Introduction

It is generally believed that the excessive emission of greenhouse gases has led to global warming worldwide. The unreasonable use of energy by human beings results in the release of a large number of greenhouse gases, such as carbon dioxide, to enter the atmosphere, which leads to the warming of the earth and destroys the normal process of the carbon cycle (Bauer et al. 2016; Shen 2017). Climate change characterized by global warming has become an international environmental issue of great concern. Countries have gradually attached importance to the development of a low-carbon economy, and China is also actively exploring the specific path to realize the development of a low-carbon economy (Zhang et al. 2022). China’s total carbon emissions account for approximately 25% of global carbon emissions. As the world’s largest carbon emitter, China’s progress in carbon emission intensity still cannot offset the increase in total carbon emissions caused by economic growth and energy consumption. The contradiction between economic growth and carbon emission reduction is prominent (Xiao et al. 2022). China has promised that its carbon emissions would peak by 2030 and that it would achieve carbon neutrality by 2060.

The combustion of fossil energy is the main source of carbon dioxide emissions. Although countries all over the world pursue low-carbon development, energy demand is increasing at the same time. The green and low-carbon development of the energy industry is the top priority of carbon emission reduction (He and Zhang 2022). Promoting the energy consumption revolution, optimizing the energy investment structure and consumption structure, and reducing energy intensity are powerful starting points for “carbon peaking and carbon neutralization” (Du et al. 2022). As the world’s largest energy consumer and carbon dioxide emitter, China has always regarded controlling total energy consumption, optimizing energy investment structure and consumption structure, and reducing energy intensity as important ways to address climate change and ensure energy security (Wang et al. 2022a). Over the past 40 years of reform and opening up, China’s total energy consumption has been growing rapidly, but the energy intensity has been declining in most years (Wang et al. 2020a). Although China’s gross domestic product (GDP) ranks second in the world, its energy consumption and imports have surpassed those of the USA to become the first in the world; The problems of an energy shortages, environmental pollution, and ecological destruction are becoming increasingly prominent under rapid economic growth (Khan et al. 2020; Mahadevan and Sun 2020). China’s energy consumption structure is dominated by coal, which is the largest greenhouse gas emitter in the world. It is facing great pressure for carbon emission reduction and ecological protection (Wang and Gong 2020).

China has a vast territory, and there are huge differences in economic development and resource endowments in various regions, which makes carbon emissions not only show the characteristics of a large total amount, but also show the characteristics of spatial heterogeneity, and there are great differences in different regions (Xuan et al. 2020). The COVID-19 epidemic in recent years has also had a profound impact on global carbon emissions and environmental governance (Wang and Su 2020). To achieve this carbon emission reduction target, we must start from the actual economic development of each province and consider factors such as resource endowment, industrial structure, economic development level, industrial energy consumption intensity, and urbanization level among provinces (Huang et al. 2020; Ma et al. 2020). At the same time, we should also consider the spatial correlation of carbon emissions among provinces. The closer the spatial distance is, the closer the material and information exchange between different regions. When formulating carbon emission reduction policies, we should pay attention to the spatial correlation of carbon emissions to formulate scientific and reasonable carbon emission reduction policies and measures.

Given this, it is of practical importance to analyse and evaluate the regional carbon emissions in China, the spatial nature, and the spatial role of the influencing factors. The main contributions of this paper are as follows. First, this paper analyses the pathways of energy intensity, total energy investment, energy investment, and consumption structure on carbon emissions and explores how and in what way each variable affects carbon emissions. Second, this paper explores how carbon emissions are distributed in space and the dynamic characteristics of each region and verifies that carbon emissions do vary spatially. Again, from a dynamic perspective, this paper takes into account regional differences and spatial linkage characteristics, as well as the dynamic evolution of carbon emission efficiency in each province, explores the key factors influencing interprovincial carbon emission efficiency, and explores the effect of each influencing factor on carbon emissions in each province of China from a spatial and temporal perspective through a dynamic spatial Durbin model. Finally, based on the empirical study, this paper provides emission reduction strategies from the perspective of regional cooperation, which can provide theoretical support for relevant organizations to formulate policies on energy, the environment, and carbon emission reduction.

The rest of this paper is organized as follows. The “Literature review” section is the literature review. The “Data selection and model construction” section presents the data selection and model construction. The “Empirical analysis and discussion” section presents the empirical analysis and discussion. In the “Conclusion and policy implications” section, the paper is summarized, and suggestions for low-carbon development are put forwards.

Literature review

At the macro-level, there are usually three main ways to reduce carbon emissions: scale effects, technology effects, and structural effects. Among these, structure and technology are the most dominant pathways to reducing emissions.

Many scholars have mostly affirmed the impact of energy intensity on carbon emissions (Fan and Lei 2017; Gao et al. 2021). Liu et al. (2021) investigated the interprovincial transportation carbon emissions in China through an extended STIRPAT and spatiotemporal geographically weighted model and found that there are geographical differences in the effects of energy structure, industrial structure, population size, and urbanization on carbon emissions from the transportation sector, with energy intensity dominating all drivers. Quan et al. (2020) analysed the influencing factors of carbon emissions through the logarithmic mean Divisia index (LMDI) model based on panel data of China from 2000 to 2016, and the results showed that the most important influencing factors are economic growth and energy intensity and that other factors, such as population, are less influential. After examining data from 147 countries for four income groups, Li et al. (2021) found that, for all income groups, increases in energy intensity promote increases in carbon emissions.

Although reducing energy intensity can promote carbon emission reduction, the reduction of energy intensity is highly dependent on technology and difficult to achieve in a short period, so it is especially important to optimize the energy investment structure and consumption structure. The development of renewable energy promotes economic growth, has a beneficial impact on the environment and is very beneficial for reducing carbon emissions (Li et al. 2022b; Wang et al. 2022b).

Many scholars’ studies have shown that optimizing the energy structure is an effective way to achieve carbon emission reduction Sun and Ren (2021) analysed data from 1985 to 2016 in China by building an autoregressive distribution lag model (ARDL) and found that the optimization of the energy consumption structure can slow the increase in carbon emissions. Lin and Agyeman (2019) found that the main driver of the increase in Ghana’s carbon emissions was a shift in energy consumption from biofuels to fossil fuels. The reform of the energy consumption structure can achieve significant carbon reduction. Some scholars have also discussed the regional differences in the relationship between energy structure and carbon emissions. For example, Li et al. (2018) used geographically weighted regression (GWR) to study how to optimize the energy price policy to reduce regional carbon emissions. The results showed that the energy structure had been improving in economically developed or energy shortage regions. In addition relatively less developed or energy-rich areas have been deteriorating. The magnitude of energy efficiency is different, and the improvement of energy efficiency has different effects on carbon emissions (Li et al. 2022a).

The analysis above shows that improvement in the energy mix is an important pathway for carbon reduction (Zhou and Xu 2022), in the form of reducing the share of coal, oil, and natural gas consumed and increasing the share of low-carbon energy such as wind. Increasing energy investment, on the one hand, can increase investment in energy technology research and development, improve energy efficiency, reduce energy intensity, and promote carbon emission reduction (Mazzaferro et al. 2020). On the other hand, the energy investment structure can be adjusted to vigorously invest in the development of renewable energy such as solar energy, wind energy, and geothermal energy, in order to promote the consumption of low-carbon energy and effectively optimize the energy consumption structure (Pramanik et al. 2019).

Guo et al. (2021) investigated the impact of green innovation investment in China’s provincial-level energy sector from 1995 to 2017 and found that China was able to curb carbon emissions and slow environmental degradation by shifting investment towards green innovation and the economy towards sustainable energy. He et al. (2021) found that R&D investments can contribute to energy efficiency improvements and energy intensity reductions and thus achieve carbon reduction targets in the industrial sector as soon as possible. Rodgers (2021) uses statistical methods to study the optimal investment plan of renewable energy supporting energy independence and an emission reduction strategy, and the results show that targeted investment in renewable energy research and the development of higher education structures can effectively achieve the goal of carbon emission reduction. Ma et al. (2021) argue that increased energy investments can not only contribute directly to carbon reduction but also have an indirect effect through renewable energy channels and technological advances. Structural changes in trade, energy, economy, and society will have a profound impact on carbon emissions (Li et al. 2021).

In general, most scholars have focused on the impact of the energy mix on carbon emissions, emphasizing the importance of developing and utilizing renewable energy (Xia et al. 2021; Zeng et al. 2021), but there are still some shortcomings in the studies, including the relationship between energy consumption and carbon emissions being mostly studied from the perspective of energy consumption, and fewer studies have been conducted on carbon emissions from the perspective of energy investment. The few studies that have been conducted focus more on total energy investment (Zhu and Zhang 2021) and less on the structure of energy investment; the impact of renewable energy use on carbon emissions is mainly analysed from the policy level, and there is a lack of empirical analysis; most existing studies ignore the spatial factor (Wang et al. 2020b) and the traditional nonspatial regression method The traditional nonspatial regression methods may lead to errors. At the same time, carbon emissions are spatially and temporally dependent, and the spatial and temporal effects cannot be ignored. Therefore, this paper uses a dynamic spatial Durbin model to investigate the impact of total energy investment and structure on carbon emissions. Therefore, this paper can provide some references for research in related fields.

Data selection and model construction

Variable selection and data sources

China’s economic development has been transformed from the high-speed growth stage to the high-quality development stage. At present, how China regulates the urgent relationship between the environment, resources, and economic development under the premise of achieving high-quality economic growth, accelerating low-carbon economic transformation, and improving provincial carbon emission efficiency has become an important issue of concern for many economists. Among the provinces in China, due to their resource endowment, economic development level, ecological environment protection, and so on, various aspects of huge differences in the environment affect the ability to meet people’s increasing demand at the same time and must also take into account provincial differences, as well as considering ways that the spatial linkage between adjacent provinces may also have a good driving effect on each other, promoting the efficiency of carbon emissions, the scientific measurement of provincial carbon emissions, the discovery of key influencing factors and dynamic evolution characteristics, and the provision of a referenceable analytical basis for the formulation of scientific emission reduction policies. This topic takes 2005–2017 as the sample research period and 30 provinces in China as the research sample, and Tibet, Hong Kong, Macao, and Taiwan are not included in the scope of this paper due to a large number of missing statistics.

The explained variable selected in this paper is carbon emissions (C), and the explanatory variables are population size (P), urbanization (U), economic development level (GDPPC), industrial structure (IS), and energy use and investment status indicators, which are represented by four indicators in this paper: energy intensity (E), energy industry investment (EI), energy consumption structure (ES), and energy industry investment structure (EIS). The data used are from the China Energy Statistical Yearbook and China Statistical Yearbook Fig. 1.

Fig. 1
figure 1

Spatial distribution of provincial carbon emissions in China

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Construction of the spatial econometric model

  • (1) Spatial correlation analysis of carbon emission levels

Spatial correlation is used to measure the degree of data aggregation in space, show the distribution and interaction of spatial data, and is also the basis of constructing the spatial econometric model. Two main tools are used to determine spatial correlation: one is a global correlation, often using Moran’s I index, which analyses the overall distribution state of spatial data; the other is a local spatial correlation, often using Moran’s scatter plot test, which measures the local area.

To determine whether there is regional correlation and spatial dependence of data in space, the global Moran index is often used:

$$I=\frac{\sum_{i=1}^{n}\sum_{j=1}^{n}{W}_{ij}({Y}_{i}-\overline{Y })({Y}_{j}-\overline{Y })}{{S}^{2}\sum_{i=1}^{n}\sum_{j=1}^{n}{W}_{ij}}$$
(1)

where Yi denotes the observed value of the ith province, n denotes the total number of observed provinces, Wij is the weight matrix after normalization, and \(\overline{Y }\) and S2 represent the mean and variance, respectively. The calculated Moran’s I index takes values between − 1 and 1. When it is negative, it indicates the existence of a negative spatial correlation between different regional variables; when it is positive, there is a positive spatial correlation; 0 indicates the absence of a spatial relationship.

Local spatial correlation can analyse the relationship between the indicator variables of a province and neighbouring provinces and detect spatial differences caused by spatial correlation to compensate for the lack of global spatial correlation. To understand the local spatial agglomeration, the local Moran’s I index can be used to perform the local spatial correlation test. The calculation formula is:

$${I}_{i}=\frac{({Y}_{i}-\overline{Y })}{{S}^{2}}\sum\nolimits_{j=1}^{n}{W}_{ij}({Y}_{j}-\overline{Y })$$
(2)

A positive Ii indicates that regions with similar values cluster together, i.e. regions with high (low) values are surrounded by adjacent regions with high (low) values; a negative Ii indicates that regions with dissimilar attribute values cluster together, i.e. regions with low (high) values are surrounded by adjacent regions with high (low) values. The Moran scatter diagram is drawn according to the measured “local Moran’s I”. The abscissa is the current observation value of each region, and the ordinate is the spatial lag value. It is divided into four quadrants: high value adjacent to a high value (H–H), low value adjacent to a high value (L–H), low value adjacent to a low value (L-L), and high value adjacent to a low value (H–L).

  • (2) Model setting

When constructing a spatial panel model, it is necessary to determine the dependent variable, independent variables, and random errors, which term should be introduced as the spatial lag term. Therefore, performing correlation tests and selecting an appropriate spatial panel model are important steps in our model analysis. The basic steps of spatial panel model selection are as follows: first, LM tests the panel model; second, the types of models.

Panel data have the advantage of being able to carry out the modelling of the dynamic behaviour of the individual. Most economic theory states that the current status of the individual is not only affected by the existing environment but will also be affected by the environment at the same time; therefore, the dynamic panel model in the lag of dependent and independent variables to add items reflects the dynamic effect of the dependent variable. According to the STIRPAT model and the variables determined above, the basic econometric model constructed is shown in Eq. (3).

$$\mathrm{lnCE}={\beta }_{0}+{\beta }_{1}\mathrm{lnE}+{\beta }_{2}\mathrm{lnEI}+{\beta }_{3}\mathrm{lnES}+{\beta }_{4}\mathrm{lnEIS}+{\beta }_{5}\mathrm{lnP}+{\beta }_{6}\mathrm{lnU}+{\beta }_{7}\mathrm{lnGDPPC}+{\beta }_{8}\mathrm{lnIS}+\upvarepsilon$$
(3)

where β0 is a constant, βi is the coefficient of the independent variable, and ε is the random error.

Because of the spatial correlation of provincial carbon emissions, this paper uses spatial panel models to study the effects of energy investment, energy consumption, and energy consumption structure on carbon emissions. Compared with previous studies, this paper considers the impact of time lag, space lag, and time lag on current regional carbon emissions, so we choose a dynamic spatial measurement model. There are many kinds of spatial panel models, and the spatial econometric models based on spatial dependence are the dynamic spatial lag model (DSLM), dynamic spatial error model (DSEM), and dynamic spatial Durbin model (DSDM). The three models have different emphases and economic connotations. The DSLM model contains the spatial lag term of the explained variable, which will directly act on the explained variable through the spatial transmission mechanism, focusing on the spatial spillover effect of the explained variable. The DSEM contains the spatial lag term of the error term, which will produce a spatial interaction effect, focusing on the spatial dependence caused by the omission of variables. The DSDM takes into account the spatial dependence of explained variables and explanatory variables as well as the spatial spillover effects of random shocks at the same time; that is, the spatial dependence effects may come from the endogenous and exogenous interaction effects between regions and the autocorrelation of error terms, which integrates the advantages of DSEM and DSLM.

The DSDM model can be expressed as Eq. (4), which can be simplified to DSLM or DSEM under certain conditions.

$${\mathrm{lnCE}}_{it}={\beta }_{0}+\mathrm{\alpha ln}{CE}_{i,t-1}+\mathrm{\rho Wln}{CE}_{it}+{\beta }_{1}\mathrm{ln}{EC}_{it}+{\beta }_{2}\mathrm{ln}{EI}_{it}+{\beta }_{3}\mathrm{ln}{ES}_{it}+{\beta }_{4}\mathrm{ln}{EIS}_{it}+{\beta }_{5}\mathrm{ln}{P}_{it}+{\beta }_{6}\mathrm{ln}{U}_{it}+{\beta }_{7}\mathrm{ln}{GDPPC}_{it}+{\beta }_{8}\mathrm{ln}{IS}_{it}+{\theta }_{1}\mathrm{Wln}{EC}_{it}+{\theta }_{2}\mathrm{Wln}{EI}_{it}+{\theta }_{3}\mathrm{Wln}{ES}_{it}+{\theta }_{4}\mathrm{Wln}{EIS}_{it}+{\theta }_{5}\mathrm{Wln}{P}_{it}+{\theta }_{6}\mathrm{Wln}{U}_{it}+{\theta }_{7}\mathrm{Wln}{GDPPC}_{it}+{\theta }_{8}\mathrm{Wln}{IS}_{it}+{\varepsilon }_{it}$$
(4)

where εit denotes the spatial error term, ρ represents the spatial autoregressive coefficient, β0 is the intercept term, W denotes the spatial weight matrix, i = 1, 2,…, N (N = 30) denotes the 30 Chinese provinces under study, t = 1, 2,…, T (T = 13) denotes the year under study, and βi is the coefficient before θi is a variable.

The partial derivative of the expected value of the dependent variable for the kth unit in the model yields the following equation for the spatial effect.

$$\mathrm{SDE}={[{\left(1-\rho W\right)}^{-1}({\beta }_{k}{I}_{N}+{\theta }_{k}W)]}^{\overline{d} }$$
(5)
$$\mathrm{SIE}={[{\left(1-\rho W\right)}^{-1}({\beta }_{k}{I}_{N}+{\theta }_{k}W)]}^{\overline{rsum} }$$
(6)
$$\mathrm{LDE}={[{\left(\left(1-\alpha \right)I-\rho W\right)}^{-1}({\beta }_{k}{I}_{N}+{\theta }_{k}W)]}^{\overline{\overline{d}}}$$
(7)
$$\mathrm{LDE}={[{\left(\left(1-\alpha \right)I-\rho W\right)}^{-1}({\beta }_{k}{I}_{N}+{\theta }_{k}W)]}^{\overline{\overline{rsum}}}$$
(8)

\(\overline{d }\) is the mean value of the diagonal elements in a matrix. \(\overline{rsum }\) is the row and average value of off-diagonal elements in a matrix. Other variables have the same meanings as above.

  • (3) Spatial weight matrix construction

The establishment of the spatial weight matrix is the basis for spatial analysis. Describing the interactions between units in space and between neighbouring things in the form of a matrix and how to quantify the proximity of each unit is the problem that needs to be solved by the spatial weight matrix.

Generally, the construction of a spatial weight matrix is based on two methods: one is based on the distance function to construct a spatial weight matrix, which is based on geographical distance or economic distance between cells, but this method is very subjective for variable selection and is not conducive to model setting and parameter estimation; the other is based on the adjacency relationship to construct a spatial weight matrix, which is based on whether the cells are adjacent to each other, and if so, the adjacency matrix is assigned to 1; otherwise, it is assigned to 0. This method applies to polygonal spatial units, is simple and intuitive, and can objectively describe the proximity of each unit. Considering that the thesis takes each province in China as the research object, and that the neighbouring provinces have a deeper degree of mutual influence on energy consumption, environmental management, and financial development, the first-order Queen adjacency matrix, which is the most commonly used and intuitive, is chosen to construct the spatial weight matrix.

Empirical analysis and discussion

Measurement of the spatial distribution state of carbon emissions in China

As shown in Fig. 2, China’s total carbon emissions have been increasing, with a steeper curve and a faster increase in carbon emissions between 2005 and 2011 and a flatter curve and a significantly lower increase in carbon emissions between 2011 and 2017. From the kernel density distribution in Fig. 2, it can be seen that the shape of the three distribution curves has changed significantly, and the kernel density distribution tends to “flatten” more and more. First, the peaks of the three curves change significantly and show a decreasing trend, indicating that the provinces whose carbon emission efficiency is near the central value are gradually decreasing; second, compared with 2005, the values of carbon emissions reaching the peak in 2011 and 2017 are constantly shifting to the left, carbon emissions show a decreasing trend, and the magnitude of the decrease is obvious. Third, the two ends of the three curves become fatter and more significant between 2012 and 2015, indicating that the provinces with low carbon emissions and those with high carbon emissions are increasing, and this trend of regional differentiation is gradually strengthened.

Fig. 2
figure 2

China’s carbon emission growth curve from 2005 to 2017 and kernel density plots in selected years

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Spatial autocorrelation test results

The spatial autocorrelation test reflects the spatial clustering characteristics of carbon emission efficiency in 30 provinces, and the change in Moran’s I index in different years reflects its spatial evolution trend. The carbon emissions of 30 provinces were used as the study variables. The Moran’s I index was used to measure its spatial autocorrelation coefficient values in 2005–2017 and to test its significance. The global spatial autocorrelation coefficient values and significance test results for 2005–2017 were obtained using GeoDa software, and the results are shown in Table 1.

Table 1 Global Moran’s I values of carbon emissions in 2005–2017
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As seen from the table, the Moran’s I indices in China from 2005 to 2017 all pass the significance test at the 5% level, and the Moran’s I indices are all positive, which indicates that the level of carbon emissions in China is not spatially random but spatially interdependent and shows a clustering trend. The carbon emission levels are similar between neighbouring regions. This also illustrates the necessity of using spatial econometric models to study the effects of energy intensity, energy investment and its structure, and energy consumption structure on carbon emissions.

To demonstrate the spatial local correlation of provincial carbon emissions in China, three-time points are selected in this paper, 2006, 2011, and 2016, and the Moran scatter plots of carbon emissions in each province are visualized and combined with LISA maps, as shown in Figs. 3 and 4. Figure 3 shows that the number of provinces in “high-high agglomeration” and “low-low agglomeration” is overwhelming, which is consistent with the global test results and confirms the positive spatial correlation of carbon emissions in China. As seen from the figure, Sichuan is of the “L-L” type in all 3 years of observation, while Shandong, Hebei, and Henan are always of the “H–H” type. Xinjiang was “L-L” in 2006 and 2011 and became “H–L” in 2016. Anhui was “L–H” in 2006 and 2011 and became “H–H” in 2016. Guangdong was “H–L” in 2006. Shanxi was “H–H” in both 2011 and 2016. All of these provinces passed the 5% significance test.

Fig. 3
figure 3

Moran scatter plots of carbon emission levels of provinces in China

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Fig. 4
figure 4

Local LISA cluster map and LISA significance map of the carbon emission level

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Through the above analysis, it can be seen that the H–H type is mainly distributed in the industrial bases in northern China, and these provinces gather a large number of high energy-consuming industries and energy-consuming enterprises, such as electric power, iron, steel, and building materials, but the technology is backwards; the level of scientific research is low, and the innovation ability is insufficient. In summary, the spatial distribution of carbon emission levels in China at the present stage shows a diminishing positive autocorrelation, with clusters in “H–H” and “L-L”. In the future, China should focus on provinces with high carbon emission levels and actively explore their carbon reduction potential.

Stationarity test

To avoid the problem of pseudo-regression, the unit root test should be carried out before panel regression analysis. In this paper, the LLC test, ADF-Fisher test, and Stata16.0 were applied to the variables to clarify the stability of related variables. In addition, the null hypotheses of these three tests all contain a unit root, and the test results of each variable are shown in Table 2. According to the results of the unit root test, the null hypothesis of the unit root is rejected at the 10% confidence level; that is, all relevant variables are stable, and there is no false regression phenomenon.

Table 2 Unit root test results
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Testing and selection of spatial panel models

As seen from Table 3, all of the results of the LM tests pass the significance test at the 5% level, indicating that spatial effects should be considered. The results of the robust LM-error and robust LM-lag tests are both significant, and the original hypotheses are also rejected for both the LM-lag and LM-error tests. The original hypothesis of the nonspatial effect econometric model is rejected, and both DSEM and DSLM models can be chosen. Considering that DSDM has broader economic significance and can better describe the spatial spillover effects of regional carbon emissions and the direct and indirect effects of factors such as energy investment on carbon emissions, we choose DSDM for the empirical analysis in this paper. Next, we present a dynamic spatial panel model of the impact of total energy investment and its structure on carbon emissions and conduct another Wald test on whether the DSDM model can be simplified to the DSEM or DSLM model.

Table 3 The LM test results of the space panel model
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Table 4 shows the estimation results of the DSDM. The R2 of the model is 0.9569, which indicates that the model fits well. The log-likelihood is 634.64, which indicates that the DSDM is more accurate in estimating the model parameters. The Wald test is used to determine whether the spatial Durbin model can degenerate into a spatial error model or a spatial lag model, and it is found that the Wald spatial lag and Wald Wald spatial lag and Wald spatial error both pass the significance test at the 1% confidence level, indicating that the DSDM cannot degenerate into the DSEM or DSLM model and that the DSDM model is more suitable to perform the estimation of explanatory variables.

Table 4 Estimation results of the dynamic spatial Durbin model and test results
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The LR test can determine whether there are significant fixed effects in time and space. As seen from Table 4, both LR spatial lag and LR spatial error pass the significance test at the 1% confidence level, indicating that there are spatial individual fixed effects and temporal fixed effects in the model. Furthermore, the Hausman test is used to determine whether the DSDM model should use spatiotemporal dual fixed effects or random effects, and the Hausman test results are significant at the 1% level, so the DSDM model with spatiotemporal dual fixed effects is supported. Therefore, the DSDM model with double fixed effects is more suitable for estimating the spatial panel data in this paper.

Analysis of the parameter estimation results of each factor on carbon emissions

The dynamic spatial effect is the focus of this paper. The time lag term, spatial effect term, and spatiotemporal lag term of carbon emissions all have significant effects. Therefore, it is necessary to consider the dynamic spatial effect. As seen from Table 4, based on the characteristics of the time dimension, the first-order lagged term of carbon emissions has a driving force of 0.5068% on the current period carbon emissions at the 1% significance level, indicating that the change in carbon emissions in each province has obvious path-dependent characteristics and that the increase in carbon emissions in the current period will lead to a continued increase of carbon emissions in the next period, i.e. China’s regional carbon emissions have continuous positive dynamic characteristics, thus exhibiting a “snowball effect”. Furthermore, the effectiveness obtained from carbon emission reduction in the current period will also have a positive impact on carbon emission reduction in the later period; based on the spatial dimension characteristics, the coefficient of the spatial effect of carbon emissions at the 1% significance level is 0.1837, indicating that every 1% increase in carbon emissions from neighbouring provinces will lead to a 0.1837% increase in carbon emissions in the region, indicating that there is an obvious spatial agglomeration effect of provincial carbon emissions. Based on the time lag effect, the time lag coefficients of carbon emissions are all significantly negative, indicating that the increase in carbon emissions in neighbouring provinces in the previous period has a driving effect on the decrease of carbon emissions in the current period, implying that the increase in carbon emissions in neighbouring provinces has a “warning effect” on the region. This may be due to the strong spatial correlation of carbon emissions and the comprehensive consideration of government performance, which leads the relevant departments to take measures to ensure that the local carbon emissions are not affected by the carbon emissions of neighbouring provinces.

The energy intensity of a province also has a significant impact on its carbon emissions, with an estimated parameter value of 0.5043. This indicates that, for every 1% increase in energy intensity, carbon emissions will increase by 0.5043%, indicating that changes in energy intensity have a significant impact on the level of carbon emissions. Reducing energy intensity by improving the technology of the energy industry can effectively reduce carbon emissions. Investment in the energy industry will not only have a dampening effect on carbon emissions in the region but also carbon emissions in neighbouring regions. Huang et al.’s research also proved this conclusion (Huang et al. 2020). Each 1% increase in energy investment will cause a 0.0023% reduction in carbon emissions in the region and a 0.0131% reduction in carbon emissions in neighbouring regions. This indicates that increasing energy investment is beneficial for improving the technology of the energy sector and thus reducing carbon emissions in the region and neighbouring regions. The energy consumption structure also has a significant impact on carbon emissions, with an elasticity coefficient of 0.2762, indicating that a 1% increase in the energy consumption structure with coal, oil, and natural gas as the main sources of consumption will lead to a 0.2762% increase in carbon emissions in the region. This conclusion is consistent with the research results of Rong et al. (2020) and Yang and Wang (2020), but there is no quantitative conclusion. The energy consumption structure is another important factor affecting the level of carbon emissions. The energy investment structure of a province positively affects the carbon emission level of the province and negatively affects the carbon emission level of neighbouring provinces with parameter estimates of 0.0062 and − 0.0176, respectively. It shows that every 1% increase in the energy investment structure with coal and oil industries as the main investment objects will cause the carbon emission level of the province to increase by 0.0062% and will make the carbon emission level of neighbouring provinces 0.0176% lower. This result indicates that an increase in investment in traditional energy industries will lead to an increase in the consumption of traditional energy in the province and a shift of traditional energy from neighbouring provinces to the province, which will have a dampening effect on the carbon emissions of neighbouring provinces.

Each 1% increase in population increases the local carbon emissions by 0.5412% and reduces the carbon emissions of neighbouring provinces by 0.4995%. This indicates that along with the increase in population, a large influx of factors from neighbouring areas into the local area will significantly increase the local carbon emissions and reduce the carbon emission level of neighbouring areas. The increase in economic development in the province also has a significant impact on the level of carbon emissions in the local and neighbouring provinces. Liu et al. (2020) and Xue (2020) also found that the increase in population and urbanization level promoted the growth of carbon emissions. A 1% increase in GDP per capita will cause a 0.5962% increase in carbon emissions in the local region and a 0.1166% increase in carbon emissions in the neighbouring regions. China’s current economic development is relatively rugged. The rapid economic development of individual regions may drive the linkage development of neighbouring regions, and through the spatial spillover effect, the carbon emission efficiency of neighbouring regions is promoted and driven, driving the flow of talent factors and production factors in neighbouring regions, which in turn improves the carbon emission level of neighbouring regions.

Analysis of the long-term and short-term effects of each factor

The greatest advantage of the dynamic spatial panel model is that it can estimate the effects of explanatory variables on the explained variables in the long and short term. When there is a spatial spillover effect, it can estimate the effect of explanatory variables such as energy intensity, energy industry investment, and energy consumption structure on local carbon emissions in addition to the degree of the effect of the variables on carbon emissions in neighbouring provinces, to judge whether there is a spatial spillover effect of both explanatory variables on the explanatory variables. Therefore, the degree of effects of explanatory variables, such as the current situation of the energy industry on carbon emissions and carbon emission intensity is further estimated, and the specific results are shown in Table 5.

Table 5 Direct and indirect effects of each variable affecting carbon emissions
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Among them, the short-term and long-term effects denote the short-term immediate effects of the relevant variables on carbon emissions and the long-term effects with time lags, respectively. The direct effect represents the spatial feedback effect, i.e. the effect of the explanatory variables on carbon emissions in neighbouring provinces and the effect of neighbouring provinces on carbon emissions in this province; the indirect effect represents the spatial spillover effect, i.e. the effect of the explanatory variables in neighbouring provinces on carbon emissions in this province or the effect of changes in the explanatory variables in this province on carbon emissions in neighbouring provinces. The obtained results are slightly different from the spatial estimation results because, in the spatial estimation, the spatial lagged terms of the independent variables are the spatially weighted values of each province and the neighbouring provinces, ignoring the inclusion of a large amount of interaction information between neighbouring regions.

The results show that the absolute values of the long-term effects of each variable on the carbon emission level are greater than the absolute values of the short-term effects, indicating that each explanatory variable has a greater effect on the carbon emission level in the long term and presents a more far-reaching impact.

Energy intensity has a positive and significant effect on carbon emissions in the province in both direct and indirect effects, indicating that the reduction in energy intensity has a significant inhibitory effect on the increase in carbon emission elements. Both in the long term and the short term, reducing energy intensity will promote the improvement of the carbon emission situation in this province and neighbouring provinces. China’s interprovincial carbon emissions possess a strong spatial agglomeration, and regions with more energy consumption have a concentration of high-energy-consuming industries. With the advancement of technology, energy intensity is significantly reduced, which in turn further inhibits the increase in carbon emission levels. With the development of the economy, people are increasingly concerned about the quality of the environment. We will strengthen the effectiveness of environmental regulations; shut down, merge, and transfer some high-pollution and high energy-consuming enterprises; and encourage enterprises to strengthen the development of low-emission technologies. In addition, from the calculation results, it can be seen that the reduction of provincial energy intensity will reduce the carbon emissions of neighbouring provinces and that there is a “demonstration effect”. This may be due to the high technological compatibility due to industrial agglomeration. Neighbouring provinces can introduce advanced local technology and management experience. This allows neighbouring provinces to enjoy the spatial spillover effects of technological progress. In the development and utilization of low-carbon technologies, technology exchange can take place between neighbouring provinces, and there is a large number of researchers and capital technology in the region, which can further promote the development of the low-carbon economy. Increasing investment in new energy and clean energy fields, reducing energy intensity, and increasing energy efficiency are conducive to controlling carbon emissions in each province.

The coefficients of both short-term and long-term direct effects of energy investment are significantly positive, but the coefficients of indirect effects are not significant, which indicates that energy investment has a suppressive effect on local carbon emissions and no significant effect on neighbouring provinces, which is because, with the increase in energy investment, R&D investment in advanced energy technologies, innovation ability, and the ability to put energy technologies into use are enhanced, which leads to the enhancement of the transition ability from traditional energy to new energy, thus having a certain adjustment to the energy structure and increasing the use of clean energy, which effectively promotes carbon emission reduction, but significant spatial spillover has not yet been formed.

The direct effect of the energy consumption structure on carbon emissions in the province is significantly positive in the short and long term, but the indirect effect is significantly negative. This shows that the optimization of the energy structure will reduce local carbon emissions, which is conducive to carbon emission reduction. The spatial spillover of the energy consumption structure is significantly negative, which can be explained by the warning effect. The increase in the proportion of traditional energy consumption leads to the deterioration of the surrounding environment, which will increase the demand for environmental governance in the surrounding area, and the surrounding governments will strengthen the supervision of laws and regulations to reduce carbon emissions.

The coefficients of both the short- and long-term direct effects of the energy investment structure are positive, and the indirect effects are negative. Both in the long term and the short term, the indirect effects are much larger than the direct effects. The increase in investment in the traditional energy sector is mostly in the large energy-consuming provinces with a high degree of industrial agglomeration. To further improve the scale effect, the proportion of traditional energy investment increases, and the traditional energy industry in the neighbouring provinces is transferred to the local area so that although the local carbon emission increases less, it will significantly reduce the carbon emission in the neighbouring areas, which is beneficial to the overall carbon emission reduction in China.

The short- and long-term direct effects on the population are significantly positive, and the indirect effects are significantly negative. This indicates that, as the population increases, factors and industries concentrate, and the demand for energy increases, thus increasing local carbon emissions, while the loss of factors and industries in the surrounding areas reduces carbon emissions in the nearby areas. In both the short and long term, the direct and indirect effects of economic growth on carbon emissions are significantly positive. This is inseparable from the current rough economic development in China. The economic development of a region will inevitably drive the flow of factors and industries in the surrounding areas, which will increase the level of carbon emissions in the region.

Conclusion and policy implications

Based on Chinese provincial panel data from 2005 to 2017, this paper analyses the impact of total energy investment and structure on carbon emissions in the region and neighbouring regions using a spatial econometric model. First, the Moran test and Moran scatter plot are used to test that there is indeed a positive spatial correlation of carbon emissions; then, two tests, LLC and ADF-Fisher, are used to conduct unit root tests on the data; second, based on spatial panel econometric model estimation and testing, it is clarified which spatial econometric model is the most appropriate; finally, the Hausman test is conducted to determine that the use of a fixed-effect dynamic spatial Durbin model study is reasonable and to further analyse its spatial spillover effect.

The results show that the coefficients of the time lag term, the coefficient of the spatial effect, and the coefficient of the time lag of carbon emissions are all significant, so the dynamic spatial effect should be considered. The absolute values of the long-term effects of each variable on carbon emission levels are larger than the absolute values of the short-term effects, indicating that each explanatory variable presents a more far-reaching effect on carbon emission levels. Reducing energy intensity through energy technology investment can effectively suppress carbon emissions in this province and neighbouring provinces. Increasing energy investment can effectively reduce the level of carbon emissions in the province. The optimization of the energy consumption structure in the province can effectively promote carbon emission reduction in the province but will have a suppressing effect on carbon emission reduction in neighbouring provinces. An increase in the proportion of investment in traditional energy sources in the province will increase the carbon emissions in the province and decrease the carbon emissions in neighbouring provinces. In both the short and long term, population growth and economic growth will have a negative impact on carbon emission reduction in both the province and neighbouring provinces.

In conclusion, the analysis in this chapter shows that there is a spatial spillover effect of the factors influencing carbon emission efficiency in China, with intra and interregional interactions; the carbon emission efficiency of different provinces is also affected by each influencing factor with some variability. Specific analysis and policy recommendations are given below.

  1. (1)

    Strengthen intraregional collaboration to promote global long-term carbon reduction. The empirical results are based on a dynamic spatial effect test: on the one hand, there is a significant spatial agglomeration effect of carbon emissions. On the other hand, the parameter estimation results of the time lag term, space lag term, and spatiotemporal lag term are significant. This indicates that local last-period carbon emissions, current-period carbon emissions of neighbouring provinces, and last-period carbon emissions of neighbouring provinces have significant effects on local current-period carbon emissions. Therefore, the spatial interaction of carbon emissions should not be neglected in the process of low-carbon development, and the first step should be to strengthen the cooperation and exchange between regions, especially learning from government carbon emission reduction policies, enterprises’ carbon emission reduction behaviours, technological innovation, and green credit investment by financial institutions, to carry out low-carbon activities according to local conditions. Second, attention should be given to the time-dependent characteristics of carbon emissions in China. Low-carbon activities should be carried out with a focus on their long-term impact, and government officials should take into account both current and future performance considerations, concretely implement carbon emission reduction policies promulgated by higher authorities, and increase carbon emission reduction behaviours according to local conditions. Enterprise technology reform and financial institutions’ capital flow should try to avoid carbon behaviours that only consider current interests and are not conducive to long-term development.

  2. (2)

    Expand the influence of the demonstration effect and enhance the strength of the warning effect. The strong support for carbon emission reduction from a factor change in a neighbouring region will have a “demonstration effect” on the region, while the obstruction of carbon emission reduction will also have a “warning effect” on the region. Therefore, to expand the “demonstration effect” and enhance the “warning effect”, we can start from the following aspects: on the one hand, strengthen regional cooperation and enhance praise. Promoting the exchange and cooperation of carbon emission reduction activities between regions can effectively expand the influence of the “demonstration effect”. At the same time, we should increase the praise and publicity of effective carbon emission reduction behaviours, promote more regions to learn and follow suit, and incorporate the effectiveness of local carbon emission reduction into the performance evaluation system of government officials. On the other hand, the punishment for unfavourable behaviours of low-carbon development should be increased, by increasing the punishment for local governments’ inaction and even sabotage of the low-carbon process and by increasing the weighting of such unfavourable behaviours in the performance evaluation system, to increase the “warning effect” on neighbouring regions.

  3. (3)

    Coordinate energy investment in each province and optimize the energy investment structure. China, at this stage, can reduce its energy intensity by increasing investment in energy technology research and development, especially technology to improve energy-use efficiency and low-carbon production, thus promoting carbon emission reduction. The proportion of clean energy consumption in China is low, and the country should vigorously promote the use of clean energy and increase investment in the research and development of new clean energy to optimize the energy consumption structure. In terms of technology, the need for independent innovation is the main focus, supplemented by the introduction of technology. Compared with independent research and development, the introduction of advanced technology is undoubtedly the most rapid way to improve technology, but the introduction of technology in each region needs to be measured, not to blindly pursue the high-end and novel technology, to examine whether the region can absorb the advanced technology; if there is no matching bearing body, it will produce a waste of technology. Therefore, the establishment of an integrated production and operation mode of industry–academia research helps the digestion, absorption, and reinvention of technology. According to the field investigation, the R&D plan is formulated, and the detailed project plan is made jointly with the school and enterprises. The low-carbon technology developed will be piloted by technicians, and after passing an examination, the technology will be put into large-scale use. It is also import to strengthen interregional technology exchange and cooperation, realize technology spillover, realize the complementary advantages between regions, and form the “advantage” of the large-scale low-carbon development mode. Different provinces have different characteristics in terms of the degree of coordination between total energy investment and structure and carbon emission coupling, which should be analysed in specific issues. Shandong, Shanxi, Hebei, and other provinces are large energy-consuming provinces with a high degree of industrial agglomeration; so to further improve the scale effect, the proportion of traditional energy investment can be appropriately increased. Since the direct effect of the energy investment structure is much smaller than the indirect effect, this will increase the carbon emissions of this province in a small amount but can significantly reduce the carbon emissions of neighbouring provinces, which is beneficial to the overall carbon emission reduction work in China.

This paper studies the impact of various factors on carbon emissions from a dynamic perspective. It is hoped that more practical factors, such as the impact of the COVID-19 epidemic in recent years, will be considered in future research.