Heterogeneous and Interactive Effects of Multi-Governmental Green Investment on Carbon Emission Reduction: Application of Hierarchical Linear Modeling

Abstract

Although both prefectural governmental green investment (GGI_city) and provincial governmental green investment (GGI_prov) have potentially diverse impacts on prefectural cities’ carbon emission reduction (CER), previous studies have rarely examined the effects of governmental green investment (GGI) on different indicators of CER such as total carbon dioxide emissions (CE), carbon emissions intensity (CEI) and per capita carbon emissions (PCE) in the context of prefectural cities nested in provinces in China. In our research, six hierarchical linear models are established to investigate the impact of GGI_city and GGI_prov, as well as their interaction, on CER. These models consider eight control factors, including fractional vegetation coverage, nighttime light index (NTL), the proportion of built-up land (P_built), and so on. Furthermore, heterogeneous impacts across different groups based on provincial area, terrain, and economic development level are considered. Our findings reveal the following: (1) The three indicators of CER and GGI exhibit significant spatial and temporal variations. The coefficient of variation for CEI and PCE shows a fluctuating upward characteristic. (2) Both lnGGI_city and lnGGI_prov have promoted CER, but the impact strength of lnGGI_prov on lnCE and lnPCE is more pronounced than that of lnGGI_city. GGI_prov can strengthen the effect of GGI_city significantly for lnCE. Diverse control variables have exerted significant impacts on the three indicators of CER, albeit with considerable variation in their effects. (3) The effect of GGI on CER is significantly heterogeneous upon conducting grouped analysis by provincial area size, terrain complexity, and economic development level. The interaction term lnGGI_city:lnGGI_prov is stronger in the small provincial area group and simple terrain group. Among the control variables, economic Development Level (GDPpc), the logarithm of gross fixed assets investment (lnFAI), NTL, and P_built exhibit particularly pronounced differences across different groups. This study provides a robust understanding of the heterogeneous and interactive effects of GGI on CER, aiding in the promotion of sustainable development.

1. Introduction

Global warming presents a grave risk to both natural ecosystems and human societies, largely orchestrated by the emissions of greenhouse gases, notably carbon dioxide [1,2]. The task of realizing carbon emission reduction (CER) is a globally significant issue, particularly in the case of countries like China. This is due to the fact that China is the largest emitter of greenhouse gases globally, accounting for one-third of global emissions in 2023, and is distinguished by its extensive fossil energy usage and comparably slow-paced progression in green technology [3]. Releasing CER requires the provinces, cities, and autonomous regions to increase investment in environmental protection, reduce energy consumption, and promote high-quality economic development [4,5,6]. Green investment, as a form of direct regulatory environmental policy instrument, is a key component in promoting carbon emission reduction and environmental governance in the new era [7]. Therefore, in the context of China’s “carbon peaking and carbon neutrality” strategy, clarifying the comprehensive impact of multi-governmental green investment (GGI) on CER is very important in the context of global efforts to reduce carbon emissions [8,9] and needs to be further studied.

In recent years, numerous indices have been developed from multiple perspectives to measure CER [10,11]. These indices often consider aspects such as the type of economic activity (e.g., energy production, industrial processes), the greenhouse gas involved (e.g., carbon dioxide, methane), and the emissions intensity (emissions per unit of output) [12]. Some commonly used indices in the multidimensional CER process index system include total carbon dioxide emissions (CE) [13], carbon emissions intensity (CEI) [14], per capita emissions (PCE) [15], carbon emissions decoupling, and so on. And previous international literature has scrutinized carbon emissions with different determinants [16], such as the impacts of urbanization [17,18], energy use [19], renewable energy consumption [20,21], foreign direct investments [22], technological innovation [23], economic growth [24,25,26], population density [27], green finance [28,29,30], fractional vegetation coverage, nighttime light index [14], and so on. Among these determinants, GGI holds a significant role in CER, which has been indicated in the previous study [12,31,32]. Furthermore, they also demonstrate the varied impacts of GGI on the different CER indicators [31]. On the one hand, multilevel GGI can directly promote CER, as well as play an educative role, such as funding projects that encourage green household consumption, thereby indirectly diminishing household consumption of carbon-intensive goods. On the other hand, governments could increase investment in strategically leveraging energy transformation, renewable energy technologies, among others, to mitigate carbon emissions [33]. Consequently, GGI plays a complex yet pivotal role in CER [12].

Previous studies have applied different methods from multiple spatial scales and multiple research angles to evaluate the complex relationship between different determinants and CER [34,35]. Among these methods are regression analysis, dynamic spatial panel models [24], the Granger causality test, threshold effect models [36], geographic weighted regression [37,38], quantile regression analysis [39], partially linear functional-coefficient models [32], and so on [40]. Additionally, studies have utilized several decomposition methods, such as structural decomposition analysis, indicator decomposition analysis [41], and other various econometric models [42,43], such as the LMDI equation [44,45], IPAT equation, PLS–STIRPAT model [46]. Altogether, these investigations have played an indispensable role in shaping our understanding of the relationship between GGI and CER [47], and they have also been instrumental in providing valuable policy recommendations that have greatly assisted governmental decision-making processes [12]. However, statistical relationships may indeed change based on the different models, variables, spatial and temporal aspects, index measurement, sample selections, and so on, even sometimes, some contradictory conclusions may indeed emerge, implying the complexity of the relationship between GGI and CER [48]. Possible reasons for such outcomes most likely stem from the failure of considering the data’s hierarchical nested structure, which can lead to misconstrued interpretations [49,50]. Taking into account the data’s hierarchical nested structure can provide a more accurate and nuanced understanding of the relationship between GGI and CER.

Most of the existing studies are based on the same level of data, such as national, regional, provincial, and prefectural city scales, to study the relationship between GGI and CER [34,51]. However, the panel data used in these prior studies exhibits a multi-layered, nested feature that is typical of a multi-governmental management system [52,53]. In such a system, economic and social development at the lower levels, such as prefectural cities, are influenced by policies and strategies set by the higher provincial level [49]. The accuracy of the estimated results can be impacted negatively if we ignore these key characteristics. Moreover, when looking at different levels of administrative divisions, it is important to consider the possibility of interactive effects between variables at these different levels [54]. This cross-level interactive impact of GGI on CER is often overlooked and should be taken into account in studies.

It is a crucial point to note that the effect of multi-level GGI on CER does not align with the assumptions of a normal distribution, variance homogeneity, and independent random errors between individuals [55]. That means traditional linear regression models, which rely on these assumptions, are not adequate to handle panel data with multi-layer nested features. Such a situation calls for “multilevel analysis”, which includes analytical approaches such as random effects, random coefficient models, and mixed-effects models [56]. Among them, the Hierarchical Linear Model (HLM), developed in the 1990s, has proven particularly suitable for accurately estimating panel data with nested features [50,57]. As a result, a considerable number of studies have adopted multi-level linear models to simulate the multi-level relationship of factors in various fields, such as education [58], economic development [59,60], social management [61], and environmental quality [62]. HLM has made some progress in methodological innovation, such as advancing from two-level models to three hierarchical linear models [56] or combining HLM with GWR to develop a hierarchical and geographically weighted regression (HGWR) model [63]. The adaptability of the multi-level linear model is proposed to fit the situations where prefectural cities are nested in provinces [64]. However, there has been a sparse application of the hierarchical linear model to analyze the multi-level relation between GGI and CER, unfortunately [65].

The diversity of China’s regional characteristics—spanning natural resource endowments, social and demographic conditions, economic development, industrial structure, and characteristics of energy utilization—inherently results in a great variation in the CER process across different regions [66]. Since the performance of the reform and opening up policy in mainland China, there has been a significant disparity in the pace and intensity of urban development and the quality of natural resources and environmental preservation across different provinces [67]. These factors directly and indirectly affect the relationship between multi-level GGI and CER [68,69]. Therefore, it is important to examine whether and how this relationship varies across regions that differ in area sizes, terrain topography, and economic development levels [47], which may facilitate the local contextualization of GGI to enhance its role in promoting sustainability. These examinations would provide new insights into the heterogeneous and cross-level interactive effects of GGI on CER, particularly with regard to the three indicators of CER.

In this study, three-level hierarchical linear models are used to investigate the interaction between multi-level GGI and CER. The core contributions of our study, distinguishing it from prior research, are threefold: (1) The creation of six hierarchical linear models aimed at examining GGI’s impact on three key CER indicators: CE, CEI, and PCE. (2) We conducted a comprehensive analysis to investigate the influence of both provincial and prefecture-level GGI on CER, and how provincial-level governmental green investment (GGI_prov) exerts an indirect impact on the prefecture cities’ CER via the prefecture-level governmental green investment (GGI_city). (3) We explored how the heterogeneous impact of GGI on CER differs across regions with different area sizes, terrain complexity, and levels of economic development. The research contributes to offering a point of reference for relevant departments to develop policies on GGI and CER, aiding governmental efforts in implementing CER policies tailored to different regions.

2. Selection of Variables and Data Sources

2.1. Selection of Variables

2.1.1. Selection of Explained Variables

In line with recent research [12], we utilized three indicators of CER—CE, CEI, and PCE—as dependent variables. These measures reflect the real-world trajectory of CER in Chinese prefecture-level cities from various perspectives. In the regression model, the logarithmic form of three indicators was taken:

(1)

The logarithm of total carbon dioxide emissions (lnCE): lnCE considers the logarithm of the sum of carbon emissions generated by direct energy, electric energy, transportation, and heat energy for each prefecture-level city as its total carbon emissions [34].

(2)

The logarithm of carbon emissions intensity (lnCEI): lnCEI refers to the logarithm of carbon emissions per unit GDP [70]. lnCEI offers insights into the environmental cost associated with GDP production. If a region or country demonstrates decreasing carbon emissions per GDP unit while the economy is growing, it suggests the adoption of a low-carbon development model. This index allows us to measure the impact of the nature and trajectory of China’s GGI on low-carbon development.

(3)

The logarithm of per capita carbon emissions (lnPCE): lnPCE measures the logarithm of the ratio of total carbon emissions to the population of prefecture-level cities [15]. Excluding the influence of population size, lnPCE offers insight into the effectiveness of carbon emission reduction from a relative change perspective.

2.1.2. Selection of Core Explanatory Variable

The green investment (GI), recognizes the total expenditure on energy conservation and environmental protection within its domain [7]. Previous research has presented several definitions of green investment but lacks an all-encompassing approach for its calculation in the theoretical field. A majority of existing studies primarily use environmental protection investment as a metric, incorporating the notion of productive green investment (i.e., investment in water conservation construction and forest management) and the volume of green enterprise financing to represent green investment holistically. This paper focuses on GGI, defined as government-funded investments aimed at curbing environmental pollution [12]. This covers investment in urban environmental infrastructure construction (including gas, central heating, drainage, landscaping, urban sanitation, etc.), industrial pollution source control (encompassing waste gas, wastewater, solid waste, and noise control), and investment in pollution prevention and control of new projects (including the construction of “three simultaneous” projects). The explanatory variables are the logarithm of governmental green investment at the city level (lnGGI_city) and the logarithm of governmental green investment at the provincial level (lnGGI_prov).

2.1.3. Selection of Control Variables

To control outside influences on the regression outcomes between GGI and CER, according to the references [7,12,14,15], eight indicators were selected as control variables for this study to ensure the model’s validity and precision: economic development level (GDPpc), the logarithm of gross fixed assets investment (lnFAI), the logarithm of the total energy consumption (lnTEC), proportion of the secondary industry in GDP (GDP2), proportion of the tertiary industry in GDP (GDP3), the logarithm of fractional vegetation coverage (lnFVC), nighttime light index (NTL), and proportion of build-up land (P_built).

2.2. Data Sources

The carbon emissions are sourced from the Emissions Database for Global Atmospheric Research (EDGAR), which is based on the most recent version 8.0 (https://edgar.jrc.ec.europa.eu/dataset_ghg80, accessed on 16 October 2024). The original spatial resolution of EDGAR 8.0 is 0.1 degrees by 0.1 degrees. The GGI_city and GGI_prov are obtained from the China Statistical Yearbook and the China Environmental Statistical Yearbook. GDP, the total population, gross fixed assets investment, the total energy consumption, GDP2, and GDP3 are from National and provincial statistical yearbooks, China Science and Technology Statistical Yearbook, and China Energy Statistical Yearbook. The land use data is obtained from the Zenodo database (https://www.zenodo.org, accessed on 20 August 2024) with a spatial resolution of 30 m. The nighttime lighting data comes from the Global Change Scientific Research Data Publishing System (https://geodoi.ac.cn/WebCn/Default.aspx, accessed on 18 November 2024), with a spatial resolution of 1 km. Fractional vegetation cover data is obtained from the Satellite Application Center for Ecology and Environment, MEE (https://data.tpdc.ac.cn/zh-hans/data/f3bae344-9d4b-4df6-82a0-81499c0f90f7, accessed on 2 November 2024), with a spatial resolution of 250 m. All data were collected for the 18-year period from 2003 to 2020.

To deal with the less problematic data gaps, an interpolation process called the AutoRegressive Integrated Moving Average model (ARAMA) was applied. After this data cleansing process, 333 prefecture-level cities and 31 provinces in mainland China, covering the period from 2003 to 2020, constitute the final research samples. The final research samples include a total of 5994 observations at the prefecture level. Apart from the time trend, all variables have been centered for full sample estimation before the actual estimation step, to ensure accuracy and efficiency in the research analysis. The time trend term was represented as an increment from 1 to 18, symbolizing the base period to the end of the sample. We conducted a test on the data using the Variance Inflation Factor (VIF) and found that the VIF values were not greater than 10, indicating the absence of severe multicollinearity among the independent variables.

Table 1. Descriptions and statistical information of variables.

Variable	Symbol	Measurement	Mean Value	Standard Deviation	Min	Max
The logarithm of total carbon dioxide emissions	lnCE	The logarithm of total carbon dioxide emissions	16.512	1.113	13.198	19.479
The logarithm of carbon emissions intensity	lnCEI	The logarithm of total carbon emissions/total GDP	9.867	0.931	6.262	13.218
The logarithm of per capita carbon emissions	lnPCE	The logarithm of total carbon emissions/total population	10.827	0.951	8.208	13.878
The logarithm of governmental green investment at the prefectural level	lnGGI_city	The logarithm of total energy conservation and environmental protection expenditure at the prefectural level	2.832	0.527	0.847	3.929
The logarithm of governmental green investment at the provincial level	lnGGI_prov	The logarithm of total energy conservation and environmental protection expenditure at the provincial level	11.112	1.632	5.041	16.028
Economic development level	GDPpc	GDP/Population (ten thousand CNY/per person)	3.714	3.323	0.069	31.974
The logarithm of gross fixed assets investment	lnFAI	The logarithm of gross fixed assets investment	15.406	1.409	4.949	18.992
The logarithm of the total energy consumption	lnTEC	The logarithm of the total energy consumption by the material production sectors and non-material production sectors	11.091	1.055	5.749	13.601
Proportion of the secondary industry in GDP	GDP2	the percentage of GDP contributed by the secondary sector, which includes manufacturing and construction.	0.453	0.122	0.000	0.910
Proportion of the tertiary industry in GDP	GDP3	the proportion of the tertiary industry (services sector) in GDP	0.396	0.100	0.000	0.839
The logarithm of fractional vegetation coverage	lnFVC	The logarithm of sum of vegetation area	4.345	0.449	1.596	4.596
Nighttime light index	NTL	The logarithm of sum of nighttime light	0.702	1.677	0.000	20.472
Proportion of build-up land	P_built	Proportion of build-up land	0.059	0.072	0.000	0.441

presents descriptions and statistical information of variables. Upon examination of these statistics, it can be noted that the standard deviation of the selected variables, after undergoing logarithmic transformations, appears relatively small. This observation suggests that the substitution of the logarithmic value into the regression model to further dismantle the impact relation is justifiable and empirically sound.

3. Research Methodology

3.1. Standard Deviation Index and Coefficient of Variation

When studying regional disparities, the standard deviation index and coefficient of variation are often employed. The standard deviation index S (standard deviation) and the coefficient of variation CV (coefficient of variation) measure the variability from both absolute and relative perspectives [34]. The formulas for the standard deviation index and coefficient of variation are as follows:

$$S=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left(Y_i-\overline{Y}\right)}}$$

(1)

$$CV={\displaystyle \frac{S}{\overline{Y}}}$$

(2)

where n is the total number of spatial units; $Y_i$ represents the observed value for the i-th spatial unit; and $\overline{Y}$ is the average of $Y_i$. A larger value of S indicates a greater absolute disparity, and a larger value of CV indicates a greater relative disparity.

3.2. Construction of Three Hierarchical Linear Models

To investigate the impact of GGI on CER, the multi-level linear model proves to be a more favorable empirical research method [56,59]. Three hierarchical linear models have been constructed at the provincial and prefectural levels. These models include the unconditional means model, the random intercept model, the complete model, the linear growth model, the linear growth model with random effects, and the complete linear growth model.

Table 2. Summarizes the six models with their key characteristics.

Model Classification	Model Name	Model Number	Key Characteristics
no growth model	unconditional means model	Model 1	This type of model analyzes the overall mean, describing the distribution of the dependent variable across all levels without any conditioning effects.
	random intercept model	Model 2	By extending Model 1, prefecture-level factors are introduced.
	the complete model	Model 3	By extending Model 2, Model 3 incorporates lnGGI_prov, directly impacting CER at the prefecture-level city and lnGGI_prov, and serves to modulate the relationship between lnGGI_city and the CER of the prefecture-level city.
growth model	the linear growth model	Model 4	Expounding on the foundation of Model 1, the linear growth model incorporates time as an independent variable.
	the linear growth model	Model 5	By extending Model 4, prefecture-level factors are introduced.
	the complete linear growth model	Model 6	By extending Model 5, Model 6 incorporates lnGGI_prov, directly impacting CER at the prefecture-level city and lnGGI_prov, and serves to modulate the relationship between lnGGI_city and the CER of the prefecture-level city.

summarizes the six models with their key characteristics.

3.2.1. Model 1: The Unconditional Means Model

An unconditional means model is also known as the null model. This type of model analyzes the overall mean, describing the distribution of the dependent variable across all levels without any conditioning effects. It was first developed to verify whether there are significant differences in CER in different provinces.

The unconditional means model can be expressed as follows:

Level 1:

$$CE{R}_{\mathrm{tij}}={\pi }_{0\mathrm{ij}}+e_{tij}$$

(3)

Level 2:

$${\pi }_{0ij}={\beta }_{00j}+{\mu }_{0ij}$$

(4)

Level 3:

$${\beta }_{00j}={\gamma }_{000}+{\mu }_{00j}$$

(5)

where the response variable carbon emissions ($CE{R}_{\mathrm{tij}}$) of Equation (3) is the CER of the prefecture-level city i, namely, lnCE, lnCEI, and lnPCE. t represents the year, i represents the prefecture-level city, and j represents the province. ${\pi }_{0\mathrm{ij}}$ is the intercept of the first level model and $e_{tij}$ is the random disturbance term. ${\beta }_{00j}$ is the mean value of the intercept in the second level model, while ${\mu }_{0ij}$ is the random error to test the difference of ${\pi }_{0ij}$ between individuals. ${\gamma }_{000}$ is the mean value of the intercept in the three-level model, while ${\mu }_{00j}$ is the random error to test the difference of ${\beta }_{00j}$ between individuals.

3.2.2. Model 2: The Random Intercept Model

By extending Model 1, a random intercept model can be established, wherein prefecture-level factors are introduced. Nevertheless, the unique feature of this model is that it permits intercepts to demonstrate random variation across different levels, encapsulating intra-group dependency and heterogeneity.

The random intercept model can be expressed as follows:

Level 1:

$$CE{R}_{\mathrm{tij}}={\pi }_{0\mathrm{ij}}+e_{tij}$$

(6)

Level 2:

$${\pi }_{0ij}={\beta }_{00j}+{\beta }_{01j}{\mathrm{lnGGI}\text{\_}\mathrm{city}}_{ij}+{\displaystyle \sum _{\mathrm{m}}^{\mathrm{m}=8}{\beta }_{0\mathrm{m}j}}control\_variable{s}_{ij}+{\mu }_{0ij}$$

(7)

Level 3:

$$\left\{\begin{array}{l}{\beta }_{00j}={\gamma }_{000}+{\mu }_{00j}\\ {\beta }_{01j}={\gamma }_{010}\\ {\beta }_{0\mathrm{m}j}={\gamma }_{0\mathrm{m}0}\end{array}\right.$$

(8)

where ${\mathrm{lnGGI}\text{\_}\mathrm{city}}_{ij}$ is the core explanatory variable on $CE{R}_{\mathrm{tij}}$, $control\_variables$ are the control variables; m represents the number of control variables; ${\beta }_{01j}$ and ${\beta }_{0\mathrm{m}j}$ stand for the coefficient of each variable, while ${\gamma }_{010}$ and ${\gamma }_{0m0}$ are the mean value of the intercept in the three-level model.

For the sake of simplification, this paper sets ${\beta }_{01j}$ and ${\beta }_{0\mathrm{m}j}$ as the invariant slope, indicating the estimated parameters of corresponding prefecture-level variables at the provincial level are constant; there is no random component.

3.2.3. Model 3: The Complete Model

This study incorporates lnGGI_prov, directly impacting CER at the prefecture-level city. To maintain model simplicity, it is not necessary to establish interactions between the province-level factor and all prefecture-level factors. Instead, lnGGI_prov serves to modulate the relationship between lnGGI_city and the CER of the prefecture-level city, thereby promoting clarity and conciseness in the modeling framework.

The complete model can be expressed as follows:

Level 1:

$$CE{R}_{\mathrm{tij}}={\pi }_{0\mathrm{ij}}+e_{tij}$$

(9)

Level 2:

$${\pi }_{0ij}={\beta }_{00j}+{\beta }_{01j}{\mathrm{lnGGI}\text{\_}\mathrm{city}}_{ij}+{\displaystyle \sum _{\mathrm{m}}^{\mathrm{m}=8}{\beta }_{0\mathrm{m}j}}control\_variable{s}_{ij}+{\mu }_{0ij}$$

(10)

Level 3:

$$\left\{\begin{array}{l}{\beta }_{00j}={\gamma }_{000}+{\gamma }_{001}{\mathrm{lnGGI}\text{\_}\mathrm{prov}}_j+{\mu }_{00j}\\ {\beta }_{01j}={\gamma }_{010}+{\gamma }_{011}{\mathrm{lnGGI}\text{\_}\mathrm{prov}}_j+{\mu }_{01j}\\ {\beta }_{0\mathrm{m}j}={\gamma }_{0\mathrm{m}0}\end{array}\right.$$

(11)

where ${\mathrm{lnGGI}\text{\_}\mathrm{prov}}_j$ is the core explanatory variable on carbon emissions ($CE{R}_{\mathrm{tij}}$), while ${\gamma }_{001}$ and ${\gamma }_{011}$ are the coefficients of ${\mathrm{lnGGI}\text{\_}\mathrm{prov}}_j$ in the three-level model.

3.2.4. Model 4: The Linear Growth Model

Expounding on the foundation of Model 1, the linear growth model incorporates time as an independent variable. This addition facilitates an examination of whether the dependent variable exhibits a linear trend over time. To maintain model simplicity, the time trend is rendered as an invariant slope. This implies that the estimated parameters corresponding to the time trend term remain constant at the prefectural level, absent any random component.

The linear growth models can be expressed as follows:

Level 1:

$$CE{R}_{\mathrm{tij}}={\pi }_{0\mathrm{ij}}+{\pi }_{1\mathrm{ij}}Tim{e}_t+e_{tij}$$

(12)

Level 2:

$$\left\{\begin{array}{l}{\pi }_{0ij}={\beta }_{00j}+{\mu }_{0ij}\\ {\pi }_{1\mathrm{ij}}={\beta }_{10j}\end{array}\right.$$

(13)

Level 3:

$$\left\{\begin{array}{l}{\beta }_{00j}={\gamma }_{000}+{\mu }_{00j}\\ {\beta }_{10j}={\gamma }_{100}\end{array}\right.$$

(14)

where $Tim{e}_t$ is the time trend term on carbon emissions ($CE{R}_{\mathrm{tij}}$). ${\pi }_{1\mathrm{ij}}$ stands for the coefficient of $Tim{e}_t$. ${\beta }_{10j}$ is the mean value of the intercept in the second-level model.

3.2.5. Model 5: The Linear Growth Model with Random Effects

The linear growth models with random effects can be expressed as follows:

Level 1:

$$CE{R}_{\mathrm{tij}}={\pi }_{0\mathrm{ij}}+{\pi }_{1\mathrm{ij}}Tim{e}_t+e_{tij}$$

(15)

Level 2:

$$\left\{\begin{array}{l}{\pi }_{0ij}={\beta }_{00j}+{\beta }_{01j}{\mathrm{lnGGI}\text{\_}\mathrm{city}}_{ij}+{\displaystyle \sum _{\mathrm{m}}^{\mathrm{m}=8}{\beta }_{0\mathrm{m}j}}control\_variable{s}_{ij}+{\mu }_{0ij}\\ {\pi }_{1\mathrm{ij}}={\beta }_{10j}\end{array}\right.$$

(16)

Level 3:

$$\left\{\begin{array}{l}{\beta }_{00j}={\gamma }_{000}+{\mu }_{00j}\\ {\beta }_{01j}={\gamma }_{010}\\ {\beta }_{0\mathrm{m}j}={\gamma }_{0\mathrm{m}0}\end{array}\right.$$

(17)

3.2.6. Model 6: The Complete Linear Growth Model

The complete linear growth models can be expressed as follows:

Level 1:

$$CER={\pi }_{0\mathrm{ij}}+{\pi }_{1\mathrm{ij}}Tim{e}_t+e_{tij}$$

(18)

Level 2:

$$\left\{\begin{array}{l}{\pi }_{0ij}={\beta }_{00j}+{\beta }_{01j}{\mathrm{lnGGI}\text{\_}\mathrm{city}}_{ij}+{\displaystyle \sum _{\mathrm{m}}^{\mathrm{m}=8}{\beta }_{0\mathrm{m}j}}control\_variable{s}_{ij}+{\mu }_{0ij}\\ {\pi }_{1\mathrm{ij}}={\beta }_{10j}\end{array}\right.$$

(19)

Level 3:

$$\left\{\begin{array}{l}{\beta }_{00j}={\gamma }_{000}+{\gamma }_{001}{\mathrm{lnGGI}\text{\_}\mathrm{prov}}_j+{\mu }_{00j}\\ {\beta }_{01j}={\gamma }_{010}+{\gamma }_{011}{\mathrm{lnGGI}\text{\_}\mathrm{prov}}_j+{\mu }_{01j}\\ {\beta }_{0\mathrm{m}j}={\gamma }_{0\mathrm{m}0}\end{array}\right.$$

(20)

4. Results

4.1. Spatial and Temporal Variations of CER and GGI

Figure 1 and Figure 2 present the spatial distribution of CE, CEI, and PCE, as well as GGI_city and GGI_prov in the years 2003, 2012, and 2020. As indicated by Figure 1, the three indicators of CER processes exhibit significant spatial and temporal variations. In terms of space, high values of CE are primarily concentrated in the central region, particularly around the Beijing metropolitan area. High values of CEI are concentrated in Inner Mongolia and Gansu, while high values of PCE are found in Inner Mongolia. Temporally, both CE and PCE show a significant increasing trend, while CEI displays a decreasing trend.

As indicated by Figure 2, GGI_city and GGI_prov exhibit significant spatial and temporal variations, with both following roughly the same distribution patterns. In terms of spatial distribution, both GGI_city and GGI_prov show a characteristic of higher values in the east and lower values in the west. Over time, both GGI_city and GGI_prov display a significant increasing trend, particularly for GGI_prov.

Figure 3 presents the standard deviation index and coefficient of variation for CE, CEI, PCE, GGI_city, and GGI_prov from 2003 to 2020. As indicated by Figure 3, the standard deviations of CE, PCE, GGI_city, and GGI_prov show an increasing trend year by year, while the standard deviation of CEI displays a fluctuating downward trend. The coefficient of variation for CEI and PCE shows a fluctuating upward characteristic, whereas the coefficient of variation for CE exhibits a fluctuating downward characteristic. GGI_city and GGI_prov, on the other hand, exhibit characteristics of fluctuation within a certain level.

4.2. Preliminary Analysis Result

In the preliminary analysis, the estimation results are reported in

Table 3. Results of models without a time trend.

Model	lnCE			lnCEI			lnPCE
	Model 1	Model 2	Model 3	Model 1	Model 2	Model 3	Mode 1	Model 2	Model 3
lnGGI_city		0.157 ***	0.013		−0.409 ***	−0.336 ***		0.176 ***	0.007
GDPpc		0.03 ***	0.009		−0.186 ***	−0.167 ***		0.03 ***	−0.007
lnFAI		0.093 ***	0.003		−0.117 ***	−0.067 ***		0.115 ***	0.003
lnTEC		0.206 ***	0.107 ***		0.056 ***	0.1 ***		0.211 ***	0.103 ***
GDP2		0.008	0.003		−0.192 ***	−0.192 ***		0.044 ***	0.04 ***
GDP3		−0.009	−0.045 ***		−0.18 ***	−0.157 ***		0.011	−0.038 ***
lnFVC		0.242 ***	0.181 ***		0.198 ***	0.218 ***		0.168 ***	0.106 ***
NTL		−0.051 ***	−0.035 ***		0.005	−0.001		−0.095 ***	−0.08 ***
P_built		0.144 ***	0.136 ***		0.078 ***	0.118 ***		0.093 ***	0.024
lnGGI_prov			0.284 ***			−0.166 ***			0.365 ***
lnGGI_city:lnGGI_prov			−0.02 ***			−0.004			−0.002
Cons	−0.065	−0.007	0.030	0.012	0.004	−0.002	0.014	0.055	0.094
first level	0.295	0.166	0.157	0.479	0.224	0.223	0.330	0.197	0.188
second level	0.768	0.671	0.735	0.757	0.786	0.788	0.841	0.883	0.850
third level	0.626	0.358	0.365	0.525	0.433	0.416	0.470	0.722	0.710
ICC	0.769	0.777	0.810	0.639	0.782	0.781	0.738	0.869	0.867
-Log likelihood	3849	−2405	−2886	9021	940	879	5078	−370	−849

Note: *** means 1% significance level.

and

Table 4. Results of models with a time trend.

Model	lnCE			lnCEI			lnPCE
	Model 4	Model 5	Model 6	Model 4	Model 5	Model 6	Model 4	Model 5	Model 6
lnGGI_city		0.063 ***	0.015		−0.354 ***	−0.337 ***		0.054 ***	0.009
GDPpc		0.009	0.009		−0.173 ***	−0.167 ***		0.004	−0.007
lnFAI		0.034 ***	0.004		−0.081 ***	−0.067 ***		0.039 ***	0.003
lnTEC		0.173 ***	0.102 ***		0.073 ***	0.101 ***		0.17 ***	0.098 ***
GDP2		0.022 **	−0.001		−0.201 ***	−0.191 ***		0.062 ***	0.036 ***
GDP3		−0.048 ***	−0.043 ***		−0.157 ***	−0.158 ***		−0.039 ***	−0.035 ***
lnFVC		0.2 ***	0.186 ***		0.226 ***	0.217 ***		0.096 ***	0.112 ***
NTL		−0.048 ***	−0.034 ***		0.004	−0.001		−0.092 ***	−0.078 ***
P_built		0.107 ***	0.135 ***		0.097 ***	0.118 ***		0.039	0.024
lnGGI_prov			0.326 ***			−0.173 ***			0.409 ***
lnGGI_city:lnGGI_prov			−0.019 ***			−0.004			−0.002
Cons	−0.484 ***	−0.266 ***	0.089	0.723 ***	0.156	−0.013	−0.433 ***	−0.276 **	0.159
Time	0.044 ***	0.026 ***	−0.006 **	−0.075 ***	−0.015 ***	0.001	0.047 ***	0.033 ***	−0.006 *
first level	0.178	0.161	0.157	0.264	0.223	0.223	0.214	0.192	0.188
second level	0.770	0.700	0.737	0.763	0.792	0.787	0.843	0.842	0.853
third level	0.626	0.381	0.373	0.525	0.456	0.415	0.470	0.547	0.742
ICC	0.847	0.798	0.813	0.765	0.789	0.780	0.813	0.840	0.872
-Log likelihood	−1553	−2657	−2880	2637	900	889	443	−666	−843

Note: *** means 1% significance level, ** means 5% significance level, * means 10% significance level.

. Table 3 presents the outcomes of Models 1, 2, and 3, illustrating lnCE, lnCEI, and lnPCE respectively, without the time trend being taken into account. Conversely, Table 4 displays the results of Models 4, 5, and 6 with a time trend. Table 3 and Table 4 report the parameter estimation results, the variance components of each level, the intra-class correlation coefficient (ICC), which reflects the ratio of intra-group variance to the total variance and the -Log likelihood statistics, which reflects how well a statistical model fits a set of observations.

From Table 3, it can be pointed out that the ICC of Model 1 for lnCE accounts for approximately 76.9% = (0.768² + 0.626²)/(0.295² + 0.768² + 0.626²) of the overall differences, the ICC of Model 1 for lnCEI and lnPCE are 63.9% and 73.8%. This signifies high internal group correlation, which corroborates the suitability of employing a hierarchical linear model to manage the nested data. Among the outcomes, the variations at the prefectural level and provincial level for lnCE display a superior explanatory power for the overall variations, followed by lnPCE and lnCEI. The substantive contributions of provincial-level variables to lnCE, lnCEI, and lnPCE are noticeable from the random effects portion, but less than prefectural-level variables. With the gradual addition of explanatory variables, the ICC shows an upward trend, indicating that the differences between the prefectural-level and provincial-level variables exhibit a stronger explanatory power for the variations in CER, and in addition, the measurement of the -Log likelihood system gradually becomes smaller, indicating that the model fitting degree gradually becomes better.

Overall, diverse control variables have exerted significant impacts on the three indicators of CER, albeit with considerable variation in their effects. lnFVC and lnTEC consistently exhibit positive and significant effects across all three indicators. Conversely, the effects of other variables are more variable; for instance, GDP2 demonstrates no significant impact on lnCE, exhibits a significant negative effect on lnCEI, and shows a significant positive effect on lnPCE.

Lastly, upon scrutinizing GGI variables, lnGGI_city and lnGGI_prov are found to be statistically significant. Upon excluding lnGGI_prov and lnGGI_city exhibits significant effects on all three indicators. However, upon the inclusion of lnGGI_prov, the impacts of lnGGI_city become insignificant for lnCE and lnPCE. They both exert positive impacts on lnCE and lnPCE, and a notable negative influence on lnCEI. The interaction term lnGGI_city:lnGGI_prov is statistically significant for lnCE, while lnCEI and lnPCE are not statistically significant. Specifically, the elasticity of lnGGI_city with respect to lnCE is 0.013, while the elasticity of lnGGI_prov with respect to lnCE is 0.284, indicating a stronger effect for the latter. For every 1% increase in lnGGI_prov, the elasticity of lnGGI_city with respect to lnCE decreases by 0.02%. The elasticity of lnGGI_city with respect to lnCEI is −0.336, and the elasticity of lnGGI_prov with respect to lnCEI is −0.166, with the former showing a more pronounced effect. For every 1% increase in lnGGI_prov, the elasticity of lnGGI_city with respect to lnCEI increases by 0.182%. lnGGI_city does not have a significant impact on lnPCE, whereas the elasticity of lnGGI_prov with respect to lnPCE is 0.365, indicating a stronger effect for the latter. For every 1% increase in lnGGI_prov, the elasticity of lnGGI_city with respect to lnPCE decreases by 0.002%.

From Table 4, the time variable appears to significantly influence lnCE, lnCEI, and lnPCE, except in Model 6 for lnCEI, suggesting a notable time-delay effect on these metrics. In comparison to Models 1, 2, and 3 without a time trend, Models 4, 5, and 6 with a time trend show a considerable increase in the ICC for lnCE. However, for lnPCE and lnCEI, the differences in ICC are not conspicuously significant. When the time variable is introduced, the changes in the ICC values across different models are not significant, which further substantiates the strong correlation between the time variable and driving variables. Another insight drawn from the -Log likelihood system indicates an improved fitting degree for Model 4 when compared to Models 1, 2, and 3. In contrast, for the -Log likelihood of Models 4 and 5, the differences when compared to Models 2 and 3 are relatively unremarkable. An intriguing finding is that upon incorporating the time trend variable, the elasticity of lnGGI_prov exhibits an enhancement. For instance, concerning lnCE, the elasticity of lnGGI_prov with respect to lnCEI amounts to 0.326, whereas it is 0.284 in Model 3 of lnCE. The interaction term lnGGI_city:lnGGI_prov remains stable, with no significant difference whether a time trend is included or not.

4.3. Heterogeneity Analysis

To further consider potential biases in the data, this paper attempts to exclude the four municipalities directly governed by the Central Government, namely Beijing, Tianjin, Shanghai, and Chongqing. The authors find that although there are slight differences in the model estimates when these municipalities are excluded, the main conclusions remain consistent with those obtained without excluding them, further validating the reliability of the results.

4.3.1. Estimation Results Based on Provincial Area Differences

The study carefully considers the varying sizes of provinces and, as a result, divides the sample data into separate categories defined by size, namely, large provincial area group and small provincial area group. The large provincial area group includes Qinghai, Sichuan, Gansu, Inner Mongolia, Xinjiang, Heilongjiang, Yunnan, and Tibet, all of which cover territories exceeding 300,000 square kilometers. The remaining provinces are classified as the small provincial area group. The large provincial area group contains 1890 observations and the small provincial area group contains 4104 observations. From Table 3 and Table 4, in order to avoid being overly extensive and confusing, as well as considering due to space constraints, Models 1, 2, 3, 4, and 5 are not presented below. Only the results of Model 6 across different groupings are presented.

Table 5. Estimation results from Model 6 for lnCE, lnCEI, and lnPCE based on differences in provincial area.

Model	The Large Provincial Area Group			The Small Provincial Area Group
	lnCE	lnCEI	lnPCE	lnCE	lnCEI	lnPCE
lnGGI_city	−0.049 ***	−0.503 ***	−0.033	0.038 **	−0.215 ***	0.021
GDPpc	0.082 ***	−0.092 ***	0.074 ***	−0.03 ***	−0.226 ***	−0.039 ***
lnFAI	0.025 *	−0.072 ***	0.010	0.000	−0.059 ***	0.009
lnTEC	0.054 ***	0.101 ***	0.043 **	0.197 ***	0.09 ***	0.23 ***
GDP2	−0.013	−0.202 ***	0.015	0.008	−0.181 ***	0.047 ***
GDP3	−0.019	−0.142 ***	−0.019	−0.062 ***	−0.163 ***	−0.057 ***
lnFVC	0.164 ***	0.197 ***	0.112 ***	0.21 ***	0.224 ***	0.065
NTL	−0.305 ***	−0.364 ***	−0.401 ***	−0.011	0.026 **	−0.051 ***
P_built	0.164	0.316 *	−0.008	0.179 ***	0.123 ***	0.1 ***
lnGGI_prov	0.376 ***	−0.034	0.495 ***	0.205 ***	−0.247 ***	0.219 ***
lnGGI_city:lnGGI_prov	−0.018 ***	−0.015 *	0.017 ***	−0.03 ***	0.013 **	−0.037 ***
Cons	−0.037	0.106	0.573	−0.032	−0.105	−0.261 **
Time	−0.013 ***	−0.008	−0.015 ***	0.008 **	0.004	0.015 ***
first level	0.155	0.252	0.182	0.154	0.203	0.185
second level	0.822	0.854	0.966	0.688	0.755	0.786
third level	0.451	0.524	0.972	0.272	0.356	0.401
ICC	0.851	0.800	0.912	0.780	0.775	0.808
-Log likelihood	−957	780	−344	−2076	−83	−719

Note: *** means 1% significance level, ** means 5% significance level, * means 10% significance level.

presents outcomes from Model 6 in the group estimation context for lnCE, lnCEI, and lnPCE, respectively. Each row and column in these tables follow the same reporting paradigm as those in Table 3 and Table 4.

Based on Table 5, it is evident that there are significant changes in the results between the large provincial area group and the small provincial area group. First of all, from the perspective of ICC and -Log likelihood system results, noticeable differences can be observed between the groups. When compared to the complete sample estimation, the large provincial area group reveals an increased ICC value, while the small provincial area group demonstrates a decrease. Moreover, the prefectural city level explains a larger proportion of the overall variance in the small provincial area group than in the large provincial area group. Secondly, the time variable has passed the statistical significance tests universally. Additionally, significant disparities exist in the results across control variables for different groups. For instance, GDPpc exhibits contrasting effects, P_built is insignificantly correlated in the large provincial area group, yet significantly correlated in the small provincial area group. The direction of influence exerted by lnFAI also varies in certain models. Finally, lnGGI_city exhibits significant variations across different groupings. The coefficient of lnGGI_prov has increased for the larger provincial area group, it has decreased for the smaller provincial area group. The interaction term lnGGI_city:lnGGI_prov have both reached statistical significance.

It is evident that there are significant changes in the results of lnCEI in different groups. Firstly, the patterns of ICC for lnCEI in different groups are essentially identical to those for lnCE. Secondly, the time variable failed to pass statistical significance tests. Moreover, notable differences in coefficients of control variables are observed in different groups. NTL exhibits a negative effect in the large provincial area group but significantly positively influences the small provincial area group. P_built also demonstrates considerable variation in significance across different groupings. Lastly, lnGGI_city exerts a more pronounced effect in the large provincial area group, whereas lnGGI_prov has a more significant impact in the small provincial area group. The interaction term lnGGI_city:lnGGI_prov has both achieved statistical significance, leading to a marked negative effect in the large provincial area group, while in the small provincial area group, it induces a significant positive effect.

It is evident that there are significant changes in the results of lnPCE in different groups. Firstly, the patterns of ICC for lnPCE in different groups are essentially identical to those for lnCE and lnCEI. Secondly, the time variable successfully passes statistical significance tests, yielding results consistent with those for lnCE. Furthermore, the coefficients for the control variables are largely consistent with the results obtained for lnCE. Notably, GDPpc exhibits effects in different directions across various groups, while P_built shows significant differences in significance levels. Lastly, lnGGI_city exerts a more pronounced effect in the small provincial area group, whereas lnGGI_prov has a more significant impact in the large provincial area group, in contrast to the results obtained for lnCEI. The interaction term lnGGI_city:lnGGI_prov has both achieved statistical significance, leading to a marked negative effect in the small provincial area group, while in the large provincial area group, it induces a significant positive effect. This is also contrary to the results obtained for lnCEI.

4.3.2. Estimation Results Based on Provincial Terrain Differences

Given the varying terrain in China, this study classifies the samples into two categories: complex terrain group and simple terrain group. This classification is based on each province’s position across the Three-step Terrain Model. Provinces with more intricate terrain—mainly located in the first and second steps—include Sichuan, Guizhou, Yunnan, Gansu, Ningxia, Inner Mongolia, and Shaanxi. All other provinces are considered part of the simple terrain group. The complex terrain group contains 2304 observations and the simple terrain group contains 3690 observations.

Table 6. Estimation results from Model 6 for lnCE, lnCEI, and lnPCE based on provincial terrain differences.

Model	Complex Terrain Group			Simple Terrain Group
	lnCE	lnCEI	lnPCE	lnCE	lnCEI	lnPCE
lnGGI_city	−0.030	−0.394 ***	−0.015	0.05 ***	−0.261 ***	0.032 *
GDPpc	0.078 ***	−0.104 ***	0.07 ***	−0.041 ***	−0.25 ***	−0.047 ***
lnFAI	0.036 **	−0.074 ***	0.026	−0.008	−0.052 ***	−0.006
lnTEC	0.073 ***	0.122 ***	0.068 ***	0.148 ***	0.059 ***	0.161 ***
GDP2	−0.042 ***	−0.294 ***	0.006	0.016	−0.153 ***	0.05 ***
GDP3	−0.064 ***	−0.269 ***	−0.038 **	−0.031 ***	−0.096 ***	−0.032 ***
lnFVC	0.176 ***	0.161 ***	0.146 ***	0.25 ***	0.403 ***	−0.098
NTL	−0.195 ***	−0.256 ***	−0.32 ***	−0.004	0.038 ***	−0.046 ***
P_built	0.045	0.044	−0.050	0.191 ***	0.135 ***	0.093 ***
lnGGI_prov	0.299 ***	−0.296 ***	0.445 ***	0.328 ***	−0.008	0.355 ***
lnGGI_city:lnGGI_prov	−0.018 ***	−0.02 ***	0.014 **	−0.031 ***	0.025 ***	−0.036 ***
Cons	0.027	−0.282	0.643 *	−0.034	−0.030	−0.24 **
Time	−0.003	0.024 ***	−0.012 **	−0.006 *	−0.024 ***	0.001
first level	0.168	0.249	0.197	0.146	0.196	0.177
second level	0.831	0.868	0.979	0.679	0.744	0.767
third level	0.514	0.501	0.952	0.193	0.197	0.206
ICC	0.850	0.802	0.905	0.774	0.751	0.781
-Log likelihood	−807	889	−78	−2236	−298	−950

Note: *** means 1% significance level, ** means 5% significance level, * means 10% significance level.

presents outcomes from Model 6 of the complex terrain group and simple terrain group for lnCE, lnCEI, and lnPCE.

Based on Table 6, it is evident that there are significant changes in the results between the complex terrain group and the simple terrain group. First of all, the patterns of ICC for lnCE in different groups based on provincial terrain differences are essentially identical to those for lnCE in different groups based on provincial area differences. Secondly, the time variable failed to pass statistical significance tests in the complex terrain group for lnCE. Additionally, significant disparities exist in the results across control variables for different groups. For instance, GDPpc and GDP2 exhibit contrasting effects. Finally, lnGGI_city demonstrates more pronounced effects in the simple terrain group, while the impact of lnGGI_prov remains relatively consistent across different groups. The interaction term lnGGI_city:lnGGI_prov has achieved statistical significance and exerts a stronger influence in the simple terrain group.

There is a stark disparity in the results of lnCEI in different terrain groups. Firstly, the patterns of ICC for lnCEI in different groups also are essentially identical to those for lnCE. Secondly, significant variations in the coefficients of control variables are evident across various groups. Moreover, NTL exhibits a negative effect in the complex terrain group but a significant positive influence in the simple terrain group. P_built has only achieved statistical significance in the simple terrain group. Lastly, lnGGI_city exerts a more pronounced effect in the complex terrain group, whereas lnGGI_prov failed to pass statistical significance tests in the simple terrain group. The interaction term lnGGI_city:lnGGI_prov has both achieved statistical significance, leading to a marked negative effect in the complex terrain group, while in the simple terrain group, it induces a significant positive effect.

There is a stark disparity in the results of lnPCE in different groups. Firstly, the patterns of ICC for lnPCE in different groups are essentially identical to those for lnCE and lnCEI. Secondly, the time variable failed to pass statistical significance tests in the simple terrain group. Furthermore, the coefficients for the control variables exhibit substantial differences with the results obtained for lnCE and lnCEI, particularly for NTL and P_built. Finally, lnGGI_city exhibits a more pronounced effect within the simple terrain group, in contrast to lnGGI_prov, which has a more substantial impact in the complex terrain group. The interaction term lnGGI_city:lnGGI_prov has achieved statistical significance, resulting in a marked negative effect in the simple terrain group, and a significant positive effect in the complex terrain group.

4.3.3. Estimation Results Based on the Difference of Provincial Economic Development Level

Taking into account the varying levels of economic development across regions, this study categorizes the provinces into two distinct groups—a high economic development group and a low economic development group—primarily based on their 2020 GDP, with a threshold of 210 billion yuan, and also considering their location in the central and western regions of China. Provinces with less developed economies, including Ningxia, Gansu, Yunnan, Inner Mongolia, Shaanxi, Sichuan, Guizhou, Guangxi, Tibet, Xinjiang, and Jiangxi, are classified as the low economic development group. All other provinces belong to the high economic development group. The low economic development group contains 2394 observations, and the high economic development group contains 3600 observations.

Table 7. Estimation results from Model 6 for lnCE, lnCEI, and lnPCE based on differences in economic development levels.

Model	Low Economic Development Group			High Economic Development Group
	lnCE	lnCEI	lnPCE	lnCE	lnCEI	lnPCE
lnGGI_city	−0.045 **	−0.383 ***	−0.047 *	0.067 ***	−0.278 ***	0.063 ***
GDPpc	0.074 ***	−0.108 ***	0.067 ***	−0.055 ***	−0.249 ***	−0.075 ***
lnFAI	0.045 ***	−0.063 ***	0.028	−0.009	−0.058 ***	−0.004
lnTEC	0.094 ***	0.133 ***	0.102 ***	0.103 ***	0.066 ***	0.081 ***
GDP2	−0.027	−0.272 ***	0.024	0.001	−0.17 ***	0.03 **
GDP3	−0.072 ***	−0.266 ***	−0.044 **	−0.031 ***	−0.104 ***	−0.034 ***
lnFVC	0.158 ***	0.139 ***	0.121 ***	0.163 ***	0.225 ***	−0.099 *
NTL	−0.158 ***	−0.232 ***	−0.257 ***	−0.008	0.036 ***	−0.049 ***
P_built	−0.059	0.074	−0.183 *	0.167 ***	0.114 ***	0.059 **
lnGGI_prov	0.237 ***	−0.393 ***	0.357 ***	0.402 ***	−0.003	0.494 ***
lnGGI_city:lnGGI_prov	−0.024 ***	−0.027 ***	0.003	−0.007 *	0.025 ***	0.006
Cons	−0.257	−0.546 ***	0.100	0.139	0.106	0.091
Time	0.006	0.036 ***	0.002	−0.015 ***	−0.022 ***	−0.015 ***
first level	0.176	0.255	0.205	0.138	0.188	0.171
second level	0.829	0.861	0.973	0.673	0.724	0.753
third level	0.405	0.353	0.832	0.333	0.438	0.651
ICC	0.829	0.773	0.889	0.803	0.792	0.853
-Log likelihood	−643	1035	94	−2477	−526	−1100

Note: *** means 1% significance level, ** means 5% significance level, * means 10% significance level.

presents outcomes from Model 6 of the complex terrain group and the simple terrain group for lnCE, lnCEI, and lnPCE.

Based on Table 7, it is evident that there are significant changes in the results for lnCE between groups. First of all, the patterns of ICC for lnCE likewise align with the aforementioned findings. Secondly, the time variable failed to pass statistical significance tests in the low economic development group for lnCE. Additionally, control variables such as GDPpc, lnFAI, GDP2, and P_built exhibit significant disparities across different groups. Finally, both lnGGI_city and lnGGI_prov exert more substantial effects in the high economic development group. The interaction term lnGGI_city:lnGGI_prov has achieved statistical significance and exerts a stronger influence in the low economic development group.

Based on the information presented in Table 6, there is a stark disparity in the results of lnCEI in different terrain groups. Firstly, the differences in ICC across groups are minimal, contrasting significantly with the outcomes observed for lnCE. Secondly, all control variables exhibit substantial variations across different groups, with particularly notable differences observed for NTL and P_built Lastly, lnGGI_city exerts a more pronounced effect in the low economic development group, whereas lnGGI_prov in Model 6 within the low economic development group exerts a strong effect, the interaction term lnGGI_city:lnGGI_prov has achieved statistical significance. However, its direction of effect varies across different groups.

There exists a significant divergence in the results of lnPCE across various groups. Firstly, the patterns of ICC for lnPCE in different groups are essentially identical to those for lnCE. Secondly, the time variable failed to pass statistical significance tests in the low economic development group. Furthermore, among the control variables, GDPpc and lnFAI, GDP2, lnFVC, and P_built exhibit particularly pronounced differences across different subgroups. Finally, in the high economic development group, lnGGI_city and lnGGI_prov demonstrate a more pronounced effect. However, the interaction term lnGGI_city:lnGGI_prov did not achieve statistical significance.

5. Discussion

5.1. Influence of GGI on CER

Based on our research, we found that both GGI_city and GGI_prov promote the CER of the prefecture-level cities. The primary reason is that GGI signifies governmental support for businesses engaged in environmental products and services [12]. Such support expedites the transformation of traditional energy firms, prompting them to allocate more resources towards CER. Moreover, GGI mitigates the allocation of capital to polluting enterprises and reduces environmental litigation costs, thereby fostering increased social investment in green production and CER. An intriguing finding is that lnGGI_city and lnGGI_prov have differential impacts on different CER indicators. Specifically, lnGGI_city and lnGGI_prov exert a strong positive influence on lnCE and lnPCE, while they have a weak negative effect on lnCEI. Notably, the impact strength of lnGGI_prov on lnCE and lnPCE is more pronounced than that of lnGGI_city. Conversely, the influence of lnGGI_prov on lnCEI is less intense than lnGGI_city. Thus, it is imperative to consider a variety of CER indicators when evaluating the impact of GGI on these indicators. Furthermore, lnGGI_prov significantly moderates the effect of lnGGI_city on lnCE. The rationale underlying the interaction term lnGGI_city:lnGGI_prov is elucidated as follows: the GGI initiatives undertaken by provincial governments that enhance carbon emissions reduction (CER) in prefecture-level cities are pivotal. On the one hand, GGI_prov can extend the benefits to a wider demographic, allowing a greater number of citizens to partake in public utilities, thereby fostering CER at the prefecture level. Alternatively, the GGI activities by provincial governments facilitate the establishment of a closely integrated hierarchical organizational framework, which further supports CER efforts in subordinate jurisdictions.

Upon grouped analysis by provincial area size, terrain complexity, and economic development level, significant heterogeneous impacts on the effect of GGI on CER are observed. Based on provincial area differences, the effect of lnGGI_city on lnCE, lnCEI, and lnPCE is more pronounced in the large provincial area group. Conversely, in the large provincial area group, the effect of lnGGI_prov on lnCE and lnPCE is stronger, but for lnCEI, it is weaker. The interaction term lnGGI_city:lnGGI_prov has both reached statistical significance, indicating that lnGGI_prov significantly influences the effect of lnGGI_city on CER, with the patterns of influence varying across different indicators and groups. The reasons for this may include spatial limitations in larger provinces that often restrict the reach of many investment services, thereby reducing the extent of provincial investment support. These services may not fully extend to all prefecture-level cities. Furthermore, a lack of administrative efficiency and effective public management within the intricate hierarchical organization might introduce barriers to the delivery of public services.

Under the influence of provincial terrain differences, in the complex terrain group, the effects of lnGGI_city on lnCE and lnPCE are weaker, but for lnCEI, it is stronger. This is markedly different from the results based on provincial area differences. In the complex terrain group, the effect of lnGGI_prov on lnCE is weaker, but for lnCEI and lnPCE, the effects are stronger. The interaction term lnGGI_city:lnGGI_prov significantly influences lnCE, lnCEI, and lnPCE, which is consistent with the results based on provincial area differences. The reason may be that in regions with simple terrain, infrastructure such as transportation is convenient, and public services are efficient, which facilitates the radiating effect of lnGGI_prov.

Under the influence of economic development level, in the high economic development group, the effects of lnGGI_city and lnGGI_prov on lnCE and lnPCE are stronger, but for lnCEI, it is weaker. This aligns well with the findings related to provincial terrain differences. The interaction term lnGGI_city:lnGGI_prov significantly influences lnCE and lnCEI but not lnPCE. This differs notably from the impacts of provincial area size and terrain complexity. The reason may be that, in regions with higher economic development, the governmental green investment activities of prefecture-level cities are very active, while the relative scale of GGI_prov is relatively modest.

5.2. Policy Implications

Our findings emphasize that the three CER indicators each reflect issues at distinct levels. Consequently, tailored measures should be proposed for each specific CER objective. Furthermore, there is room to consider the development of a comprehensive indicator that captures the holistic picture of CER. Significantly, our findings highlight the interactive effects of cross-level GGI, taking into account the spatial nesting hierarchy of administrative divisions, which is often overlooked [56]. It is essential for governmental green investments to not only persistently augment the scale of environmental protection expenditures but also to strategically consider the interplay between provincial and prefectural-level governments in shaping CER. This necessitates a thoughtful optimization of the allocation ratios of green investments by both provincial and prefectural-level governments to ensure the most effective environmental outcomes.

The influence of GGI on CER also needs to be adapted to local conditions and take into account regional disparities. When allocating GGI at the sub-provincial level, it is essential to consider local factors such as provincial area size, terrain complexity, and economic development level [12]. Evidently, differences in provincial area, terrain, and provincial economic development level exert significant heterogeneous impacts on the effect of GGI on CER. This underscores the necessity of making differentiated arrangements for GGI based on different conditions. In provinces with larger areas, for lnCE and lnPCE, it is advisable to increase lnGGI_prov. For lnCEI, the focus should be on increasing lnGGI_city. In provinces with complex terrain, the effect of GGI on lnCE is relatively low, thus the emphasis should be on increasing GGI in the simple terrain group. For lnCEI, both lnGGI_city and lnGGI_prov should be increased. For lnPCE, the focus should be on increasing lnGGI_prov. In provinces with a low level of economic development, the effect of GGI on lnCE and lnPCE is relatively low, thus the emphasis should be on increasing GGI in the high-level development group. For lnCEI, both lnGGI_city and lnGGI_prov should be increased. If the aim is to leverage lnGGI_prov to stimulate lnGGI_city, the promotional effect will be stronger in the small provincial area group and the simple terrain group.

5.3. Limitations

There are some limitations in this study. Firstly, the acquisition of county-level data on GGI and CER presents notable challenges, which has resulted in the absence of a county-level analysis within this research framework. Secondly, the comprehensiveness of the control variables is potentially insufficient. This study has considered only eight control variables due to constraints in data collection, which may have overlooked other driving forces. Thirdly, the research has not taken into account the potential non-linear dynamics of the relationship between GGI and CER, such as the possibility of an inverted U-shaped relationship, nor has it examined the spatial spillover effects of governmental green investment on emissions. Fourthly, the lack of detailed and specific data is evident, as the terms GGI_city and GGI_prov have not been further broken down or subcategorized in a manner similar to GDP2 and GDP3, thereby limiting the depth and comprehensiveness of the analysis. Finally, the study discerns a significant influence of the temporal variable on CE and PCE and identifies a robust correlation with the GGI variables. Future research is encouraged to incorporate models that account for the temporal effects to provide a more nuanced understanding of these dynamics.

6. Conclusions

Based on the panel data from 333 prefecture-level cities in China collected from 2003 to 2020, this study developed three-level hierarchical linear models to examine GGI on CER. This study explores the impact of GGI_city and GGI_prov on the CER of prefecture-level cities, and how GGI_prov acts on the GGI_city on CER across regions with different provincial area sizes, terrain complexity, and economic development levels. The result shows the following:

(1)

The three indicators of CER and GGI exhibit significant spatial and temporal variations. High values of CE and PCE are primarily concentrated in the central region, while high values of CEI are concentrated in Inner Mongolia and Gansu. Both GGI_city and GGI_prov show a characteristic of higher values in the east and lower values in the west. The coefficient of variation for CEI and PCE shows a fluctuating upward characteristic.

(2)

Both lnGGI_city and lnGGI_prov have promoted CER, but the impact strength of lnGGI_prov on lnCE and lnPCE is more pronounced than that of lnGGI_city. lnGGI_prov can strengthen the effect of lnGGI_city significantly for lnCE. lnGGI_city and lnGGI_prov exert a strong positive influence on lnCE and lnPCE, while they have a weak negative effect on lnCEI. Diverse control variables have exerted significant impacts on the three indicators of CER, albeit with considerable variation in their effects.

(3)

The effect of GGI on CER is significant heterogeneous upon conducting grouped analysis by provincial area size, terrain complexity, and economic development level. The effect of lnGGI_city on lnCE, lnCEI, and lnPCE and the effect of lnGGI_prov on lnCE and lnPCE are stronger in provinces of large areas. In the complex terrain group, the effects of lnGGI_city and lnGGI_prov on lnCE and the effects of lnGGI_city on lnPCE are weaker, but the effects of lnGGI_city and lnGGI_prov on lnCEI and the effects of lnGGI_prov on lnPCE are stronger. In the high economic development group, the effects of lnGGI_city and lnGGI_prov on lnCE and lnPCE are stronger, but for lnCEI, it is weaker. The interaction term lnGGI_city:lnGGI_prov is stronger in the small provincial area group and the simple terrain group than in the large provincial area group and the complex terrain group. Among the control variables, GDPpc, lnFAI, NTL, and P_built exhibit particularly pronounced differences across different groups.