Effect of Forestry Carbon Offset Policy on Sharing the Pressure of Emission Reduction: Findings from China

Abstract

The forestry carbon offset policy has been implemented for a short time, and in order to study its optimization mechanism and pressure-sharing emission reduction effect, this paper applies the directional distance function to calculate the marginal abatement cost of each province/city based on the panel data of 30 provinces/cities in China from 2000 to 2020. Then, we utilize the synthetic control method to analyze the forestry carbon offset policy by taking Beijing, Guangdong, and Fujian as a natural experiment. Finally, placebo tests and differences-in-differences tests were used to verify the experiment’s effectiveness. The study has the following results. (1) The forestry carbon offset policy is a Pareto improvement after integrating multiple benefits. The proportion of FCS offset should be increased, and government subsidies should be reduced when carbon quotas are tightened, followed by the gradual inclusion of more industries and enterprises in the scope of mandatory emission reductions. (2) The impact of forestry carbon offset policy on sharing the abatement pressure has regional heterogeneity, which is affected mainly by geographical location, economic level, and industrial structure. It can be obtained that the forestry carbon offset policy has shared the pressure for emission reductions in Guangdong and Fujian. This study provides a theoretical basis for promoting forestry carbon offset policies and their coupling with other carbon-reduction policies.

1. Introduction

The carbon trading scheme endows carbon emission rights with commodity attributes and makes them circulate in the carbon trading market, which promotes the liquidity and allocation of funds and resources between different industries and regions [1,2,3,4]. The report of the United Nations Intergovernmental Panel on Climate Change (IPCC) pointed out that negative emission technologies play an important role in the process of reducing emissions, and forestry carbon sinks (FCS) are the most accessible means [5,6]. Therefore, the carbon neutralization mechanism of carbon sink trading is widely considered to relieve the pressure of emission reduction effectively. Compared with other carbon sink products, FCS increases economic, social, and ecological benefits but also faces some challenges. (1) Wildfires that occur during the contract period of an FCS project will likely result in carbon credits being canceled and the project failing. (2) The paradox of FCS emission reduction and offsetting: from a certain point, FCSs are viewed as a means of allowing fossil fuels to continue to be burned. If the enterprise purchases unlimited forestry carbon credits to balance its emissions from fossil fuel combustion, it becomes a tool for the enterprise to absolve itself of responsibility, rather than truly fulfilling its emission-reduction obligations.

Emission-controlled enterprises (ECEs) have to make abatement plans to relieve abatement pressures through various abatement methods. Among the indirect abatement pathways, the price of purchasing FCSs is usually advantageous. Unlike other countries, China’s forestry carbon offset policy is still in the developmental stage and is not yet perfect. Since 2011, FCS has been promoted gradually with the launch of the Chinese carbon market pilot and has been incorporated into Chinese Certified Emission Reduction (CCER) projects. To simplify the procedures and reduce the cost of project development, Beijing, Guangdong, and Fujian have carried out the pilot and practice of the forestry carbon offset policy. In particular, after the CCER project was put on hold in 2017, these three provinces/cities became the focus areas for the implementation of the offset supplementation mechanism with their FCS products as other types of carbon sink products came to a halt. FCS projects not only provide forest farmers with extra income and employment opportunities but also provide ECEs with a new channel to reduce carbon emission [7,8,9].

The marginal contribution of the paper is to enrich the research on the impact of FCS-related policies on carbon emissions reduction. Studies on carbon trading policies have focused more on the effects of policies on carbon emission reduction but neglected the fact that the trading mechanism provides multiple pathways to reduce emission reduction costs. Therefore, this paper not only identifies the role of FCS in carbon emission reduction but also evaluates the effect of the policy based on the forestry carbon offset mechanism. By analyzing the dynamic optimization mechanism of the forestry carbon offset mechanism, this study provides a reference for the design of policies related to forestry carbon offset policy and bridges forestry carbon offset policy and other carbon reduction policies.

The rest of this paper is organized as follows. Section 2 presents the background of this study. Section 3 describes the methodology used in this study. The selection of variables and their data sources are described in Section 4. The main results are analyzed and tested in Section 5. Section 6 concludes the paper and discusses policy implications.

2. Literature Review and Mechanism Analysis

2.1. Literature Review

FCS is an important way to achieve carbon neutrality, which realizes the integration of forest ecological protection and the benefits to farmers and other supply entities. Meanwhile, forest ecological products have significant positive externalities, and the forest ecological incentive mechanism established through market-based means is of great significance in improving the ecological compensation system and reducing the financial pressure on the state. At present, most of the research on FCS aims to measure the carbon sequestration potential of forests [10] and the pricing of FCS [11], and argue that the ecological benefits of FCS projects outweigh the economic benefits [7].

In the area of carbon trading, relevant studies have focused on the economic and environmental impacts generated by carbon trading, exploring the effectiveness of policies related to carbon trading and the effects of their implementation. Most of the studies on the direct or indirect effect of emission reduction are based on policy evaluation [12]. (1) The direct effect is the impact on the output of pollutants. Most studies evaluated the emission reduction effect [13] or air pollution control effect [14] in pilot provinces/cities, used DID to test the impact of environmental policies and economic aggregation on emission reduction, assessed the carbon trading pilot policies and the synergistic emission reduction effect of regional pollutants [15], and studied the emission reduction effect of carbon emission trading policies [12]. Other studies have dynamically analyzed the effects of carbon emission reduction policies from the perspective of industry heterogeneity. (2) The resultin gvariable of the indirect effect is not unique, such as energy utilization [16] and technological innovation [17]. At present, studies have examined the direct effects of policies, using methods such as DID [18], propensity score matching (PSM) [14], and integrated evaluation analysis [19] to measure the impact of policies on emission reductions.

Studies on forestry carbon offset policies have found a positive correlation between the proportion of FCS offset and its price [20]. Therefore, China should hasten the integration of FCS into the national carbon emission unified market and boost the trading price through policy design and market adjustment. In addition, for FCS to play its role in reducing the carbon-neutral cost of society, China should raise the amount of FCS used to offset carbon emission allowances (CEAs) in ECEs [20]. However, the offset proportion should not be too large. This is due to carbon offsets being widely used by individuals, corporations, and governments to mitigate their greenhouse gas emissions on the assumption that offsets reflect equivalent climate benefits achieved elsewhere. Thus, rather than encouraging companies to innovate technologically to reduce emissions, forest offsets program creates incentives to generate offset credits that do not reflect real climate benefits [21]. It is improves global welfare when a region introduces such an offset mechanism, with an optimal conversion rate below 1 [22]. In addition, the implementation of a forestry carbon offset policy increases the operating costs of forest land and has obvious accounting problems [23,24]. The carbon sink generated by the project only offsets 1.22% of the total regional CO₂ emissions, and there is still a need to increase its carbon sequestration potential [25]. Other studies have explored the role of forestry carbon offset policies in voluntary markets [26].

In summary, there is a lack of quantitative research on the specific mechanism and effect of FCS in carbon emission reduction, and studies have yet to include FCS market policies and ECEs’ demand response in the same analytical framework. Meanwhile, these studies only argue that the CEA requirements of carbon trading policies reduce carbon emissions (direct effect) by ignoring that the trading mechanism provides more diverse emission reduction paths, which can share the pressure of emission reduction effectively (the indirect effect). Therefore, the effects of the implementation of FCS projects in achieving national emission reduction targets have not been demonstrated fully. In addition, studies have pointed to the need to accelerate the effective integration of FCS into carbon trading policies and to increase the offset proportion but have not revealed the specific mechanisms by which this works.

2.2. Forestry Carbon Offset Policy and Optimization Mechanisms

The carbon offset policy refers to the offsetting of carbon emissions in the carbon trading process for emission reduction projects that are being implemented or have been filed for approval, after the verification and determination of emission reductions. China has implemented the pilot and practice of the forestry carbon offset policy successively in three regions to simplify the process and reduce costs: Beijing Certified Emission Reduction (BCER), Pu Hui Certified Emission Reduction (PHCER), and Fujian Forestry Certified Emission Reduction (FFCER).

(1) BCER. The Beijing Carbon Emissions Trading Pilot Project was officially launched in 2013, and FCS was included as an important offsetting mechanism in carbon emissions trading. In 2014, the policy of “Beijing Municipal Carbon Offset Management Measures” clarified that forest management projects and carbon sink afforestation projects in Beijing after 16 February 2005 can participate in the city’s carbon trading for offsetting. As can be seen from the data published by the Beijing Environmental Exchange, from December 2014 to June 2021, the price of FCS in Beijing fluctuated widely (RMB 8.4/tonne–RMB 57.2/tonne), with a volume of 140,000 tonnes, a transaction amount of RMB 5.27 million, and an average transaction price of RMB 32.35/tonne.

(2) PHCER. In 2015, the “Implementation Plan for the Guangdong Province Carbon Inclusion Pilot Scheme” was released, and the first batch of pilot cities were identified in January 2016. In April 2017, the “Interim Measures for the Management of Certified Emission Reductions under the Carbon Inclusion Scheme” proposed that, in terms of the relationship between local and provincial PHCER, local PHCER with a cumulative total of 500 tonnes or more can be converted into provincial PHCER for trading within the province. According to the Guangdong Provincial Department of Ecology, the number of PHCER transactions and transaction prices have been rising. As of 30 June 2021, the recorded emission reduction volume of PHCER in Guangdong Province reached 1,919,700 tonnes, of which FCS projects were as high as 92%; the transaction volume was 6,216,700 tonnes, which has a price advantage compared to CEA in the same period and therefore has good development prospects.

(3) FFCER. Fujian is the province with the highest forest cover in China, which has led to a relatively large number of FCS projects in Fujian Province. A total of 156,000 tonnes of FFCER were sold the day they went online in 2016, with a transaction value of RMB 2.88 million. In terms of the implementation effect, the total emission reduction volume of the recorded FCS projects in Fujian is 2,906,900 tonnes, the number of FCS transactions is 2,753,500 tonnes and the transaction amount is RMB 40,550,600, which can account for 10% of the offset ratio generated in the province, which is twice as much as the offset volume of other types of projects. Nationwide, Fujian Province ranks among the top in terms of the amount and number of FCS transactions.

Carbon trading originates from emissions trading and is an environmental regulation method that follows the Coase property theorem. Based on the “Structure-Conduct-Performance” (SCP) analysis paradigm from modern industrial economics, subjects have various transaction behaviors in different trading markets. The number of transaction entities, the scale of industry concentration, and entry/exit barriers will all have an impact on the market behavior of transaction entities. Different transaction behaviors will have an impact on the structure and performance of markets. Conversely, performance will further affect market behavior and market structure. Therefore, among the nine types of mechanisms in the FCS international and domestic markets, the forestry carbon offset policy has become the most widely used trading method in China at present.

Carbon trading mainly occurs in the mandatory trading market, which is more active than the voluntary trading market, where the forestry carbon offset policy also plays a role in trading with the constraints of CEA. The nature of trading under market behavior is a game between the supply side and the demand side, the outcome of which has a direct impact on the performance of the policy. Existing research suggests that China should accelerate the incorporation of FCS into the national carbon market and increase the price of trading and the proportion used for offsets through policy design and market adjustments [20]. However, it fails to reveal the coordination mechanism involved. Therefore, we use a game model to analyze the market equilibrium of FCS under market and governance mechanisms, and then explore how FCS offset policies should be dynamically integrated with carbon trading policies.

Assumption 1: (1) When ECEs choose to purchase FCS to meet the carbon emission allowance (CEA) requirements (the probability is x), and while forest farmers participate in the FCS project, the ECEs need to pay the cost of purchasing FCS $C_f=\theta \tilde{E}{P}_f$, where $\tilde{E}$ is the CEA requirement of ECEs, $\theta$ is the proportion of offset by purchasing FCS, $0<\theta <0.1$, and $P_f$ is the unit price of FCS in the carbon trading market. The technological innovation cost incurred by the ECE’s technological emission reduction is assumed to be $C_t$, and $C_t=T(E-\theta \tilde{E})$, where E is the carbon emissions of ECSs ($E\le (1+\theta )\tilde{E}$) and T is the unit cost of technical emission reduction. When forest farmers do not participate in FCS projects, ECEs can meet the CEA requirements by purchasing carbon sinks certified by other offset projects, and paying $C_e=\theta \tilde{E}{P}_e$, where $P_e$ is the transaction unit price of carbon sinks generated by other offset projects. (2) When ECEs rely entirely on technology to reduce emissions (the probability is $1-x$), the cost is assumed to be $C_t^{\prime }=ET$.

Assumption 2: (1) When forest farmers participate in FCS projects (the probability is y), they can carry out under-foresting economic activities and obtain forest income $R_f$; also, the forest farmer can obtain FCS income through the carbon trading market $C_f$. During this process, forest farmers need to bear the initial cost $C_b$. (2) When they do not participate in FCS projects (the probability is $1-y$), forest farmers can obtain timber income $R_w$, and the cost is $C_w$.

To sum up, the matrix of benefits for both the supply and demand sides of FCS is shown in

Table 1. Revenue matrix.

	x	1 − x
y	($-C_t-C_f+M$, $C_f+R_f-(1-\phi )C_b$)	$(-C_t^{\prime },R_f-(1-\phi )C_b)$
$1-y$	$(-C_t-C_e,R_w-C_w)$	$(-C_t^{\prime },R_w-C_w)$

.

From Table 1, the replication dynamic equation for both supply and demand is given by

$$\begin{array}{cc}\hfill F\left(x\right)& ={\displaystyle \frac{\mathrm{d}x}{\mathrm{d}t}}=x(E_{\left(x\right)}-{\overline{E}}_x)\hfill \\ \hfill & =x(1-x)\{y(-C_t-C_f+M)\hfill \\ \hfill & +(1-y)(-C_t-C_e)-C_t^{\prime }\}\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill F\left(y\right)& ={\displaystyle \frac{\mathrm{d}y}{\mathrm{d}t}}=y(E_{\left(y\right)}-{\overline{E}}_y)\hfill \\ \hfill & =y(1-y)\{x[C_f+R_f-(1-\phi )C_b]\hfill \\ \hfill & +(1-x)[R_f-(1-\phi )C_b]-R_w+C_w\}\hfill \end{array}$$

(2)

The equilibrium point of the system (Equation (3)) can be determined by means of the Jacobi matrix:

$$J=\left[\begin{array}{cc}{\displaystyle \frac{\partial F\left(x\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(x\right)}{\partial y}}\\ {\displaystyle \frac{\partial F\left(y\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(y\right)}{\partial y}}\end{array}\right]$$

(3)

where

$$\begin{array}{cc}\hfill {\displaystyle \frac{\partial F\left(x\right)}{\partial x}}& =(1-2x)\{y(-C_t-C_f+M)\hfill \\ \hfill & +(1-y)(-C_t-C_e)-C_t^{\prime }\}\hfill \\ \hfill {\displaystyle \frac{\partial F\left(x\right)}{\partial y}}& =x(1-x)(-C_t-C_f+M+C_t+C_e-C_t^{\prime })\hfill \\ \hfill {\displaystyle \frac{\partial F\left(y\right)}{\partial x}}& =y(1-y)[C_f+R_f-(1-\phi )C_b.\hfill \\ \hfill & -R_f+(1-\phi )C_b]\hfill \\ \hfill {\displaystyle \frac{\partial F\left(y\right)}{\partial y}}& =(1-2y)\{x[C_f+R_f-(1-\phi )C_b].\hfill \\ \hfill & +(1-x)[R_f-(1-\phi )C_b]-R_w+C_w\}\hfill \end{array}$$

(4)

If supply and demand are in equilibrium, $(1,1)$ is an evolutionarily stable strategy. From the determination of Equation (3), the conditions for the equilibrium of the system can be obtained as shown in Equation (5):

$$\begin{array}{cc}\hfill & \mathrm{tr}J=-R_f+(1-\phi )C_b+R_w-C_w-M+C_t-C_t^{\prime }<0\hfill \\ \hfill & \det J=[C_f+R_f-(1-\phi )C_b-R_w+C_w][C_t^{\prime }-C_t-C_f+M]>0\hfill \end{array}$$

(5)

From Equation (5), we canobtain

$${\displaystyle \frac{R_w-C_w+(1-\phi )C_b-R_f}{\theta \tilde{E}}}<P_f<{\displaystyle \frac{M}{\theta \tilde{E}}}+T$$

(6)

When the CEA tightening policy is implemented, $\tilde{E}$ decreases. It can be found through Equation (6) that $P_f$ increases. At this time, it is possible to appropriately reduce the government subsidy M and increase the proportion of FCSs that can be used for offsets $\theta$, which will not only alleviate the financial pressure on the government but also alleviate the reduced emissions pressure on ECEs.

When more industries, enterprises, or regions are included in the scope of emission control, both $\tilde{E}$ and T increase. In this case, $P_f$ may decrease, and an increase in $\theta$ will further decrease $P_f$, which will affect the incentives for FCS projects. This negative effect is better eliminated when there are fewer government subsidies (i.e., market mechanism plays a dominant role), with an active market and greater price volatility.

Therefore, in the early stage of policy development, the implementation of the CEA tightening policy should be the main focus, and with an increase in the FCS offset proportion and a reduction in government subsidies, to realize the transfer from government-led to market-led, followed by the gradual inclusion of more industries and enterprises in the scope of mandatory emission reduction.

3. Research Design

The basic idea of the research design was to construct a “counterfactual” control unit based on existing data and the target unit and to assess the effect of the policy by comparing the difference between the target and control units after implementation. Specifically, we considered the forestry carbon offset policy as a quasi-natural experiment conducted by the government, with the pilot provinces and cities defined as the experimental group and others unaffected by the policy as the control group.

Three points are made here.

(1) Carbon trading policies reduce carbon emissions and increase pressure to reduce emissions.

The carbon trading policy allows for the trading of CEA between low- and high-emitting enterprises. Although this has relieved the pressure on enterprises to reduce emissions to some extent, this is based on the relative carbon emission constraint. Overall, numerous studies have shown that China’s carbon trading policy has been effective in reducing carbon emissions since its implementation in 2011 due to the CEA constraint but has also increased the pressure on enterprises to reduce emissions.

(2) Forestry carbon offset policies have effectively shared the pressure to reduce emissions in the context of CEA constraints.

To ease the pressure on ECEs to reduce emissions, certified emission reductions from CCER projects can be used to offset carbon emissions from ECEs. However, the core of the carbon market mechanism is the total control of allowances, and CCERs, as a complementary offsetting mechanism, are usually underpriced compared to the cost of reducing emissions from ECEs. If the offset proportion is too high, it will increase the total supply and change the supply and demand of allowances in the carbon market, thus affecting the market price of allowances, so the offset proportion is often limited to 5%–10%. Since the suspension of China’s CCER projects in 2017, only three regions, Beijing, Fujian and Guangdong, have FCS projects available for offsetting. In addition, we will further verify whether the reduced pressure to reduce emissions is caused by carbon trading policies or other policies through a placebo test and a DID test. In the placebo test, equal treatment is carried out for provinces and cities that have implemented carbon trading but not forestry carbon offsetting policies for control purposes.

(3) Abatement pressure is represented by marginal abatement costs

The forestry carbon offset policy is supplemented by the substitution effect of carbon sinks so the marginal cost of increase is less than the marginal reward, sharing the pressure of emission reduction. When the carbon emission reduction cost is higher, the emission reduction expenditure increases, which increases the emission reduction pressure. Therefore, the emission reduction pressure can be expressed by the marginal abatement costs (MACs). The MAC is the price that the system needs to pay for emission reduction, and it is an important indicator to measure the emission reduction potential [27,28,29]. The calculation of MAC not only includes the level of economic development, labor force, and energy consumption from the perspective of input but also takes into account the total regional economic output and carbon dioxide emissions from the perspective of output. Therefore, the abatement pressure is expressed by MAC.

3.1. Measuring the Impact of the Forestry Carbon Offset Policy on the Emission Reduction Pressure

The synthetic control method synthesizes a virtual control group by predicting variables and evaluates the effect of policy implementation by comparing the difference between the experimental group and the control group [30,31]. The experimental group in this paper is provinces/cities where the forestry carbon offset policy is implemented. First, a counterfactual synthetic control group similar to the experimental group before the implementation of the forestry carbon offset policy was fitted. Second, the implementation effect of the forestry carbon offset policy was evaluated by comparing the differences between the experimental group and the synthetic control group after the forestry carbon offset policy was implemented. At present, the main provinces/cities in China that implement the forestry carbon offset policy are Beijing, Guangdong, and Fujian. Therefore, Beijing, Guangdong, and Fujian are selected as experimental groups.

Assume that the MAC of provinces/cities $i(i=1,2,\dots ,K+1)$ in period $t(t=1,2,\dots ,T+1)$ are $C_{it}$. $C_{it}^N$ is the MAC of province/city i when FCS is not implemented in period t, and $C_{it}^Y$ is the MAC of province/city i when FCS is implemented in period t. Let

$$C_{it}=C_{it}^N+D_{it}{\alpha }_{it}$$

where ${\alpha }_{it}$ is the emission reduction pressure shared by the forestry carbon offset policy. $D_{it}$ is a virtual variable of whether to implement the forestry carbon offset policy. If province/city i implements the forestry carbon offset policy when $t=T_0$, then $D_{it}=1$; otherwise, $D_{it}=0$. Therefore, for province/city i that has not implemented the forestry carbon offset policy, let $D_{it}=0$ and $C_{it}=C_{it}^N(t=1,2,\dots ,T)$. As for province/city i in the control group, let $C_{it}=C_{it}^N,t\in [1,T_0]$ and $C_{it}=C_{it}^Y=C_{it}^N+{\alpha }_{it},t\in [T_0,T]$ before and after implementing the forestry carbon offset policy. Hence,

$${\alpha }_{it}=C_{it}^Y-C_{it}^N=C_{it}-C_{it}^N$$

Assuming that province 1 implements the forestry carbon offset policy at period $t=T_0$, and the remaining K provinces/cities do not implement it, then ${\alpha }_{1t}=C_{1t}^Y-C_{1t}^N=C_{1t}-C_{1t}^N(T_0+1\le t\le T)$, which means estimating $C_{1t}^Y$. $C_i{t}^N$ can be estimated by using a factor model [30,31]:

$$C_{it}^N={\delta }_t+{\beta }_t{X}_i+{\lambda }_t{\mu }_i+{\epsilon }_{it}$$

(7)

where ${\delta }_t$ is the time-fixed effect; $X_i$ is the observable control variable that is not affected by forestry carbon offset policy; ${\beta }_t$ is the parameter to be estimated; ${\lambda }_t{\mu }_i$ is the interactive fixed effect, where ${\lambda }_t$ and ${\mu }_i$ are the unobservable common factor and fixed effect, respectively; ${\epsilon }_{it}$ is an unobservable temporary shock, and $\mathbb{E}\left({\epsilon }_{it}\right)=0$.

Determining the weight vector $W={(w_2,\dots ,w_{K+1})}^{\prime }$ is the key to estimating $C_{1t}^N$, where $w_k>0(k=2,\dots ,K+1)$ and $w_2+\cdots +w_{K+1}=1$. According to the outcome variable of each province/city in the control group, there is

$$\sum _{k=2}^{K+1}{w}_k{C}_{kt}={\delta }_t+{\beta }_t\sum _{k=2}^{K+1}{w}_k{X}_k+{\lambda }_t\sum _{k=2}^{K+1}{w}_k{\mu }_k+\sum _{k=2}^{K+1}{w}_k{\epsilon }_{kt}$$

(8)

Suppose the vector $W^{*}={(w_2^{*},\dots ,w_{K+1}^{*})}^{\prime }$ satisfies

$$\sum _{k=2}^{K+1}{w}_k^{*}{C}_{k1}=C_{11},\sum _{k=2}^{K+1}{w}_k^{*}{C}_{k2}=C_{12},\dots ,\sum _{k=2}^{K+1}{w}_k^{*}{C}_{k{T}_0}=C_{1T_0}$$

(9)

and

$$\sum _{k=2}^{K+1}{w}_k^{*}{X}_k=X_1$$

(10)

If ${\sum }_{t=1}^{T_0}{\lambda }_t^{\prime }{\lambda }_t$ is non-singular, then:

$$\begin{array}{cc}\hfill C_{1t}^N-\sum _{k=2}^{K+1}{w}_k^{*}{C}_{kt}& =\sum _{k=2}^{K+1}{w}_k^{*}\sum _{s=1}^{T_0}{\lambda }_t{\left(\sum _{n=1}^{T_0}{\lambda }_n^{\prime }{\lambda }_n\right)}^{-1}{\lambda }_s^{\prime }({\epsilon }_{ks}-{\epsilon }_{1s})\hfill \\ \hfill & -\sum _{k=2}^{K+1}{w}_k^{*}({\epsilon }_{kt}-{\epsilon }_{1t})\hfill \end{array}$$

(11)

If the period before the implementation of the policy is longer than the period after the implementation, the mean value on the right side of Equation (11) will tend to 0, so the period ${\sum }_{k=2}^{K+1}{w}_k^{*}{C}_{kt}$ after the implementation of the forestry carbon offset policy can be used as the unbiased estimator of $C_{1t}^N$. Therefore, the estimation of the pressure-sharing effect of emission reduction for provinces/cities implementing the forestry carbon offset policy is

$$\widehat{{\alpha }_{1t}}=C_{1t}-\sum _{k=2}^{K+1}{w}_k^{*}{C}_{kt},t\in [T_0+1,\dots ,T]$$

(12)

Hence, the key to estimating ${\widehat{\alpha }}_{1t}$ is to calculate $W^{*}={(w_2^{*},\dots ,w_{K+1}^{*})}^{\prime }$. The solution of $W^{*}$ is that the eigenvectors of the experimental group are within the convex set of eigenvectors of other provinces/cities outside the policy implementation. The synthetic control vector $W^{*}$ is usually calculated by solving an approximate solution. Therefore, let $M={(m_1,\dots ,m_{T_0})}^{\prime }$ and the linear combination before policy implementation ${\overline{C}}_i^M={\sum }_{t=1}^{T_0}{m}_t{C}_{it}$. If $m_1=m_2=\cdots =m_{T_0-1}=0$ and $m_{T_0}=1$, then ${\overline{C}}_i^M=C_{i{T}_0}$, which means the value of the outcome variable is the value at a point before the policy is implemented. If $m_1=m_2=\cdots =m_{T_0-1}={\displaystyle \frac{1}{T_0}}$, then ${\overline{C}}_i^M=T_0^{-1}{\sum }_{t=1}^{T_0}{C}_{it}$, which means the value of the outcome variable is the mean value before the policy was implemented. A linear combination of P vectors is $M_1,M_2,\dots ,M_P$; let $Z_1={(X_1^{\prime },{\overline{C}}_i^{M_1},\dots ,{\overline{C}}_i^{M_P})}^{\prime }$ be the $(r+P)\times 1$-dimensional eigenvector of the provinces/cities that implement the forestry carbon offset policy before the policy is implemented. Similarly, let $Z_0$ be a matrix of $(r+P)\times K$, which covers the eigenvectors corresponding to K provinces/cities that have not implemented the forestry carbon offset policy; i.e., the k-th column of $Z_0$ is ${(X_k^{\prime },{\overline{C}}_i^{M_1},\dots ,{\overline{C}}_i^{M_P})}^{\prime }$. Therefore, $W^{*}$ can be calculated by minimizing the distance $\Vert Z_1-Z_{0}W\Vert$ between $Z_1$ and $Z_{0}W$ such that $w_k\ge 0$, where $k=2,\dots ,K+1$ and $w_2+\cdots +w_{k+1}=1$. This paper calculates the distance according to Abadie’s method, i.e., $\Vert Z_1-Z_{0}W\Vert =\sqrt{{(Z_1-Z_{0}W)}^{\prime }V(Z_1-Z_{0}W)}$, where V is a symmetric positive semi-definite matrix.

Finally, the Root Mean Square Prediction Error was constructed to measure the degree of difference between the forestry carbon offset policy in provinces/cities and their synthetic control groups. The calculation formula is

$$RMSPE=\sqrt{{\displaystyle \frac{1}{T}}{\displaystyle \sum _{t=1}^T}{(C_{1t}-{\displaystyle \sum _{k=2}^{K+1}}{w}_k{C}_{kt})}^2}$$

(13)

3.2. Measurement of Marginal Abatement Costs

The measurement of MAC can be divided into two categories: (1) dynamic simulation models based on GDP growth rate and energy consumption. The main ones are the MARKAL-MACRO model and the Global Trade and Environment Model (GTEM). Such methods construct different models, set different assumptions, and often produce different results. (2) The analysis of abatement costs based on input–output efficiency, commonly calculated by DEA methods, mainly includes the DEA model based on Slacks-Based Measure (SBM) and Directional Distance Function (DDF). Compared to non-parametric DEA, DDF estimates the production frontier with the advantage of being differentiable and is generally used for MAC measurements between industries or regions. In addition, DDF is an improvement on the Shepard distance function. The DDF allows the consensual output to increase while reducing the non-consensual output, breaking a major limitation of the Shepard distance function, and is therefore used widely in the estimation of the shadow price of pollutants [32]. Therefore, the DDF is used in this paper to measure MAC.

DDF represents the maximum possible proportion of the expected output (undesired output) to increase (decrease) when the input is given [33,34]. Let the input be x, and $x\in R_{+}^N$ is the input vector; y is the expected output, and $y\in R_{+}^M$ is the expected output vector; b is the undesired output, and $y\in R_{+}^U$ is the undesired output vector; the production set is $P\left(x\right)\in \left[\right(y,b):x\to (y,b\left)\right]$, where $P\left(x\right)$ is all feasible input–output vectors. When $x=0$, $y=0$ exists as well. $P\left(x\right)$ must satisfy the following properties: (1) strong disposability of x. When x increases, $P\left(x\right)$ does not decrease, which means if $x^{\prime }\in x$, then $P\left(x\right)\supseteq P\left(x^{\prime }\right)$. (2) The zero correlation of y and b. When y is produced, b must be produced. If $(y,b)\in P\left(x\right)$ and $b=0$, then $y=0$. (3) The weak joint disposability of y and b. At a given input x, reducing b requires a proportional reduction in y. (4) The disposability of y. If $(y,b)\in P\left(x\right)$ and $y_0\le y$, then $(y_0,c)\in P\left(x\right)$. Based on the above properties, we define DDF:

$$\overrightarrow{D_0}(x,y,b:g_y,-g_b)=max[\beta :(y+\beta g_y,b-\beta g_b)\in P\left(x\right)]$$

(14)

$g=(g_y,-g_b)$ is the direction vector, and $g\ne 0$.

DDF can be solved with quadratic functions or transcendental logarithmic functions. Quadratic functions are differentiable and therefore more flexible than logarithmic functions. Therefore, this paper uses the quadratic functions to solve the DDF [35]. The shadow price of pollutants is

$$q=-p\times {\displaystyle \frac{\partial D(x,y,b:g_y,-g_b)/\partial b}{\partial D(x,y,b:g_y,-g_b)/\partial y}}$$

(15)

where p is normalized to be 1.

MAC is calculated based on three inputs and two outputs.

Input variables: capital ($x_1$); labor ($x_2$); energy ($x_3$).

Output variables: gross regional product (y); carbon emissions (b).

Direction vector: $g=(1,-1)$.

Therefore, the quadratic DDF of province k in period t is

$$\begin{array}{cc}\hfill \overrightarrow{D_0}(x^{kt},y^{kt},b^{kt}:1,-1)& ={\alpha }_0+\sum _{n=1}^3{\alpha }_n{x}_n^{kt}+{\beta }_1{y}^{kt}+{\gamma }_1{b}^{kt}\hfill \\ \hfill & +{\displaystyle \frac{1}{2}}\sum _{n=1}^3\sum _{n^{\prime }=1}^3{\alpha }_{n{n}^{\prime }}{x}_n^{kt}{x}_{n^{\prime }}^{kt}+{\displaystyle \frac{1}{2}}{\beta }_2{\left(y^{kt}\right)}^2\hfill \\ \hfill & +{\displaystyle \frac{1}{2}}{\gamma }_2{\left(b^{kt}\right)}^2+\sum _{n=1}^3{\delta }_n{x}_n^{kt}{y}^{kt}\hfill \\ \hfill & +\sum _{n=1}^3{\eta }_n{x}_n^{kt}{y}^{kt}+\mu y^{kt}{b}^{kt}\hfill \end{array}$$

(16)

Objective function:

$$\begin{array}{cc}\hfill min& \sum _{k=1}^K\sum _{t=1}^T[\overrightarrow{D_0}(x^{kt},y^{kt},b^{kt}:1,-1)-0]\hfill \\ \hfill \mathrm{s}.\mathrm{t}.& \overrightarrow{D_0}(x^{kt},y^{kt},b^{kt}:1,-1)\ge 0,k=1,2,\dots K;t=1,2,\dots ,T\hfill \\ \hfill & {\displaystyle \frac{\partial D(x^{kt},y^{kt},b^{kt}:1,-1)}{\partial b}}\ge 0,k=1,2,\dots K;t=1,2,\dots ,T\hfill \\ \hfill & {\displaystyle \frac{\partial D(x^{kt},y^{kt},b^{kt}:1,-1)}{\partial y}}\le 0,k=1,2,\dots K;t=1,2,\dots ,T\hfill \\ \hfill & {\displaystyle \frac{\partial D(x^{kt},y^{kt},b^{kt}:1,-1)}{\partial x_n}}\ge 0,k=1,2,\dots K;t=1,2,\dots ,T;n=1,2,3\hfill \\ \hfill & {\beta }_1-{\gamma }_1=-1;{\beta }_2=\mu ={\gamma }_2;{\delta }_n={\eta }_n;n=1,2,3\hfill \\ \hfill & {\alpha }_{n{n}^{\prime }}={\alpha }_{n^{\prime }n};n,n^{\prime }=1,2,3\hfill \end{array}$$

(17)

4. Data

The sample for this paper is 30 provinces, cities, and autonomous regions in China from 2000 to 2020, excluding Hong Kong, Macao, Taiwan, and Tibet.

4.1. Result Variables

The three inputs are capital, labor, and energy; the two outputs are regional economic scale and carbon dioxide emissions. The process of indicator selection and data processing is as follows.

(1) Expected output (y). Taking 2000 as the base period, the GDP of each province/city is obtained by a deflator. The data are selected from the China Statistical Yearbook from 2001 to 2021.

(2) Carbon dioxide emissions (b). Carbon dioxide emissions were estimated using the methods recommended in the IPCC Guidelines for National Greenhouse Gas Emissions Inventories, where regional carbon dioxide emissions are calculated as

$$C{O}_2=\sum _{i=1}^m{E}_i\times NC{V}_i\times C{C}_i\times CO{F}_i\times {\displaystyle \frac{44}{12}}$$

(18)

where $C{O}_2$ is the emission to be estimated; i is the type of energy fuels, including coal, coke, crude oil, gasoline, kerosene, diesel, fuel oil, and natural gas; $E_i$ is the physical quantity of energy consumption; $NC{V}_i$ is the average low calorific value; $C{C}_i$ is the carbon content; $CO{F}_i$ is the carbon oxidation factor; ${\displaystyle \frac{44}{12}}$ is the conversion factor.

(3) Capital ($x_1$). The capital stock is estimated using the “perpetual inventory method” [36]. The data are selected from the China Statistical Yearbook and the Statistical Yearbook of various provinces/cities from 2001 to 2021.

(4) Labor ($x_2$). The number of employees at the end of the year published by the Statistical Yearbook of each province/city from 2001 to 2021 is used to represent the labor force.

(5) Energy ($x_3$). The data are selected from the China Energy Statistical Yearbook from 2001 to 2021.

4.2. Control Variables

The determinants of MAC of the synthetic control group were as consistent as possible with those of the experimental group. Studies have shown that factors such as energy structure, industrial structure, urbanization rate, transportation, R&D intensity, and carbon emission intensity significantly affect MAC [37]. Therefore, based on combining existing research, this paper further considers the economic development level of provinces/cities and the impact of innovation output on MAC and selects the following variables as control variables.

(1) Economic level (EL). On the one hand, due to the scale effect, there is a positive correlation between the level of economic development and carbon dioxide emissions; on the other hand, provinces/cities with high economic levels have relatively perfect emission reduction technology, which is conducive to reducing carbon dioxide emissions. The economic level is represented by the per capita GDP in the China Statistical Yearbook from 2001 to 2021.

(2) Carbon emission intensity (CEI). MAC is inversely proportional to carbon emission intensity [28], which can be measured by the ratio of carbon dioxide emissions to GDP. The data are selected from the China Energy Statistical Yearbook and China Statistical Yearbook from 2001 to 2021.

(3) Energy structure (ES). Provinces/cities that consume coal mainly often have many alternative emission reduction schemes and have a large space for emission reduction, so the MAC of those areas is relatively lower. The proportion of coal consumption is used to represent the energy structure, and the data are selected from the China Energy Statistical Yearbook from 2001 to 2021.

(4) Industrial structure (IS). The development of the secondary industry needs to consume a lot of fuel, aggravating environmental pollution, but it also has more space for emission reduction and more emission-reduction measures. The industrial structure is represented by the proportion of the secondary industry. The data are selected from the China Statistical Yearbook from 2001 to 2021.

(5) Urbanization rate (UR). Carbon dioxide emissions are related to urbanization rates. Compared with rural areas, cities are populated more densely. The rapid development of industrialization increases carbon emissions, and the regional conduction effect brought about by the increase in productivity will also have an impact on the regional economy [38]. In addition, cities can also reduce carbon dioxide emissions with technologies and alternative energy sources [3]. The data are selected from the China Statistical Yearbook from 2001 to 2021.

(6) Traffic factor (TF). Vehicle exhaust is a major source of carbon emissions. It has been shown that pollution is positively related to the number of cars in cities. The number of private cars is used to represent the traffic factor, and the data come from the China Statistical Yearbook from 2001 to 2021.

(7) Research and development intensity (R&D). The R&D input/GDP indicator is used to measure R&D intensity. R&D subsidies are an important industrial policy that drives innovation and strengthens competition in various countries [39]. R&D intensity is positively correlated with regional technological progress and economic growth [11]. Since ECEs have CEA requirements, ECEs have to achieve emission reduction requirements through technological innovation. In addition, although technological progress has improved the efficiency of emission reduction, the marginal contribution rate will gradually decrease. Hence, the possibility of reducing emission reduction costs using technology will decrease. The data are selected from the China Science and Technology Statistical Yearbook from 2001 to 2021.

(8) Innovation Output (IO). Technological progress needs to be measured not only from the input but also from the output. The innovation output is represented by the number of patents [39], and the data are selected from the China Science and Technology Statistical Yearbook from 2001 to 2021.

5. Results and Robustness Test

5.1. Results

5.1.1. Analysis of the Results of the MAC

The linear programming problem in Equation (17) is solved using Python + Gurobi, and all variables are standardized in consideration of the convergence problem of the linear programming solution. The standardized data represent the input–output set $(x,y,b)=(1,1,1)$, which means that the average input obtains the average output. Then, the unknown parameters are estimated in Equation (16), and the MAC of 30 provinces/cities from 2000 to 2020 are calculated using Equation (15). Figure 1 shows the MAC by provinces/cities in China in 2005, 2010, 2015 and 2020.

As can be seen from Figure 1, the MAC is directly proportional to economic development. As China’s economy continues to develop, provinces/cities with higher MAC gradually shift from the central to the southeastern coast, forming the first ladder with the highest MAC; the second ladder with higher MAC gathers in the central region; the remaining provinces/cities form the third and fourth ladders. In addition, the evolution of MAC by provinces/cities reflects the changing pattern of economic development in China, with the tertiary sector taking shape gradually and clustering on the southeast coast, which has also become the region with the highest MAC in the country.

The MAC is higher in Beijing, Zhejiang, Shanghai, Jiangsu, and Guangdong, where the provinces/cities are developed more economically and the economic cost per unit of non-consensual output reduction is greater. The highest MAC in Beijing and Shanghai is due to their low industrial share and high economic capacity. Therefore, they have effectively improved pollution control and abatement facilities, resulting in less room for carbon abatement and greater difficulty in reducing carbon emissions. Liaoning launched a low-carbon-emission pilot in July 2010, and with the innovation of emission reduction technology and the initial investment of funds, the cost of emission reduction in Liaoning has been reduced effectively. In the central region, Hubei province has a higher MAC because its energy structure is dominated by coal, which makes it more difficult to reduce emissions. Western regions such as Guizhou, Xinjiang, Shaanxi, and Ningxia are less economically developed and thus have a lower economic cost per unit of non-consensual output reduction. In addition, western regions such as Guizhou and Yunnan, where agriculture and tourism are better integrated, produce low economic output relative to traditional agriculture, and thus, the economic cost of reducing one unit of carbon emissions is lower.

According to the theory of comparative advantage, the western regions will be the sellers of carbon emissions with the most potential, while the eastern regions are more likely to be the buyers of carbon emissions. In addition, the pricing mechanism of carbon emissions trading in the future may affect the industrial layout. By optimizing the industrial structure, it is likely that the eastern regions will gradually shift their high-emission secondary industries to the central and western regions and accelerate the development of tertiary industries.

5.1.2. Analysis of the Effect of Forestry Carbon Offset Policy on Sharing the Pressure to Reduce Emissions

For the implementation of the forestry carbon offset policy, “synthetic Beijing” was fitted using control variables from 2000 to 2013, “synthetic Guangdong” from 2000 to 2015, and “synthetic Fujian” from 2000 to 2016. The synthetic Beijing is weighted by Shanghai (0.874), Zhejiang (0.073), and Sichuan (0.053); the synthetic Guangdong is weighted by Zhejiang (0.862) and Jiangxi (0.138); the synthetic Fujian is weighted by Shanghai (0.039), Jiangsu (0.532), Zhejiang (0.1), Hainan (0.145), Chongqing (0.074) and Qinghai (0.11). In Figure 2, the solid line indicates the MAC of the experimental group; the dashed line indicates the MAC of the synthetic control group, and the vertical dashed line indicates the year when the forestry carbon offset policy was implemented.

In Figure 2, the gap between the dashed and solid lines is large before the implementation of the forestry carbon offset policy in Beijing. The fittedness between Beijing and synthetic Beijing is low, which is mainly because Beijing has the highest level of economic development, openness to the outside world, and urbanization in the country, which makes it difficult to be fitted perfectly by weighting other provinces and cities. It is difficult for Beijing to study the effect of forestry carbon offset policy through the SCM. Through the solid line in Figure 2, we can find that the overall emission reduction pressure in Beijing is in an upward stage, so we only analyze this trend and the current status of forestry carbon offset policy in Beijing. Since the implementation of the carbon trading policy in 2013, CEA requirements have greatly increased the pressure of emission reduction in Beijing, and BCER has failed to share the pressure of emission reduction effectively, which is due to two reasons. (1) According to the data of the Beijing Environmental Exchange, the transaction volume and transaction price of FCS have fluctuated greatly since the implementation of the policy in 2014. The transaction volume of FCS in Beijing from 2016 to 2017 was tiny. The transaction price decreased continuously from 2016 to 2019, and from 37.75 RMB/ton to 10.8 RMB/ton in 2019. The transaction volume and average price of FCS in Beijing fell to the lowest level ever in 2019. The instability of the volume and transaction price of FCS makes it difficult to achieve the expected effect of policy implementation. (2) Beijing has a low industrial share and a strong economic capacity and has improved its pollution control and emission reduction facilities effectively. This has led to less space for carbon reduction and greater difficulty in carbon reduction, which leads to a high MAC. In addition, compared to Guangdong and Fujian, Beijing has fewer forest resources, so the supply of FCS is unstable as trading is limited to local FCS projects.

It can be found from Figure 2 that before the implementation of the forestry carbon offset policy, there was no significant difference in the MAC between Guangdong and synthetic Guangdong. After the implementation of the policy in 2016, Guangdong’s MAC was lower than that of synthetic Guangdong, indicating that Guangdong has been effective in sharing the pressure to reduce emissions since the implementation of the forestry carbon offset policy. Guangdong is a major economic province in China, and the secondary industry is the backbone of Guangdong. As the pressure on carbon emissions intensifies, technological innovation to reduce emissions in Guangdong has tended to be efficiency-based innovation, which means that the huge energy demand is relieved temporarily by improving energy efficiency. However, due to the difficulty of optimizing the energy structure, and even its deterioration for the sake of economic development, Guangdong is experiencing gradually the consequences of energy saving rather than emission reduction. Therefore, FCS as an offsetting mechanism will play an important buffering role in the process of Guangdong’s energy structure transition. In 2016, Guangdong’s MAC decreased slightly, while in 2017, it decreased significantly, due to the introduction of the “Interim Measures for the Management of Certified Emission Reductions under the Carbon Inclusion Scheme” in 2017, which further clarified that local PHCER could be converted into provincial PHCER for offsetting, equivalent to the CCER generated in the province. This takes over the moratorium on CCER projects for the year effectively. In addition, in 2018, Guangdong’s MAC rose slightly and then turned to a downward trend in 2019, due to the suspension of the provincial PHCER filing applications by the Guangdong Development and Reform Commission in August 2018 in order to further improve the system and the resumption of filing applications from early 2019.

As the province with the highest forest cover in China, Fujian has a large number of FCS projects. This can be seen in Figure 2: before the implementation of the forestry carbon offset policy, the solid line and the dashed line overlap basically, which means a high degree of fittedness between Fujian and synthetic Fujian. The implementation of the forestry carbon offset policy in Fujian was clarified by the publication of the Pilot Program of Forestry Carbon Sink Trading in Fujian Province in 2017. After the implementation of the forestry carbon offset policy, the abundant forest resources have laid a solid foundation for the development of forestry carbon trading in Fujian, and the forestry carbon offset policy has a clear effect on sharing the pressure of emission reduction in Fujian.

To summarize, the implementation of the forestry carbon offset policy has effectively mitigated the increase in MAC in Fujian and Guangdong though the CEA requirement has increased the pressure on the pilot regions to reduce carbon emissions as a result of the carbon reduction policy. However, the implementation of the forestry carbon offset policy in Beijing has not been effective. The differences in implementation results, taking into account regional heterogeneity, will be further analyzed in the following sections.

5.2. Robustness Test

5.2.1. Placebo Test

The placebo test is a useful way of determining whether the difference between the experimental and synthetic control groups is due to policy or other factors. The core of the placebo test is to assume that all provinces/cities in the control group have implemented forestry carbon offset policy and toperform a synthetic control analysis for each province separately by calculating the difference between the synthetic and true values $\widehat{gap}$. It is assumed that $t_1$ is the period before the policy is implemented and $t_2$ is the period after the policy is implemented. If ${\widehat{gap}}_{1t}$ in the experimental group in the period $t_2$ is caused by the forestry carbon offset policy, the decrease in ${\widehat{gap}}_{1t}$ should be greater than the decrease in ${\widehat{gap}}_{kt}$ in the other control provinces/cities in the placebo test, thus indicating that the forestry carbon offset policy is effective in reducing MAC. If the difference between ${\widehat{gap}}_{1t}$ and ${\widehat{gap}}_{kt}$ in period $t_1$ is large, the difference in period $t_2$ may also be due to poor fitness and is not related to the implementation of the forestry carbon offset policy. To avoid differences due to large fitting errors, provinces/cities in the control group with RMSPE values over five times were excluded. The test results are shown in Figure 3.

In Figure 3, if the trend of the solid black line is lower than the dashed grey line after the implementation of the forestry carbon offset policy, it means that the effect of the forestry carbon offset policy in sharing emission reductions is significant. The significance test is to construct a statistic of the number of grey dashed lines whose lower edge exceeds the solid black line divided by the total number of grey dashed lines. The statistic is recorded as $P\left(\varphi \right)$. Figure 3 shows that the pressure-sharing effect of emission reduction in Fujian and Guangdong is generated by the forestry carbon offset policy. The results of the placebo test are shown in

Table 2. Analysis of the effect of the SCM and DID methods on the sharing of emission reduction pressure by the forestry carbon offset policy.

Test		Intensity of Shared Pressure to Reduce Emissions
		Guangdong	Fujian
Mean effect of SCM and placebo test	${\widehat{gap}}_{mean}$	−753.07 ***	−505.14 ***
	Number of grey lines along the lower edge	25	25
	Total number of grey lines	0	0
	$P\left(\varphi \right)$	0	0
	Placebo test	Significant	Significant
DID effect and testing	$trea{t}_{it}\times perio{d}_{it}$	−178.95 *	−302.5 *
	Control variables	Yes	Yes
	Double fixation	Yes	Yes
	_cons	86,546.48 **	17,227.16 **
	Adj $R^2$	0.9817	0.9913
	DID test	Significant	Not significant
Comparison of robustness tests		Consistent	Consistent
Policy effectiveness conclusion		Valid	Valid

Note: (1) “Total number of grey lines” and “Number of grey lines at the lower margin” correspond to the placebo test in Figure 3, and ${\widehat{gap}}_{mean}$ marked with *** indicates a significant placebo test; (2) $trea{t}_{it}\times perio{d}_{it}$ and _cons marked with *, **, and *** indicate significant at 10%, 5% and 1% respectively; (3) “Robustness test comparison” is based on whether the signs of the coefficients of ${\widehat{gap}}_{mean}$ and $trea{t}_{it}\times perio{d}_{it}$ are consistent; (4) “Policy effectiveness conclusion” is based on the SCM and placebo test.

. The placebo effect of Guangdong and Fujian is significant.

5.2.2. SCM-DID Test and Measurement of Net Policy Effects

The SCM has a significant advantage in the selection of control groups and can ensure parallel trends between the experimental and synthetic control group outcome variables, which is a prerequisite for the use of the DID method. To compare with the SCM method and to check the robustness of the SCM method, the SCM-based DID method is further used to conduct robustness tests and to compare the analysis with the conclusions drawn from the SCM. The provinces/cities implementing the forestry carbon offset policy were selected as the experimental group, and the provinces/cities in the synthetic group constructed by the SCM method were used as the control group. The DID method was set as follows:

$$C_{it}={\xi }_0+{\xi }_1\times trea{t}_{it}\times perio{d}_{it}+\sum _{k=1}^8{\tau }_k{X}_{it}^k+{\sigma }_{it}$$

(19)

where $C_{it}$ is the outcome variable; $perio{d}_{it}$ is the time dummy variable; $period=0\mathrm{or}1$ before or after the implementation of the forestry carbon offset policy, respectively; $trea{t}_{it}$ is the between-group dummy variable; $treat=1$ for provinces/cities implementing the forestry carbon offset policy; $treat=0$ for synthetic provinces/cities constructed by the SCM method; $trea{t}_{it}\times perio{d}_{it}$ is the cross-sectional term (double difference term); ${\xi }_1$ is the net effect of the forestry carbon offset policy; $X_{it}$ is the control variable, including economic level, energy structure, carbon intensity, industrial structure, urbanization rate, transportation factor, R&D intensity, and innovation output; and ${\sigma }_{it}$ is the residual term.

In Table 2, the coefficients of the Guangdong DID and Fujian DID are the DID effect, which has the same sign as the mean effect of the synthetic control analysis, indicating that the two tests are in the same direction. Hence, the forestry carbon offset policies in Guangdong and Fujian are effective.

5.3. Analysis of Heterogeneity

The effects generated by the policy are heterogeneous due to differences in geographic location, urbanization rate, economic level, industrial structure, and environmental awareness among provinces/cities, which also leads to regional heterogeneity in the forestry carbon offset policy.

The implementation of the forestry carbon offset policy in Fujian and Guangdong is better than that in Beijing. There are nine provinces/cities in China that have a forest coverage rate of more than 50%. In the sixth to ninth inventory of China’s forest resources, Fujian ranked first in terms of a forest coverage rate of 66.8%. Its forest stock also ranks in the top ten in China. Guangdong’s forest coverage is in the top nine in China, with a high forest coverage rate of 53.52% in the ninth forest inventory. The 6th–9th China Forest Resources Report shows that the forest coverage rate and forest stock in Fujian and Guangdong are much higher than those in Beijing. In addition, due to the different types of forest stock, the carbon sequestration capacity is also different. Among the living wood stock, Fujian has a high forest stock of over 90%. The number of trees per unit area of forest stock is high, so the carbon sequestration capacity is higher than other stock types, which also makes it very suitable for developing FCS projects. Therefore, there are relatively more FCS projects in Fujian and Guangdong. However, Fujian belongs to the hilly region of southeastern China. Although it has a large area of forest coverage, the province consists mainly of mountains and hills and has the smallest proportion of plains and few fields. Therefore, Fujian province has the smallest population among the southern coastal provinces/cities. And the size of the population has an impact on the consumption of energy, which in turn affects the number of carbon emissions.

Based on the National Bureau of Statistics of China, Beijing’s GDP per capita is much higher than that of Guangdong and Fujian, and the share of the secondary industry in Beijing is much lower than that of Guangdong and Fujian. The industrial share is an important indicator of the industrial structure of each province/city. Over 50% of China’s economic growth is driven by the secondary sector, but provinces/cities with a higher industrial share are more dependent on resources. The secondary sector requires a large number of fossil fuels, so provinces/cities with a higher share of secondary sector emissions have more room for emissions reduction, such as using clean energy or developing the tertiary sector. While economic growth affects carbon emissions through scale effects, it also has an impact on MAC through technological and structural effects. Beijing has gone through three stages of industrialization, a modern integrated service center, and internationalization, while following the laws of economic development and serving the requirements of the national strategy. With the synergistic development of Beijing, Tianjin, and Hebei, the continuous optimization of Beijing’s industrial structure is beginning to bear fruit, with the share of secondary industry decreasing from 38.06% in 2000 to 15.8% in 2020, and progress has been made in the development of highly sophisticated industries. Provinces/cities with a high level of economic development and low emissions have a high level of accumulated human and financial wealth, the financial capacity to support the improvement of pollution control and emission reduction facilities, and the advantage of technological innovation and talent support. Provinces/cities with average or lower levels of economic development prefer to purchase FCS to meet CEA requirements and maximize their returns, as they do not have the advantage of technical facilities and related human resources, and upgrading their emission reduction technologies would be costly. Therefore, there are two main reasons for the poor implementation of the forestry carbon offset policy in Beijing: (1) ECEs are more likely to meet CEA requirements through technological innovation and do not use FCS as an important way to reduce carbon emissions. (2) The forestry carbon offset policy has a low spillover effect on policies such as environmental regulation and financial subsidies, thereby weakening the expectations of banks and other financing institutions and thus reducing the intensity of FCS development.

6. Conclusions and Policy Implications

This paper applies the DDF to calculate the marginal abatement cost of each province/city based on the panel data of 30 provinces/cities in China from 2000 to 2020. Then, we utilize the SCM to analyze the forestry carbon offset policy by taking Beijing, Guangdong, and Fujian as a natural experiment. Finally, placebo tests and DID tests were used to verify the effectiveness of the results.

6.1. Conclusions

We find the following main conclusions. (1) The forestry carbon offset policy is a Pareto improvement after integrating multiple benefits. The proportion of FCSs offset should be increased and government subsidies should be reduced when carbon quotas are tightened, followed by the gradual inclusion of more industries and enterprises in the scope of mandatory emission reductions. (2) The forestry carbon offset policy reduces the MAC in Guangdong and Fujian. The placebo test and DID test ensure that the effect of the forestry carbon offset policy on the MAC of the implementing provinces/cities is not caused by other factors. The impact of the forestry carbon offset policy on MAC has regional heterogeneity, which is affected mainly by geographical location, economic level, and industrial structure.

6.2. Policy Implications

The conclusions of the paper have implications for implementing the forestry carbon offset policy in China. (1) Our conclusions will improve the forestry carbon offset policy in terms of both depth and breadth. In terms of depth, the development and trading stages of FCS projects should be further improved. In terms of breadth, following the pace of the construction of the national carbon trading mechanism, on the one hand, the carbon trading market covering all provinces/cities where FCS projects are located should be accelerated, so that its price advantage can play a role in sharing the pressure of emission reduction by the forestry carbon offset policy. On the other hand, some provinces/cities are unable to develop FCS projects due to their geographical location and other special factors but have a demand for emission reduction. Therefore, provinces/cities with abundant FCS projects, such as Fujian, should be matched with such provinces/cities, and regional regulation should be carried out according to their characteristics, forming a “one-to-one” or “one-to-many” matching mode between regions abundant and scarce forest resources. (2) There is a dynamic relationship between the forestry carbon offset policy and the carbon trading policy. In the process of including more industries and regions in the scope of emission reduction, an increase in the carbon offset percentage will not necessarily have a positive effect on the trading market, and it is safest to adjust the offset percentage when only the CEA is adjusted. (3) Since the emission reduction effect of the forestry carbon offset policy is regionally heterogeneous, the forestry carbon offset policy should be implemented in a differentiated manner. For provinces/cities with a higher level of economic development and a lower share of secondary industries, there is less space for emission reduction, so the proportion of FCS offsets should be increased appropriately. For provinces/cities with abundant forest resources, on the one hand, relevant incentives can be developed to further increase the development potential of FCS projects; on the other hand, regional optimization can be allocated to produce a spillover effect and clarify the direction of the flow of resources and funds between regions to avoid idle resources due to insufficient demand.

6.3. Limitations and Future Directions

Our paper studies the effect of forestry carbon offset policy. However, other aspects need to be considered in the future. First, we have considered the implementation effect of forestry carbon offset policy, but it is closely related to other carbon policies, and future research should explore the links between them. Second, based on the mechanism analysis in this study, we can obtain the conditions for the optimization of forestry carbon offset policy through model research in the future.