#### 5.1. The EKC Estimation

In the EKC studies, if the per capita GDP and its’ quadratic and cubic terms are included as the independent variables of the traditional panel data regression model, then each region (province/city) will have the same shaped EKC, while the intercept (fixed effects) will enable the EKC to shift up and down vertically for different regions. However, there is no reason to assume that different regions in China are experiencing the same CO_{2}-income relationship, given the differences in socio-economics, culture, geography, climate, etc. that exist across these regions. Therefore, this study adopts an alternative and less restrictive random coefficients model that shows the cross-provincial heterogeneities in the shape of the income-CO_{2} nexus.

All the empirical results in this study are generated through Stata 15.

Table 3 presents estimates of Equations (3)–(5) by the random coefficients approach. The linear, squared and cubic income coefficients in the cubic model are highly significant, thus the cubic model specification is superior to the quadratic and linear specifications because the linear and quadratic models are naturally nested in the cubic model. The

χ^{2}-statistics (test of parameter constancy with the null hypothesis:

β_{1j} =

β_{2j} = … =

β_{mj}) overwhelmingly reject that the independent variables are the same for each province. Hence, in order to know the extent to which such an “average” nonlinear (cubic) nexus is meaningful/representative, the province-specific estimations were conducted (shown in

Appendix Table 1 and

Table 2). As one can see, despite the heterogeneities across the provinces, only a small part of them are not subject to cubic relationships. Therefore, the following analysis of the GDPT-CO

_{2} emissions nexus is based around the cubic specification result.

Evidence from the cubic model result highlights signs of the three income terms: negative (−0.113), positive (1.819) and negative (−9.430). This depicts an inversely N-shaped dynamics, which would imply potential EKC dynamics for the GDPT-CO

_{2} relationship with double turning points well inside the total per capita income range (see

Table 2, the ln

GDPT ranges from 3.354 to 7.596 while the corresponding ln

GDPT of the N-shape’s lower and higher peak are approximately 4.369 and 6.371). To put this in a practical way, in China, the developed provinces (generally with a GDPT over 58,470 Yuan, the second turning point) are currently experiencing a monotonic decrease in CO

_{2} emissions while the developing regions are experiencing an increase and the increasing trend would be curbed when the total per capita income reaches around 58,470 Yuan (the 1995 constant prices), then the emissions would start to decrease.

The explanations for the environmental quality improvements after income reaching a threshold (the transitions from second phase to the third phase in the inverse-N dynamic) includes the following: people are willing to pay more for environmental quality as their income rises [

35]; increasing levels of income lead to peoples’ environmental awareness which brings higher environmental pressures on the political agenda [

66]; the economic composition alters with an increase of income, while the secondary industry loses more importance against services [

67]; higher levels of wealth are more often associated with higher levels of technological eco-efficiency, led by changes in material and energy consumption patterns [

68].

#### 5.2. Driving Forces and the Underground Economic Impacts

The EKC can be regarded as a simplified description of multiple socioeconomic factors influencing environmental quality in general and the CO

_{2} emissions in particular [

68]. Rothman [

69] and Torras and Boyce [

70] integrate several factors into their analysis framework to show that the relationship between economic development and environmental quality depends on the effectiveness of the structure, technology advancement and the scale of the economy. The Scale effects tend to aggravate environmental degradation but the structural (when the tertiary industry dominates) and technological effects can offset this effect, so the environmental quality starts to improve at higher income levels, as suggested by the EKC theory.

In the EKC study, the threshold regression technique makes the examination of the threshold effects led by endogenous factors (e.g., technology, economic structure, etc.) suitable from an econometric perspective. Another side benefit of this method is that marginal effects of underground economic scale on CO_{2} emissions can be verified and estimated by indicating the lnGDPT term as the threshold parameter in the indicator function. In this way, the potential interaction and mixed effects between the underground and total economic scale can be overcome.

Table 4 provides the results from threshold tests (F

_{1}, F

_{2}, and F

_{3}, along with their bootstrapped

p-values) based on statistical inference introduced in

Section 4.3. The regression models with the triple-threshold are overwhelmingly rejected by their

F-statistics (with

p-values of 0.608 and 0.656). On the other hand, the

F-tests (F

_{1}) for a single threshold are strongly significant (with

p-values of 0.038 and 0.006), while the

F-tests (F

_{2}) for a double threshold are also significant (with

p-values of 0.048 and 0.018). This provides convincing evidence that there are two thresholds (structural breakpoints) in the empirical relationship. For the remainder of the analysis, this paper works with the double threshold models that can be written as the piecewise function.

It is interesting to note the estimated threshold values are almost the same for both Equations (14) and (15). Estimated coefficients and their OLS t-statistics are listed in

Table 5. Parameter estimates are similar in two different specifications of the regime-dependent variable, which suggests that the threshold regression results are robust. The coefficient of primary interest is the one on the underground economic scale (ln

GDPN), and its point estimates in both models are around 0.16, which suggests that the CO

_{2} emissions are positively related to the scale of the underground economy. Ceteris paribus, a 10% increase in the per capita underground economy would lead to a 1.6% increase in the CO

_{2} emission level in China. In general, there exist many waste emissions activities in the underground economic sectors, for example, resource extraction, transportation by scrapped vehicles, as well as the production in small-scale and informal factories. These firms are usually beyond the supervision of the environmental department [

5]. Hence, a larger scale of the underground economy implies a higher level of CO

_{2} emissions.

The other interest is on economic structure and technological efficiency. Their parameter estimates suggest that the CO

_{2} emission level is positively and non-linearly related to the secondary industry ratio and energy intensity, with low per capita income level provinces (the provinces with an ln

GDPT lower than 4.7, 10,994.72 RMB) having smaller coefficients (

str: 0.006 vs. 0.010; ln

EI: 0.323 vs. 0.343) than the typical provinces (the provinces with an ln

GDPT between 4.7 and 5.6). Not surprisingly, the provinces with high-income levels (the provinces with ln

GDPT higher than 5.6, 27,042.64 RMB) have the highest coefficient of 0.013 and 0.363. Since the secondary industry is energy- and pollution-intensive, the higher the share of secondary industry in GDP is, the higher the level of CO

_{2} emissions would be. Technological progress (energy intensity, the technological effects index, is negatively related to the level of technological advancement) has evident impacts on the upgrade of the energy consumption structure and the energy efficiency of a country. Generally, the more progressive the technology is, the fewer the resources consumed for producing the same output would be and the lower the energy intensity would be, and thus, the lower corresponding CO

_{2} emissions would be [

20,

71].

In fact, Chinese provinces with a higher level of income are usually associated with a lower proportion of secondary industry and higher technological eco-efficiency. Overall, the secondary industry ratio and energy intensity have been decreasing during the sampled period, thus the structural and technological effects drive a continuous reduction in CO_{2} emissions. Moreover, with the increase of total income, the structural and technological effects become more and more obvious. Specifically, after the income (lnGDPT) reaches 4782 (11,934.28 RMB), the structural effect is roughly 66% greater than its initial level and 116% greater than the initial level when the income reaches 5635 (28,005.89 RMB). Similarly, after the income reaches the first threshold, the technical effect is about 6% greater than its initial level, and 12% greater than its initial level after income reaches the second threshold. Parenthetically, it is worth noting that the structural breaking points (thresholds) of the structural and technological effects lie between the inverse-N EKC’s turning points. This indicates that the industrial structure and technology tend to exert beneficial effects before the CO_{2} emissions decrease.