We selected CE as the dependent variable in this study. The indicator of CE was calculated through the material balance algorithm recommended by the Intergovernmental Panel on Climate Change (IPCC, 1990), which takes into account the consumption of several major fossil fuels, such as coal (including coal and coking coal), natural gas, and petroleum (including kerosene, diesel, crude oil, fuel oil, and gasoline). The CE calculation formula is presented in Eqn. 1:

(1)$$\mathrm{CE}={\sum }_{\mathrm{i}}{\mathrm{m}}_{\mathrm{i}}\times {\delta }_{\mathrm{i}}\times 12/44$$

Where m_i is the annual consumption of the i-th major carbon emitting energy source. $\delta$_i denotes the carbon emission factor (CEF) of the i-th fossil fuels, which is the average value provided in Table 1. The factor 12/44 is the mass fraction of carbon in one unit of carbon dioxide. Energy consumption data is sourced from the China Stock Market & Accounting Research (CSMAR) database and the China Energy Statistical Yearbook, while the CE coefficient is sourced from the CE coefficient guidelines of major authoritative energy accounting institutions. In addition, we calculate regional carbon emission intensity (CEI). Regional CEI is the amount of CE per unit of output, accounting for the level of gross domestic product (GDP). The formula for regional CEI is shown in Eqn. 2:

(2)$$\mathrm{CEI}=\mathrm{CE}/\mathrm{GDP}$$

Where GDP denotes the annual gross domestic product of each provincial administrative unit, obtained from the National Bureau of Statistics of China.

We chose GC as the independent variable of this research. Currently, scholars often use the proportion of interest expenses in six high energy consuming industries to the total interest expenses of industrial enterprises above designated size when measuring GC (Tan et al, 2022b). The effectiveness of utilizing the interest expenditure share of high-energy-consumption industries as a proxy variable for green credit policy intensity lies in the mechanism that when regulators tighten green credit policies, commercial banks will systematically reduce credit allocation to high-energy-consumption, high-pollution, and overcapacity sectors. This credit rationing mechanism directly results in decreased total loan volume accessible to high-energy-consumption industries, consequently diminishing their proportional share in aggregate interest expenditures. The reduction in this indicator value reflects the policy effect of structural reallocation of credit resources from traditional polluting industries to green and low-carbon sectors, with lower numerical values indicating stronger enforcement intensity of green credit policies. Therefore, we calculate GC according to this method. Moreover, these six high energy consuming industries include chemical raw material and chemical product manufacturing, electricity and heat production and supply, black metal smelting and rolling processing, petroleum processing coking and nuclear fuel processing, non-ferrous metal smelting and rolling processing, and non-metallic mineral products. The data used to calculate GC is primarily drawn from the China Statistical Yearbook, the China Industrial Statistical Yearbook, the China Energy Statistical Yearbook, and statistical yearbooks of various provinces and cities in China, as well as the Fourth National Economic Census of China. Interpolation was applied to supplement minor missing data from 2017.

We selected IS, TA and EE as the mediating variables in this study. Following the methodological framework established by Liu et al (2019), we operationalized industrial structure upgrading through the Industrial Structure Upgrading Index (ISUI). The index construction involves: (1) assigning differentiated weights to primary, secondary, and tertiary industries; (2) applying weighting coefficients through multiplication by their respective proportions. The ISUI metric exhibits positive directional alignment, where elevated values correspond to enhanced industrial structure upgrading. The formal mathematical specification appears in Eqn. 3:

(3)$$\mathrm{IS}=\sum {\mathrm{q}}_{\mathrm{i}}\times \mathrm{i}={\mathrm{q}}_1\times 1+{\mathrm{q}}_2\times 2+{\mathrm{q}}_3\times 3$$

Where q_i denotes the proportion of the i-th industry.

As for TA, we measured it by the sum of internal R&D expenditures within the region divided by GDP. R&D expenditure is divided into internal expenditure and external expenditure. Internal expenditure refers to all expenses actually used within the unit to carry out R&D activities, while external expenditure refers to the actual expenses incurred by outsourcing R&D activities to external entities. To avoid double counting between the implementing unit and the commissioning unit, the data refers only to internal R&D expenditures by implementing units.

As for EE, we measured it by total energy supply divided by GDP, which refers to energy consumption per unit of GDP in each province. This reflects the degree of energy utilization in a country’s economic activities, indicating changes in economic structure and EE.

The data for mediating variables is from the Energy Database of China, the National Bureau of Statistics of China, the China Energy Statistical Yearbook, the China Science and Technology Statistical Yearbook and so on.

Control variables refer to variables that are not the main focus of the study but may affect the dependent variable. By introducing control variables, researchers can more accurately estimate the impact of independent variables on the dependent variable, reducing omitted variable bias. With reference to relevant studies, we chose population density (PD), openness level (OPL), and economic development level (EDL) as the control variables of this research. According to existing literature, these three control variables will have an impact on CE. As for PD, we measured it by the total population divided by the area of each province (Wang et al, 2023). PD will reflect the population density of a province and also reflect the level of urbanization. As for OPL, we used the proportion of the total import and export volume to the current GDP of each province as a representation (Lei et al, 2023). The higher the degree of OPL, the more advanced domestic and foreign technologies and development concepts can be introduced, and it can also contribute to the development of cross-border GF cooperation. As for EDL, we measured it by GDP divided by total population of each province (Sun and Zeng, 2023). EDL reflects the consumption level of the people in each province. The data for control variables are obtained from the National Bureau of Statistics of China, the CSMAR database, the China Statistical Yearbook, the China Environmental Statistical Yearbook, the China Industrial Statistical Yearbook, the China Energy Statistical Yearbook, and statistical yearbooks of various provinces and cities in China, as well as the Fourth National Economic Census of China. For individual missing data, interpolation was used to fill gaps. For the convenience of browsing, each specific variable is defined in Table 2.

For the convenience of calculation, we took the logarithm of all variables. The descriptive statistics of variables are shown in Table 3. Table 3 shows that the mean of lnCE is 5.493, the standard deviation is 0.751, the minimum value is 3.076 and the maximum value is 6.843. Additionally, there is a significant difference in lnEE, lnPD and lnOPL.

In order to test the direct impact of GC on CEI, we constructed the model in Eqn. 4:

(4)$${\mathrm{lnCE}}_{\mathrm{i},\mathrm{t}}={\mathrm{a}}_0+{\mathrm{a}}_1\ln {\mathrm{GC}}_{\mathrm{i},\mathrm{t}}+\sum _{\mathrm{j}=1}{\beta }_{\mathrm{j}}{\mathrm{X}}_{\mathrm{j},\mathrm{i},\mathrm{t}}+{\text{µ}}_{\mathrm{i}}+{\gamma }_{\mathrm{t}}+{\epsilon }_{\mathrm{i},\mathrm{t}}$$

Where a₀ refers to the constant; a₁ and $\beta$_j denote the coefficients of the explanatory variables. Moreover, lnCE_i,t, lnGCL_i,t and X_j,i,t refer to the value of CE, GC and j-th variable for i-th province of China in year t. µ_i, $\gamma$_t, and $\epsilon$_i denote the individual effects, time effects, and stochastic error term, respectively.

The commonly used research methods for analyzing mediating effect are stepwise regression, the Sobel method, and the bootstrap method. This research uses the first method to analyze the relationship between GC and CE from the perspectives of the individual mediating effects of IS, TA, and EE. The mediating effect model based on stepwise regression is constructed in Eqns. 5,6,7,8,9,10:

(5)$$\ln {\mathrm{IS}}_{\mathrm{i},\mathrm{t}}={\mathrm{b}}_0+{\mathrm{b}}_1\ln {\mathrm{GC}}_{\mathrm{i},\mathrm{t}}+\sum _{\mathrm{j}=1}{\beta }_{\mathrm{j}}{\mathrm{X}}_{\mathrm{j},\mathrm{i},\mathrm{t}}+{\text{µ}}_{\mathrm{i}}+{\gamma }_{\mathrm{t}}+{\epsilon }_{\mathrm{i},\mathrm{t}}$$

(6)$$\ln {\mathrm{CE}}_{\mathrm{i},\mathrm{t}}={\mathrm{c}}_0+{\mathrm{c}}_1\ln {\mathrm{GC}}_{\mathrm{i},\mathrm{t}}+\ln {\mathrm{IS}}_{\mathrm{i},\mathrm{t}}+\sum _{\mathrm{j}=1}{\beta }_{\mathrm{j}}{\mathrm{X}}_{\mathrm{j},\mathrm{i},\mathrm{t}}+{\text{µ}}_{\mathrm{i}}+{\gamma }_{\mathrm{t}}+{\epsilon }_{\mathrm{i},\mathrm{t}}$$

(7)$$\ln {\mathrm{TA}}_{\mathrm{i},\mathrm{t}}={\mathrm{d}}_0+{\mathrm{d}}_1\ln {\mathrm{GC}}_{\mathrm{i},\mathrm{t}}+\sum _{\mathrm{j}=1}{\beta }_{\mathrm{j}}{\mathrm{X}}_{\mathrm{j},\mathrm{i},\mathrm{t}}+{\text{µ}}_{\mathrm{i}}+{\gamma }_{\mathrm{t}}+{\epsilon }_{\mathrm{i},\mathrm{t}}$$

(8)$$\ln {\mathrm{CE}}_{\mathrm{i},\mathrm{t}}={\mathrm{e}}_0+{\mathrm{e}}_1\ln {\mathrm{GC}}_{\mathrm{i},\mathrm{t}}+\ln {\mathrm{TA}}_{\mathrm{i},\mathrm{t}}+\sum _{\mathrm{j}=1}{\beta }_{\mathrm{j}}{\mathrm{X}}_{\mathrm{j},\mathrm{i},\mathrm{t}}+{\text{µ}}_{\mathrm{i}}+{\gamma }_{\mathrm{t}}+{\epsilon }_{\mathrm{i},\mathrm{t}}$$

(9)$$\ln {\mathrm{EE}}_{\mathrm{i},\mathrm{t}}={\mathrm{f}}_0+{\mathrm{f}}_1\ln {\mathrm{GC}}_{\mathrm{i},\mathrm{t}}+\sum _{\mathrm{j}=1}{\beta }_{\mathrm{j}}{\mathrm{X}}_{\mathrm{j},\mathrm{i},\mathrm{t}}+{\text{µ}}_{\mathrm{i}}+{\gamma }_{\mathrm{t}}+{\epsilon }_{\mathrm{i},\mathrm{t}}$$

(10)$$\ln {\mathrm{CE}}_{\mathrm{i},\mathrm{t}}={\mathrm{g}}_0+{\mathrm{g}}_1\ln {\mathrm{GC}}_{\mathrm{i},\mathrm{t}}+\ln {\mathrm{EE}}_{\mathrm{i},\mathrm{t}}+\sum _{\mathrm{j}=1}{\beta }_{\mathrm{j}}{\mathrm{X}}_{\mathrm{j},\mathrm{i},\mathrm{t}}+{\text{µ}}_{\mathrm{i}}+{\gamma }_{\mathrm{t}}+{\epsilon }_{\mathrm{i},\mathrm{t}}$$

Where b₀, c₀, d₀, e₀, f₀, and g₀ refer to constants; b₁, c₁, d₁, e₁, f₁ and g₁ denote the coefficient of the variables. Moreover, lnIS_i,t, lnTA_i,t and lnEE_i,t refer to the values of IS, TA, and EE for i-th province of China in year t. In order to eliminate the influence of heteroscedasticity, logarithmic transformation is applied to all variables.

There are generally four types of matrices commonly used in the empirical literature on spatial econometrics: binary adjacency weight matrix (also known as 0-1 weight matrix), inverse distance weight matrix, economic weight matrix and nested matrix. The earliest spatial econometric model in foreign literature is the 0-1 weight matrix (Getis, 2009), which is also widely used in China. The 0-1 weight matrix is divided into two categories: first-order adjacency and high-order adjacency. The first-order adjacency matrix assumes that spatial interactions will occur as long as there are non-zero length common boundaries between spatial sections. Researchers believe that a spatial effect should also occur within a certain distance range around a given spatial cross-section, and beyond a given threshold distance, the spatial effect between regions can be ignored. Therefore, this research extends the definition of spatial weights as follows:

(11)

where, w_i,j is the spatial weight matrix, i and j are the spatial section number. i, j$\in$[1, n], and n is the number of spatial sections. Moreover, d_i,j denotes the distance between i-th and j-th spatial section, and d denotes a certain distance range. This article adopts the above method, using the latitude and longitude of provincial administrative regions to create a 0-1 weight matrix, that is, if regions are adjacent within a threshold distance, it takes 1, otherwise it takes 0. In the construction of spatial econometric models, the selection of a binary adjacency weight matrix (0-1 matrix) fundamentally stems from its straightforward construction logic and suitability for characterizing strong spatial adjacency relationships. The investigation focuses on the geographical distribution characteristics of 30 Chinese provincial units, where administrative boundary adjacency demonstrates notable prominence. The adjacency matrix effectively captures direct spatial interdependencies between regions through its binary operationalization. By dichotomously assigning weights based on territorial contiguity, the 0-1 matrix circumvents potential estimation biases inherent in geographical distance matrices that may arise from topographical heterogeneity, transportation network disparities, or asymmetrical economic interactions. Furthermore, this matrix configuration has been extensively employed in seminal spatial econometric literature, possessing both classical theoretical underpinnings and empirical validation, thereby satisfying the preliminary verification requirements for spatial effect existence in exploratory research. Although geographical distance matrices can delineate the continuity of physical separation, their construction necessitates precise geospatial coordinate computations that may introduce superfluous complexity while inadequately reflecting practical pathways of policy transmission and economic spillover effects. Consequently, this study adopts the 0-1 matrix to streamline spatial relationship representation, achieving an optimal balance between model robustness and explanatory efficacy.

In addition, this study also requires the use of Moran’s Index (Moran’s I) for spatial autocorrelation test. The formula is shown in Eqn. 12:

(12)$$\text{Moran’s I}=\frac{\mathrm{n}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{i},\mathrm{j}}\left({\mathrm{x}}_{\mathrm{i}}-{\mathrm{x}}_{\mathrm{m}}\right)\left({\mathrm{x}}_{\mathrm{j}}-{\mathrm{x}}_{\mathrm{m}}\right)}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{i},\mathrm{j}}{\left({\mathrm{x}}_{\mathrm{i}}-{\mathrm{x}}_{\mathrm{m}}\right)}^2}$$

Where i and j refer to the i-th and j-th province of China, n denotes 30 provinces of China and w_i,j is the spatial weight matrix. Additionally, x and x_m refer to a variable and its mean value. Moran’s I ranges from 0 to 1.

The spatial econometric model is divided into Spatial Error Model (SEM), Spatial Lag Model (SLM), and SDM. For the convenience of calculation, this study currently uses the SDM with fixed effect and tests the rationality of the model settings in the following section. The construction of SDM is as follows:

(13)$$\ln {\mathrm{CE}}_{\mathrm{i},\mathrm{t}}={\beta }_0+\rho \mathrm{W}\ln {\mathrm{CE}}_{\mathrm{i},\mathrm{t}}+{\beta }_1{\mathrm{GC}}_{\mathrm{i},\mathrm{t}}+\sum {\beta }_{\mathrm{j}}{\mathrm{X}}_{\mathrm{j},\mathrm{i},\mathrm{t}}+{\mathrm{W}}^{\prime }{\mathrm{GC}}_{\mathrm{i},\mathrm{t}}\delta +\sum {\mathrm{W}}^{\prime }{\mathrm{X}}_{\mathrm{j},\mathrm{i},\mathrm{t}}{\delta }_{\mathrm{j}}+{\text{µ}}_{\mathrm{i}}+{\gamma }_{\mathrm{t}}+{\epsilon }_{\mathrm{i},\mathrm{t}}$$

Where i and t denote province and year; $\beta$₀, $\rho$ and $\beta$₁ refer to constant, the coefficient of spatial autoregression and the coefficient of independent variable. W is 0-1 weight matrix and W’ denotes the spatial lag term of one variable. $\beta$_j and $\delta$_j refer to the coefficient of control variables and spatial lag term. $\gamma$_t denotes the time fixed effect.

To better understand the trend of CEI changes, we shifted the sample observation period forward by five years. Hence, we calculated the average CEI of 30 provincial-level administrative regions in China from 2003 to 2022. Regarding spatial distribution, the CEI of the northern part of China is higher than the southern part, and the CEI of the western part of China is higher than the eastern part, forming a geographical feature of “higher north and lower south, higher west and lower east” (Zhang A et al, 2022). Shanxi, Nei Mongol, Guizhou, and Ningxia consistently exhibit high CEI values. For example, as an old industrial zone and an important energy production base in China, Shanxi’s CEI reached 6.4 tons/10,000 yuan in 2020. However, under long-term environmental constraints, its CEI decreased by 48% compared to the initial level. In contrast, Guangdong, Sichuan, Chongqing and other regions have consistently maintained lower CEI levels, which reflects differences in regional CE and economic structures. The CEI of most other provinces is below 1 ton/10,000 yuan. It is worth mentioning that Xinjiang’s CEI has remained relatively high and stable, with small fluctuations. However, in recent years, an upward trend has emerged, which cannot be ignored (Yu et al, 2021).

In terms of temporal trends, China’s overall CE has shown a continuous upward trend, rising from 8.3 billion tons of standard coal in 2006 to over 11.4 billion tons of standard coal in 2022. This indicates that while China is rapidly developing its economy, its energy consumption is also increasing. From 2006 to 2008, the overall CE level in China remained relatively stable, with a modest growth rate. Between 2008 and 2012, China’s economy expanded rapidly, and energy demand surged. During this period, the average annual growth rate of CE was 7.06%, and the total CE remained high. After 2012, the overall growth rate of China’s CE slowed, and although the total CE continued to increase, the average annual growth rate dropped to only 0.67%. This suggests that in recent years, while China has continued to pursue economic growth, environmental awareness has become increasingly embedded in public consciousness. China’s ecological focus on green development and the promotion of low-carbon production and lifestyles has yielded notable results (Su D et al, 2023; Tan et al, 2022a).

Compared to CE, CEI has shown a consistent downward trend. From 2006 to 2008, due to China’s vigorous development of green and sustainable concepts, the decline was significant. Since 2009, the rate of decline has moderated but remained steady. This suggests that in recent years, for the same level of output, China’s energy consumption and CE have continuously declined due to technological advances, IS adjustments, and improvements in EE.

Consistent with the preceding analysis, we calculated the average GC of 30 provincial-level administrative regions in China from 2003 to 2022. Regarding the industrial interest expenses of China’s six high-energy consuming industries, the electricity and heat production and supply industry has the largest share of interest expenses, while the petroleum, nuclear fuel processing, and smelting industry has the smallest share. In addition, energy consumption in the eastern region of China is generally higher than in other regions (Su T et al, 2023). Energy use in the power and heat industry, chemical products sector, and non-ferrous metal smelting industry is relatively high in the western region. The central region, dominated by coal-rich provinces, exhibits energy concentration in industries such as power generation, heating, and smelting. As for GC, detailed data are presented in Table 4. The proportion of GC in eastern Chinese provinces is relatively low, while in western provinces such as Gansu, Qinghai, and Yunnan, where energy development constitutes a large share of the economy, the proportion of GC is high. This may be due to the relatively advanced economy in eastern China, which features more large state-owned enterprises and listed companies, diverse financing channels, and a richer economic structure, with a lower reliance on indirect financing (Song et al, 2021). In contrast, there are relatively more small and medium-sized enterprises (SMEs) in the less developed central and western regions, where the economic structure is more concentrated. GC continues to play a key role in supporting the development of these SMEs.

Table 9 shows the values of Moran’s I of GC and CE from 2008 to 2022. It can be seen that there is a significant positive spatial correlation between GC and CE in the 30 provincial-level administrative regions of China during the sample period. Therefore, the next step of spatial effect analysis can be carried out.

Model selection is required before constructing a spatial econometric model (Fischer and Getis, 2010). This study first conducted the Lagrange Multiplier (LM) test, as shown in Table 10, and found that the results of both the SEM and SLM were significant. Therefore, the SDM that combines the advantages of both models was selected. Then, this study conducted the Wald test. The result of the Wald test for SLM is 32.63, with a p-value of 0.000. Besides, the result of the Wald test for SEM is 34.19 while its p-value is 0.000. Thus, the null hypothesis that SDM can be degraded to SLM or SEM is rejected. Eventually, this study continued with the Hausman test and the result was 33.89, which led to the rejection of the null hypothesis of random effects at the 1% significance level.

Compared to SEM and SLM, SDM is capable of simultaneously capturing the spatial lag effect of the dependent variable and the spatial spillover effect of the independent variables, which is particularly crucial when examining the impact of green credit policies on carbon emissions. Green credit policies not only influence carbon emissions within the local region but may also generate spillover effects on neighboring regions through mechanisms such as technology diffusion and industrial linkages. By incorporating the spatial lag term of the independent variables, SDM provides a more comprehensive depiction of such spatial interactions. SDM can be regarded as a generalized form of SEM and SLM, as it can degenerate into either SEM or SLM when specific parameters are set to zero. This flexibility allows SDM to adapt to a broader range of research scenarios, especially when the sources of spatial dependence are uncertain. In this study, the Wald test confirmed that SDM cannot degenerate into SLM or SEM, further substantiating the rationale for selecting SDM. The estimation results of SDM not only decompose direct and indirect effects but also more accurately reflect the spatial spillover effects of green credit policies, offering significant guidance for formulating regionally coordinated green finance policies. Therefore, based on theoretical completeness and empirical considerations, this study selects SDM as the primary analytical tool to more comprehensively reveal the mechanisms and spatial effects of green credit policies on carbon emissions.

Table 11 shows the results of spatial spillover effects. The direct effect refers to the degree of impact of a variable in the local area on CE in the local area, the indirect effect refers to the degree of impact of a variable in the surrounding area on CE in the local area, and the total effect refers to the overall degree of impact of a variable in the local area and surrounding areas on CE in the local area.

According to Table 11, the regression coefficients for the direct effect, indirect effect, and total effect of GC are –0.130, –0.287, and –0.417, respectively, and all passed the significance test at the 1% level. This indicates that the higher the proportion of GC, the more it can reduce CE. The possible reason for this is that GC guides funds towards low-carbon and environmentally friendly green industries and projects by providing preferential loan conditions, while limiting the development of high-pollution and high energy-consumption industries. This funding allocation method helps promote the green transformation of IS, reduce the proportion of high-carbon industries, and thus reduce regional CE. In addition, GC can promote exchanges and cooperation in green technology between the local and surrounding areas, and generate demonstration effects. By sharing green technology achievements and experiences, regions can promote the improvement of regional technological levels and reduce CE in surrounding areas. Therefore, GC can reduce CE in the local and surrounding areas.

As for control variables, PD and EDL both contribute to an overall increase in CE. The possible reason for this is that population expansion and economic development can cause consumption and production expansion effects, leading to an increase in household consumption, an expansion of enterprise production scale, stimulating economic development and generating more carbon dioxide, resulting in an overall increase in CE. OPL can effectively reduce CE in the local and surrounding areas. The possible reason for this is that OPL has promoted international trade and technological exchanges, allowing domestic enterprises to introduce and absorb advanced foreign technologies, including clean energy technology, energy conservation and emission reduction technology, and so on. The introduction and application of these technologies can help reduce CE in the production process. In addition, with the increasing awareness of environmental protection, green consumption and low-carbon living have gradually become new trends in society. OPL enables domestic consumers to access more green products and services, thereby promoting the popularization of green consumption and low-carbon living, thus helping to reduce CE in surrounding areas.

To further validate the robustness of the empirical results, this study used dummy variables as replacement indicators for GC variables. Starting from the official implementation of GC in 2012, the value of GC indicators before 2012 is 0, and the value of GC indicators after 2012 is 1. Table 13 shows the estimation results for replacing the GC variable with a dummy variable. Compared with the benchmark regression data, although the coefficient size of GC has changed, it still has a significant negative impact on CE at the 1% level. Therefore, the results of the benchmark regression are valid and robust.

To verify the robustness of the empirical results again, this paper adopted the method of changing the sample time from 2003–2022 to 2013–2022. Table 14 shows the estimation results for replacing the sample period. Compared with the benchmark regression data, although the coefficient size of GC has changed, it still has a significant negative impact on CE at the 1% level. Therefore, the results of the benchmark regression are also valid and robust.

To verify the robustness of the spatial effects, we replaced the spatial weight matrix. Therefore, we replaced the spatial weight matrix with the economically and geographically nested spatial weight matrix, which can comprehensively consider the impact of geographical distance and economic development level. The formula for this matrix is as follows:

(14)$${\mathrm{w}}_{\mathrm{i},\mathrm{j}}^{\mathrm{eg}}\{\begin{array}{c}\hfill \frac{1}{{\mathrm{d}}_{\mathrm{i},\mathrm{j}}\left|{\mathrm{G}}_{\mathrm{i}}-{\mathrm{G}}_{\mathrm{j}}\right|},\text{if}\mathrm{i}\ne \mathrm{j}\hfill \\ \hfill 0,\text{if}\mathrm{i}=\mathrm{j}\hfill \end{array}$$

Where d_i,j denotes the distance between i-th and j-th province. Moreover, G_i and G_j refer to the real GDP of i-th and j-th province. Table 15 presents the estimation results for replacing the spatial weight matrix. Compared with Table 11, the signs and significance levels of all variables remain largely unchanged. Therefore, the results of the spatial effects are valid and robust.