Benchmark regression analysis
We analyzed the multicollinearity problem by variance inflation factor (VIF). According to the test results in Table 3, only the VIF and DF2 variables had a larger VIF. The fact that the VIFs of the other variables were all less than 10 suggests that there was no major multicollinearity issue in the system (Zhao et al. 2020). Although, as the variance of the estimator increases, the regression coefficient is still significant. Meanwhile, since the application of panel data can help avoid the problem of multicollinearity, the F statistics are all significant, and the multicollinearity problem in the model has little impact on the conclusion of the analysis. Adding quadratic terms to the regression model helps reduce the bias of missing variables and better explains the real problem.
Table 3
Variance inflation factor (VIF)
| DF | DF2 | FDI | GOV | HC | FI | IS | Mean |
VIF | 16.44 | 16.15 | 1.71 | 1.70 | 1.49 | 1.40 | 1.26 | 5.74 |
1/VIF | 0.061 | 0.062 | 0.586 | 0.587 | 0.670 | 0.713 | 0.792 | 0.172 |
The regression model's regression results are presented in Table 4. When only the linear relationship is considered, Model 1 indicates that the coefficient for DF is notably positive. By adding the square terms of the explanatory variable to model 2, we find that the numerical finance coefficients are significantly negative, and the square terms are significantly positive. The results of the Hausman test support the use of fixed effects for the data. Therefore, based on Model 2, Model 3 controls for time and province effects, and Model 4 adds control variables and the regression results are still consistent with the above. There is a U-shaped relationship between DF and GEE. This suggests that although DF inhibits the improvement of GEE in the short term, it will promote GEE as its scale expands. The finding echoes the EKC hypothesis (Kaika and Zervas 2013) and verifies Hypothesis 1. In addition, the average value of DF during the sample period is 2.091 to the left of the inflection point DF = 2.294, indicating that the relationship between DF and green economic efficiency in China is still in a critical period of inhibition to facilitation effect.
Possible reasons for this are that in the early stages of DF development, the policies of the supporting regulatory incentive system are yet to be perfected, and the efficiency of capital allocation is low, hindering green economic efficiency; in addition, DF promotion requires massive digital technology equipment and infrastructure, whose production and use may increase carbon emissions, energy consumption, and e-waste production. However, the DF boom will lead to scaled-up investment and increasingly efficient resource allocation, promoting technological R&D and innovation within green enterprises by directing capital flows to improve green economic efficiency (Zhao et al. 2020). Therefore, DF can be a powerful tool in advancing China's green economy in the long run.
Table 4
Regression results of the direct effects of digital finance on green economy efficiency
Variable | Explained variable: GEE |
Model 1 | Model 2 | Model 3 | Model 4 |
DF | 0.527*** | −0.699*** | −2.060*** | −2.662*** |
| (0.070) | (0.228) | (0.700) | (0.809) |
DF2 | | 0.301*** | 0.473*** | 0.580*** |
| | (0.061) | (0.063) | (0.086) |
IS | | | | 1.774 |
| | | | (1.184) |
FI | | | | 0.387** |
| | | | (0.163) |
GOV | | | | 2.340** |
| | | | (1.025) |
FDI | | | | −15.284*** |
| | | | (2.966) |
HC | | | | 0.615** |
| | | | (0.284) |
cons | 0.672*** | 1.632*** | 2.097*** | −0.420 |
| (0.136) | (0.190) | (0.284) | (0.801) |
Province Fixed Effect | No | No | Control | Control |
Time Fixed Effect | No | No | Control | Control |
N | 300 | 300 | 300 | 300 |
r2 | 0.208 | 0.284 | 0.644 | 0.692 |
F | 56.219 | 34.956 | 42.528 | 35.747 |
t statistics in parentheses; *p < 0.10; **p < 0.05; ***p < 0.01 |
Unlike the existing studies that directly test the significance of the quadratic coefficients, this paper tests the U-shaped nonlinear relationship based on the “three-step” method suggested by Haans et al. (2016). First, determine whether the quadratic term of the independent variable is significant. Second, whether the U-shaped curve satisfies the requirement that the slope is negative when the independent variable is small (e.g., at the endpoints of the left interval) and positive when the independent variable is large (e.g., at the endpoints of the right interval). Third, whether the inflection point of the U-shaped curve is within the range of the independent variable value. Table 5 shows that Models 2 − 4 passed the U-shaped relationship test.
Table 5
U-shaped relationship test
| Model2 | Model3 | Model4 |
t-value | 2.86 | 2.78 | 3.14 |
P>|t| | 0.002 | 0.003 | 0.001 |
Inflexion point | 1.16 | 2.176 | 2.294 |
confidence interval (95%) | [0.67193324; 1.4038583] | [0.92718456; 3.0332014] | [0.1833; 4.319276] |
The slope on both sides of the curve | −0.5888159***, 1.905151*** | −1.886333***, 2.028223*** | −2.449496***, 2.351406*** |
nonlinear relationship | U-shape | U-shape | U-shape |
The scope of DF | [0.1833; 4.319276] |
Endogeneity and robustness tests |
The model may have endogeneity problems due to reverse causation and omitted variables. On the one hand, DF promotes GEE, which will help improve corporate profits and promote financial activities, such as money management and investment. Therefore, GEE improvements may have an adverse effect on DF, leading to the reverse causality problem. On the other hand, although the impact from the county and time level is controlled as much as possible in the regression model, the dependent variable may still be interfered with by other factors. Concerning existing studies, this paper uses the following instrumental variables to deal with the endogeneity problem. (1) Digital finance lagged one period (IV1). In terms of time, Since the level of digital financing last year was not affected by the efficiency of the green economy this year, its use as a tool variable can eliminate the negative effects of the reverse causality problem (Li et al. 2021). (2) Referring to the treatment of Zhang et al. (2019), the distance from the provincial capitals to Hangzhou is adopted as an instrumental variable (IV2). Since distance is a constant, to use this instrumental variable in the process of fixed effects estimation, the above distance is multiplied by the year variable (Nunn and Qian 2014). The regression results in columns (1)−(2) of Table 6 show that after adopting the instrumental variable, there is still a significant U-shaped influence relationship between DF and GEE.
In addition, this paper also performs robustness tests by shrinking the tails on the upper and lower 1% quartiles for the main variables. The regression results in column (3) of Table 5 indicate that the direction and significance of the regression coefficients for DF do not change significantly, which further proves the robustness of the benchmark results.
Table 6
Endogeneity and robustness tests
Variable | Explained variable: GEE |
(1) | (2) | (3) |
DF | −6.213*** | −14.541** | −2.803*** |
| (2.294) | (5.912) | (0.786) |
DF2 | 0.899*** | 1.794*** | 0.589*** |
| (0.273) | (0.594) | (0.085) |
IS | 1.631 | 1.061 | 1.625 |
| (1.635) | (1.489) | (1.165) |
FI | 0.623** | 0.817* | 0.387** |
| (0.285) | (0.448) | (0.160) |
GOV | 3.718 | 10.219** | 2.324** |
| (2.306) | (4.092) | (1.009) |
FDI | −13.311 | −7.758 | −14.750*** |
| (8.758) | (5.939) | (2.919) |
HC | 0.992** | 1.534*** | 0.531* |
| (0.497) | (0.454) | (0.279) |
cons | 2.522 | 6.356** | −0.145 |
| (1.710) | (2.991) | (0.786) |
N | 270 | 270 | 300 |
r2 | | | 0.693 |
F | | | 35.824 |
Heterogeneity analysis |
The varying degrees of economic growth and lack of access to financial resources between different areas result in substantial disparities in the effect of DF on green economic productivity. To explore whether DF narrows or exacerbates the regional green economic efficiency development gap, this paper uses the median economic development level to group the samples and test the heterogeneous impact of DF on green economic efficiency.
Table 7 illustrates the coefficient of DF in column (1). The quadratic term has a significantly positive coefficient, suggesting that DF and GEE in underdeveloped regions have a U-shaped correlation, with an inflection point of 2.159, 0.068 higher than that of the whole country. In developed regions, the coefficient of the primary term in column (2) is significantly positive, which means that DF is positively related to green economic efficiency. It is evident that for regions with weaker economic development, before crossing the inflection point, the lack of environmental supervision and the digital divide may temporarily exacerbate the gap in green economic efficiency among regions; however, after crossing the inflection point, developed DF can be an effective supplement to traditional finance by playing its long-tail effect, increasing the access to funds for micro and small businesses to stimulate creativity, and improving the effectiveness of the green economy in underdeveloped areas (Li and Pang 2023; Zhu et al. 2023). Therefore, in the long run, DF can become a late-coming advantage for less-developed regions to catch up with developed provinces and play an inclusive role in filling the green economy development gap.
Table 7
Regional differences in the impact of digital inclusive finance on green economic efficiency
Variable | Undeveloped regions | Developed regions |
(1) | (2) |
DF | −3.063*** | 1.275** |
| (1.044) | (0.627) |
DF2 | 0.709*** | |
| (0.139) | |
IS | −0.075 | 4.098 |
| (1.162) | (3.541) |
FI | 0.352** | 2.828*** |
| (0.165) | (0.830) |
GOV | 3.393** | −2.892** |
| (1.560) | (1.445) |
FDI | −27.815*** | −11.200** |
| (4.414) | (5.427) |
HC | 0.633* | −0.246 |
| (0.334) | (0.446) |
cons | 0.217 | −0.259 |
| (0.813) | (2.225) |
N | 150 | 150 |
r2 | 0.743 | 0.748 |
F | 21.306 | 23.535 |
The intermediary effect of technological innovation
Table 8 shows that the coefficients of digital finance and its quadratic term in columns (1)−(2) are both negative and positive; both are statistically significant at the 1% level, suggesting that DF has a U-shaped influence on TI. To alleviate the possible endogeneity problem in the model, columns (3)−(4) were empirically tested using the instrumental variable method, with the instrumental variable being DF lagged by one period. The regression results remain robust. This echoes the relationship between DF and GEE, upholding Hypothesis 3.
Table 8
Results of the mediation effect test
Variable | OLS | IV |
TEC | GEE | TEC | GEE |
(1) | (2) | (3) | (4) |
DF | −7.226*** | −1.640** | −12.501*** | −4.637** |
| (1.928) | (0.784) | (4.074) | (1.813) |
DF2 | 1.410*** | 0.381*** | 1.941*** | 0.655*** |
| (0.206) | (0.089) | (0.356) | (0.167) |
IS | 6.497** | 0.856 | 6.735** | 0.782 |
| (2.822) | (1.128) | (3.361) | (1.445) |
FI | −0.065 | 0.396** | 0.215 | 0.596*** |
| (0.388) | (0.154) | (0.487) | (0.208) |
GOV | −9.922*** | 3.743*** | −6.620** | 4.552*** |
| (2.444) | (0.998) | (2.993) | (1.278) |
FDI | 27.389*** | −19.157*** | 28.263*** | −16.874*** |
| (7.070) | (2.879) | (7.861) | (3.478) |
HC | −1.937*** | 0.889*** | −1.217 | 1.145*** |
| (0.678) | (0.272) | (0.799) | (0.340) |
TI | | 0.141*** | | 0.126*** |
| | (0.025) | | (0.029) |
_cons | 7.365*** | −1.461* | 12.706*** | 0.920 |
| (1.909) | (0.777) | (3.044) | (1.377) |
N | 300 | 300 | 270 | 270 |
r2 | 0.692 | 0.727 | | |
F | 35.595 | 39.717 | | |
Table 9 presents the results of the Bootstrap tests. The estimated coefficients of the interaction terms of Bootstrap sampling 1000, 2000, and 5000 tests are all significant, and none of the confidence intervals of the mediation effect contain 0, indicating that TI partially mediates the relationship between DF and GEE. Hypothesis 3 is tested again.
Table 9
Bootstrap test of the nonlinear intermediary effect
Intermediary variable | Nonlinear mediation effect | Bootstrap sampling count | The lower limit of the confidence interval | The upper limit of the confidence interval |
Technological innovation | 0.8449626 | 1000 | 0.4395223 | 1.250403 |
0.8449626 | 2000 | 0.4325646 | 1.257361 |
0.8449626 | 5000 | 0.423627 | 1.266298 |
The moderating effect of environmental regulation |
Table 10 reports the regression results of Eq. (5). First, the regression coefficients for the secondary terms of DF on the efficiency of the green economy and the interaction terms of environmental regulation are significant (λ5 = − 0.303, p < 0.05). Second, examining the shift in the U-shaped curve between DF and green economy, the values of regression coefficients in Table 9 are substituted into δ GEE*/ δEN, which can be obtained as δGEE*/ δEN = − 0.06 / (0.662 − 0.606EN)2<0. This indicates that the inflection point moves to the left as the moderating variable EN increases. Therefore, the U-shape of DF and green economic efficiency is positively moderated by environmental regulation, and Hypothesis 3 is verified.
Table 10
Regulatory effects of environmental regulation
| (1) |
GEE |
DF | −0.747*** |
| (0.207) |
DF2 | 0.331*** |
| (0.071) |
EN | −0.259 |
| (0.414) |
DF×EN | 0.844* |
| (0.479) |
DF2×EN | −0.303** |
| (0.148) |
FI | 0.259 |
| (0.217) |
GOV | 2.229* |
| (1.151) |
IS | 1.087 |
| (0.942) |
FDI | −15.073 |
| (10.018) |
HC | −0.029 |
| (0.081) |
cons | 0.634 |
| (0.670) |
N | 300 |
Furthermore, this paper analyzes the moderated role of the curve using a simple slope diagram. Figure 3 shows the curve relationship between DF and GEE under different environmental supervision levels. When environmental supervision is low (EN = M − 1SD), the value of DF at the inflection point is 1.126. When the level of environmental regulation is high (EN = M + 1SD), the value of DF at the inflection point is 0.838. This result shows that the inflection point moved to the left within the range of the value of DF (0.183, 4.319), which once again verifies Hypothesis 3.
The change in the slope of the curve was also analyzed. Since β4 is significantly negative, the U-shaped curve becomes flat. As shown in Fig. 3, before point D, the implementation of stringent environmental regulations amplifies the beneficial effects of DF on the effectiveness of the green economy. However, after point D, low-intensity environmental regulation is more conducive to green economic efficiency, indicating that a high level of DF is compatible with low-intensity environmental regulation.
The possible reason is that, on the one hand, with the development of DF, the financial environment is gradually improved, there is a more efficient allocation of resources, the industrial structure is relatively reasonable, and the development trend of industrial green transformation is satisfactory (Geng et al. 2023). This ensures that green development is less dependent on environmental regulation. On the other hand, the development of DF can improve information transparency (Aziz and Naima 2021; Yu et al. 2022). With better information disclosure policies, green enterprises can stimulate their intrinsic motivation to develop emission reduction technology and continuously improve product quality, producing innovative compensation effects later. In this case, DF does full justice to its market regulation role and promotes the improvement of green economic efficiency. This reduces the government's financial and regulatory burden, allowing it to take a leading role in the market economy instead of being a guiding force. At this time, excessive environmental regulation will, in turn, inhibit market activity, hindering the proper distribution of resources and hampering the effectiveness of the green economy. This is in accordance with our national situation, which emphasizes the development of DF and encourages the market to play a more prominent role in promoting the transformation of the green economy.