3.4.3. Comprehensive Discussion

The above analysis of the spatio-temporal evolution of carbon emissions and land economic efficiency in each region shows that regions with high land economic efficiency generally do not have low carbon emissions (for example, Figures 3a and 7a). This suggests that even in eastern China, it is difficult to achieve better land–economy–environment synergy. Such a conclusion contradicts hypothesis H1. However, this may not be the case as the map analysis requires a quantitative analysis of the econometric model. Furthermore, the study shows that the level of land economic efficiency in each region does not usually ge<sup>t</sup> worse as time progresses, but rarely breaks through to "high efficiency". This suggests that the level of land economic efficiency in eastern China tends to be at the same level, indirectly reflecting the fact that each region in eastern China is actually improving its own land economic efficiency.

**Figure 7.** Spatio-temporal evolution map of land economic efficiency. (**a**) Beijing, Tianjin and Shanghai. (**b**) Shandong Province. (**c**) Zhejiang Province. (**d**) Fujian Province.

**Figure 8.** Spatio-temporal evolution map of land economic efficiency in Hebei Province.

**Figure 9.** Spatio-temporal evolution map of land economic efficiency in Jiangsu Province.

**Figure 10.** Spatio-temporal evolution map of land economic efficiency in Guangdong Province.

#### **4. Empirical Design and Results**

*4.1. Model Design*

This study involves data from 84 prefecture-level cities and municipalities from 2011–2017, and therefore uses a panel regression model. Referring to the C-D production function [66], the main regression model (Equation (5)) is developed.

$$
\ln \text{Carbon}\_{it} = \alpha + \beta \text{Land}\_{-} \triangle \text{coE}\_{it} + \gamma \ln \text{Control}\_{it} + \varepsilon\_{it} \tag{5}
$$

where *i* denotes prefecture-level city *i* and *t* denotes year. *Carbonit* denotes carbon emissions, *Land* \_ *EcoEit* denotes land economic efficiency and *Controlit* denotes control variables, which in this study refer to foreign capital utilization intensity (Fore\_CUI) and innovation intensity (Inno\_I). *εit* denotes the random disturbance term.

Each region in the study has its own unique underpinnings, such as policies and culture, and these unique attributes may change over time. Therefore, in this study, *θt* and *σi* are added to Equation (5). *θ<sup>t</sup>*, which can control for changes over time, represents time fixed effects, and *σi*, which controls for regional idiosyncrasies, represents spatial fixed effects.

$$
\ln \text{Carb}\_{il} = a + \beta \text{Land}\_{-} \text{EcoE}\_{il} + \gamma \ln \text{Control}\_{il} + \theta\_l + \sigma\_i + \varepsilon\_{il} \tag{6}
$$

Equation (6) is used to test hypothesis H1, and this study proposes hypothesis H2 on the basis of hypothesis H1. In order to implement the process, this study constructs dummy variables (*D*), where, if region *i* belongs to the most economically developed group of regions in eastern China, *D* = 1; otherwise, *D* = 0. The specific equation is as follows:

$$
\ln \text{Carbon}\_{\text{it}} = \pi + \beta\_1 \text{Land}\_{-} \text{EcoE}\_{\text{it}} + \beta\_2 \text{D} \ast \text{Land}\_{-} \text{EcoE}\_{\text{it}} + \gamma \ln \text{Control}\_{\text{it}} + \theta\_{\text{l}} + \sigma\_{\text{i}} + \varepsilon\_{\text{it}} \tag{7}
$$
