Spatial Analysis of CO₂ Shadow Prices and Influencing Factors in China’s Industrial Sector

Abstract

Reducing emissions through the invisible hand of the market has become an important way to promote sustainable environmental development. The shadow price of carbon dioxide ($C{O}_2$) is the core element of the carbon market, and its accuracy depends on the micro level of the measurement data. In view of this, this paper innovatively uses enterprise level input-output data and combines the stochastic frontier method to obtain $C{O}_2$ shadow prices in China’s industrial sector. On this basis, the impacts of research and development (R&D) intensity, opening up level, traffic development level, population density, industrial structure, urbanization level, human resources level, degree of education, and environmental governance intensity on shadow price are discussed. In further analysis, this study introduces a Spatial Durbin Model (SDM) to evaluate the spatial spillover effects of $C{O}_2$ shadow price itself and its influencing factors. The research results indicate that market-oriented emission abatement measures across industries and regions can reduce total costs, and it is necessary to consider incorporating carbon tax into low-carbon policies to compensate for the shortcomings of the carbon Emission Trading Scheme (ETS). In addition, neighboring regions should coordinate emission abatement tasks in a unified manner to realize a sustainable reduction in $C{O}_2$ emissions.

1. Introduction

In November 2024, the 29th Conference of Parties to the United Nations Framework Convention on Climate Change was held, and the issue of greenhouse gas emissions such as $C{O}_2$ once again became the focus of attention from all sectors of society. According to the latest annual Greenhouse Gas Bulletin of the World Meteorological Organization, greenhouse gas concentrations reached a new record in 2023. Among them, the global average surface $C{O}_2$ concentration was 151% of the preindustrial level. The accumulation rate of $C{O}_2$ in the atmosphere increased by 11.4% within 20 years, exceeding any period in human history. As a major responsible developing country, China has always regarded actively responding to climate change as an inherent requirement to achieve its own sustainable development. In 2020, China put forward the “dual carbon” goals, that is, China strives to peak its $C{O}_2$ emissions before 2030 and aims to realize neutrality before 2060. Against the backdrop of continuously rising $C{O}_2$ emissions, China has set a carbon neutrality goal that will take 40 years to achieve, which is half the time required by developed countries and poses great challenges. The establishment of this $C{O}_2$ emission reduction target not only promotes the innovation of green and low-carbon technologies, but also presents requirements for the innovation of policy systems.

Economically, the reason for excessive $C{O}_2$ emissions is the absence of a carbon pricing mechanism, which makes it impossible to realize the optimal allocation of $C{O}_2$ emissions through the “invisible hand” of the market. Therefore, the government needs to take action to address the problem of market failure. There are two main ways to promote $C{O}_2$ emission reduction through economic means [1]. One is to levy a carbon tax based on the theory of the Pigouvian tax; the other is to establish a carbon ETS guided by the Coase theorem. When setting carbon tax rates and the prices in carbon ETS, the shadow prices can be used as a reference [2]. In environmental economics, the $C{O}_2$ shadow price represents the marginal cost of abating an additional unit of emissions. It measures the marginal abatement cost [3]. Only when shadow prices of various economic entities are equal can the above two emission reduction means achieve economic effectiveness. Therefore, accurately measuring $C{O}_2$ shadow prices in the industrial sectors is an important guarantee of achieving effective emission reduction in the industrial system. In addition, $C{O}_2$ emissions and their greenhouse effects have the characteristic of spatial correlation across regions. Thus, exploring the spatial dependence of $C{O}_2$ shadow prices in neighboring economies is of great significance for regional collaborative emission reduction.

However, on the one hand, most existing studies are based on provincial and municipal input-output tables and energy consumption data at the macro level [4,5,6], and the measurement results are quite different from the real marginal abatement costs. On the other hand, most scholars have only explored the factors that influence the shadow price [7,8], and few articles in the literature have paid attention to the spatial effects of the shadow price itself and its influencing factors.

Therefore, this study may provide the following marginal contributions. First, after matching the China Industrial Enterprises Database and the Integrated Database of Pollutant Discharges in China’s Manufacturing Industry, we use the micro-enterprise data to enhance the accuracy of calculation results. Second, spatial econometric models are introduced to quantify the regional distribution differences of shadow price, and SDM is used to explore the impacts of factors on $C{O}_2$ shadow prices across regions. Finally, we put forward policy suggestions for coordinated emission reduction at the industrial and regional levels.

This paper is structured as follows: Section 2 presents a review of the available relevant literature; Section 3 outlines the models used to estimate the shadow price of $C{O}_2$ and analyze the spatial spillover effects of shadow price and its influencing factors; Section 4 describes the process of variable construction and data matching; Section 5 presents the measurement results and conducts empirical analysis; and Section 6 summarizes the research findings and proposes policy recommendations.

2. Literature Review

In order to realize national low-carbon transformation, it is essential to comprehensively utilize government supervision and market-oriented measures while introducing advanced emission reduction technologies. Among them, the shadow price of $C{O}_2$ may be a tool that can play a key role [9]. In the academic community, there are three categories of measurement models: the engineering economy model [10,11], the energy economy model [12,13], and the efficiency analysis model [14,15].

The engineering economy model refers to the model in which experts in the field, taking the latest available technologies as the reference benchmark, adopt engineering methods to conduct a discounted assessment of alternative emission reduction measures (such as energy-saving renovation and energy substitution). Then, cost-effective schemes are aggregated based on emission reduction targets, thereby obtaining the shadow price of $C{O}_2$ [16]. This method is generally used for the selection of solutions for specific projects, and the accuracy of its assessment results depends on the subjective judgment of experts [17]. The energy economy model employs either a partial or general equilibrium framework. Within this model, $C{O}_2$ emission constraints are systematically varied. The corresponding shadow price is then endogenously determined by these constraint changes [18]. This model usually couples modules such as energy, economy, and environment [19]. The efficiency analysis model constructs a production possibility set incorporating $C{O}_2$ emissions. This framework applies production theory under current technological and economic constraints. From this set, the model computes the shadow price of $C{O}_2$ [20].

The three models mentioned above have their respective advantages and disadvantages. Due to their different construction mechanisms, they are suitable for estimating $C{O}_2$ shadow prices with different connotations [21]. At present, the main ways for China’s industrial sectors to abate emissions (such as reducing output) all involve the production processes of enterprises. The efficiency analysis model precisely combines the production theory of micro-firms with environmental economics. This model encourages firms to increase desired outputs while reducing the quantity of undesired outputs, which is consistent with the production decisions of real-world enterprises. Therefore, this study employs an efficiency analysis model to derive the shadow price of industrial $C{O}_2$ emissions. The derivation utilizes firm-level input-output data under prevailing technological and economic constraints.

As for the efficiency analysis model, the existing literature can be divided into two major research streams: regions and industries. From the regional perspective, Zhang et al. [22] found that the shadow price presented an upward trend during the sample period, and the $C{O}_2$ emission reduction cost in high-income regions was significantly higher than others. Similarly, Ao et al. [23] calculated the $C{O}_2$ shadow price at the provincial level, and found that there was a large difference in emission reduction costs among regions. Total $C{O}_2$ reduction costs decreased when low-cost regions undertook greater mitigation burdens. Conversely, high-cost regions should receive lower reduction allocations to enhance system-wide efficiency. Given the relationship between $C{O}_2$ emission and economic growth, which was encapsulated in the shadow price, Wu and Lin [24] classified 29 provinces of China into three groups. Their analysis advocated for region-specific environmental policies and $C{O}_2$ reduction targets, given substantial inter-provincial heterogeneity in abatement potential.

From the industrial perspective, He et al. [25] established a measurement framework for agricultural greenhouse gas emissions. Based on measuring agricultural emission reduction costs, they examined possible influencing factors on $C{O}_2$ shadow prices from three dimensions: economy, technology, and policy. Wang et al. [26] selected relevant data from the construction industry and its upstream material supply industry to estimate the direct and overall $C{O}_2$ shadow price. The results implied that the manufacturing industry providing construction materials had significant emission reduction potential. Additionally, coal-fired power generation is also a high-energy-consuming and high-emission industry. Using cross-sectional data for 648 Chinese coal power plants, Du et al. [27] pointed out that state-owned enterprises exhibited the lowest values of $C{O}_2$ shadow prices, contrasting sharply with non-state-owned operators. They noted that if all power plants operated efficiently, total emissions could be abated by 44%. For the industrial sector concerned in this paper, Shen et al. [28] calculated the $C{O}_2$ shadow prices of industrial sectors in different regions by using provincial input-output data and concluded that the industrial $C{O}_2$ shadow prices are continuing to rise.

Based on a review of the existing literature, the following observations can be made: first, studies on $C{O}_2$ shadow prices in regional and industrial sectors predominantly use macro-level data. However, on the one hand, macro data cannot accurately reflect the specific input-output dynamics of local enterprises, leading to lower accuracy in the calculated shadow prices; on the other hand, the efficiency analysis model is constructed based on micro manufacturer production theory, and the use of macro data does not match its construction mechanism. Second, when discussing regional differences in $C{O}_2$ shadow prices, existing research only conducts simple comparative analyses of measurement results. It does not introduce spatial econometric models, failing to quantitatively assess the regional distribution of shadow prices and the mutual influences between regions. Third, when exploring the influencing factors on $C{O}_2$ shadow prices, previous studies have not considered the potential spatial effects of these factors. That is, while explanatory variables may affect the shadow prices in their own regions, they may also influence the explained variables in adjacent regions through spatial spillover effects. Therefore, this paper will use micro-enterprise data to measure industrial $C{O}_2$ shadow prices and introduce spatial econometric models to investigate the inter-city spillover effects of shadow prices and their influencing factors.

3. Research Methods

3.1. Theoretical Analysis

In economics, the market serves as a means of allocating resources, with market prices reflecting social value. However, on the one hand, many valuable goods and services (such as clean air, wildlife habitats, and fishery resources) lack a market; on the other hand, due to the existence of externalities, the prices of some goods traded in the market cannot effectively measure their value. For instance, coal-fired power generation causes environmental pollution, but electricity prices do not reflect the social cost of air pollution. To compensate for the inadequacies of market prices, the concept of shadow prices has been introduced.

Pollution emissions constitute inevitable byproducts of production under current technologies. No production process achieves desired economic outputs without generating undesirable residuals. The economic literature formally models this duality: desirable outputs (economic goods) and undesirable outputs (pollution) are jointly produced. These outputs exhibit weak disposability [29]: efficient production units cannot reduce undesirable outputs without proportionally sacrificing desirable outputs. Consequently, pollution abatement entails an economic output trade-off, representing the opportunity cost of emissions reduction. This opportunity cost manifests practically as the shadow price of pollution. Formally, the shadow price quantifies the marginal opportunity cost (foregone desirable output) when reducing one unit of undesirable output. Higher shadow prices indicate greater economic sacrifice per unit of emissions abated.

Based on the principle of maximizing income, rational producers will adjust the allocation of input factors to place their outputs at the Production Possibility Frontier (PPF). The slope at any point on the PPF is the ratio of the prices of different outputs at that production level. Figure 1 shows the measurement of shadow prices in a scenario of expected output (g) and unexpected output (b), where $P\left(x\right)$ is the PPF.

As shown in the figure, the PPF slope of this observation point is equal to the negative ratio of the shadow price of pollutant ($p^b$) to the ideal output shadow price ($p^g$), which is also known as the standardized shadow price of defective output. The negative sign indicates that people are willing to spend money to reduce the production of pollutants. Assuming that the shadow price of ideal output is equal to its market price, the absolute shadow price of unexpected output can be obtained. The shadow price of pollutants indicates the amount of expected output that needs to be abandoned in order to reduce one unit of adverse output while keeping production efficiency constant. The larger its absolute value, the more people agree to give up output to remove one unit of pollution.

When the unexpected output is $C{O}_2$, its shadow price can be regarded as the marginal cost of emission reduction, as well as the carbon tax rate and carbon trading price. For example, Chen [30] calculated the optimal carbon tax rates based on the difference between shadow prices under carbon emission reduction targets and the current prices. Therefore, estimating the shadow price of $C{O}_2$ can provide a reference for the introduction and improvement of carbon pricing mechanisms.

3.2. Calculation of $C{O}_2$ Shadow Prices

In the production process, $C{O}_2$ is an undesirable output. The associated shadow price represents the marginal economic sacrifice—expressed as output reduction or revenue loss—required to decrease emissions by one unit. Prevailing methodologies employ the output distance function (D). This metric quantifies the technical efficiency gap between observed production levels and the PPF, generally defined as:

$$D\left(x,y,w\right)=inf\left\{\phi >0:\left(x,{\displaystyle \frac{y}{\phi }},w\right)\in T\right\}$$

(1)

where T is the production possibility set. T determines how input set (x) is combined for production to obtain output vectors $\left(y,w\right)$. In this article, y represents the desirable output, which refers to industrial added value and changes with the variation in $\phi$. w represents the undesirable output, which refers to $C{O}_2$ emissions.

Based on the advantages of parametric methods such as differentiability, statistical inference, and insensitivity to outliers [31,32], this paper uses a parametric output distance function for estimation. When selecting a specific functional form, considering that the translog production function has advantages such as no need for a prior setting of directional vectors [33] and no strong disposability assumptions for output variables [34,35], this study adopts a translog functional form to parameterize the output distance function. The specification is given below:

$$\begin{array}{cc}\hfill lnD\left(x,y,w\right)={\alpha }_0& +{\sum }_{k=1}^K{\alpha }_{k}ln{x}_{ki}+{\displaystyle \frac{1}{2}}{\sum }_{k=1}^K{\sum }_{l=1}^K{\alpha }_{kl}ln{x}_{ki}ln{x}_{li}+{\sum }_{m=1}^M{\beta }_{m}ln{y}_{mi}\hfill \\ \hfill & +{\displaystyle \frac{1}{2}}{\sum }_{m=1}^M{\sum }_{n=1}^M{\beta }_{mn}ln{y}_{mi}ln{y}_{ni}+{\sum }_{r=1}^R{\gamma }_{r}ln{w}_{ri}\hfill \\ \hfill & +{\displaystyle \frac{1}{2}}{\sum }_{q=1}^R{\sum }_{s=1}^R{\gamma }_{qs}ln{w}_{qi}ln{w}_{si}+{\sum }_{k=1}^K{\sum }_{m=1}^M{\delta }_{km}ln{x}_{ki}ln{y}_{mi}\hfill \\ \hfill & +{\sum }_{k=1}^K{\sum }_{r=1}^R{\epsilon }_{kr}ln{x}_{ki}ln{w}_{ri}+{\sum }_{m=1}^M{\sum }_{r=1}^R{\rho }_{mr}ln{y}_{mi}ln{w}_{ri}\hfill \end{array}$$

(2)

Due to the unobservability of the distance function, the parameters in the Equation (2) cannot be directly estimated. Therefore, it is necessary to derive the homogeneity of y based on the distance function:

$$\begin{array}{cc}\hfill -lny& =lnD\left(x,1,w\right)-lnD\left(x,y,w\right)\hfill \\ \hfill & ={\alpha }_0+{\sum }_{k=1}^K{\alpha }_{k}ln{x}_{ki}+{\displaystyle \frac{1}{2}}{\sum }_{k=1}^K{\sum }_{l=1}^K{\alpha }_{kl}ln{x}_{ki}ln{x}_{li}+{\sum }_{r=1}^R{\gamma }_{r}ln{w}_{ri}\hfill \\ \hfill & +{\displaystyle \frac{1}{2}}{\sum }_{q=1}^R{\sum }_{s=1}^R{\gamma }_{qs}ln{w}_{qi}ln{w}_{si}+{\sum }_{k=1}^K{\sum }_{r=1}^R{\epsilon }_{kr}ln{x}_{ki}ln{w}_{ri}+u_i+{\omega }_i\hfill \end{array}$$

(3)

Then, the random frontier analysis method is used to estimate the variable coefficients in Equation (3). The residual consists of two parts: $lnD\left(x,y,w\right)=-u_i$ is the inefficiency term, representing the distance between a certain enterprise and the PPF; ${\omega }_i$ is the standard error term, representing statistical noise that follows a normal distribution.

Based on the principle of enterprise profit maximization, the shadow price can be derived using the duality theory between distance and profit function. That is, the $C{O}_2$ shadow price is the solution to following maximization problem:

$$\left\{\begin{array}{c}\underset{y,w}{max}R\left(x,p_y,p_w\right)=p_{y}y+p_{w}w\hfill \\ s.c.D\left(x,y,w\right)\le 1\hfill \end{array}\right.$$

(4)

where $R\left(x,p_y,p_w\right)$ is the profit function; $p_y=\left(p_{y1},\cdots ,p_{yM}\right)$ and $p_w=\left(p_{w1},\cdots ,p_{wR}\right)$ are the shadow prices of desirable and undesirable output; $y=\left(y_1,\cdots ,y_M\right)$ and $w=\left(w_1,\cdots ,w_R\right)$ are the vectors of desired and undesired output, respectively. $p_w$ is negative, indicating a societal willingness to pay for reducing undesirable outputs. This implies an opportunity cost associated with emissions abatement.

Then, using the Lagrange multiplier method, the shadow price of $C{O}_2$ can be obtained:

$$p_{w_r}={\displaystyle \frac{p_y}{\frac{𝜕D\left(x,y,w\right)}{𝜕y}}}{\displaystyle \frac{𝜕D\left(x,y,w\right)}{𝜕w_r}}$$

(5)

Using mathematical property of ${\displaystyle \frac{𝜕lnD}{𝜕lny}}={\displaystyle \frac{y}{D}}{\displaystyle \frac{𝜕D}{𝜕y}}$, the shadow price can be rewritten as:

$$p_{w_r}=p_y{\displaystyle \frac{y}{w_r}}{\displaystyle \frac{\frac{𝜕lnD\left(x,y,w\right)}{𝜕ln{w}_r}}{\frac{𝜕lnD\left(x,y,w\right)}{𝜕lny}}}$$

(6)

$lnD\left(x,y,w\right)=ln\left[yD\left(x,1,w\right)\right]=lny+lnD\left(x,1,w\right)$ can be obtained from the homogeneity of y by the distance function, so the shadow price of unexpected output can be simplified as:

$$p_{w_r}=p_y{\displaystyle \frac{y}{w_r}}e\left(y,w_r\right)$$

(7)

where $e\left(y,w_r\right)={\displaystyle \frac{𝜕lnD\left(x,y,w\right)}{𝜕ln{w}_r}}$ is a negative value. $e\left(y,w_r\right)$ indicates the elasticity of undesirable outputs on the production frontier.

Substituting the translog output distance function, the final expression for the $C{O}_2$ shadow price is obtained:

$$p_{w_r}=p_y{\displaystyle \frac{y}{w_r}}\left[{\gamma }_r+{\displaystyle \frac{1}{2}}{\sum }_{s=1}^R\left({\gamma }_{rs}+{\gamma }_{sr}\right)ln{w}_{si}+{\sum }_{k=1}^K{\epsilon }_{kr}ln{x}_{ki}\right]$$

(8)

3.3. Spatial Effect Models of Shadow Price

$C{O}_2$ is a major component of greenhouse gases, and the impacts of its emissions have cross-regional effects. Meanwhile, emission reduction actions are non-exclusive. This means that when one city implements $C{O}_2$ emission reduction measures, the $C{O}_2$ emissions of adjacent regions will change accordingly. To quantify the cross-regional effects of $C{O}_2$ emissions, this paper introduces a spatial weight matrix into the baseline fixed-effects model and uses spatial econometric methods to identify the correlation of $C{O}_2$ shadow prices and their influencing factors in each spatial unit with other surrounding spatial units.

The benchmark regression model generally consists of three components: the explained variable, explanatory variables, and a random error term. Since each component may influence the variables through spatial dependence, scholars have constructed different spatial econometric models. Among them, the generalized nested space model takes into account all possible spatial interaction effects. The model structure is as follows:

$$\begin{array}{c}\hfill \begin{array}{c}Y=\alpha +\rho WY+\beta X+\gamma WX+\mu \\ \mu =\theta W\mu +\epsilon \end{array}\end{array}$$

(9)

where $WY$ measures the spatial correlation effect of dependent variables across different regions. The spatial lag term $WX$ captures cross-regional spillover effects, and quantifies how independent variables in one region influence dependent variables in neighboring regions. Conversely, $W\mu$ measures spatial error dependence, reflecting how unobserved shocks propagate across geographic units.

Halleck and Elhorst [36] point out that the spatial interaction between explained and explanatory variables is the main cause of spatial spillover effects, while the spatial interaction of random errors does not contain effective information about spatial spillover effects. Additionally, since the study focuses on spatial dependence of $C{O}_2$ shadow prices and their influencing factors (i.e., $WY$ and $WX$ are the key focuses of the paper), this study employs the generalized nested spatial model with $\theta =0$ (i.e., SDM). The specific form is as follows:

$$Y=\alpha +\rho WY+\beta X_i+\gamma W{X}_i+u_c+\epsilon$$

(10)

where Y is the absolute value of $C{O}_2$ shadow price and takes the logarithm; $X_i$ represents the influencing factors of shadow price; W denotes the spatial weight matrix; $WY$ captures the endogenous spatial dependence of the dependent variable; and $W{X}_i$ represents the spatial lag term of influencing factors. The coefficients $\alpha$, $\beta$, $\gamma$ quantify marginal effects, and $\epsilon$ signifies the stochastic disturbance term. $u_c$ is the spatial fixed effect, which measures the effect that varies with cities in the panel data.

If $\rho =0$, it means regional observations of the dependent variable are spatially independent, but the influencing factors in adjacent regions will affect the local shadow price. In this scenario, Equation (10) is simplified to $Y=\alpha +\beta X_i+\gamma W{X}_i+u_c+\epsilon$. The SDM degenerates into a spatial lag model of explanatory variables.

If $\gamma =0$, it implies that the spatial lag term of independent variables has no impact on the dependent variable, and spatial effects only exist among the dependent variables across regions. In this scenario, Equation (10) is simplified to $Y=\alpha +\rho WY+\beta X_i+u_c+\epsilon$. The SDM degenerates into a spatial lag model of dependent variable, also known as the Spatial Autoregression Model (SAM).

If $\rho =\gamma =0$, it means that there is no spatial effect for all variables, and Equation (10) is simplified to $Y=\alpha +\beta X_i+u_c+\epsilon$. The SDM degenerates into a standard individual fixed effects model.

Since the SDM simultaneously considers the spatial correlations of both explained variables and explanatory variables, which aligns directly with the study’s research purpose, this article adopts SDM to explore the spatial effects of $C{O}_2$ shadow prices and their influencing factors. In the empirical analysis section, model applicability is verified via specification tests to determine whether the SDM can be simplified into a SAM or a Spatial Error Model (SEM).

4. Variables and Data

This paper aims to measure the $C{O}_2$ shadow prices of industrial enterprises, and further obtain the shadow prices of the two-digit industries and prefecture-level cities. Due to the lack of $C{O}_2$ emission data at the enterprise level, this study matches the China Manufacturing Pollution Discharge Integration Database with the China Industrial Enterprises Database to obtain energy input data for some enterprises, and calculates the undesirable output of enterprises according to the Intergovernmental Panel on Climate Change (IPCC) [37,38]. According to the matching results of various indicators, the final sample covers 277 prefecture-level cities in China, with a time window from 2001 to 2007, involving 28 two-digit industries. This article takes labor l, capital k, and intermediate input f as the input factors of the production function, and considers two types of outputs: desired (i.e., industrial added value y) and non-desired (i.e., $C{O}_2$ emissions c). In order to obtain the industrial added value based on 2001, the added value of enterprises was adjusted by the producer price index of each region (see

Table 1. Descriptive statistics of input-output data.

Variable	Unit	Samples	Mean	Std.	Min.	Max.
y	100 million CNY	199,872	0.59	5.96	0	975.12
l	person	199,872	623	2573	1	402,498
k	100 million CNY	199,872	1.01	8.19	0	852.43
f	100 million CNY	199,872	1.53	9.57	0	885.71
c	Mt	199,872	0.16	3.37	0	729.6

for details).

Existing studies have partially identified the influencing factors on $C{O}_2$ shadow prices. Referring to previous research, this paper primarily examines factors such as R&D intensity $rd$, level of opening-up $fdi$, level of transportation development $pc$, population density $pd$, industrial structure $is$, level of urbanization $ul$, level of human resources $hr$, level of education $edu$, and environmental governance intensity $env$ (see

Table 2. Descriptive statistics of variables related to influencing factors.

Variable	Samples	Mean	Median	Std.	Min.	Max.
$rd$	1939	−3.555	−3.251	1.732	−16.12	2.045
$fdi$	1939	−0.176	0.435	3.255	−16.12	4.253
$pc$	1939	1.4	1.587	1.254	−11.51	4.745
$pd$	1939	5.696	5.823	0.906	1.548	9.356
$is$	1939	3.795	3.828	0.237	3.309	4.154
$ul$	1939	3.359	3.334	0.487	2.502	4.221
$hr$	1939	3.762	3.785	1.303	0.793	6.06
$edu$	1939	4.6	4.601	0.005	4.586	4.605
$env$	1939	−2.382	−2.429	0.222	−3.438	−0.098

for details). The relevant data in this paper are extracted from databases such as the Carbon Emission Accounts and Datasets, CEIC Data’s China Premium Database, and the China Urban Statistical Yearbook. It should be noted that when constructing the environmental governance intensity variable, this article incorporates three indicators: green coverage rate of built-up areas, sulfur dioxide removal rate, and pollution abatement expenditure share. Based on the calculation of the weights of each indicator by the entropy method, the score of urban environmental governance intensity is obtained by using the linear weighting method.

$rd$ is expressed as the ratio of the annual R&D capital stock to the total industrial output value during the sample period. This study estimates R&D capital stock using Zhang’s [39] perpetual inventory method. Firstly, the annual scientific and technological expenditure of each prefecture-level city in the China Urban Statistical Yearbook is selected as the R&D investment. Secondly, the national R&D price index is used as the R&D investment price index. Then, the R&D capital stock $K_0$ in the base period (2001) is obtained according to the formula $K_0=I_0/\phantom{I_0\left(g+\delta \right)}\left(g+\delta \right)$, where $I_0$ denotes the scientific and technological expenditure in 2001 and $\delta$ is the R&D capital depreciation rate (20.6%) [40]. Due to data limitations, the annual R&D investment growth rate is used as a proxy for R&D capital stock growth g [41]. Finally, $K_t=K_{t-1}\left(1-\delta \right)+I_t$ is used to measure the annual R&D capital stock. For missing data, this article uses linear interpolation to fill in the gaps.

5. Empirical Analysis

Based on the stochastic frontier analysis method described earlier and micro-enterprise data, this paper obtains the estimated values of each coefficient in the output distance function. The results show that most regression coefficients are statistically significant (see Appendix A 

Table A1. The coefficient estimation results of the production distance function.

Variable	Estimated Coefficient
ll	−0.429 ***
	(0.029)
lk	−0.123 ***
	(0.018)
lf	0.015
	(0.018)
lc	−0.094 ***
	(0.013)
ll_2	−0.064 ***
	(0.005)
lllk	−0.018 ***
	(0.003)
lllf	0.074 ***
	(0.003)
lllc	−0.005 ***
	(0.002)
kk_2	−0.025 ***
	(0.002)
lklf	0.034 ***
	(0.002)
lklc	0.002
	(0.001)
ff_2	−0.137 ***
	(0.002)
lflc	0.010 ***
	(0.001)
cc_2	−0.005 ***
	(0.001)
Constant	−2.927 ***
	(0.134)
Observations	200 771

Standard errors in parentheses. *** p < 0.01.

for details), so the industrial $C{O}_2$ shadow prices calculated by Equation (11) are reliable. This section will discuss the differences in shadow prices at the industrial and regional levels, and quantitatively analyze the spatial effects of shadow prices and their influencing factors.

5.1. Shadow Prices of $C{O}_2$ in Industrial Sector

Based on enterprise input-output data, the $C{O}_2$ shadow prices of 28 two-digit industries in the industrial sector are estimated. The results show significant differences in shadow prices among industries (see Figure 2 for details). The $C{O}_2$ shadow price of the petroleum and natural gas extraction is the highest, with an average shadow price of CNY 4664.41/ton during the sample period. In addition, industries such as instruments, meters cultural and office machinery (CNY 1369.04/ton), electronic and telecommunications equipment (CNY 1339.43/ton), and other manufacturing (CNY 1034.71/ton) also have $C{O}_2$ shadow prices exceeding CNY 1000/ton. Higher shadow prices indicate that these industries have higher marginal costs of $C{O}_2$ emission reduction, greater difficulties, and less emission reduction potential. A possible reason is that most of these industries are capital-intensive industries, and their $C{O}_2$ emission intensity is already at a low level.

Figure 2 also shows that industries such as gas production and supply, nonmetal mineral products, and petroleum processing and coking have relatively low $C{O}_2$ shadow prices, at CNY 72.09/ton, CNY 90.12/ton, and CNY 100.13/ton, respectively. The main reason for the low shadow prices in these industries is that they are energy-intensive industries with high $C{O}_2$ emissions during production, and enterprises can achieve one unit of $C{O}_2$ emission reduction by taking simple measures. Therefore, industries with low shadow prices are usually characterized by low emission reduction difficulty, small opportunity cost, and large emission abatement potential. In the process of realizing emission reduction in the industrial sector, local governments can start with industries with lower shadow prices and gradually reduce emissions from easy to difficult.

5.2. Regional Shadow Prices of $C{O}_2$

There are also significant differences in China’s $C{O}_2$ shadow prices at the provincial level, after calculating the annual average of $C{O}_2$ shadow prices in the provincial administrative regions (see Figure 3). The five regions with higher shadow prices are Hainan (CNY 914.62/ton), Chongqing (CNY 736.78/ton), Sichuan (CNY 592.38/ton), Fujian (CNY 581.61/ton), and Guangdong (CNY 571.32/ton). The five regions with lower shadow prices are Ningxia (CNY 95.14/ton), Xinjiang (CNY 95.17/ton), Gansu (CNY 135.49/ton), Heilongjiang (CNY 136.2/ton), and Yunnan (CNY 147.06/ton). Among them, Hainan exhibits the highest value, while Ningxia shows the lowest. The price differential between these extremes approximates a tenfold ratio. This indicates that marginal abatement costs for $C{O}_2$ reduction exhibit substantial inter-regional disparity. This variation stems from the following determinants: On the one hand, provinces with high shadow prices generally have a higher level of economic development, meaning that emission reduction in economically developed regions causes greater economic losses; on the other hand, compared to regions dominated by the service industry (such as Hainan), provinces dominated by secondary industry (such as Heilongjiang) have large $C{O}_2$ emissions, and the scale effect makes the economic cost of abating each ton of $C{O}_2$ emissions relatively small. Intuitively, when the total amount of emission reduction is constant, reducing emissions more in areas with lower shadow prices and less in areas with higher prices can maximize economic benefits.

5.3. Spatial Effects of $C{O}_2$ Shadow Prices in Prefecture-Level Cities

The Moran’I is an indicator for measuring the spatial correlation of variables, reflecting the degree of similarity of a certain attribute value among adjacent regions in space. The global Moran’I measures a comprehensive result of spatial spillover effects across all regions, and its specific calculation formula is as follows:

$$Mora{n}^{\prime }I={\displaystyle \frac{{\sum }_{i=1}^n{\sum }_{j=1}^n{w}_{ij}\left(Y_i-\overline{Y}\right)\left(Y_j-\overline{Y}\right)}{S^2{\sum }_{i=1}^n{\sum }_{j=1}^n{w}_{ij}}}$$

(11)

Among them, $S^2={\displaystyle \frac{1}{n}}{\sum }_i^n{\left(Y_i-\overline{Y}\right)}^2$; $Y_i$ is the $C{O}_2$ shadow price of city i, $Y_j$ represents the $C{O}_2$ shadow price of city j, which is adjacent to city i, $\overline{Y}$ is the average shadow prices of all cities, and w is the spatial weight matrix.

Tobler’s First Law of Geography posits universal spatial interdependence. Its intensity follows an inverse-distance gradient, where nearer phenomena demonstrate stronger statistical dependence. Therefore, this paper constructs a spatial weight matrix using the reciprocal of the distance ($d_{ij}$) between the geographic central positions of city i and city j, that is:

$$w_{ij}=\left\{\begin{array}{c}0,i=j\hfill \\ 1/\phantom{1d_{ij}}{d}_{ij},i\ne j\hfill \end{array}\right.$$

(12)

The global Moran’I of $C{O}_2$ shadow prices for each year (see Appendix A 

Table A2. The global Moran’I of $C{O}_2$ shadow price.

Year	Moran’I	p-Value
2001	−0.005	0.214
2002	0.005	0.014
2003	0.015	0
2004	0.016	0
2005	0.036	0
2006	0.004	0.005
2007	0.002	0.089

for details) shows that the Moran’s indices for all years except 2001 pass the 10% significance test. This indicates that the city-level $C{O}_2$ shadow prices from 2002 to 2007 were not randomly distributed, and econometric regression models ignoring spatial correlation would violate the assumption of mutual independence of explanatory variables. A positive Moran’s index suggests that cities with high shadow prices are often adjacent to other high-shadow-price cities, while cities with relatively low shadow prices are generally close to cities with even lower shadow prices. Therefore, the selection of spatial econometric models has certain rationality and accuracy.

5.4. Fixed Effect Analysis of Influencing Factors

This section will analyze the influencing factors on $C{O}_2$ shadow prices, including R&D intensity, population density, environmental governance intensity, level of opening-up, industrial structure, level of urbanization, level of transportation development, level of human resources, and level of education. To avoid regression result bias caused by multicollinearity, this paper conducts a Variance Inflation Factor (VIF) test on the explanatory variables. As shown in the Appendix A 

Table A3. VIF test.

Variable	VIF	1/VIF
ln$hr$	1.71	0.586
ln$ul$	1.66	0.603
ln$pc$	1.51	0.661
ln$rd$	1.53	0.655
ln$pd$	1.38	0.726
ln$edu$	1.28	0.783
ln$is$	1.37	0.728
ln$fdi$	1.23	0.816
ln$env$	1.04	0.964
Mean	1.41	0.725

, the VIF values of all variables are far less than 10, meaning that the issue of multicollinearity among influencing factors can be ignored in the empirical analysis.

To compare the differences between models, this section first performs ordinary least squares estimation on all influencing factors. The regression results in first column of

Table 3. The regression results of influencing factors.

	FE	SAM	SEM	SDM
ln$rd$	0.061 ***	0.041 ***	0.043 ***	0.032 *
	(0.016)	(0.015)	(0.016)	(0.016)
ln$fdi$	−0.015 **	−0.013 **	−0.012 **	−0.011 **
	(0.006)	(0.006)	(0.006)	(0.006)
ln$pc$	0.099 ***	0.081 ***	0.075 ***	0.079 ***
	(0.020)	(0.018)	(0.019)	(0.018)
ln$pd$	−0.224 *	−0.293 **	−0.316 ***	−0.307 **
	(0.133)	(0.120)	(0.121)	(0.121)
ln$is$	0.994 ***	0.635 ***	0.602 ***	0.576 ***
	(0.178)	(0.164)	(0.175)	(0.175)
ln$ul$	0.352 **	0.081	0.058	0.044
	(0.147)	(0.135)	(0.145)	(0.147)
ln$hr$	0.122 ***	(0.022)	(0.030)	(0.056)
	(0.036)	(0.035)	(0.040)	(0.040)
ln$edu$	−9.633 ***	(0.687)	1.762	2.043
	(3.418)	(3.186)	(4.606)	(4.685)
ln$env$	0.082	0.053	0.037	0.051
	(0.086)	(0.077)	(0.078)	(0.078)
Constant	38.968 **
	(15.752)
$\rho$		0.710 ***		0.366 ***
		(0.066)		(0.137)
$\lambda$			0.826 ***
			(0.049)
std.		0.254 ***	0.255 ***	0.252 ***
		(0.008)	(0.008)	(0.008)
Observations	1939	1939	1939	1939

Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

show that educational level plays a decisive role in reducing $C{O}_2$ shadow prices. A general improvement in educational level implies an enhancement in public awareness regarding emission reduction. On the one hand, this reduces the difficulty in advancing government’s $C{O}_2$ reduction measures; on the other hand, it increases low-carbon behaviors among the public in production and consumption processes, thereby lowering the emission reduction costs reflected by shadow prices. Therefore, local governments at all levels should unswervingly prioritize education and increase investment in the education sector.

Industrial structure constitutes the primary driver of elevated $C{O}_2$ shadow prices. The regression coefficient of 0.994 indicates that a 1% increase in the proportion of secondary industry will lead to a 0.994% rise in $C{O}_2$ shadow prices. The secondary industry exhibits high energy and emission intensity. Its economic significance creates an abatement trade-off; that is, greater GDP contribution correlates with higher difficulty and opportunity costs of emission reduction. Urbanization level is the second largest positive influencing factor (with a regression coefficient of 0.352). A possible reason is that with an improvement in urbanization level, the construction and improvement of infrastructure will increase demand for high-energy-consumption and high-carbon emission products (such as cement), and the increased demand for $C{O}_2$ emissions raises $C{O}_2$ shadow prices.

Population density is the second largest negative factor influencing $C{O}_2$ shadow prices, with a regression coefficient of −0.224, meaning that a 1% increase in population density will reduce $C{O}_2$ shadow prices by 0.224%. This is because $C{O}_2$ emissions exhibit scale effects, with the larger the population per square kilometer and the corresponding $C{O}_2$ emissions, the lower the cost of decarbonization, resulting in a decrease in $C{O}_2$ shadow price. At the same time, the degree of regional openness will also significantly lower $C{O}_2$ shadow prices, with a regression coefficient of −0.015. This means that a 1% increase in foreign direct investment will reduce the shadow price by 0.015%. Therefore, adhering to opening-up is conducive to the realization of decarbonization. An increase in regional openness will lower the barriers to the introduction of advanced $C{O}_2$ reduction technologies, and the widespread application of new technologies will drive down the economic burden of achieving emission reduction targets.

Subsequently, the influencing factors that have a significant positive correlation with shadow prices are, in order, the level of human resources, the level of transportation development, and R&D intensity. The level of human resources is quantified by the number of college students per 10,000 population, reflecting structural economic advancement, specifically the high-tech industry’s share in industrial composition. The regression coefficient of 0.122 indicates that a 1% increase in the proportion of college students will lead to a 0.122% increase in shadow prices. Due to the characteristics of high value-added and low energy consuming in high-tech industries, the costs and difficulties of implementing $C{O}_2$ emission reduction in this field are high, resulting in a relatively high shadow price of $C{O}_2$. R&D intensity measures a city’s expenditure level on science and technology, with a regression coefficient of 0.061. This means that a 1% increase in R&D intensity will increase the shadow price by 0.061%. Higher values of this variable correlate with increased regional R&D expenditure on abatement technologies. Concurrently, technological intensification raises the opportunity cost per unit of $C{O}_2$ reduction. This paper uses per capita car ownership to calculate the level of transportation development. Since new energy vehicles were not commercially promoted during the sample period, the increase in per capita car ownership indicates an increase in demand for $C{O}_2$ emission, which will lead to greater difficulties in emission reduction, as well as an increase in $C{O}_2$ shadow prices and marginal emission reduction costs. Specifically, the regression results show that for every 1% increase in the proportion of gasoline vehicles, the shadow price increases by 0.099%.

Furthermore, the regression coefficient of environmental governance intensity is also positive, meaning that strict environmental policies will increase the $C{O}_2$ shadow price and further reduce social demand for $C{O}_2$ emissions, thereby promoting the realization of $C{O}_2$ emission reduction. However, the policy variable’s coefficient estimate is statistically insignificant at conventional levels. This indicates that the environmental policies of prefecture-level cities are relatively lenient and yield no statistically discernible effect on local $C{O}_2$ shadow prices, making it impossible to further reduce $C{O}_2$ emissions through price mechanisms.

5.5. Spatial Effect Analysis of Influencing Factors

Based on the fixed-effects regression, this section explores the spatial effects of $C{O}_2$ shadow prices and their influencing factors. To verify the necessity of spatial effect analysis at the model level, this paper conducts the LM test for model selection. The Moran’s index is statistically significant at the 1% level, confirming dependence on both local determinants and neighboring cities’ shadow prices. The results of Lagrange multiplier and robustness tests also significantly reject both spatial error and spatial lag null hypotheses. This suggests that spatial correlations should be considered when studying the shadow price of $C{O}_2$ and its influencing factors.

SAM, SEM, and SDM cover all approaches to introduce spatial weights into the baseline regression model. To maintain generality, this paper presents all of the models’ regression results in Table 3. It can be observed that both the spatial autoregressive coefficient ($\rho$) and the spatial autocorrelation coefficient ($\lambda$) are significantly positive at the 1% level. This indicates that, on the one hand, a high $C{O}_2$ shadow price in surrounding cities will raise the shadow price in the local region; on the other hand, adjacent cities will exert a positive influence on $C{O}_2$ shadow price in the local area through neglected factors in the random error term. Additionally, the autoregressive coefficient (0.710) of spatial lag model is notably larger than the estimated result of SDM (0.366). This suggests that if the spatial spillover effects of explanatory variables (i.e., influencing factors of $C{O}_2$ shadow prices) in surrounding areas on the local dependent variable (i.e., $C{O}_2$ shadow price) are ignored, the model will overestimate the degree of interaction between $C{O}_2$ shadow prices in different regions.

In the benchmark regression, the estimated coefficient values reflect the marginal effects of various influencing factors on $C{O}_2$ shadow price. However, after adding the spatial weight matrix, the regression coefficients of independent variables cannot fully capture the marginal impact of each factor on shadow prices. Therefore, it is necessary to decompose the spatial effects (see

Table 4. Decomposition of spatial effects.

	SAM			SDM
	Direct	Indirect	Total	Direct	Indirect	Total
ln$rd$	0.041 ***	0.106 **	0.147 **	0.033 **	0.34	0.369 *
	(0.02)	(0.05)	(0.06)	(0.02)	(0.21)	(0.21)
ln$fdi$	−0.013 **	−0.035 *	−0.048 **	−0.012 **	0.05	0.04
	(0.01)	(0.02)	(0.02)	(0.01)	(0.18)	(0.18)
ln$pc$	0.084 ***	0.218 **	0.302 ***	0.084 ***	1.485 ***	1.569 ***
	(0.02)	(0.10)	(0.10)	(0.02)	(0.51)	(0.51)
ln$pd$	−0.297 **	(0.79)	−1.091 *	−0.305 ***	1.30	1.00
	(0.12)	(0.50)	(0.58)	(0.12)	(2.64)	(2.65)
ln$is$	0.641 ***	1.657 **	2.298 ***	0.582 ***	2.35	2.937 *
	(0.16)	(0.71)	(0.79)	(0.17)	(1.73)	(1.71)
ln$ul$	0.09	0.22	0.31	0.06	3.70	3.76
	(0.13)	(0.38)	(0.51)	(0.15)	(2.54)	(2.51)
ln$hr$	(0.02)	(0.07)	(0.10)	(0.06)	−1.478 **	−1.538 **
	(0.04)	(0.12)	(0.15)	(0.04)	(0.70)	(0.70)
ln$edu$	(0.76)	(1.37)	(2.13)	2.00	14.84	16.84
	(3.01)	(8.74)	(11.57)	(4.45)	(16.59)	(16.13)
ln$env$	0.06	0.15	0.22	0.06	2.03	2.09
	(0.08)	(0.22)	(0.29)	(0.08)	(1.53)	(1.54)

Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

for details).

The direct effect refers to the impact of local factors on the local $C{O}_2$ shadow price, including feedback effects. That is, after a factor influences the shadow prices of surrounding areas through spillover effects, changes in the shadow prices of neighboring regions in turn cause changes in the local shadow price. By comparing Table 3 and Table 4, it can be seen that after introducing the spatial weight matrix, variables such as R&D intensity, openness level, transportation development level, population density, and industrial structure still exert a substantial effect on local $C{O}_2$ shadow price, while factors such as the level of urbanization, the level of human resources, the level of education, and environmental governance intensity no longer have a significant effect on the local shadow price. This indicates that ignoring spatial effects would overestimate the influence of these factors. Prefecture-level cities can regulate their local $C{O}_2$ shadow prices by controlling the above significant factors, but their impacts on other regions require further discussion.

Regarding the indirect effects and total effects, the SAM and the SDM did not yield consistent regression results. Therefore, model tests are required to confirm whether the SDM can be reduced to a SAM or SEM. The results show that the LR test rejects the null hypotheses that the SDM can be degenerated to the SAM and the SEM, respectively. Therefore, subsequent analysis will be based on the regression results of the SDM.

Indirect effects represent cross-boundary influences, which means predictors in adjacent regions alter the outcome variable locally, reflecting spatial spillover effects. Table 4 shows that both the indirect and direct effects of transportation development level are significantly positive. This implies that before the popularization of new energy vehicles, the more per capita car ownership in neighboring cities, the greater difficulty of $C{O}_2$ emission reduction in the local city. This indicates that $C{O}_2$ emission problems caused by vehicle exhaust are not limited to the local area but are challenges commonly faced by surrounding cities. The indirect effect of human resource level is significantly negative, with a coefficient of −1.478 indicating that a 1% increase in the human resource level of neighboring cities will reduce the local $C{O}_2$ shadow price by 1.478%. This suggests that local governments can reduce the $C{O}_2$ shadow prices of other cities besides their own by improving local human resource level and increasing the proportion of high-tech industries.

The total effect aggregates both direct and indirect effects. According to the regression results of the SDM, R&D intensity, the level of transportation development, industrial structure, and the level of human resources exert measurable impacts on the shadow price of $C{O}_2$ in all cities. Among them, adjusting the level of transportation development and human resources appropriately can not only reduce the emission reduction costs in the local region. but also potentially help neighboring cities achieve low-cost $C{O}_2$ reduction. This result also confirms that free riding behavior has a significant implementation motivation in the process of $C{O}_2$ reduction.

6. Conclusions

This paper takes stochastic frontier analysis as the theoretical foundation and uses micro-enterprise data to calculate the $C{O}_2$ shadow prices of 28 two-digit industries in China and 277 prefecture-level cities from 2001 to 2007. Then, this study uses the Moran’I to test the spatial dependence of $C{O}_2$ shadow prices in sample cities, and employs a SDM to investigate the spillover effects of shadow prices and their determinants. Synthesizing the analytical outcomes, this study derives several actionable policy prescriptions:

(1) Levying a carbon tax and improving the market-oriented mechanism for $C{O}_2$ emission reduction.

Significant heterogeneity persists in industrial $C{O}_2$ shadow prices across both sectoral classifications and geographic regions. For example, the petroleum and natural gas extraction has the highest shadow price of $C{O}_2$ (CNY 4664/ton), while the gas production and supply has the lowest (CNY 72/ton). At the provincial level, Hainan has the highest shadow price (CNY 914.62/ton), and the Ningxia has the lowest (CNY 95.14/ton), with a price difference approaching tenfold.

The huge heterogeneity of $C{O}_2$ shadow prices across industries and regions mean that there is significant room for carbon tax levying among different industries and regions. Specifically, carbon taxes slightly lower than their own marginal emission reduction costs should be imposed on regions and industries with high $C{O}_2$ shadow prices, and the emission reduction requirements for these entities should be appropriately relaxed. At the same time, emission reduction efforts should be strengthened in regions and industries with lower shadow prices, and subsidies should be provided to these entities for the introduction of green and low-carbon technologies through government transfer payments afterwards. On the one hand, the carbon tax system directly promotes $C{O}_2$ emission abatement by raising the input price of fossil energy factors, stimulating enterprises to improve energy efficiency and use clean energy. On the other hand, it indirectly achieves the goal of $C{O}_2$ reduction by redistributing government tax revenues to support the R&D of decarbonization technologies and new energy. In the long run, the integration of carbon taxation with ETS accelerates structural transitions in both industry and energy systems, thereby enabling the green transformation of industry.

(2) Taking multiple approaches to reduce regional emission reduction difficulties.

Without considering spatial spillover effects, the $C{O}_2$ shadow prices of prefecture-level cities are affected by multiple factors, including R&D intensity, population density, environmental governance intensity, opening-up level, industrial structure, the level of urbanization, level of transportation development, level of human resources, and education level. Among them, R&D intensity, the level of transportation development, industrial structure, urbanization level, and human resources level have significant positive effects on shadow prices; opening-up level, population density, and degree of education exert critical negative effects.

Therefore, effective emission reduction requires concurrent regulation of abatement cost determinants. This integrated approach improves policy efficacy while lowering implementation barriers. For example, increasing the degree of openness can strongly reduce shadow prices, thereby lowering the difficulty of emission reduction. Therefore, all regions should actively introduce advanced emission reduction technologies from other countries and regions, especially in cities with high shadow prices and high emission reduction costs. Although the model results show that increasing R&D investment will raise emission reduction costs, in the long run, the increase in government R&D expenditure will promote technological advancement and the innovation of emission reduction technologies, thereby achieving the goal of $C{O}_2$ reduction while adjusting the local industrial structure. In addition, the increase in the proportion of heavy industrial enterprises and fuel-powered vehicles in a region will significantly raise $C{O}_2$ shadow prices and increase the difficulty of emission reduction. Therefore, cities with high shadow prices and high emission reduction costs should prohibit the construction of new heavy industrial enterprises and restrict the sale of fuel-powered vehicles, assist local industries to carry out structural adjustment and low-carbon transformation, and encourage the R&D and launch of new energy vehicles.

(3) Coordinating emission reduction to achieve efficient and fair $C{O}_2$ reduction.

In terms of geographic space, the shadow price of $C{O}_2$ exhibits a “high-high” and “low-low” clusters domination. This pattern confirms substantial cross-regional spillovers. Among the factors influencing shadow prices, R&D intensity, the level of transportation development, industrial structure, and the level of human resources can affect the shadow prices of neighboring regions. In contrast, opening-up level and population density only have an inhibitory effect on the local $C{O}_2$ shadow price.

The spatial spillover effects of $C{O}_2$ shadow prices and their influencing factors indicate that collaborative emission reduction across regions is more effective. For example, the positive indirect effect of per capita vehicle ownership on shadow prices implies that a decrease in the number of vehicles in neighboring cities will lower the difficulty of emission reduction in the local area. Therefore, adjacent local governments should jointly negotiate and promote the cross-regional construction of infrastructure such as charging stations and charging piles to facilitate the substitution of electric vehicles for fuel vehicles and share the dividends of low emission reduction costs. Additionally, the negative spillover effect of human resource level on $C{O}_2$ shadow prices suggests that the larger talent pool and proportion of high-tech industries in surrounding areas will lower the local emission reduction costs. This means that neighboring regions should strengthen talent exchange and sharing, jointly develop high-tech industries, and achieve low-cost emission reduction together. However, the spatial spillover effects of shadow prices also indicate that free-riding behavior may occur as regions fulfill their emission reduction targets. Therefore, while coordinating and collaborating, local governments at all levels should clarify their respective emission reduction responsibilities and supervise each other to achieve win-win cooperation.