Measurement and Spatial Econometric Analysis of Forest Carbon Sequestration Efficiency in Zhejiang Province, China

Abstract

Maximizing the carbon sequestration of forested land is important for achieving carbon neutrality. Although some studies have discussed forest carbon sequestration efficiency (FCSE) from the perspective of total factor production, it is being increasingly recognized that forestland use regulates sequestration and emissions. When viewing forestland use as input and carbon emissions as output, there is a lack of empirical evidence on FCSE and its influencing factors. Here, a superefficiency slacks-based measurement model was applied to estimate FCSE for 66 counties in Zhejiang Province, China. The influencing factors and spatial spillover effects of FCSE were also analyzed using a spatial autocorrelation model. The findings showed that over the sample observation period, county FCSE ranged from 0.199 to 1.258, with considerable gaps. The global Moran’s I index showed that county-level FCSE was markedly spatially autocorrelated. Spatially, forestland use, cutting, pests, and diseases had negative spatial spillover effects on FCSE, whereas average annual temperature and precipitation displayed positive spillover effects. These findings suggest that the overall coordination of forest resource supervision and management among counties should be strengthened. The implementation of forestry management models aimed at consolidating or increasing forest carbon sequestration should be emphasized to improve forest quality, thereby promoting FCSE enhancement.

1. Introduction

Climate change is a ubiquitous problem faced by humanity. Recently, the Working Group I report of the Intergovernmental Panel on Climate Change (IPCC) reiterated that current global average surface temperatures were 1.09 °C higher than in 1850–1900 [1], and to limit warming to ≤1.5 °C by 2050, approximately 1 billion ha of forest had to be added [2]. Forest ecosystems are the most critical global terrestrial carbon pools [3,4] and play an indispensable role in absorbing atmospheric CO₂ in terrestrial ecosystems [5]. The Kyoto Protocol adopted in 1997 proposed the forest carbon sink as an important way to achieve carbon sequestration and required the strengthening of forest protection and sustainable management. Scholars have conducted extensive research on forest carbon sink development from the perspectives of institutional freedom [6], regional CO₂ allocation [7], future socioeconomic, regulatory, and policy changes [8], and for promoting long-term forest growth [9], and have recognized that natural climate solutions (NCS) are an important part of climate change mitigation. Therefore, forestland use practices of cultivating, developing, and protecting forest resources represent important pathways to enhance forest carbon sequestration capacity [10].

Specifically, the rational use of forestland (e.g., afforestation, tending, and sustainable management) can effectively increase the forest carbon sink potential [11]. Particularly, afforestation is the most cost-effective way to increase terrestrial carbon sink potential [12]. In developing countries, reforestation of degraded lands will help reduce atmospheric CO₂ concentrations [13]. Further, the implementation of appropriate forest management practices can also enhance biomass carbon stocks [14,15]. Tong et al. [16] corroborated these findings, noting that 72% of the regional carbon sink contribution was primarily from newly established forests, as well as forest growth within existing stands and deforested areas. However, forests are both carbon sinks and carbon sources. Wood harvesting removes biomass from standing trees, and the carbon in wood is oxidized and emitted to the atmosphere as CO₂ [17]. Events such as forest fires, pests, diseases, droughts, etc., can also interfere with the forest carbon balance, and lead to carbon emissions from standing tree stocks [18,19]. In addition, emissions from forest degradation are an important source of CO₂, and are equivalent to approximately one-third of those from deforestation [20]. To cope with these situations, at the 13th Conference of the Parties of the United Nations Framework Convention on Climate Change (UNFCCC), countries around the world have identified reducing emissions from deforestation and forest degradation (REDD) as an important and feasible climate change mitigation strategy.

It can be seen that NCS are receiving increasing attention [10], and forestry has been identified as one of the main focus areas to achieve climate change mitigation goals. The forestry department shoulders multiple tasks such as implementing ecological protection and restoration and providing forest ecosystem services. A series of forestry policies are aimed at mitigating climate change, for example, the introduction of forest carbon sink subsidies and carbon tax policies to encourage afforestation [21], support sustainable forestry development through community forest management to increase carbon sequestration [22], strengthen cutting management to control carbon balance [23], and introduce climate-smart forestry to guide forest management [24]. The National Forestry and Grassland Administration (NGFA) released the “2019 Forestry and Grassland Policies and Actions to Address Climate Change” white paper, pointing out that resource cultivation and resource protection should be strengthened and efforts made to increase carbon sink functions and reduce carbon emissions [25]. However, the cost-effectiveness of afforestation and the contribution of engineering measures and forest management activities to increasing forest carbon stocks vary across regions [26]. In addition, the focus of forestry is to invest capital in areas with high productivity [27]; therefore, it is necessary to consider maximizing forest-based carbon sequestration (collectively referred to as forest carbon sequestration efficiency—FCSE) under a given set of input conditions. FCSE reflects the relative change of forest carbon sequestration in forestland use, and its core idea is to achieve maximum forest carbon sequestration when forestland use inputs (such as afforestation and tending) are optimal [28]. The analysis of FCSE is important for effectively measuring the value of forestry inputs and outputs, rationalizing forestry policies, and improving the efficiency of capital investment.

The forestry input–output efficiency is an important index of economic efficiency that influences the subsequent forestry management decisions [29]. The input–output efficiency of forestry generally takes the three traditional production factors of land, labor, and capital as inputs and measures them according to the data envelopment analysis (DEA). For example, Chen and Yao [30] used the slack-based measure (SBM) model to measure the forestry ecoefficiency of 31 provinces in China and found that the ecoefficiency increased by an average of 1.2% per year. Zhong and Wang [31] used the panel data of 30 provinces to measure the total factor productivity (TFP) of the forestry industry in China and empirically found that the TFP had a spatial spillover effect and its impact on CO₂ emissions of energy consumption was “inverted U-shaped”. Lin and Ge [32] regarded CO₂ emissions from the forestry production process as undesired output and measured the TFP of forestry in Chinese provinces with forestry output and forest carbon sinks as the desired outputs. The results of the study showed that the TFP of forestry was higher when both forestry output and forest carbon sink were used as outputs. The government is actively making efforts to enhance the function of forest carbon sinks while promoting the development of the forestry industry. Yin et al. [27], Xue et al. [33], and Yao et al. [34] took China’s provinces as decision-making units (DMUs) and used forest area, forestry labor, and forestry investment as inputs to measure FCSE, but their selection of output indicators were different. Yin et al. used the gross output value of forestry and the volume of forest carbon sequestration as outputs, Xue et al. selected the gross output value of forestry and value of forest carbon sequestration, and Yao et al. only used forest carbon sequestration as an output. Their studies showed marked differences in FCSE between provinces, with relatively high efficiency values in the southern and northeastern forested areas. Huang, et al. [35] proposed the hybrid game cross-efficiency evaluation model and applied it to FCSE evaluation to reduce the overevaluation from the perspective of self-evaluation. In addition, some scholars have enriched the connotation of the input–output system and used it to measure carbon sequestration efficiency. For example, Long et al. [36] used afforestation and reforestation, forest tending, and forest harvesting as inputs to measure the carbon sequestration efficiency of eight counties. Susaeta et al. [37] used natural factors such as climate, age of the forest stand, tree density, and site index as inputs and calculated the ecosystem services output efficiency and forest carbon sequestration in southern loblolly pine forests.

Research on the influencing factors can help direct efforts aimed at improving carbon sequestration efficiency [38]. Thus, existing research can be summarized based on the following perspectives: forestland use including afforestation [11], timber production [39], cutting [40], and sustainable management [41]; natural environment factors including climate conditions [42], forest degradation [43], and forest growth rate [44]; social development factors including population mobility [11], urbanization rates [45], and economic development [46].

Due to the similarities in climatic conditions, topography, production patterns, and forestry policies in adjacent regions [31], there is spatial variability in forest carbon stocks [47] and spatial differences in carbon sequestration efficiency [48]. Spatial econometric models can capture regional heterogeneity and thus analyze the drivers. Du et al. [49] and Xue et al. [50] pointed out that forest carbon sinks between countries and provinces had spatial spillover effects; therefore, formulating common coping strategies with surrounding regions can promote the improvement of these sinks. Yin et al. [27] analyzed the driving factors of FCSE using panel data from various provinces in China and found that efficiency had spatial spillover effects and that per capita GDP, urbanization, and road network length had important positive effects on FCSE.

In summary, although extensive studies have been conducted on forest carbon sequestration, laying a solid foundation for our collective understanding, much room for improvement remains. From a research perspective, only a few papers have focused on the production efficiency of forest carbon sequestration, and in the measurement of efficiency, carbon sequestration was typically recognized by researchers as a desirable output, while forest carbon emissions were ignored as an undesirable output. If forest carbon emissions are considered, the analysis of FCSE would be more comprehensive and systematic. In terms of research scale, most studies have been conducted at the provincial or larger scale, and cannot reveal smaller-scale heterogeneity patterns, whereas county-level FCSE studies remain rare. Therefore, it is important to discuss FCSE under the output of forest carbon emissions and analyze the influencing factors by taking the county as the entry point.

In China, the county is the most basic administrative unit for conservation and utilization of forest resources. Particularly in southern China, one of the most active forest management regions in the world [51], counties have diverse natural resources and complex socioecological environments. Moreover, with the flow of forestry capital and the popularization of technology, policymakers formulate policies and guidelines based on the region as a whole, resulting in a synergistic effect; thus, assessing county-level differences in FCSE and its influencing factors can offer direct guidance for forestry macro policy formulation as well as the consolidation and enhancement of forest carbon sink capacity in accordance with local conditions. Therefore, this study examined the FCSE of 66 counties in Zhejiang Province, China, a southern collective forested area, adopting the superefficiency slack-based measure (Super-SBM) model with undesirable outputs and empirically analyzing both the influencing factors and spillover effects through a spatial econometric model, quantitatively revealing the effects of forestry production input characteristics on FCSE. This study enriches the current research on FCSE by providing scientific references and targeted suggestions for forestland use to optimize FCSE.

2. Materials and Methods

2.1. Study Area

Zhejiang Province is located on the southeastern coast of China, in the subtropical monsoon humid climate zone, and is rich in photothermal resources and abundant in precipitation. The province spans 105,500 km², is comprised of approximately 70% hilly mountains, and includes 11 cities, as well as 90 counties. In 2020, the forested area of Zhejiang Province was estimated as 60,800 km², equivalent to a forest coverage rate of 61.17%, with a forest stock volume of 378 million m³ (Figure 1). Zhejiang Province is also one of the most economically developed provinces in China, with an estimated per capita GDP of CNY 100,600 in 2020; however, rapid urbanization and industrialization pose great challenges to forestland use and management.

2.2. Methods

2.2.1. Super-SBM Model with Undesirable Outputs

Because traditional DEAs assume the maximization of output, it is not applicable to situations with an undesired output in the production process, nor does it consider the slackness of input–output variables. In light of this, Tone [52] proposed a service level agreement (SLA)-based measure SBM model, and further proposed the Super-SBM model to resolve the issue of the traditional SBM model not being able to evaluate and rank multiple simultaneously valid DMUs. Accordingly, when setting the FCSE of the n = 66 counties, each was regarded as DMU_j (j = 1, 2,..., n), while the counties were recorded as DMU_k. Each DMU used m inputs [x_i (I = 1, 2,..., m)] to obtain s₁ desired outputs [y_r (r = 1, 2,..., s₁)], and s₂ undesired outputs [b_u (u = 1, 2,..., s₂)]. The matrices were defined as: $X=\left[x_1,x_2,\cdots ,x_n\right]\in R^{m\times n}$, $Y=\left[y_1,y_2,\cdots ,y_r\right]\in R^{s_1\times n}$, and $B=\left[b_1,b_2,\cdots ,b_u\right]\in R^{s_2\times n}$. Under constant return to scale conditions, the calculation of the Super-SBM model with undesirable outputs is shown in Equation (1):

$$\begin{array}{l}{\rho }^{*}=\min \frac{1+\frac{1}{m}{{\displaystyle \sum }}_{i=1}^m\frac{s_i^{-}}{x_i^t}}{1-\frac{1}{s_1+s_2}\left({{\displaystyle \sum }}_{r=1}^{s_1}\frac{s_r^{g+}}{y_{rk}^t}+{{\displaystyle \sum }}_{u=1}^{s_2}\frac{s_u^{b-}}{b_{uk}^t}\right)}\\ s.t\{\begin{array}{l}{{\displaystyle \sum }}_{j=1,j\ne k}^n{x}_{ij}{\lambda }_j-s_i^{-}\le x_{ik} i=1,2,\cdots ,m\\ {{\displaystyle \sum }}_{j=1,j\ne k}^n{y}_{rj}{\lambda }_j+s_r^{+}\le y_{rk} r=1,2,\cdots ,s_1\\ {{\displaystyle \sum }}_{j=1,j\ne k}^n{b}_{uj}{\lambda }_j-s_u^{b-}\le b_{uk} u=1,2,\cdots ,s_2\\ 1-\frac{1}{s_1+s_2}\left({{\displaystyle \sum }}_{r=1}^{s_1}\frac{s_r^{g+}}{y_{rk}^t}+{{\displaystyle \sum }}_{u=1}^{s_2}\frac{s_u^{b-}}{y_{uk}^t}\right)>0\\ \lambda ,s_i^{-},s_r^{g+},s_u^{b-}\ge 0\end{array}\end{array}$$

(1)

where ρ* is the FCSE score, λ represents the weight vector of the jth DMU, and $s_i^{-}$, $s_r^{g+}$, and $s_u^{b-}$ are the slack variables of the input, desirable output, and undesirable output, respectively. Here, if ρ* ≥ 1, the DMU was considered effective, while 0 ≤ ρ* < 1 indicated an ineffective DMU.

Scientific and effective forestland use is an important way to improve the potential of forest carbon sequestration. Forestland use as an input indicator to measure FCSE can provide a decision basis for optimizing the input allocation of forestland use, thereby maximizing the output of forest carbon sinks. Therefore, MATLAB R2018a v.9.4 (MathWorks Inc., Natick, MA, USA) was used to calculate county-level FCSE for Zhejiang Province from 2016 to 2019 according to the following input and output parameters.

Input indicators: afforestation, reforestation, protection of existing forests, and tending to forests are the primary practices of forestland management in southern China [53]. Accordingly, the present study divided the input indicators of forestland use into afforestation + reforestation, forest tending, and forest management. (1) Afforestation + reforestation refers to the process of forestland use that adds to or restores forest cover each year. As it is difficult to distinguish afforestation and reforestation from existing data, this study used afforestation data as a proxy. (2) Forest tending are measures taken to promote tree growth, improve stand composition, and increase forest productivity. Here, our study used the sum of the areas for tending cutting, regeneration cutting, low-yield forests, and low-efficiency forest transformation to indicate this value. (3) Forest management is an important contributor to carbon stock biomass increases and enhancing these practices represents a practical method for increasing carbon sequestration [54]. According to the definition of forest management in the Marrakech Accords, if a forest is directly or indirectly subjected to anthropogenic impacts, it can be considered under at least one component of forest management. As an important collective forested area in southern China, Zhejiang Province has implemented collective-forestland tenure reform to provide >95% forestland management rights to individual households that manage their forestland to improve both productivity and forest volume [55]. Accordingly, this study used the total forested area as an input indicator for forest management. The data for afforestation, reforestation, and forest tending areas were obtained from the Zhejiang Forestry Statistical Report, while the total forested area was derived from the annual forest resources vector map provided by the Zhejiang Bureau of Forestry.

Output indicators: the input indicators, while contributing to forest carbon sequestration, may also produce carbon emissions under natural and unnatural mortality events, that is, including positive externalities (e.g., carbon sinks), as well as negative externalities (e.g., carbon sources). (1) Forest carbon sequestration removes CO₂ through photosynthesis and is arguably an important forest ecosystem service; therefore, carbon sequestration was selected as the desired output for this study. (2) Forest carbon emissions, considered here via individual mortality, were further divided into two categories: natural and unnatural mortality [56]. All forest mortality leads to carbon emissions through standing tree decomposition. Accordingly, forest carbon emissions were selected as the undesirable outputs. Forest carbon sequestration and emissions were calculated using Equations (2) and (3), respectively:

$$C={{\displaystyle \sum }}_i^n{A}_i·per{V}_i·BCE{F}_i·\left(1+R_i\right)·C{F}_i+{{\displaystyle \sum }}_j^2{A}_j·perAG{B}_j·\left(1+R_j\right)·C{F}_j$$

(2)

$$OC={{\displaystyle \sum }}_i^n{A}_i·per{V}_i·C{R}_i·BCE{F}_i·\left(1+R_i\right)·C{F}_i$$

(3)

where C is the carbon storage in the forest ecosystem (tC); A_i is the area of the ith-type tree species (hm²); perV_i is the storage volume per unit area of the arbor forest (m³·hm⁻²); BCEF_i is the biomass conversion and expansion factor of the ith tree species; R_i is the root-to-shoot ratio of the ith tree species; CF_i is the carbon fraction of dry matter for the ith tree species; CR_i is the tree loss rate of the ith tree species; while A_j, perAGB_j, R_j, and CF_j are the bamboo forest (j = 1) or shrub forest (j = 2) area (hm²), biomass per unit area (t·hm⁻²), root-to-shoot ratio, and carbon content coefficient, respectively.

The data sources for A_i, A_bamboo, A_shrub, and perV_i were derived from the annual forest resources vector map provided by the Zhejiang Bureau of Forestry, while CR_i was adopted from those for pine, fir, and broad-leaved tree species obtained from the annual continuous forest inventory in Zhejiang Province. The data for perAGB_bamboo and perAGB_shrub were acquired from the Announcement on Forest Resources and their Ecological Function Values in Zhejiang Province (2016 to 2019), while the BCEF, R, and CF parameters were derived from the land use change and forestry greenhouse gas inventory of The People’s Republic of China Second National Communication on Climate Change [57].

2.2.2. Spatial Correlation Analysis

According to Tobler’s First Law of Geography, everything is related to everything else, but this relationship increases with geographic proximity [58]. Historical research has revealed substantial heterogeneity in the spatial distribution of forests. Further, forest carbon sinks have been found to maintain spatial spillover effects [49], with the explained variable used in the present study (FCSE) displaying a more pronounced spatial transmission effect [32]. In addition, some studies have found a strong correlation between socio-economic development among different regions. If the explained variables are spatially autocorrelated, the use of spatial econometric methods is essential [59,60,61] to account for estimation bias. In the present study, the Global Moran’s Index (I) was used to check and assess the spatial autocorrelation of county-level FCSE values. The Local Moran’s Index (I) was used to draw the map of the local indicators of spatial association (LISA) to describe the local clustering characteristics of FCSE. The map of the LISA includes four categories: high–high and low–low which indicate positive spatial autocorrelations and high–low and low–high which indicate negative spatial autocorrelations. Furthermore, to better reflect the spatial dependence characteristics and test the robustness of the research results, the contiguity weight matrix $W_{ij}^1$, distance weight matrix $W_{ij}^2$, and economic weight matrix $W_{ij}^3$ were selected for spatial econometric analyses for which the calculations are shown in Equations (4)–(7):

$$W_{ij}^1=\{\begin{array}{c}1\\ 0\end{array} \begin{array}{c}if i and j are contiguity\\ otherwise\end{array}$$

(4)

$$W_{ij}^2=e^{-\frac{d_{ij}}{d_{\min }}}$$

(5)

$$W_{ij}^3=W_{ij}^2·\mathrm{diag}\left(\frac{{\overline{E}}_1}{\overline{E}},\frac{{\overline{E}}_2}{\overline{E}},\cdots ,\frac{{\overline{E}}_n}{\overline{E}}\right)$$

(6)

$${\overline{E}}_i=\frac{1}{t_1-t_0+1}{{\displaystyle \sum }}_{t=t_0}^{t_1}{E}_{it}$$

(7)

where d_ij is the Euclidean distance from the government seat of county i to that of county j; d_min is the shortest Euclidean distance between the county government seats; t₁ is the end of the study; t₀ is the base period of the study; ${\overline{E}}_n$ is the mean GDP of county i from 2006 to 2019; and $\overline{E}$ is the mean GDP of all counties.

2.2.3. Spatial Econometric Model

Spatial econometric models can effectively address the spatial dependencies that are not acquired by linear regression analyses. The most commonly used spatial panel models include the spatial Durbin model (SDM), spatial autoregressive model (SAR), and spatial error model (SEM). The general form of the SDM, SAR, and SEM is Equations (8), (9), and (10) and (11), respectively:

SDM:

$$Y=\rho WY+\theta WX+\beta X+\epsilon \epsilon ~N\left(0, {\delta }^2{I}_n\right)$$

(8)

SAR:

$$Y=\rho WY+\beta X+\epsilon \epsilon ~N\left(0, {\delta }^2{I}_n\right)$$

(9)

SEM:

$$Y=\beta X+\mu$$

(10)

$$\mu =\rho W\mu +\epsilon \epsilon ~N\left(0, {\delta }^2{I}_n\right)$$

(11)

where Y is the dependent variable; W is the spatial weight matrix after standardization; X is the independent variables; ρ is the spatial autocorrelation coefficient; θ is the exogenous interaction coefficient; β is the spatial regression coefficient; μ is the disturbing term; ε is the random error and belongs to N(0, δ²I_n); and I_n is the n-order identity matrix. Both the SAR and SDM can estimate the direct and indirect effects of explanatory variables, where the direct effects refer to the influence of local influencing factors on the nearby FCSE, and the indirect effects (i.e., spatial spillover) can be explained in two ways: the county-level influencing factors on the FCSE of neighboring counties and the influencing factors of the neighboring counties on the county of interest. The calculation methods of direct effects and indirect effects based on the SAR are as follows:

$$y={\left(I_n-\rho W\right)}^{-1}X\beta +{\left(I_n-\rho W\right)}^{-1}\epsilon$$

(12)

Equation (12) is the general form of the SAR. Suppose X contains K explanatory variables, and denote the rth explanatory variable as x = (x_1r x_2r …x_nr) (n × 1 column vector), then Xβ = ${\displaystyle \sum }_{r=1}^K{X}_r{\beta }_r$; therefore, Equation (12) can be rewritten as:

$$y={{\displaystyle \sum }}_{r=1}^K{S}_r\left(W\right)x_r+{\left(I_n-\rho W\right)}^{-1}\epsilon$$

(13)

where S_r(W) = β_r (I_n−ρW)⁻¹. Equation (13) can be rewritten as:

$$\left[\begin{array}{c}{y}_1\\ \begin{array}{c}{y}_2\\ \begin{array}{c}⋮\\ y_n\end{array}\end{array}\end{array}\right]=\left[\begin{array}{ccc}\begin{array}{cc}{S}_r{\left(W\right)}_{11}& S_r{\left(W\right)}_{12}\end{array}& \cdots & S_r{\left(W\right)}_{1n}\\ \begin{array}{cc}\begin{array}{c}{S}_r{\left(W\right)}_{21}\\ ⋮\end{array}& \begin{array}{c}{S}_r{\left(W\right)}_{22}\\ ⋮\end{array}\end{array}& \begin{array}{c}\cdots \\ \cdots \end{array}& \begin{array}{c}{S}_r{\left(W\right)}_{2n}\\ ⋮\end{array}\\ \begin{array}{cc}{S}_r{\left(W\right)}_{n1}& S_r{\left(W\right)}_{n2}\end{array}& \cdots & S_r{\left(W\right)}_{nn}\end{array}\right]\left[\begin{array}{c}{x}_1\\ \begin{array}{c}{x}_2\\ \begin{array}{c}⋮\\ x_n\end{array}\end{array}\end{array}\right]+{\left(I_n-\rho W\right)}^{-1}\epsilon$$

(14)

where S_r(W)_ij is the influence of the variable x_jr in region j on the explained variable in region i. The partial differential equation is as follows:

$$\frac{\partial y_i}{\partial x_{jr}}=S_r{\left(W\right)}_{ij}$$

(15)

In Equation (14), the direct effect of the Kth explanatory variable is the average value of each element of the main diagonal in the matrix, and the indirect effect of the Kth explanatory variable is the average value of all elements in the matrix except the elements of main diagonal. This study used Stata v.16.0 (StataCorp LLC, College Station, TX, USA) to estimate the three models described above.

Referring to the studies of Yin et al. [27] and Zhong and Wang [31], this study set the possible influencing factors (with an accompanying list of descriptive statistics presented in

Table 1. Descriptive statistical analysis of the possible influence factors of forest carbon sequestration efficiency.

Variable Name	Symbol	Mean	Std. Dev.	Min	Max
Forest carbon sequestration efficiency	FCSE	0.5918	0.2942	0.1508	1.4348
Forestland use inputs	inputs	0.6241	0.5126	0.0028	2.7389
Average annual temperature (°C)	temper	17.9085	0.4920	16.9778	19.0520
Average annual precipitation (mm)	precip	1652.3628	225.4909	1178.7659	2511.8375
Scale of forestry economic development (104 CNY)	gross	2.7500	3.2871	0.0386	21.5468
Economic development (104 CNY)	gdppc	7.9636	2.6399	3.3014	17.2508
Urbanization level (%)	urban	0.4938	0.1576	0.1162	0.8200
Forest cutting (104 m3)	cut	2.7971	4.2541	0.0042	28.6034
Forestry labor inputs (104 capita)	labor	0.5215	0.5436	0.0034	2.9876
Forestry investment (104 CNY)	invest	0.6365	0.7026	0.0049	5.6151
Forest pests and diseases (hm2)	pest	1.1620	0.8494	0.0000	3.5047

), including forestland use inputs, climatic conditions, scale of forestry economic development, economic development, urbanization level, forest cutting, forestry labor input, forestry investment, forest pests, and diseases. The detailed information of the influencing factors is shown in the Supplementary Materials. To help normalize the data for enhanced comparability, this study explored the logarithm values of all variables, where the occurrence area of forest pests and diseases was the logarithm after adding 1 to the original data.

3. Results

3.1. Spatiotemporal Characteristics of Forest Carbon Sequestration

Our study calculated annual county-level forest carbon sequestration and carbon emissions from 2016 to 2019, using Equations (2) and (3), and the results are shown in the Supplementary Materials. The forest carbon sequestration in all counties was higher than carbon emissions. Specifically, Chun’an, Longquan, and Lin’an had the highest total forest carbon sequestration, with a combined total of 19,978.58 × 10⁴ tC, accounting for 15.97% of the total in Zhejiang Province over the study period. Since the forested area and growing stock of these three counties were among the top five in the province, their corresponding forest resources were relatively rich, and the resulting carbon sequestration was large. In terms of forest carbon emissions, Yongjia, in the district of Ningbo, and Jiande had the highest total of 352.41 × 10⁴ tC, accounting for 16.45% of the total in Zhejiang Province over the study period. Pine wood nematode disease is highly prevalent in these counties; thus, it is likely that forest pests and diseases are the proximate causes for the high forest carbon emissions in these areas. Conversely, Jiashan, Pinghu, and Haiyan had the lowest total forest carbon sequestration and forest carbon emissions totaling 125.67 × 10⁴ tC and 0.14%, and 1.28 × 10⁴ tC and 0.06%, respectively. Notably, these counties are all located in the Hangjiahu Plain in the north of Zhejiang Province, which is dominated by cultivated lands, rivers, and urbanized land cover with fewer forested resources.

3.2. Evaluation of FCSE in Zhejiang Province

Annual FCSEs in the counties of Zhejiang Province ranged from 0.1993 to 1.2576 and displayed important differences among them (Figure 2). Fenghua maintained the highest mean FCSE (1.2576). A further 12 counties, including Qingyuan, Sanmen, and the district of Shaoxing, also had above-average FCSE values, ranging between 0.8 and 1.0. An additional 16 counties had FCSE scores falling between 0.6 and 0.79, whereas 21 counties scored between 0.4 and 0.59. The FSCE of Cangnan showed the lowest average score of 0.199. In terms of the annual change rates, the FCSE of 52 counties displayed a downward trend over the study period, while those of three counties, namely Jingning, Qingyuan, and Shangyu, were relatively stable, with an average change rate of nearly 0%. The FCSE of the remaining nine counties, including the districts of Jiaxing, Xiaoshan, and Fuyang increased to varying degrees.

When FCSE does not reach one, the cause of FCSE efficiency loss can be analyzed by slack variables. The slack variable S⁻ of each input is divided by the corresponding input variable to obtain the ratio of input redundancy. The slack variables S^g+ for desired outputs and S^b− for undesired outputs are divided by the corresponding output volumes to obtain the ratios of desired output deficiency and undesired output excess, respectively. The calculation results are shown in Supplementary Materials. From the calculation results, the output redundancy rate of carbon sequestration in all counties was zero, which indicated that the expected output deficiency was not the cause of FCSE loss, and the main causes of efficiency loss were afforestation + reforestation redundancy (redundancy rate 48.1%) and forest tending redundancy (47.7%).

A visualization of the annual FCSE results using the Jenks Natural Breaks method shows the evolutionary characteristics from 2016 to 2019 (Figure 3a–d). Based on the county-level FCSE averages from 2016 to 2019 (Figure 3e), the map of the LISA (Figure 3f) was drawn using the Local Moran’s I index to reveal spatial autocorrelation patterning. The analysis revealed that most counties showed stable or decreasing trends of FCSE from 2016 to 2019. The highest FCSE values were primarily observed in the southwest and northeast regions of the province, whereas overall FCSE values were lowest in the southeastern coastal region. Based on the spatial clustering, the high–high type was mainly concentrated in the southwest region, the northeast region showed a coexistence of both high–high and low–low types, while Yuhuan in the southeast was the only low–high type.

3.3. Results of Spatial Econometrics Analysis

3.3.1. Spatial Effects

The Global Moran’s I index was used to test the spatial correlation of FCSE across the 66 counties of the Zhejiang Province using a set of contiguity, distance, and economic weight matrices (

Table 2. Global Moran’s I of forest carbon sequestration efficiency under different weight matrices.

Weight Matrices	Variables	FCSE in 2016	FCSE in 2017	FCSE in 2018	FCSE in 2019
Contiguity weight matrix	Global Moran’s I	0.266	0.343	0.195	0.218
	z-score	3.519	4.864	2.719	3.013
	p-value	0.002	0.001	0.007	0.004
Distance weight matrix	Global Moran’s I	0.160	0.452	0.204	0.284
	z-score	1.444	4.231	1.809	2.453
	p-value	0.074	0.000	0.035	0.007
Economic weight matrix	Global Moran’s I	0.200	0.460	0.208	0.303
	z-score	1.805	4.379	1.879	2.653
	p-value	0.036	0.000	0.030	0.004

). The results showed that the I value for county FCSEs under the three spatial weight matrices over the analysis years were all positively significant, indicating a significant positive spatial autocorrelation. Thus, county-level FCSE in Zhejiang Province displayed strong spatial autocorrelation, thereby supporting the use of a spatial econometric model for empirical analysis.

3.3.2. Analysis of Spatial Panel Regressions

As it is impossible to preverify the existence or form of the spatial relationships, the Wald test, likelihood ratio (LR) test, and Bayesian information criterion (BIC) were used for model selection in this study [62,63]. Hausman’s test also suggested that fixed effects estimates should be used. To avoid the influence of unobservable county heterogeneity factors and temporal changes, the time-fixed and space-fixed spatial econometric models were used for estimation, in accordance with the methods of Yuan, et al. [64]. The Wald and LR tests showed that the three spatial weight matrices were not significant, indicating that they could successfully be degenerated into SEM or SAR models. Furthermore, comparing the BIC of the SEM and SAR models for the three spatial weight matrices revealed that the SAR model with the contiguity and distance weight matrices had the smallest BIC, whereas the SEM with the economic weight matrix had the smallest BIC. Accordingly, the SAR model was chosen for both the contiguity (Model 1) and distance weight matrix (Model 2), while the SEM was chosen for the economic weight matrix (Model 3). Ultimately, Model 2 was selected, as it produced the smallest BIC value. Therefore, the remainder of this study focused on the empirical results of the SAR model for the distance weight matrix.

From the regression results (

Table 3. Forest carbon sequestration efficiency influencing fitting results.

Variables	Model 1	Model 2	Model 3
inputs	−0.2085 ***	−0.1799 ***	−0.1559 ***
	(0.0602)	(0.0586)	(0.0600)
temper	10.8363 **	8.5354 *	5.1929
	(5.1245)	(4.9909)	(6.4591)
precip	0.3255	0.4375 **	0.5498 **
	(0.2058)	(0.1981)	(0.2750)
gross	0.3667 *	0.2817	0.2772
	(0.1994)	(0.1941)	(0.1917)
gdppc	−0.1202	−0.1038	0.0060
	(0.3813)	(0.3695)	(0.3891)
urban	−0.2065	−0.0415	−0.0466
	(0.2344)	(0.2300)	(0.2394)
cut	−0.2006 ***	−0.2062 ***	−0.2228 ***
	(0.0334)	(0.0322)	(0.0334)
labor	−0.1534	−0.0372	−0.0454
	(0.1816)	(0.1762)	(0.1707)
invest	0.0335	0.0024	0.0004
	(0.0760)	(0.0736)	(0.0756)
pest	−0.1482 **	−0.1806 ***	−0.2719 ***
	(0.0724)	(0.0692)	(0.0862)
rho	0.4320 ***	0.3654 ***
	(0.0689)	(0.0505)
sigma2_e	0.0486 ***	0.0457 ***	0.0455 ***
	(0.0043)	(0.0041)	(0.0041)
Log-likelihood	18.7930	24.1794	23.5544
R2	0.3490	0.3343	0.2929
BIC—lag	29.3253	18.5526	20.0224
BIC—error	32.0257	20.6591	19.8025

Notes: Parenthetical values are t-statistics. ***, **, * represent significance at the 1%, 5%, and 10% levels, respectively.

), the spatial autoregressive coefficient rho values were positive and significant at the 1% level in both the contiguity and distance weight matrices; thus, there was a significant spatial association and positive spillover effect of FCSE between counties. The conclusions also illustrated the need to use a spatial econometric model to analyze the influencing factors of county-level FCSE values to account for estimate biases. The effects of average annual temperature and precipitation, as well as the scale of forestry economic development were positively significant in only some of the spatial weight matrices. In fact, the regression results of the spatial econometric models, based on the spatial weight matrices, showed that both significance and degree of significance for each explanatory variable did not change markedly over the analysis period, indicating the robustness of the constructed model.

3.3.3. Direct, Indirect, and Total Effects on FCSE

LeSage and Pace [65] argue that point estimation can lead to parameter estimation bias. Simultaneously, when spatial spillover effects exist, changes in certain influencing factors will not only impact the local FCSE, but also those of neighboring counties. Therefore, to further dissect this spatial interaction, this study separated the estimated results into total, direct, and indirect effects (

Table 4. Effect decomposition results.

Variables	Model 2-SAR (Distance Weight Matrix)
	Total Effect	Direct Effect	Indirect Effect
inputs	−0.2800 ***	−0.1902 ***	−0.0898 ***
	(0.0940)	(0.0639)	(0.0332)
temper	13.0955 *	8.9051 *	4.1903 *
	(7.5598)	(5.1412)	(2.5253)
precip	0.7247 **	0.4897 **	0.2350 **
	(0.3116)	(0.2038)	(0.1142)
gross	0.4366	0.2978	0.1388
	(0.2987)	(0.2038)	(0.0981)
gdppc	−0.1597	−0.1080	−0.0517
	(0.5695)	(0.3847)	(0.1870)
urban	−0.0333	−0.0249	−0.0084
	(0.3662)	(0.2476)	(0.1201)
cut	−0.3264 ***	−0.2211 ***	−0.1053 ***
	(0.0573)	(0.0355)	(0.0268)
labor	−0.0583	−0.0410	−0.0173
	(0.2858)	(0.1930)	(0.0940)
invest	0.0156	0.0107	0.0049
	(0.1144)	(0.0768)	(0.0381)
pest	−0.2823 **	−0.1913 **	−0.0909 **
	(0.1118)	(0.0745)	(0.0400)

Notes: Parenthetical values are t-statistics. ***, **, * represent significance at the 1%, 5%, and 10% levels, respectively.

). The total effect of forestland use input, cutting, and pest damage on FCSE were all significant (p < 0.05). Further, the direct and indirect effects of these three explanatory variables showed similarly negative effects (p < 0.05). Thus, each of these factors not only decreased regional FCSE, but also reduced it in neighboring areas. The total, direct, and indirect benefits of the average annual temperature and precipitation on FCSE values were all significantly positive (p < 0.10), indicating that the influence of climate factors on FCSE was regional. Precipitation and temperature are affected by altitude, underlying surface, and latitude, which vary regionally. Since suitable climatic conditions aid forest growth and the study area has relatively high temperatures and abundant precipitation, being situated on the eastern coast of China, there is an accumulation of spillover effects and a regional impact on FCSE.

4. Discussion

4.1. Differences in Forest Carbon Sequestration Efficiencies

The results of the FCSE calculations are directly related to the input–output indicator systems used. For example, Lin and Ge [32] and Yin, Gong, Gu, Deng and Niu [27] measured FCSE from the perspective of total factor productivity, using total forestry output values and carbon sequestration as the output indicators. Comparatively, this study calculated FCSE from the perspective of forestland use. When assessing the carbon cycle of a forested ecosystem and if undesired outputs of forest carbon emissions are ignored, then the resulting carbon sequestration efficiency will almost always be overestimated. Accordingly, forest carbon emissions as an undesired output were considered in this study to derive more accurate FCSE results. Substantial spatial heterogeneity in FCSE was also observed across the study area. Chun’an, Longquan, Lin’an, Qingyuan, and Yongjia had the highest forest carbon sequestration values, and their corresponding FCSE values were all higher than the provincial average. Importantly, these areas are rich in forest resources, where forestry is a key sector, thereby promoting forest carbon sequestration and likely increasing productivity [36]. Conversely, except for Qingyuan County, the FCSE values were <1.0, indicating that there was necessarily no link between high forest carbon sequestration and high FCSE values, as indicated by previous studies [66]. In terms of spatial patterning, the key forestry region of Zhejiang Province (approximately 80% forest cover) displayed the highest FCSE values. Here, the abundance of forest resources and forestry investments by the government help sustain the high levels of FCSE observed. However, it cannot be ignored that high investments face larger input costs, which may also lead to lower FCSE. For this reason, the government should consider a bottom-up financial investment to promote the sustainability of higher FCSE. For example, it should strengthen the construction of ecological welfare forestland and natural forest management, and appropriately increase the minimum standards of compensation for ecological welfare forestland and subsidies for stopping cutting, management, and protection of natural commercial forests, so as to mobilize the enthusiasm of individual households and communities for forest management. In addition, it is necessary to help enhance the scientific and technological investment at the grassroots level, especially in state-owned forest farms, and to carry out differentiated technology promotion and application to stimulate forestry carbon sink development. Alternatively, the southeastern coastal areas with lower FCSE values are more severely affected by natural disasters (e.g., typhoons and storm surges) and there are greater occurrences of forest pests and diseases, which all contribute to the observed local decrease in forest quality.

FCSE can be used to measure the changes in forest carbon sequestration caused by forestland use behavior in the forestry sector. Increasing forest carbon stocks too rapidly may reduce their future carbon sequestration capacity [67]. Especially in the context of climate change, forest managers should promote long-term forest growth rather than maximizing short-term carbon accumulation [9]. Since a more unstable climate is expected to occur in the future [68], rapid and large-scale inputs and an indiscriminate maximization of carbon storage may not be able to adapt to future climate change, increasing the risk of carbon loss due to wildfires, insect pests, and meteorological disasters. FCSE helps to indirectly understand the contribution of forestry work such as afforestation and tending to greenhouse gas emission reduction and provides an effective reference for the rational arrangement of forestry policies to adapt to regional economic development conditions and future climate change.

4.2. Factors Influencing FCSE

A new round of forest rights system reform has seen the allocation of land use rights of collective forested lands in China to local farmers. Consequently, the division of public welfare forests has exacerbated the already fragmented forestland, creating a lack of economies of scale [69]. Previous research examining Zhejiang Province found that small-scale operations tend to lead to increased forest nurturing inputs and increased forestland management costs [70], thus generating greater input redundancy and resulting in lower FCSE. The goal of promoting sustained growth in forest cover and forest stocks can stimulate local governments to increase afforestation inputs and forest tending; however, too many inputs can have diminishing benefits in promoting forest ecosystem functions [71]. As pointed out by Tong et al. [16], large-scale afforestation may have adverse effects on ecosystems; therefore, inputs can only contribute to FCSE enhancement if they are maintained at a certain level, which is consistent with findings elsewhere [36]. Due to the relatively small differences in forest resource endowment between neighboring counties, proximate regions are more likely to experience a catch-up effect in forest ecological construction [72], which can inherently bring about an excessive amounts of inputs. Moreover, labor transfer, investment allocation, as well as science and technology promotion are also linked between neighboring counties [73], thus creating a convergence effect on regional FCSE. Therefore, it is clear that due to different endowments of forest resources, economic development levels, and forestry development plans in different counties the input of afforestation and reforestation, forest tending, and forest management may not necessarily improve the carbon sequestration efficiency in all counties. Accordingly, different regions should improve the carbon sequestration capacity of forests through differentiated inputs.

Forest felling inherently changes the structure of forestlands, as mature forests are replaced by younger trees, resulting in a net carbon sink loss [74], a decrease in forest ecosystem carbon stocks [75], and a reduction of the FCSE of the region. Notably, forest cutting also has spatial spillover effects. If the number of felled trees in a county increases, the pressure of forest cutting may be transferred to neighboring counties by strictly controlling the consumption of the quota for forest cutting and purchasing wood from neighboring areas, thereby reducing the FCSE of the neighboring counties. The occurrence of forest pests and diseases also can result in a marked reduction of vegetation gross primary productivity, as well as the release of large amounts of CO₂ from the decomposition of dead trees, thereby decreasing overall carbon sequestration [76]. Pine wood nematode disease has a relatively strong spatial spillover effect due to the regional transmission of pine brown Aspergillus, which can present regional aggregations and concentrated contiguous outbreaks in space. In 2019, 53 counties in the province were within pine wood nematode disease epidemic areas, and the occurrence of this disease in this region also impacted surrounding areas, increasing forest carbon emissions and reducing the overall FCSE of the larger region.

The empirical results show that precipitation and temperature have spillover effects. In Zhejiang Province, precipitation and temperature are relatively synchronous throughout the year and exhibit agglomeration where a county is affected by the climatic elements of neighboring counties, which in turn has an impact on tree growth. Further, when rainfall is abundant, the associated higher temperatures can promote plant growth and increase forest productivity [77]. Precipitation is beneficial for increasing biomass, carbon density, and carbon accumulation in forests [78], and related studies have also pointed out that higher precipitation can promote vegetation productivity [79]. This study found a significant positive correlation between FCSE, mean annual temperatures, and mean annual precipitation, further supporting these findings.

5. Conclusions

Based on the Super-SBM model of undesired output, this study calculated the FCSEs for each of the 66 counties in Zhejiang Province from 2016 to 2019. A spatial econometric model was used to analyze the most important factors influencing these values, as well as the existence of any spatial spillover effects. The results showed that because the terrain of Zhejiang Province is inclined from southwest to northeast, the southwest and central regions are dominated by hills, and the northeast and eastern regions are dominated by plains, forest resources were also concentrated in the southwest and central regions. Correspondingly, these regions had high forest carbon stocks. In addition, the county-level FCSE in Zhejiang Province was generally low and regional development was unbalanced and showed a decreasing trend. Further, county FCSE values were significantly spatially autocorrelated, displaying local clustering over the sample observation period. Forest-use inputs, cutting, as well as pests and diseases all displayed significant negative spatial spillover effects, whereas the average annual temperature and precipitation had significantly positive spillover effects. Based on the above conclusions, this study proposes the following policy implications.

First, considering the negative spillover effects of forestland use inputs, forest carbon sequestration should be regarded as a key factor during forest resource allocation, for which the input structure should be reasonably improved by implementing a forest quality precision improvement project and strengthening the cultivation of large-diameter forest resources to promote the improvement of forest quality. Second, in view of the negative spillover effects of forest cutting, pests, and diseases observed here, the sustainable management of forest resources, with an equal emphasis on protection and utilization, should be carried out, forest felling should be controlled, inter-regional interactions should be emphasized, and the collaborative monitoring and regional joint prevention of pine wood nematode disease in contiguous areas should be strengthened. Third, the advantages of climatic resources should be used to guide and inspire state-owned forest farms, forestry enterprises, and other entities to manage the forest carbon sinks for optimal FCSE, thereby promoting carbon sinks in the surrounding areas via the radiation of driving effects. Finally, in view of the significant spatial correlation of FCSE, cross-regional forest carbon sink cooperation should be intensified, including improving the spatial layout of nature protected areas to strengthen forest resource protection, and promoting the synergy of adjacent regions in the construction of forest urban agglomerations and ecological corridors.

Some shortcomings of the current study can be addressed in future analyses. It is difficult to obtain county-level forestry resource data and statistics. The use of four-year panel data in this study may only be indicative of recent changes in FCSE and not of the larger, long-term evolutionary trend. Further, the present study did not investigate whether there was a scale effect on FCSE. Future studies can be more robust when considering municipal or provincial panel data as well.