effects 99 (Corrado and Fingleton, 2012; Lesage and Fischer, 2008). Different methods of making spatial weight matrics are 100 proposed in empirical research, including the binary weight matrix, the inverse distance weight matrix, and the economic-101 based weight matrix. This paper uses the inverse squared distance matrix for the basic model in section 3. The matrix is 102 constructed as follows: 103 Where is the element of the inverse squared distance matrix , a row-normalized spatial weight matrix, 104 representing the spatial structure of connections among provinces of China. is the geographical distance between the 105 province and .

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Model specification 107 Anselin adjusted the spatial weight matrix and its trace in the LM test formula for cross-sectional data to derive the 108 LM test suitable for the spatial panel. The test statistics are as follows: is proposed to solve the previous problem, and it is widely used to describe the relationship between economic growth 116 and convergence between countries or regions. This paper establishes the following spatial panel model to examine the 117 influencing factors and spatial spillover effects of low-carbon innovation on carbon emissions in 30 provinces of China. 118 The basic model is presented as follows: is the explained variable in period , and is the matrix of the explanatory variables. The parameters , , 121 and represent the corresponding parameters of the time lag effect, the spatial lag effect, and the time-spatial lag effect 122 of the explained variable, respectively. is the spatial weight matrix. 123 It is noteworthy that the estimated coefficients are biased in the Spatial Durbin Model (same as Dynamic Spatial 124 Durbin Model); thus, the model should be decomposed into direct and indirect effects to separate the marginal effects of (SIE); long-term direct effects (LDE), and long-term indirect effects (LIE) can be expressed as: where ̅ denotes the mean diagonal element of the spatial weight matrix, denotes an identify matrix, and ̅̅̅̅̅̅̅ 131 denotes the operator that calculates the mean row sum of the non-diagonal element. (In our situation, = 0.) 132 Variable selection and data source 133 A sample dataset for a panel of 30 provinces from 2007 to 2017 is utilized to investigate the nexus between low-134 carbon innovation and carbon emissions (Hongkong, Macaw, Taiwan, and Tibet are not considered due to data 135 unavailability). Notably, the purpose of this study is to address the concern about whether and how low-carbon innovation 136 affects carbon emissions in China; thus, the dependent variable in this paper is carbon emissions, which is estimated by 137 the consumption of fossil fuels derived from China's Energy Statistical Yearbook (2008-2018). The estimation method is 138 proposed by the IPCC (Intergovernmental Panel on Climate Change): 139 where is the th type of fossil fuel consumption, is the net calorific value of the th type of fossil fuel, and 140 represents the carbon content of the unit heating value of the types of energy. is the carbon oxidation rate of the 141 jth fossil fuel, and 44/12 is the ratio of the molecular weight of carbon dioxide to the carbon atom. 142 The other independent variables are illustrated as follows: 143 (1) Low-carbon innovation (denoted as LCI). As the core independent variable, low-carbon innovation plays an essential 144 part in our study. Green innovation refers to a series of innovation outputs (i.e., improved products, processes, and 145 technologies) for saving energy and reducing environmental pollution (

Empirical analysis 172
The procedures of the estimations mainly consist of three steps in this paper. (1) Analyzing the spatial characteristics 173 of carbon emissions across China; (2) Verifying the existence of spatial autocorrelation, including LM tests and LR tests; 174 (3) Examing the impact of low-carbon innovation and economic growth on carbon emissions based on the DSDM, 175 including the primary and effect decomposition models. the panel. Table 3 shows the results of the panel unit root test. We conclude that the variables are stationary. 220 Hausman test is also reported in Table 5. Since rejecting the null hypothesis at the 1% significant level, the fixed effects 239 model is used to conduct the research. 240 Model V is DSDM with both time-lagged and spatial-time-lagged dependent variables. 246 The Wald and LR test confirm the validity of the Spatial Durbin Model in our analysis, and the DSDM is better than 247 the SDM from the more significant coefficients in DSDM. Moreover, it can be seen that SDM overestimates the 248 coefficient of low-carbon innovation when comparing model II and model IV. However, the insignificance of the spatial-249 time-lagged coefficient allows us to exclude model V. Furthermore, the square term of GDP introduced in model III is 250 significant, proving that model IV is better than model III. It is reasonable to use model IV in our analysis. 251 The time-lagged coefficient ( ) is positive and significant, which shows inertia on carbon emissions, meaning that 252 carbon emissions in the previous period positively affect the current period. Furthermore, the spatial-lagged coefficient 253 ( ) is significantly positive, which indicates that neighbors' carbon emissions have a positive impact on local carbon 254 emissions. The time-lagged effect of carbon emissions is greater than the spatial-lagged effect, confirming that regional 255 carbon emissions are more internally influenced by carbon emissions from local. Although there is an external influence 256 of carbon emissions from neighbors, the influence effect is disproportionate to the internal effect. 257 Although the estimated coefficients before the effect decomposition are biased, it is still meaningful to observe the 258 sign of the estimated coefficients. Concerning the effect of low-carbon innovation on carbon emissions, log and 259 log show a significantly negative impact on CO2 emissions. It can be concluded that low-carbon innovations in 260 both local and neighboring regions reduce local carbon emissions. 261 Regarding the nexus between economic developments and carbon emissions, the signs of log and log 2 are 262 positive and negative, respectively, indicating an inverted U-shaped relationship between economic development and 263 carbon emissions, which confirms the EKC hypothesis. Likewise, the economic development of neighboring regions has 264 a similar inverted U-shaped impact on local carbon emissions. 265 Finally, the coefficients of the control variables indicate that there are positive effects of population density, industrial 266 structure, energy intensity, foreign direct investment, and energy structure on carbon emissions, and exogenous interaction 267 effects of these control variables on carbon emissions are also present. 268 Table 6 Estimation results of OLS model, SDM, and DSDM. 269

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The direct, indirect, and total effects in the short-term and long-term are reported in Table 7. Regarding our critical 271 explanatory variable, the SDE of low-carbon innovation is -0.146, and the SIE is -0.253. In the short term, low-carbon 272 innovations in local and neighboring regions have collectively reduced carbon emissions. However, the greater reduction 273 effect in neighboring regions leads to a potential "free-rider" phenomenon. Even though the local environment benefits 274 from low-carbon innovation, regional policymakers have an incentive to receive only the innovations spilled over from 275 their neighbors rather than invest in low-carbon R&D themselves. Note: ***, **, and * represent statistical significance at 1%, 5%, and 10% levels, respectively; the parentheses' values represent the t-statistics.

Conclusion and policy implications 290
Previous studies have examined the nexus between low-carbon innovation, economic development, and carbon 291 emissions. However, the understanding of the dynamic relationship remains unclear. This paper investigates the 292 relationship by the Dynamic Spatial Durbin Model based on thirty Chinese provinces from 2007 to 2017. The results can 293 be concluded as follows. 294 Our evidence-based results provide significant results for the role of low-carbon innovation in reducing carbon 295 emissions in developing countries. First, we confirm the provincial agglomeration of carbon emissions through the Moran 296 index, which was corroborated in several studies (Li and Li, 2020). The provinces with high emissions mainly concentrate 297 in major economic zones and energy extraction areas. 298 Second, we find that low-carbon innovation plays a vital role in carbon emissions reduction by DSDM. After the effect 299 decomposition, we find that the spillover effects of low-carbon innovation are larger than the direct effects in the short 300 run, and regions may have short-sighted incentives to "free-riding"; however, regions can only reduce carbon emissions 301 through local low-carbon innovation in the long run. attract investment from high-tech companies (Bildirici, 2021), and the emissions trading scheme (ETS) has been proved 313 an excellent climate policy based on the experience of seven independent regional pilots (Zhu et al., 2019). However, it 314 is urgent to continually construct the national carbon emissions trading market, especially to promote more industries to 315 participate in the market. 316 Second, the externalities of low-carbon innovation require attention. Encouraging low-carbon innovation entails high 317 administrative costs for local governments targeting carbon reduction. Even though local governments are under pressure 318 from the environmental assessment of the central government concerned, it may be difficult for local enterprises to receive 319 support from local governments regarding low-carbon innovation, especially in less developed provinces, due to the 320 financial constraints of local governments. Therefore, the central government needs to increase incentives for local 321 governments, such as establishing special funds. 322 Last, energy transition need to be promoted as soon as possible. Take Shanxi as an example. It is the largest carbon-323 emitting and the highest coal-extracting province. The 30-60 target indicates that this largest emitting province needs to 324 reduce its carbon emissions as soon as possible. On the one hand, the good news is that most provinces in China have 325 now crossed the inflection point of EKC, which means that more resources are available to invest in environmental 326 protection, especially in reducing carbon emissions. On the other hand, manufacturing development is driven by electricity, 327 and China is still dominated by thermal power generation. China is currently pushing for renewable energy such as 328 photovoltaics, but thermal power needs to fill the gap between electricity demand and renewable electricity in the 329 transitional period. Therefore, promoting energy transition is urgent for policymakers. Availability of data and materials All data are received from official source. 335

Declarations 336
Ethics approval and consent to participate This paper was not previously published in any journal. It is currently not 337 under consideration by another journal. Consent to participate is not applicable. 338 Consent for publication Not applicable 339 Competing interests The authors declare no competing interests. 340 Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-341 profit sectors. 342 Competing Interests The authors declare that they have no known competing financial interests or personal relationships 343 that could have appeared to influence the work reported in this paper. 344 Appendix: Robustness test 472 Table 8 shows the DSDM estimated by two different spatial weight matrics to confirm the robustness of the previous 473 results. The spatial weighting schemes include binary spatial weight matrix ( 2 ) and inverse economic-distance matrix 474 ( 3 ). The results estimated from different spatial weight matrices are consistent, especially in that the effects of low-475 carbon innovation and economic development on carbon emissions remain consistent in Model IV, model VI and Model 476 VII. Therefore, the robustness of the model has been verified. 477 Ta ble 8 Robustness test: changing spatial weight matrix 478 Notes: ***, **, and * represent statistical significance at 1%, 5%, and 10% levels, respectively.