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Given that the 16th National Congress of the Communist Party of China was held in November 2002, it was emphasized that “development is an unyielding principle, and every opportunity must be seized to accelerate progress”. This prompted provincial governments to vigorously promote regional industrialization and urbanization. However, the accelerated process of industrialization and urbanization has led to a significant increase in energy demand and consumption, exacerbating the conflict between energy and the environment. Therefore, this study takes the year 2003 as its starting point and first calculates the EEE of each province in China. Subsequently, it investigates the impact of GTI on EEE under the influence of ER. However, the calculation of EEE requires the input indicator of capital stock, which is measured by gross fixed capital formation in this research. Unfortunately, this data is not available in the China Statistical Yearbook after 2017. To ensure data availability, the study ultimately selects data from 30 provinces and regions in China (excluding Tibet, Hong Kong, Macao, and Taiwan) from 2003 to 2017 for analysis.
A two-step approach was used to investigate the impact of GTI on EEE under the influence of ER from 2003 to 2017. Firstly, EEE in 30 provinces was measured. Secondly, the impact of GTI on EEE under the influence of ER was analyzed. It is shown in Fig. 1. This article considers EEE, SE, and PTE as explanatory variables, GTI, SubGI, and SymGI as explanatory variables, and ER as a moderating variable. Besides, gross domestic product per capita (PGDP), industrial structure (IS), foreign direct investment (FDI), energy consumption structure (ECStruc), urbanization level (Urban), R&D investment intensity (RDI), energy intensity (EI), fixed asset investment (Fix), R&D personnel input (RDP) are used as control variables.
Data description
Green technology innovation (GTI). GTI refers to the development and application of new products and technologies aimed at environmental protection, pollution reduction, energy and resource conservation, and promoting sustainable development1,50. On the other hand, green patents are inventions, utility models, and design patents with the subject of invention related to resource conservation, energy efficiency, and pollution prevention. Considering the alignment with the definition of GTI, design patents only cover product shapes and patterns, hence this study adopts the total number of green invention patents and green utility model patents to measure GTI51. As the patent granting process in China is known to be time-consuming, using the total number of patent applications can promptly and accurately reflect the willingness and motivation of enterprises to engage in GTI. Additionally, based on the essence of GTI definition, which includes both the development and promotion of new clean energy technologies, as well as improvements in ecological environment protection and resource recycling technologies, this research attempts to decompose GTI into SubGI and SymGI.
Substantive green innovation (SubGI). Substantive green technology innovation is focused on the development and adoption of environmentally beneficial technologies that result in significant reductions in resource consumption and carbon emissions. Green invention patents exhibit creativity, novelty, and energy-efficient features, aligning with the fundamental principles of substantive green innovation52. As a result, this study utilizes the quantity of green invention patent applications as a metric to assess SubGI11,53.
Symbolic green innovation (SymGI). Symbolic green innovation is aimed at responding to government environmental policies, emphasizing improvements to existing technologies but typically lacking significant positive environmental impacts. Green utility model patents refer to product or process improvements that feature energy-saving and emission reduction characteristics, aligning with the core principles of symbolic green technology innovation52,54. Hence, this study employs the quantity of green utility model patent applications as a metric to assess SymGI11,53.
Environmental regulation (ER). Based on the polluter-pays principle, China began to levy emission charges in 198255 By imposing charges on enterprises and individuals that emit pollutants, it can incentivize them to adopt more environmentally-friendly measures, reduce emissions of pollutants, and consequently mitigate environmental pollution and resource wastage. In light of this, the emission charges to GDP is used as a measure of ER.
This study integrates the exercises of several scholars to take the PGDP56, IS12, FDI44, ECStruc52, Urban56, RDI57, EI58, Fix59, RDP as control variable, the definition of each variables is shown in Table 10.
Non-radial direction distance function
In this section, the study concentrates on the computation of the dependent variable, EEE. Due to the flexibility of DEA in not requiring a specific functional form, it can effectively measure the EEE of DMU60,61. In this context, DMU refers to the 30 provinces from 2003 to 2017.
Non-radial Directional Distance Function (NDDF) is a variant of the DEA method that offers several advantages in assessing EEE. Firstly, it allows for the simultaneous consideration of multiple input and output indicators, enabling a more comprehensive evaluation of regional efficiency. Secondly, it introduces directionality, which determines the optimization direction, leading to more precise assessment results. Additionally, it permits the assignment of different weights to different input and output indicators when calculating the distance function, reflecting their importance in the evaluation process. In summary, NDDF demonstrates broader applicability when assessing EEE as it comprehensively accounts for multiple indicators and their respective weights, contributing to a more accurate assessment of the efficiency levels of businesses or regions.
The NDDF function is defined based on the principle of output expansion while minimizing pollutant emissions as follows62:
$$\overrightarrow{D}\left(K,L,E,Y,C;g\right)=sup\left\{{w}^{T}\beta :\left(\left(K,L,E,Y,C\right)+g\cdot diag\left(\beta \right)\right)\in P\right\}$$
(1)
where K, L, E are input variables, Y is desired output and C is undesired output. The input and output variables are shown as follows:
Input indicator: Capital (K). Estimate the capital stock using the perpetual inventory method34. Labor (L). Measures labor through the number of people employed at the end of each year in each region. Energy (E). Measured using the consumption of tons of standard coal in each region.
Expected output: Total output value of each province (Y). Converted from nominal GDP to 2003 constant price GDP through a price index.
Unintended output: CO2 emissions (C). CO2 emissions are calculated from the calorific value of consumption of nine energy sources: raw coal, coking coal, crude oil, gasoline, kerosene, diesel fuel, fuel oil, natural gas, and electricity.
Additionally, \({w}^{T}=\left({w}_{K},{w}_{L},{w}_{E},{w}_{Y},{w}_{C}\right)\) denotes the vector of weights for each input–output variable; \({\beta }^{T}=\left({\beta }_{K},{\beta }_{L},{\beta }_{E},{\beta }_{Y},{\beta }_{C}\right)\) denotes the slack vector of the proportion in which each input–output variable can be expanded or contracted; \({g}^{T}=\left({g}_{K},{g}_{L},{g}_{E},{g}_{Y},{g}_{C}\right)\) denotes the direction vector of the direction of input and output changes (i.e., expansion or contraction), and \(diag\left(\beta \right)\) denotes the diagonalization of the \(\beta \) vector.
EEE examines the maximum shrinkage ratio of energy inputs, undesired outputs, and the maximum expansion ratio of desired outputs with constant capital and labor inputs. Therefore, the weight vector is set to \({w}^{T}=\left(\mathrm{0,0},\frac{1}{3},\frac{1}{3},\frac{1}{3}\right)\) , and the respective direction vector is \(g=\left(\mathrm{0,0},-\mathrm{E},\mathrm{Y},-\mathrm{C}\right)\) , and the corresponding linear programming problem is as follows:
$$\overrightarrow{D}\left(K,L,E,Y,C\right)=max\left\{\frac{1}{3}{\beta }_{E}+\frac{1}{3}{\beta }_{Y}+\frac{1}{3}{\beta }_{C}\right\}$$
(2)
Similarly, the optimal solution for the relaxation variable \({\beta }_{it}^{*}={\left({\beta }_{it,K}^{*},{\beta }_{it,L}^{*},{\beta }_{it,E}^{*},{\beta }_{it,Y}^{*},{\beta }_{it,C}^{*}\right)}^{T}\) and thus the EEE for each province and region is:
$${EEE}_{it}=\frac{1}{6}\left(\frac{{Y}_{it}/{E}_{it}}{\left({Y}_{it}+{\beta }_{it,Y}^{*}{Y}_{it}\right)/\left({E}_{it}+{\beta }_{it,E}^{*}{E}_{it}\right)}+\frac{{Y}_{it}/{C}_{it}}{\left({Y}_{it}+{\beta }_{it,Y}^{*}{Y}_{it}\right)/\left({C}_{it}+{\beta }_{it,Y}^{*}{C}_{it}\right)}\right)$$
(3)
Dynamic spatial Durbin model
The literature review mentions that ER has spatial spillover effects and that CO2 generates spatial spillover due to geographic boundaries or natural winds, among other issues. In order to further illustrate the existence of spatial effects among the research variables, this article firstly analyzes the explanatory and interpreted variables by using Moran’s I index. As in Eq. (4):
$${\mathrm{Moran}}^{\mathrm{^{\prime}}}\mathrm{s I}=\frac{\mathrm{n}\sum_{\mathrm{i}=1}^{30}\sum_{\mathrm{j}=1}^{30}{\mathrm{W}}_{\mathrm{ij}}\left({\mathrm{x}}_{\mathrm{it}}-{\overline{\mathrm{x}}}_{\mathrm{t}}\right)\left({\mathrm{x}}_{\mathrm{jt}}-{\overline{\mathrm{x}}}_{\mathrm{t}}\right)}{\sum_{\mathrm{i}=1}^{30}{\left({\mathrm{x}}_{\mathrm{it}}-{\overline{\mathrm{x}}}_{\mathrm{t}}\right)}^{2}\sum_{\mathrm{i}=1}^{30}\sum_{\mathrm{j}=1}^{30}{\mathrm{W}}_{\mathrm{ij}}}$$
(4)
where \({\overline{x}}_{t}=\frac{1}{30}\sum_{i=1}^{30}{x}_{it}\), and \({x}_{it}\) are the variable to be spatially autocorrelated tested. \({W}_{ij}\) are the spatial weight matrix. To improve the accuracy of the results, three spatial weight matrices are considered in this study: the geographic neighborhood weight matrix (\({W}_{a}\)), the geographic distance weight matrix (\({W}_{b}\)), and the economic geographic distance weight matrix (\({W}_{c}\)).
Next, except for the spatial effect, there is also a time lag in CO2 emissions63,64. Thus, in order to make the empirical results more reliable, the dynamic spatial Durbin model (DSDM), which takes time and space into consideration, is adopted as the empirical model in this paper. As shown in Eqs. (5) to (10). Where, in order to have a more in-depth understanding of the effect of GTI on EEE, this article adds the quadratic term of GTI ((\({\mathrm{GTI}}_{it}\))2) into the model, the \(\sum_{j=1}^{30}{W}_{ij}{lnEEE}_{it}\), \(\sum_{j=1}^{30}{W}_{ij}{lnGTI}_{it}\), \(\sum_{j=1}^{30}{W}_{ij}{lnER}_{it}\), \(\sum_{j=1}^{30}{W}_{ij}{lnSubGI}_{it}\), \(\sum_{j=1}^{30}{W}_{ij}{lnSymGI}_{it}\), \(\sum_{j=1}^{30}{W}_{ij}{lnPTE}_{it}\) and \(\sum_{j=1}^{30}{W}_{ij}{lnSE}_{it}\) are spatial variables, \({lnControls}_{it}\) is a control variables.
$${lnEEE}_{it}={\alpha }_{0}+{\lambda }_{0}{lnEEE}_{it-1}+{\rho }_{0}\sum_{j=1}^{30}{W}_{ij}{lnEEE}_{jt}+{\iota }_{0}\sum_{j=1}^{30}{W}_{ij}{lnGTI}_{jt}+{\varpi }_{1}{lnGTI}_{it}+{\varpi }_{2}{\left({lnGTI}_{it}\right)}^{2}+\varpi {lnControls}_{it}+{\mu }_{i}+{\varepsilon }_{it}$$
(5)
$${lnEEE}_{it}={\alpha }_{0}+{\lambda }_{1}{lnEEE}_{it-1}+{\rho }_{1}\sum_{j=1}^{30}{W}_{ij}{lnEEE}_{jt}+{\iota }_{1}\sum_{j=1}^{30}{W}_{ij}{lnGTI}_{jt}+{\alpha }_{1}{lnGTI}_{it}+{\alpha }_{2}{\left({lnGTI}_{it}\right)}^{2}+{\vartheta }_{1}\sum_{j=1}^{30}{W}_{ij}{lnER}_{jt}{+\alpha }_{3}{lnER}_{it}+{\kappa }_{1}\sum_{j=1}^{30}{W}_{ij}{\mathrm{ln}\left(GTIER\right)}_{jt}+{\alpha }_{4}{\mathrm{ln}\left(GTIER\right)}_{it}+\alpha {lnControls}_{it}+{\mu }_{i}+{\varepsilon }_{it}$$
(6)
$${lnEEE}_{it}={\alpha }_{0}+{\lambda }_{2}{lnEEE}_{it-1}+{\rho }_{2}\sum_{j=1}^{30}{W}_{ij}{lnEEE}_{jt}+{\nu }_{1}\sum_{j=1}^{30}{W}_{ij}{lnSubGI}_{jt}+{\beta }_{1}{lnSubGI}_{it}+{\pi }_{1}\sum_{j=1}^{30}{W}_{ij}{lnSymGI}_{jt}+{\beta }_{2}{lnSymGI}_{it}+{\vartheta }_{2}\sum_{j=1}^{30}{W}_{ij}{lnER}_{jt}{+\beta }_{3}{lnER}_{it}+{\xi }_{1}\sum_{j=1}^{30}{W}_{ij}{\mathrm{ln}\left(SubGIER\right)}_{jt}+{\beta }_{4}{\mathrm{ln}\left(SubGIER\right)}_{it}+{\zeta }_{1}\sum_{j=1}^{30}{W}_{ij}{\mathrm{ln}\left(SymGIER\right)}_{jt}+{\beta }_{5}{\mathrm{ln}\left(SymGIER\right)}_{it}+\beta {lnControls}_{it}+{\mu }_{i}+{\varepsilon }_{it}$$
(7)
$${lnPTE}_{it}={\alpha }_{0}+{\lambda }_{3}{lnPTE}_{it-1}+{\varphi }_{1}\sum_{j=1}^{30}{W}_{ij}{lnPTE}_{jt}+{\iota }_{2}\sum_{j=1}^{30}{W}_{ij}{lnGTI}_{jt}+{\gamma }_{1}{lnGTI}_{it}+{\gamma }_{2}{\left({lnGTI}_{it}\right)}^{2}+{\vartheta }_{3}\sum_{j=1}^{30}{W}_{ij}{lnER}_{jt}{+\gamma }_{3}{lnER}_{it}+{\kappa }_{2}\sum_{j=1}^{30}{W}_{ij}{\mathrm{ln}\left(GTIER\right)}_{jt}+{\gamma }_{4}{\mathrm{ln}\left(GTIER\right)}_{it}+\gamma {lnControls}_{it}+{\mu }_{i}+{\varepsilon }_{it}$$
(8)
$${lnPTE}_{it}={\alpha }_{0}+{\lambda }_{4}{lnPTE}_{it-1}+{\varphi }_{2}\sum_{j=1}^{30}{W}_{ij}{lnPTE}_{jt}+{\nu }_{2}\sum_{j=1}^{30}{W}_{ij}{lnSubGI}_{jt}+{\delta }_{1}{lnSubGI}_{it}+{\pi }_{1}\sum_{j=1}^{30}{W}_{ij}{lnSymGI}_{jt}+{\delta }_{2}{lnSymGI}_{it}+{\vartheta }_{4}\sum_{j=1}^{30}{W}_{ij}{lnER}_{jt}{+\delta }_{3}{lnER}_{it}+{\xi }_{2}\sum_{j=1}^{30}{W}_{ij}{\mathrm{ln}\left(SubGIER\right)}_{jt}+{\delta }_{4}{\mathrm{ln}\left(SubGIER\right)}_{it}+{\zeta }_{2}\sum_{j=1}^{30}{W}_{ij}{\mathrm{ln}\left(SymGIER\right)}_{jt}+{\delta }_{5}{\mathrm{ln}\left(SymGIER\right)}_{it}+\delta {lnControls}_{it}+{\mu }_{i}+{\varepsilon }_{it}$$
(9)
$${lnSE}_{it}={\alpha }_{0}+{\lambda }_{5}{lnSE}_{it-1}+{\phi }_{1}\sum_{j=1}^{30}{W}_{ij}{lnSE}_{jt}+{\iota }_{3}\sum_{j=1}^{30}{W}_{ij}{lnGTI}_{jt}+{\eta }_{1}{lnGTI}_{it}+{\eta }_{2}{\left({lnGTI}_{it}\right)}^{2}+{\vartheta }_{5}\sum_{j=1}^{30}{W}_{ij}{lnER}_{jt}{+\eta }_{3}{lnER}_{it}+{\kappa }_{3}\sum_{j=1}^{30}{W}_{ij}{\mathrm{ln}\left(GTIER\right)}_{jt}+{\eta }_{4}{\mathrm{ln}\left(GTIER\right)}_{it}+\eta {lnControls}_{it}+{\mu }_{i}+{\varepsilon }_{it}$$
(10)
Model (5) is the model of the impact of GTI on EEE without considering ER. Model (6) is the impact of GTI on EEE under the influence of ER, corresponding to RF1 in Fig. 2 of the research framework. Model (7) is the impact of SubGI and SymGI on EEE under the influence of ER, corresponding to RF2 in Fig. 2 of the research framework. Model (8) and model (10) are the effects of GTI on PTE and SE under the influence of ER, corresponding to RF3 in Fig. 2 of the research framework. Model (9) is the effects of SubGI and SymGI on PTE under the influence of ER, corresponding to RF4 in Fig. 2 of the research framework. Where \({\alpha }_{0}\) denote the constant term; \({\lambda }_{i}\) is the time-lag effects of the explained variables; \({\varpi }_{i}\), \({\alpha }_{i}\), \({\beta }_{i}\), \({\gamma }_{i}\), \({\delta }_{i}\), and \({\eta }_{i}\) are the coefficients of the independent and control variables; \({\mu }_{i}\) is the individual fixed effect; \({\varepsilon }_{it}\) refers to the error term. \(\uprho \), \(\mathrm{\varphi }\), \(\upphi \), \(\upiota \), \(\upnu \), \(\uppi \), \(\mathrm{\vartheta }\), \(\upkappa \), represent the coefficients of spatial spillover effects of the explained variables, explanatory variables and interaction terms, respectively.
Due to the panel nature of the data, involving both time series and cross-sectional dimensions, using Ordinary Least Squares (OLS) for estimation would result in biased and inconsistent estimates19. Furthermore, Generalized Least Squares (GLS) can be applied to panel data but does not account for spatial effects, leading to biased estimates as well. Finally, spatial autoregressive model (SAR), spatial error model (SEM) and spatial Durbin’s model (SDM) all consider the influence of spatial factors. However, SAR neglects cross-variable autocorrelation, while SEM overlooks spatial dependency among variables. Hence, this study opted for SDM as the base model, extending it to incorporate lag effects, thereby forming a DSDM.
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