Fiscal decentralization, local government environmental protection preference, and regional green innovation efficiency: evidence from China

Abstract

Green technological innovation has gained in importance in regional policy making towards gaining competitive advantage and sustainable development. This paper used the data envelopment analysis method to calculate regional green innovation efficiency in China, and empirically tested the effect of fiscal decentralization through Tobit model. The regression results show that the local governments with higher fiscal autonomy would prefer to strengthen environmental protection; thus, the regional green innovation efficiency was improved. After the guidance of relevant national development strategies, these effects became more apparent. Our research provided theoretical support and practical guidance for promoting regional led green innovation, improving environmental quality, achieving carbon neutrality, and promoting the high-quality and sustainable development.

Appendix

The SBM model is represented as follows:

$$\underset{\lambda ,{s}^{-},{s}^{+}}{\mathrm{min}}\rho =\frac{1-\frac{1}{m}\sum \limits_{i=1}^{m}\frac{{s}_{i}^{-}}{{x}_{i0}}}{1+\frac{1}{s}\sum \limits_{r=1}^{s}\frac{{s}_{r}^{+}}{{y}_{r0}}}$$

(5)

subject to ${x}_{i0}=\sum \limits_{j=1}^{n}{X}_{ij}{\lambda }_{j}+{{s}_{i}}^{-},i=\mathrm{1,2},...,m$

$$\begin{array}{c}{y}_{r0}=\sum \limits_{j=1}^{n}{Y}_{rj}{\lambda }_{j}-{{s}_{r}}^{+},r=\mathrm{1,2},...s\\ {\lambda }_{j}\ge 0,{{s}_{i}}^{-}\ge 0,{{s}_{r}}^{+}\ge 0\end{array}$$

ρ in Eq. (5) represents the efficiency value. 0 <  ρ  ≤ 1. m and s are the total number of input and output indicators respectively, and ${X}_{rj}$ ${Y}_{rj}$ are the input and output amounts of the jth decision-making unit for the ith input indicator and the rth output indicator, respectively. ${\lambda }_{j}$ are the weights, and ${s}_{i}^{-} \mathrm{and }{s}_{r}^{+}$ are the slack variables for input and output, respectively.

The evaluation process of three-stage DEA model can be divided into three stages as follows.

First, a traditional DEA model is used and the slack variables of the relevant indicators are obtained.

Second, the effects of environmental variables are estimated using the stochastic frontier analysis (SFA) method as:

$$\begin{array}{c}{s}_{ij}={f}^{j}({z}_{i},{\beta }^{j})+{\nu }_{ij}+{\mu }_{ij}\\ (i=\mathrm{1,2},3,...,n;j=\mathrm{1,2},3,...,p)\end{array}$$

(6)

In formula (6), ${s}_{ij}$ represents the slack variable of the jth input of the ith decision-making unit. ${z}_{i}=({z}_{1i},{z}_{2i},...,{z}_{ki})$ represents the value of the kth environmental variable. ${\beta }^{j}$ is the parameter to be estimated for the jth input. ${\nu }_{ij}+{\mu }_{ij}$ is the compound error term, while ${\nu }_{ij}$,represents the random errors, and ${\nu }_{ij}\text{ }N(0,{\sigma }_{jv}^{2})$. ${\mu }_{ij}$ indicate management inefficiencies, and ${\mu }_{ij}\sim {N}^{+}({\mu }_{j},{\sigma }_{ju}^{2})$. ${\mu }_{ij}$ and ${\nu }_{ij}$ are independent of each other.

Subsequently, the input amount was adjusted as follows.

$$\begin{array}{c}{x}_{ij}^{A}={x}_{ij}+\left[\mathrm{max}\left[{f}^{j}\left({z}_{i},{\widehat{\beta }}^{j}\right)\right]-{f}^{j}\left({z}_{i},{\widehat{\beta }}^{j}\right)\right]+\left[\mathrm{max}\left({\widehat{v}}_{ij}\right)-{\widehat{v}}_{ij}\right]\\ \left(i=\mathrm{1,2},3,...,n;j=\mathrm{1,2},3,...p\right)\end{array}$$

(7)

In formula (7), ${x}_{ij}^{A}$ is the input after adjustment, and ${x}_{ij}$ is the input before adjustment.

Third, the efficiency value is recalculated using the adjusted relevant variables and the traditional DEA model.

The calculation steps of entropy method are as follows:

First, the original data are standardized to eliminate the dimensional differences between each indicator, and then, the standardized value of kth indicator ${X}_{itk}$ in year t of province i is obtained:

$$\theta_{itk}=\left\{\begin{array}{c}\frac{X_{itk}-{\min(X}_{itk})}{\max(X_{itk})-\min(X_{itk})},ifX_{itk}\;is\;a\;positive\;indicator\\\frac{{\max(X}_{itk})-X_{itk}}{\max(X_{itk})-\min(X_{itk})},ifX_{itk}\;is\;a\;negative\;indicator\end{array}\right.$$

(8)

$$\widetilde{{\theta }_{itk}}=\left\{\begin{array}{c}{\theta }_{itk} , if {\theta }_{itk}\ne 0\\ {\theta }_{itk}+{10}^{-4}, if{ \theta }_{itk}=0\end{array}\right.$$

(9)

Second, we can calculate the entropy of each standardized index:

$${E}_{k}=-\frac{1}{\mathrm{ln}(n)}\sum \nolimits_{i=1}^{n}\left[\frac{\widetilde{{\theta }_{itk}}}{\sum_{i=1}^{n}\widetilde{{\theta }_{itk}}}\times \mathrm{ln}\left(\frac{\widetilde{{\theta }_{itk}}}{\sum_{i=1}^{n}\widetilde{{\theta }_{itk}}}\right)\right]$$

(10)

where n represents the sample size.

Third, the entropy weight of the kth index is:

$${W}_{k}=\frac{1-{E}_{k}}{\sum_{k=1}^{m}\left(1-{E}_{k}\right)}$$

(11)

Finally, the weighted composite index ${\gamma }_{it}$ is:

$${\gamma }_{it}=\sum \nolimits_{k=1}^{m}{W}_{k}\times \widetilde{{\theta }_{itk}}$$

(12)

Please see Table 14, and 15

Table 14 GIE value-SBM model

Due to missing data, the statistical scope of this table does not include Hong Kong, Macao, Taiwan, and Tibet

Table 15 GIE value-three-stage DEA model

Due to missing data, the statistical scope of this table did not include Hong Kong, Macao, Taiwan, and Tibet