Measurement of Forest Carbon Sink Efficiency and Its Influencing Factors Empirical Evidence from China

Abstract

The efficiency and productivity improvement are the core requirements of high-quality development, while improving the efficiency of forest carbon sinks is an important means and fundamental way to achieve their high-quality development. Based on the forests and socioeconomic development data of 31 provinces (cities and districts) in China from 2004 to 2018, the biomass method and DEA-Tobit panel regression model were used to analyze the level of forest carbon stock, carbon sink and carbon sink efficiency, and factors influencing forest carbon sink efficiency in China’s provinces. The results indicated that: ① nationwide forest carbon stocks and carbon sinks increased successively while carbon density decreased. The regions with higher carbon stock, carbon sink, and carbon density were concentrated in the northeast and southwest forest areas with abundant forest resources. ② During the 7th to 9th forest inventory, the efficiency of forest carbon sinks was on a low and decreasing trend. The mean values of comprehensive efficiency in general for the 7th to 9th forest inventory periods were 0.421 and 0.336, respectively. The scale efficiency in the decomposition efficiency was above 0.650 for both inventory periods, and gradually increased, showing that the gap between the actual scale and the optimal production scale of forestry carbon sink was decreasing. The pure technical efficiency level represented the production efficiency of input factors at the optimal scale of forestry carbon sinks. The mean values of the two periods are 0.639 and 0.514, respectively, while the differences within the production frontier surface are 0.361 and 0.486, which indicates that there is input redundancy or output deficiency in the two periods as a whole. ③ The total annual precipitation and the level of socioeconomic development have significant driving effects on the improvement of forest carbon sink efficiency, while the incidence of pests and diseases, abnormal changes in temperature, afforestation area and the development of population urbanization have significant inhibiting effects on the improvement of forest carbon sink efficiency in China.

1. Introduction

To cope with climate change represented by global warming and frequent extreme weather phenomena, reducing carbon emissions, increasing carbon sinks, and achieving carbon neutrality have become prominent development goals worldwide. As the largest ecosystem on Earth, forest production activities have always been of great interest. The world’s forests are huge and persistent carbon sinks [1,2]. The expansion of forest cover and enhancement of forest productivity are crucial measures for many countries to cope with future climate change. Due to the natural growth of vegetation and ecological construction, China’s terrestrial ecosystems have played and would continue to play an important role as carbon sinks in the future. China is a large developing forestry country with abundant forest resources, and the quantity and quality of forests have been greatly improved in more than 40 years through reforms and openings. The data of the ninth national forest inventory (China Forest Inventory is a statistical project on China’s forest resources) indicated that the forest area and storage volume are among the highest in the world, while the area of planted forests still ranks first in the world. To some extent, secondary forests can buffer climate change [3]. Carbon sink capacity and potential make forests play a significant role in coping with climate change. Forest carbon sink capacity not only depends on forest growth and area expansion, but also correlates with productivity level. Forest carbon sink is one of the expected outputs obtained under total factor inputs, while forest carbon sink quality depends on not only the amount of forest carbon sequestration, but also the optimization of forest carbon sink efficiency (FCSE) under the given inputs. FCSE is influenced by both resource endowment and social development, and there are differences in FCSE in different regions. Therefore, measuring the level of FCSE and exploring its improvement path are of both theoretical and practical significance for China to achieve the carbon neutrality target and forest carbon sink development proposed for coping with climate change.

Research on forests and carbon is longstanding, as the flow, storage, and cycling of carbon in forest ecosystems were discussed in the 1870s [4], however, up to now, the research results were few and insufficient. In 1992, the United Nations Framework Convention on Climate Change (UNFCCC) began to focus on the link between forest ecosystems and climate change [5]. Subsequently, the biodiversity and carbon dioxide absorption functions of forests have received attention due to global warming [6], and forest carbon sink research has entered the stage of systematic research development. On the basis of input-output theory, scholars have conducted a series of studies on forestry efficiency [7,8,9,10]. Due to the different selection of input-output indicators and research methods, the research results obtained from different scholars were different. According to the different types of research efficiency, it is mainly divided into forestry economic efficiency, forestry ecological efficiency [11], forestry management efficiency, forestry production efficiency, and forestry carbon sequestration efficiency [12,13,14,15]. Forestry carbon sequestration efficiency is similar to the input-output indicators of other efficiency studies, which were generally based on the three elements of capital, labor, and land in the selection of evaluation indicators [15,16], with adjustments depending on the characteristics of the actual study. In particular, the land input is selected according to the research topic as forest area [17,18], afforestation and reforestation area [19], and forest land area [20], etc. Among the forest carbon sink output indicators, there are single output indicators and multiple output indicators, while the single output indicators include total forest carbon sequestration [7,19], forest stock change [21], and forest carbon sink per unit area [20], multi-output indicators include total forestry economic output value and value of carbon sequestration [16,22], desired output and non-desired output [12]. The study area ranges from individual cities, provinces, and collective forest areas to the national level. The efficiency measures in the research methods included traditional Data Envelopment Analysis (DEA) [7,23], DEA-Malmquist [16], Super-DEA evaluation model [13], stochastic frontier production function [23,24], DEA-BCC model [25], Dagun Gini coefficient and Markov chain approach [20,26], non-expected output SBM-Malmquist index [12,27], and CCR-I model of DEA [19]. Spatial distribution and spatial spillover effects are the focus of studies on the spatial characteristics of FCSE, regional differences in forest carbon sinks [15], dynamic evolutionary trends [28,29], and spatial spillover effects [30] were mostly analyzed at the provincial and national levels. Other scholars have analyzed the mechanism of forest carbon sink influence on the efficiency of forestry output [31]. The results from the published studies indicated on the influencing factors were slightly different due to the different selected factors and certain differences in the mechanisms of action [24,28,32]. For example, Yin et al. [28] analyzed the spatial influences affecting forest carbon sequestration using SDM model and found that GDP per capita, degree of urbanization, and length of road network have significant positive effects on carbon storage efficiency. Angang et al. [33] founded that near-natural forest management had a positive effect on climate change mitigation, which was different from some scholars who founded that forest management had negative effect on climate change mitigation. In contrast, some scholars observed that there was a lag period for forest carbon stock [34]. Zhang et al. [35] founded that precipitation was the main factor affecting the amount of carbon sequestered by vegetation, while Wu et al. [34] revealed that the effects of temperature and precipitation on forest carbon sequestration were not significant. It can be seen that the research on FCSE and its influencing factors is still controversial, specifically in terms of the mechanisms of natural and non-natural factors and whether they significantly affected FCSE. Therefore, further research is needed to determine the influencing factors and mechanisms of FCSE and to improve the efficiency of forest carbon sink in different development contexts of the times.

In summary, the research on forest carbon sinks mainly focus on regional differences, spatial distribution, and spatio-temporal dynamic evolution, taking the natural attributes of carbon sinks as the basis. Considering the socio-economic attributes of forest carbon sinks, it is necessary to conduct an in-depth study on whether the input and output of forest carbon sinks are reasonable as a production activity, and the influencing factors and improvement paths of forest carbon sink efficiency have not been effectively determined. To this end, this paper measures the national forest carbon sink efficiency using DEA model with forest carbon sink as output and labor force, forestry capital stock and forest area as input indicators, then analyzes the influencing factors of forest carbon sink efficiency using Tobit regression model. This is done in order to reveal the intrinsic mechanism of FCSE influenced by different factors and explore the path to achieve higher efficiency. In turn, it provides a theoretical basis for better promoting forest carbon sinks to cope with climate change and improve resource utilization.

2. Research Methods and Data Sources

2.1. Research Methods

The DEA-Tobit model was selected for this article, and is divided into two stages of empirical analysis. The first stage is DEA analysis. When efficiency measurement is carried out, forest carbon stock is selected as the output, and the DEA model is used to calculate the efficiency of forest carbon sink. The biomass conversion factor continuous function method is selected for carbon stock estimation. In the second stage, the stata16.0 software’s Tobit model was used to analyze the influencing factors of FCSE, and the above econometric model has been estimated using Stata 16.0. Accordingly, the specific research methods are as follows:

2.1.1. Biomass Conversion Factor Continuous Function Method

Based on 758 sets of research data collected on biomass and accumulation nationwide, Fang et al. (2001) [36] classified the national forest types into 21 categories and calculated the relationship between biomass expansion factor (BEF) and stand wood volume for each forest type separately. The calculation procedure is as follows:

$${\mathrm{B}}_{\mathrm{i}}{=\mathrm{BEF}}_{\mathrm{i}}{\times \mathrm{V}}_{\mathrm{i}}=(\mathrm{a}+\frac{\mathrm{b}}{{\mathrm{V}}_{\mathrm{i}}}{)\times \mathrm{V}}_{\mathrm{i}}$$

(1)

$${\mathrm{B}}_{\mathrm{itotal}}{=\mathrm{a}\times \mathrm{V}}_{\mathrm{itotal}}{+\mathrm{b}\times \mathrm{A}}_{\mathrm{itotal}}$$

(2)

where BEF_i is the biomass conversion factor, V_i is the unit accumulation of a certain tree species, $A_{\mathit{itotal}}$ is the total area of tree species i, B_i is the biomass per unit area of tree species i, and $B_{\mathit{itotal}}$ is the total biomass of a certain tree species. Both a and b are constants.

$${\mathrm{C}}_{\mathrm{i}}={\mathrm{B}}_{\mathrm{itotal}}\times {\mathrm{CF}}_{\mathrm{i}}$$

(3)

$${\mathrm{C}}_{\mathrm{j}}={{\displaystyle \sum }}_{i=1}^n{\mathrm{B}}_{\mathrm{i}}\times {\mathrm{CF}}_{\mathrm{i}}$$

(4)

where $C_i$ is the carbon stock of tree species i; CF_i is the carbon factor of tree species i; $C_j$ is the carbon stock of area j.

2.1.2. DEA

DEA is a linear programming technique proposed by Charnes et al., to deal with evaluation problems containing multiple input and output indicators [37], which are categorized into input-oriented and output-oriented. Considering the input controllability of forest carbon sinks and the limited forest resources in China, it is of great practical significance to increase the output with the given input to make more reasonable use of resources. Therefore, an input-oriented variable scale DEA model, i.e., the generalized BCC-DEA model, was used to analyze the efficiency of forest carbon sinks. The provincial domain is set as a decision unit in combination with the actual, i.e., a total of 31 decision units, which are presented by DMUi (i = 1, 2, …, n). The input is denoted by ${\mathrm{x}}_{\mathrm{j}}$ and the output is denoted by ${\mathrm{y}}_{\mathrm{j}}$. ${\mathrm{x}}_{\mathrm{ip}}$ denotes the inputs of type i input for the p-th decision unit DMUp, ${\mathrm{y}}_{\mathrm{rp}}$ denotes the outputs of type r output for the p-th decision unit DMUp. The specific model of BCC for evaluating the effectiveness of the p-th decision unit is as follows:

$$\mathrm{Min}\left[\mathsf{\theta }-\mathsf{\epsilon }\left({{\displaystyle \sum }}_{i=1}^m{\mathrm{S}}_{\mathrm{ip}}^{-}+{{\displaystyle \sum }}_{i=1}^m{\mathrm{S}}_{\mathrm{rp}}^{+}\right)\right]$$

(5)

$$\mathrm{s}.\mathrm{t}.\left\{\begin{array}{c}{{\displaystyle \sum }}_{j=1}^{\overline{n}}\overline{x_{ij}}{\lambda }_j{+\mathrm{S}}_{\mathrm{ip}}^{-}{=\mathsf{\theta }}_{\mathrm{p}}{\mathrm{x}}_{\mathrm{ip}},\mathrm{i}=1\cdots \mathrm{m}\\ {{\displaystyle \sum }}_{j=1}^{\overline{n}}d\overline{y_{rj}}{\lambda }_j{-\mathrm{S}}_{\mathrm{rp}}^{+}{=\mathrm{y}}_{\mathrm{rp}},\mathrm{r}=1\cdots \mathrm{s}\\ {{\displaystyle \sum }}_{j=1}^{\overline{n}}{\lambda }_j=1\\ {\mathsf{\lambda }}_{\mathrm{j}}\ge 0,\mathrm{j}=1,2,\cdots \mathrm{n},{\mathrm{S}}_{\mathrm{ip}}^{-}\ge 0,{\mathrm{S}}_{\mathrm{rp}}^{+}\ge 0\end{array}\right.$$

(6)

where θ denotes the efficiency value, ε is a non-Archimedean infinitesimal quantity, i denotes the decision unit input and j denotes the output; m and s denote the number of input and output indicators of the decision unit, respectively; ${\mathsf{\lambda }}_{\mathrm{j}}$ denotes the weight of each factor in the reference set; ${\mathrm{S}}_{\mathrm{ip}}^{-}$ and ${\mathrm{S}}_{\mathrm{rp}}^{+}$ denote the input slack variables and output slack variables, respectively. The “s.t.” in the mathematical formula is an abbreviation for “subject to”.

2.1.3. Tobit Model

The Tobit model was first proposed by Tobin in 1958 for analyzing econometric models under restricted explanatory variables. The FCSE measured by the DEA model is between 0 and 1, which is a restricted variable. If a dependent variable is 0, the model parameters using least squares will produce bias, while the Tobit model can avoid this situation. A Tobit model should be used to estimate the factors influencing the FCSE measurement. The specific model is as follows:

$$\mathrm{Y}=\left\{\begin{array}{l}{\mathrm{Y}}^{*}=\mathsf{\alpha }+\mathsf{\beta }\mathrm{X}+\mathsf{\mu },{\mathrm{Y}}^{*}\text{>}0\\ 0,{\mathrm{Y}}^{*}\le 0\end{array}\right.$$

(7)

where ${\mathrm{Y}}^{*}$ is the restricted dependent variable, X is the vector of independent variables, α is the vector of intercept terms, β is the vector of regression parameters, μ is the random error term, and μ~N (0,σ²).

$${\mathrm{Eff}}_{\mathrm{it}}{=\mathsf{\alpha }}_{\mathrm{i}}{+\mathsf{\beta }}_1{\mathrm{X}}_1{+\mathsf{\beta }}_2{\mathrm{X}}_2{+\mathsf{\beta }}_3{\mathrm{X}}_3{+\mathsf{\beta }}_4{\mathrm{X}}_4{+\mathsf{\beta }}_5{\mathrm{X}}_5{+\mathsf{\beta }}_6{\mathrm{X}}_6{+\mathsf{\beta }}_7{\mathrm{X}}_7{+\mathsf{\beta }}_8{\mathrm{X}}_8{+\mathsf{\epsilon }}_{\mathrm{it}}$$

(8)

where ${\mathit{Eff}}_{\mathit{it}}$ is the FCSE value, ${\mathsf{\alpha }}_{\mathrm{i}}$ is the constant term, ${\mathsf{\beta }}_1$ − ${\mathsf{\beta }}_8$ are the parameters to be estimated, and ${\mathsf{\epsilon }}_{\mathrm{it}}$ is the random error term.

2.2. Index Selection and Data Sources

2.2.1. Forest Carbon Sink Efficiency Evaluation Index System

In order to further measure the efficiency of forest carbon sinks in China, the traditional three factors, including capital, labor, and land, were selected as inputs, and forest carbon sinks were used as output indicator. Specifically, the land input of a forest carbon sink is reflected by the actual forest area during the inventory periods. The physical capital input is reflected by the forestry capital stock calculated by the Perpetual Inventory Method (PIM) in the current year. The formula for PIM is ${\mathrm{K}}_{\mathrm{it}}={\mathrm{K}}_{\mathrm{i}(\mathrm{t}-1)}\left(1-{\mathsf{\delta }}_{\mathrm{it}}\right)+{\mathrm{I}}_{\mathrm{it}}$ where ${\mathrm{K}}_{\mathrm{it}}$ represents the capital stock in year t in region i. ${\mathrm{I}}_{\mathrm{it}}$ is the forestry fixed asset investment in year t in region i, which is later deflated to a constant price-fixed asset investment using the price index for the base period of 2000. ${\mathsf{\delta }}_{\mathrm{it}}$ represent the economic depreciation rate of the i-th region in year t, which is set to 9.6% with reference to the studies of Zhang Jun et al. [38]. Labor input is reflected by excluding the employees not related to forest carbon sequestration from the end-of-year number of forestry system employees. The average annual forest carbon sink reflects the forest carbon sink output. As a result, the evaluation index system of forest carbon sink efficiency in this paper was formed, as shown in

Table 1. Forest carbon sink efficiency input–output indicators.

Indicator Layer	Indicator Type	Measurement	Units
Input index	Land	Area of forest tree species by province	10,000 ha
	Labor	Number of forestry system employees associated with forest carbon sequestration activities	10,000 people
	Forestry capital stocks	PIM of calculating current year capital stock	10,000 a
Output index	Carbon sink volume	Annual average forest carbon sink change	TgC

Note: ^a represents Yuan.

.

2.2.2. Theoretical Analysis of Factors Influencing Forest Carbon Sink Efficiency

Forest carbon sinks depend on the capacity and rate of carbon sequestration, which are essentially determined by the amount of forest resources and forestry productivity. Generally, it is influenced by a combination of natural and non-natural resource endowments [34], where non-natural endowments can be subdivided into two dimensions: social development and forest management.

(1)

Natural environmental factors

Total annual precipitation (precip, billion cubic meters): water is an essential condition for biological growth in nature, and there is a significant positive effect of precipitation on forest resources, especially in arid and semi-arid regions [39]. Average precipitation is positively correlated with forestland quality [40]. One the one hand, abundant precipitation affects FCSE by accelerating forest growth and increasing carbon storage. On the other hand, it increases carbon sinks and improves carbon sink efficiency by improving climatic conditions, increasing forest survival rate, and improving overall forest quality. In this article, the annual precipitation during the inventory period is used as a factor affecting the efficiency of forest carbon sink for analysis, which is obtained from the China Environment Statistical Yearbook of 2004–2018.

Temperature variation (temper, in degrees Celsius): temperature variation is critical to the growth of forest trees, and increasing and decreasing temperatures both have positive and negative effects on forest trees [39]. The positive effects of increasing temperatures are an increase in photosynthetic efficiency and extension of the growing season; the negative effects are the increase of water consumption and causes of problems, such as drought. Correspondingly, the negative effects of lower temperatures are shorter growing seasons, lower light, and efficiency, with the positive effects of slowing down water consumption and avoiding problems such as drought due to high temperatures. In this paper, the amount of change relative to the average temperature anomaly during the three forest inventory periods is used as a factor affecting FCSE for analysis, and the data are obtained from the China Environment Statistical Yearbook of 2004–2018.

Incidence of pests and diseases (pests in %): Forest management is key to maintaining and increasing forest carbon sinks, and forest growth affects the amount of carbon sequestered by forests [41]. An increase in the incidence of pests and diseases, a typical forest disaster, increases the damage to forests and affects the forest carbon sink capacity [42]. The occurrence of pests and diseases affects forest carbon sink efficiency by affecting forest quality and the amount of carbon sequestered by forests. Therefore, in this paper, the incidence of pests and diseases in each province were selected as one of the factors affecting forest carbon sink efficiency for research and analysis, and the data were obtained from the China Forestry Statistical Yearbook of each year.

(2)

Operation and management factors

Land use structure change (lusc, in %): Land use structural changes have a greater impact on whether an area becomes a carbon sink or a carbon source [19,43]. Land use change can affect vegetation carbon sinks [19], and carbon emissions from land use change have become one of the major sources of regional carbon emissions [44]. The total land area is relatively fixed, while changes in forest area will have an impact on the total carbon stock, as well as on the scale efficiency of forest carbon sinks, which in turn will have an impact on the overall efficiency of forest carbon sinks. In this article, the ratio of forest area to total land area is selected as one of the factors affecting FCSE for analysis, with the data obtained from the China Forestry Statistical Yearbook and the China Statistical Yearbook of 2004–2018.

Afforestation area (afforest, in 10,000 hectares): Natural forests have higher carbon stocks and carbon density than planted forests, which have a higher carbon sequestration capacity per unit area [45]. Afforestation activities are a low-cost and effective strategy to improve the carbon sequestration capacity of forests [46]. Afforestation projects are also the main way to increase forest area and scale as well as promote forest carbon sequestration and oxygen release in China presently. In this study, the area of afforestation in each province is selected as one of the factors affecting the efficiency of forest carbon sink for research and analysis, with data from the China Forestry Statistical Yearbook of 2004–2018.

The education level of forestry practitioners (education): Labor input is one of the important inputs of forest carbon sink production activities, not only in terms of the number of practitioners, however, the level of professional skills of the practitioners is also important. Human capital consists of their own education level, occupational skills, health status and work experience [47], which is often expressed by scholars using years of education. In view of the scientific and rational nature of forest carbon sink operation, in this paper, the education level of forestry practitioners in each province is selected as one of the factors affecting the efficiency of forest carbon sink, with data obtained from the China Forestry Statistical Yearbook of 2004–2018.

(3)

Social and economic development factors

Urbanization rate (urate, in %): The urbanization process leads to complex changes in carbon source sinks and affects forest carbon sinks. Carbon sink changes are mainly influenced by natural factors and land urbanization, among which population urbanization, economic urbanization, and land urbanization affects carbon emissions. Since forests are more affected by human activities, this paper selects population urbanization rate as the explanatory variable of FCSE for analysis, with the data obtained from the China Statistical Yearbook of 2004–2018.

GDP per capita (pergdp, in million dollars): Economic growth is a fundamental driver of social development which is closely related to forest carbon sinks [48]. GDP per capita is a typical indicator of the socioeconomic development of a country or a region. On the one hand, along with high-speed economic growth, it leads to natural resource consumption and environmental problems. On the other hand, it can promote the upgrading of industrial structure and technological progress, in addition to improving the forest operation management level as well as FCSE. In this paper, the GDP per capita of each province is selected as one of the factors affecting FCSE for research and analysis, with data from the China Statistical Yearbook of 2004–2018.

Total social investment (sinvest, in million yuan): Social investment contributes to the accumulation of forest ecological resources as well as promoting sustainable development of forestry. The long operation cycle and high investment risk of the forest industry make it difficult to rely on the forest’s own output to sustain forest operations in the early stage, especially as the cost of forestry ecological construction continues to increase, requiring continuous investment from social capital [49]. In this article, social investment in each province was selected as one of the factors affecting the efficiency of forest carbon sink for research and analysis, with the data obtained from the China Statistical Yearbook of 2004–2018.

The evaluation index system of factors influencing FCSE in

Table 2. Indicators of influencing factors for the forest carbon sink efficiency.

Influencing Factors	Variable Name	Indicator Description	Unit
Natural Endowment	Total precipitation	Average annual precipitation	billion cubic meters
	Temperature change	Change relative to average temperature	Celsius
	Incidence of pests and diseases	Incidence of forest pests and diseases in each region during the study period	%
Forest Management	Land Use Change	Ratio of forest area to total land area	%
	Afforestation area	Area of afforestation	10,000 ha
	The education level of forestry practitioners	Percentage of personnel with more than 9 years of education	%
Social Development	Urbanization rate	Population urbanization rate	%
	GDP per capita	GDP per capita	10,000 a
	Total social investment	Cumulative investment completed since the beginning of the year	10,000 a

Note: ^a represents Yuan.

contains three levels, respectively: total precipitation, temperature change, and pest and disease occurrence; land use change at the level of natural environmental factors, afforestation area, and education level of forestry practitioners at the level of forest management and administration; and urbanization rate and per capita GDP at the level of socio-economic development.

2.2.3. Data Sources and Data Processing

(1)

Sources of data for FCSE measurement and its influences. Considering the data availability, the forest input and output data of 31 provinces (municipalities and districts) in China from 2004 to 2018 were selected as the research samples in this paper. Wherein, the data on forest tree resources, forest area, and forest accumulation involved in the calculation of carbon sinks are obtained from the China Forest Resources Report (7th, 8th, and 9th) compiled by the Forestry Bureau of China. The data related to forestry employees, regional forest area, and forestry investment amount in each region are obtained from the China Forestry and Grassland Statistical Yearbook published from 2004–2018. The data of total precipitation and temperature change were obtained from The China Environmental Statistical Yearbook of 2004–2018. The forest area in land use change was obtained from the China Forestry Statistical Yearbook of 2004–2018, and the total land area was obtained from the China Statistical Yearbook of 2004–2018. Data on pest and disease incidence, silvicultural activities, and education level of forestry personnel were obtained from The China Forestry Statistical Yearbook of 2004–2018. Data on urbanization rate, GDP per capita, and social investment were obtained from the China Statistical Yearbook of 2004–2018.

(2)

Method of data processing. The prerequisite for scientific efficiency measurement is that the input and output of the decision-making unit need to be guaranteed to be in the same period, while the national continuous inventory of forest resources is reviewed every five years on a provincial basis. The years of continuous national forest inventory in each province are shown in

Table 3. Forest resources Inventory of China from 2004 to 2018.

Inventory Year	Inventory Provinces
2004, 2009, 2014	Jilin, Zhejiang, Anhui, Hubei, Hunan, Shaanxi, Shanghai
2005, 2010, 2015	Jiangsu, Shanxi, Liaoning, Guangxi, Guizhou, Ningxia, Heilongjiang
2006, 2011, 2016	Beijing, Hebei, Jiangxi, Gansu, Xinjiang, Tibet
2007, 2012, 2017	Tianjin, Sichuan, Yunnan, Guangdong, Shandong, Chongqing
2008, 2013, 2018	Fujian, Henan, Hainan, Qinghai, Inner Mongolia

, and the labor force, forest area, and capital stock of forest carbon sink input indicators were measured based on the general average of the corresponding years in the actual inventory years in each province because of the inconsistency of the review period.

(3)

Descriptive Statistics

The descriptive statistics of the main variables in this study are shown in

Table 4. Statistical description of variables.

Variable	N	Mean	Sd	Min	Max
crste	62	0.423	0.309	0.013	1.000
water	62	2018	1538	64.40	6850
temch	62	0.013	0.590	−1.280	1.440
forest	62	31.64	17.87	4.064	66.12
pst	62	7.286	6.045	0.380	27.20
edu	62	0.943	0.052	0.704	1.000
area	62	209,792	165,837	1228	767,145
urban	62	54.87	13.70	23.13	89.22
pergdp	62	4.790	2.404	1.654	11.88
invest	62	112.6	145.8	6.288	1029

. From Table 4, it can be seen that the mean value of FCSE is 0.309, the maximum value is 1.000, and the minimum value is 0.013. There are large differences among regions. The data of the main variables in the influencing factors, such as temperature variation (mean value of 0.013), pest incidence (mean value of 6.045%), and per capita GDP (mean value of 4.190), are within a reasonable range.

3. Results

3.1. Forest Carbon Stocks and Carbon Sinks in China

Before proceeding to presenting the empirical results, a description of the forest carbon sink development in China statistics is in order. Characteristics of the forest carbon storage, annual carbon sink increase, and carbon density of provinces in China are provided in

Table 5. Forest carbon storage, annual carbon sink increases, and carbon density of provinces in China.

Province	Carbon Stock /TgC			Annual Carbon Sink TgC/a		Carbon Density MgC/ hm2
	7th	8th	9th	Period I	Period II	7th	8th	9th
Anhui	75.127	101.417	124.969	5.258	4.710	22.629	28.166	32.850
Beijing	8.580	10.586	16.415	0.401	1.166	22.650	20.339	27.911
Fujian	241.887	307.864	354.058	13.195	9.239	31.622	40.157	44.187
Gansu	103.332	120.034	140.537	3.340	4.101	34.487	25.606	27.695
Guangdong	189.058	245.145	307.293	11.217	12.429	22.861	28.049	33.913
Guangxi	295.702	341.817	409.008	9.223	13.438	30.056	27.291	30.462
Guizhou	128.633	175.299	230.010	9.333	10.942	30.593	31.477	35.205
Hainan	47.871	54.137	81.405	1.253	5.454	28.724	30.715	43.354
Hebei	63.618	77.247	93.014	2.726	3.153	19.347	18.466	21.172
Henan	83.452	107.426	143.479	4.795	7.211	30.874	31.916	39.958
Heilongjiang	973.375	1025.236	1121.048	10.372	19.162	54.152	53.205	57.134
Hubei	144.332	200.856	253.863	11.305	10.601	29.009	34.701	35.562
Hunan	194.051	233.176	274.639	7.825	8.293	22.543	24.592	27.140
Jilin	495.848	535.008	578.087	7.832	8.616	68.856	72.635	75.679
Jiangsu	20.157	38.475	42.961	3.664	0.897	26.039	35.787	26.503
Jiangxi	246.778	276.846	322.610	6.014	9.153	26.496	28.434	32.203
Liaoning	136.364	166.581	195.815	6.043	5.847	28.378	32.537	35.136
Inner Mongolia	640.081	757.317	828.469	23.447	14.230	31.213	32.003	33.300
Ningxia	3.103	3.850	5.507	0.150	0.331	7.688	7.535	8.911
Qinghai	18.336	19.937	22.616	0.320	0.536	5.781	6.049	5.565
Shandong	39.747	49.753	50.910	2.001	0.231	19.423	19.553	19.996
Shanxi	47.145	61.047	84.323	2.780	4.655	22.645	27.610	29.858
Shaanxi	209.622	236.631	339.207	5.402	20.515	31.269	30.829	39.755
Shanghai	1.183	1.280	1.659	0.019	0.076	62.595	21.448	24.360
Sichuan	668.862	698.562	778.214	5.940	15.930	45.677	42.094	45.677
Tianjin	1.298	2.056	3.045	0.151	0.198	13.883	22.055	27.289
Xizang	846.390	849.701	861.884	0.662	2.437	60.908	58.093	58.569
Xinjiang	113.596	126.793	148.351	2.639	4.312	23.467	19.163	21.246
Yunnan	791.898	883.857	1040.895	18.392	31.408	50.762	48.624	54.378
Zhejiang	101.878	136.799	174.685	6.984	7.577	18.392	23.408	29.048
Chongqing	49.192	61.539	105.438	2.469	8.780	26.855	21.448	33.320
National average	225.177	255.041	294.659	5.973	7.923	30.641	30.451	34.108

Note: Period I and Period II indicate the seventh to the eighth and eighth to the ninth inventory period, respectively.

.

3.1.1. Forest Carbon Storage

As shown in Table 5, the forest carbon stock nationwide increased annually during 2004–2018, which was 24.021 PgC as of the 9th forest inventory. However, there are large differences in the spatial distribution of carbon stock in China. Forest carbon stocks in the northeast, northwest, and southwest regions are much higher than those in the eastern and central regions. Five provinces with large carbon stocks, including Heilongjiang, Yunnan, Inner Mongolia, Tibet, Sichuan, and Jilin, had forest carbon stocks exceeding 0.400 PgC in the period 2004–2018. The carbon stocks of Heilongjiang and Yunnan reached 1.000 PgC in the period of the 9th forest inventory, while the above five provinces accounted for 53.69%, 51.23%, and 48.50% of the national carbon stocks in the three forest inventories, respectively, with a total share of 50.91% from 2004 to 2018. It is related to the forest resource endowment, location factors, and social development level and ways in different regions. Concerning forest resource endowment, as forest resources are unevenly distributed in China, forest areas are mainly concentrated in northeast and southwest regions, which have higher forest area, storage volume, tree species, and forest density than those in northwest, north, and central regions, resulting in relatively higher total forest carbon sink. In terms of social development, with the vast area and low population density in the western region, forestry accounts for a higher proportion of local social development than in the developed eastern regions, attracting a higher degree of attention.

3.1.2. Forest Carbon Sinks

The annual average carbon sink is the average annual carbon stock change between the two inventory periods. During the period 2004–2018, the overall national forest stand biomass showed carbon sink, with a total sequestration of 2.104 PgC and annual average carbon sink of 0.210 PgC/a. During the 7th to 8th and 8th to 9th forest inventory, the increase of forest carbon sink was 0.899 PgC and 1.205 PgC, respectively, with a large increase in overall carbon sink. The annual average carbon sink increments were 5.973 TgC and 7.923 TgC, respectively. The provinces with carbon sink over 10.000 TgC/a from 2004 to 2013 were Inner Mongolia, Yunnan, Fujian, Guangdong, and Hubei. In the period of 2014–2018, there was a substantial increase in carbon sinks of provinces, with nine provinces exceeding 10.000 TgC/a, which are Yunnan, Heilongjiang, Inner Mongolia, Sichuan, Shaanxi, Guizhou, Guangxi, Guangdong, and Hubei, among which Heilongjiang and Shaanxi exceeded 20.000 TgC/a. Different from the distribution of forest carbon stock, the five provinces with higher forest carbon sinks during the study period were Yunnan, Shaanxi, Heilongjiang, Sichuan, and Inner Mongolia in order, whereas the faster growth rate was in Yunnan, Shaanxi, Heilongjiang, and Sichuan, while Inner Mongolia showed negative growth in carbon sinks compared with the previous period, and the increase in annual carbon sinks slowed down. The reasons may be that the unique climatic and topographical conditions are more suitable for forest carbon sequestration, while the carbon sink caused by the difference in forest age is not fully consistent with the distribution characteristics of forest carbon stock.

3.1.3. Forest Carbon Stock Density

During 2004–2018, the national forest carbon density exceeded 30 Mg C/hm², among which the forest carbon stock density in Fujian, Gansu, Henan, Heilongjiang, Jilin, Inner Mongolia, Shaanxi, Sichuan, Tibet, and Yunnan provinces is higher than the national average, in which four provinces, including Jilin, Tibet, Yunnan and Heilongjiang, have forest carbon stock density over 50 Mg C/hm², while the highest Jilin province is 2.247 times the national average, and the smallest among the provinces below the national average carbon density level Qinghai Province is less than 20% of the national average. Considering the overall changes during the three inventory periods, the forest carbon stock density did not have significant changes and was basically increasing, with Jilin being the highest while Tibet, Yunnan, and Heilongjiang followed. It could be due to the fact that, as far as carbon density is concerned, natural forests are larger than planted forests, and provinces such as Tibet, Yunnan, and Heilongjiang have larger natural forest areas and stockpiles, so the density of forest carbon stocks is relatively higher.

3.2. Forest Carbon Sink Efficiency Measurement Results

On the basis of the DEA model constructed in the previous section, the FCSE of 31 provinces in China was measured using deap2.1 based on the data of the 7th–9th forest inventory in China, and the results presented in

Table 6. Forest carbon sink efficiency of provinces in China.

Province	Crste		Vrste		Scale
	Period I	Period II	Period I	Period II	Period I	Period II
Anhui	0.039	0.056	0.345	0.244	0.114	0.230
Beijing	1.000	0.212	1.000	0.292	1.000	0.727
Fujian	1.000	0.640	1.000	0.648	1.000	0.987
Gansu	0.196	0.124	0.236	0.169	0.829	0.732
Guangdong	1.000	1.000	1.000	1.000	1.000	1.000
Guangxi	0.219	0.203	0.361	0.292	0.606	0.694
Guizhou	0.425	0.361	0.746	0.361	0.570	0.999
Hainan	0.296	1.000	1.000	1.000	0.296	1.000
Hebei	0.214	0.162	0.296	0.275	0.723	0.589
Henan	0.436	0.474	0.452	0.490	0.964	0.967
Heilongjiang	0.267	0.216	0.275	0.233	0.971	0.926
Hubei	0.764	0.461	1.000	0.469	0.764	0.982
Hunan	0.375	0.224	0.394	0.234	0.953	0.958
Jilin	0.347	0.254	0.402	0.256	0.863	0.991
Jiangsu	0.696	0.436	0.796	0.485	0.874	0.899
Jiangxi	0.350	0.408	0.410	0.428	0.854	0.953
Liaoning	0.488	0.297	0.507	0.320	0.962	0.927
Inner Mongolia	0.624	0.270	1.000	0.276	0.624	0.978
Ningxia	0.059	0.094	1.000	1.000	0.059	0.094
Qinghai	0.032	0.033	0.373	0.322	0.087	0.103
Shandong	0.617	1.000	0.628	1.000	0.983	1.000
Shanxi	0.013	0.254	1.000	1.000	0.013	0.254
Shaanxi	0.267	0.486	0.294	0.496	0.907	0.980
Shanghai	0.090	0.375	1.000	1.000	0.090	0.375
Sichuan	0.023	0.332	0.185	0.818	0.124	0.406
Tianjin	1.000	1.000	1.000	1.000	1.000	1.000
Xizang	1.000	1.000	1.000	1.000	1.000	1.000
Xinjiang	0.450	0.380	0.464	0.391	0.969	0.971
Yunnan	0.100	0.298	0.260	0.298	0.386	0.999
Zhejiang	0.368	0.747	1.000	0.845	0.368	0.884
Chongqing	0.300	0.379	0.385	0.402	0.778	0.942
National average	0.421	0.336	0.639	0.514	0.669	0.690

Note: Period I and Period II indicate the seventh to the eighth and eighth to the ninth inventory period, respectively.

.

In general, the average comprehensive efficiency of forest carbon sinks in the 31 provinces of China is lower. The comprehensive efficiency of forest carbon sinks reflects the ability of forests to obtain the maximum carbon sink output with the given inputs of production factors. The mean values of comprehensive efficiency in general for the 7th to 9th forest inventory periods were 0.421 and 0.336, respectively, with improvement spaces of 57.9% and 66.4% for the corresponding periods, respectively. In which the frequencies of DEA is valid (value of 1.000) in comprehensive efficiency, pure technical efficiency, and scale efficiency in period I are 5, 12 and 5, respectively, accounting for 16.12%, 38.71%, and 16.12% of the total sample. DEA is fully valid (crste, vrste, and scale are 1) in five provinces, Beijing, Fujian, Guangdong, Tianjin, and Tibet, and accounts for 16.12%. The frequencies of DEA validity (value of 1.000) in period II comprehensive efficiency, pure technical efficiency, and scale efficiency are 5, 8, and 5, respectively, accounting for 16.12%, 25.81%, and 16.12% of the total sample. The provinces with fully valid DEA (crste, vrste, and scale are all 1.000) are Guangdong, Hainan, Shandong, Tianjin, and Tibet, accounting for 16.12%. As seen above, the three provinces of Guangdong, Tianjin, and Tibet all achieved full DEA validity throughout the research periods, with their comprehensive efficiency, pure technical efficiency, and scale efficiency reaching the frontier of the production.

The pure technical efficiency reflects the technical level and management capacity as well as the reasonable degree of input and output in each province under the constant input of forest carbon sink. The mean values of the two periods are 0.639 and 0.514, respectively, while the differences with the production frontier surface are 0.361 and 0.486, which indicates that there is input redundancy or output deficiency in the two periods as a whole. The comprehensive efficiency is the product of pure technical efficiency and scale efficiency. As shown in Table 6, the mean value of pure technical efficiency is lower than the mean value of scale efficiency, which means that the current pure technical efficiency of forest carbon sink is the main factor limiting the development of FCSE, and the production technology or management technology of forest carbon sinks are not effectively utilized, which in turn cause the ineffective DEA of comprehensive efficiency. For the future, the improvement of the comprehensive efficiency of forest carbon sink mainly lies in improving its pure technical efficiency.

Compared with the pure technical efficiency, the overall scale efficiency of national forest carbon sink is higher, with the average value above 0.650 in the two inventory cycles, as well as the average scale efficiency increasing by period. It indicates that the ratio of the existing technically efficient forest-scale carbon sink to the carbon sink at the optimal scale gradually increases under a certain input of forest carbon sink, i.e., a series of afforestation, reforestation, and ecological restoration measures taken to increase forest carbon sink are effective. The provinces below the mean were Anhui, Ningxia, Qinghai, Shanxi, Shanghai, and Sichuan, with large changes in scale efficiency in both periods, of which Anhui and Shanxi were increasing period by period. The possible reasons why the scale efficiency of Ningxia, Qinghai, and Sichuan is much lower than the national average is due to the constraints of natural geographic environment. The shortage of soil, climate, and water resources make local forests of low quality, difficult to afforest, and difficult to achieve the goal of high scale efficiency of forest carbon sink. The low scale efficiency in Shanghai and Tianjin are the dual constraints of natural factors and socio-economic development. Firstly, the small area of the jurisdiction and high population density determine that a large amount of land cannot be invested in forestry activities. Secondly, as these areas mainly develop high-tech industries and engage in economic activities, the forestry industry has a long production cycle, large initial investment, and much lower economic efficiency per unit area than other industries, which cannot generate high scale efficiency.

3.3. Tobit Regression Results

Based on the Tobit model constructed in the previous section, the factors influencing the efficiency of forest carbon sinks were analyzed at the levels of social development, natural factors, and the quality of forestry practitioners, with the regression results shown in

Table 7. Empirical analysis results of influencing factors of forest carbon sink efficiency.

Variables	Coef.	S.t.	T-Value	p-Value	Confidence Interval
precip	0.046 **	0.022	2.10	0.036	0.003	0.088
temper	−0.122 **	0.021	−0.94	0.345	−0.061	0.021
lusc	0.004	0.004	1.06	0.29	−0.003	0.011
pests	−0.009 ***	0.003	−2.62	0.009	−0.016	−0.002
education	−0.048	0.029	−1.62	0.105	−0.105	0.01
afforest	−1.522 **	0.626	−2.43	0.015	−2.749	−0.295
urate	−0.615 *	0.331	−1.86	0.063	−1.265	0.034
pergdp	0.698 ***	0.2	3.48	0.00	0.305	1.09
sinvest	−0.06 **	0.025	−2.37	0.018	−0.11	−0.01
cons	1.17 ***	0.407	2.88	0.004	0.373	1.968

Note: ***, **, and * represent significance levels of 1%, 5%, and 10%, respectively.

. Several conclusions can be drawn from the results of the Tobit model as follows:

(1)

Annual total precipitation positively affects the efficiency of forest carbon sinks at a significant level of 5%, which indicates that the current increase in precipitation has a positive effect on the improvement of FCSE. There are mainly two reasons for this: on the one hand, forest growth is highly dependent on water resources. Especially for China, many provinces in northwest, southwest, northern Shaanxi, and some eastern regions belong to arid and semi-arid areas, which make it more difficult for forest trees to grow into trees, so the increase of rainfall can enhance the growth and survival rate of forest trees. On the other hand, precipitation can improve the microclimate in the region, increasing the ecosystem regulation and support services, promoting the virtuous cycle of nature, providing a suitable environment for the growth of forest trees. In turn, improving the forest quality and the overall efficiency of forest carbon sinks. As shown in the analysis, the comprehensive efficiency of forest carbon sink increases by 0.046 for every 1 trillion cubic meters of precipitation. In order to further improve the efficiency of forest carbon sinks, environmental protection needs to be enhanced and the climate environment improved.

(2)

Temperature variation negatively affects the efficiency of forest carbon sink at 5% significant level, which means that abnormal temperature variation reduces the efficiency of forest carbon sink. The appropriate temperature for forest growth is an important factor in improving the quality of the forest. Too high or too low a temperature compared to the normal temperature level in the region can affect the normal growth of the forest to some extent. Excessive temperature will increase forest water consumption and cause problems such as drought. Too low temperature will affect photosynthesis efficiency and reduce the ability of forest trees to absorb carbon dioxide and release oxygen. All of the mentioned will eventually cause the reduction of forest carbon sink, and thus reduce the efficiency of forest carbon sink. From the analysis results in Table 7, it can be seen that the comprehensive efficiency of forest carbon sink decreases by 0.122 for every degree Celsius increase in temperature variation. In order to further improve the efficiency of forest carbon sink, it is necessary to avoid excessive temperature changes in the region, and reduce extreme temperature changes by increasing environmental protection and improving the climate environment.

(3)

Afforestation area negatively affects FCSE at the 5% significant level, which indicates that an increase in afforestation area reduces FCSE. A possible reason for this is that an increase in afforestation area does not imply an increase in the carbon sequestration capacity of forests. Afforestation is generally planted through seedling cultivation, and the forest quality is not stable. Carbon stocks increased, but the increase did not exceed the increase in afforested area. This is determined by the growth and carbon sequestration characteristics of forest trees, and it is necessary to further improve the quality of afforestation area and the survival rate of forest growth. The average marginal coefficient of Tobit model shows that for every 1000 ha increase in afforestation area, the comprehensive efficiency of forest carbon sink decreases by −0.570%.

(4)

The incidence of pests and diseases negatively affects forest carbon sink efficiency at a significant level of 1%, which indicates that an increase in the incidence of pests and diseases reduces the overall efficiency of forest carbon sinks. In addition to being determined by itself, the change of forest vegetation carbon stock is also influenced by the area and incidence of forest pests and diseases [23]. The ability of forests to sequester carbon essentially depends on the ability of forests to absorb and conserve carbon. The occurrence of pests and diseases negatively affects forest growth and even causes abnormal mortality of forests, converting them from carbon sinks to carbon sources. The reduction of carbon sequestration capacity makes its carbon sink output lower with the same input of other factors, which causes the reduction of carbon sink efficiency. From the average marginal regression coefficients in Table 7, it can be seen that for every 1% increase in the incidence of pests and diseases, the comprehensive efficiency of forest carbon sink decreases by 0.900%.

(5)

The urbanization rate negatively affects FCSE at a significant level of 10%, which indicates that an increase in the urbanization rate of the population reduces the overall efficiency of forest carbon sinks. This could be attributed to the complex changes in forest carbon sink due to urbanization process. From an objective point of view, the capacity of a city is limited, and the urbanization of the population means the migration of the agricultural population to the off-farm population. In order to increase the capacity of a city, it is necessary to expand the town area. However, cities are generally established in plain areas with good natural conditions, where an increase in urban area means a decrease in the area of agricultural and forestry. Excessive urbanization has the potential of leading to a series of social and environmental problems. The intensive and industrialized production under high urbanization rate will inevitably increase the pressure of environmental development with negative effects on the growth of forest trees, forest carbon sequestration capacity, and carbon sink efficiency. From the average marginal regression coefficients in Table 7, it can be seen that each 1% increase in population urbanization rate decreases the comprehensive efficiency of forest carbon sink by 0.615%.

(6)

Total social investment negatively affects the efficiency of forest carbon sink at 5% significant level, which indicates that the increase of total social investment reduces the comprehensive efficiency of forest carbon sink. On the one hand, total social investment involves all aspects of social development, however due to the limitations in the stage of social development, the social investment is concentrated in productive investment, consumer investment, infrastructure investment, and investment in environmental protection. Compared to investments in agriculture, health care, and education, forest development investments are smaller in scale. On the other hand, the increase in total social investment means accelerated industrial development with economic growth as an intermediary, which leads to natural resource depletion and environmental problems. The current industrial structure of China still has a low proportion of tertiary industries, and the consumption of natural resources and high dependence on them makes social development and environmental protection not a complete “win-win” situation. The average marginal regression coefficient in Table 6 shows that for every 10,000 RMB increase in total social investment, the comprehensive efficiency of forest carbon sink decreases by 0.070%.

(7)

GDP per capita positively affects forest carbon sink efficiency at a significant level of 1%, which indicates that an increase in the overall level of socioeconomic development increases the comprehensive efficiency of forest carbon sinks. GDP per capita is one of the important indicators of social development level, and there is a complex internal link between economic growth and environmental development. In the early stage of social development, the economy was developed by increasing the consumption of resources, and after the economic development reached a certain level, it would bring the upgrading of industry structure and technological progress. Its effect on the efficiency of forest carbon sink is reflected in increasing environmental protection, improving forest management, and upgrading technological changes, which improve the technical efficiency and scale efficiency of forest carbon sink, and affect the comprehensive efficiency of forest carbon sink. From the analysis results, it can be seen that for every 10,000 increases in per capita GDP, the comprehensive efficiency of forest carbon sink increases by 0.698%. In order to further improve the efficiency of forest carbon sink, the level of socio-economic development needs to be accelerated.

4. Discussion

4.1. Development of Forest Carbon Sink

The conclusion indicates that forest carbon sinks in China vary among different regions, which is consistent with (Xue, 2018; Yan, 2018; Xue, 2017; Wang, 2014) [20,50,51,52]. As shown in Table 4, the national forest carbon stock increased annually during 2004–2018, but there were large differences in spatial distribution. The forest carbon stocks in the Northeast, Northwest, and Southwest regions were much higher than those in the eastern and central regions. The amount of forest carbon stock is related to the forest resource endowment, location factors, and the level and manner of social development in various regions. Inter-regional disparity is the primary factor causing regional differences of forest carbon sinks in China [20,51]. In terms of forest resource endowment, due to the uneven distribution of forest resources in China, forest areas were mainly concentrated in northeastern and southwestern regions, hence southwestern and northeastern regions are the most important carbon pool bases in China [53,54]. The forest area, stock, tree species, and forest density in these regions are higher than those in Northwest, North, and Central regions, resulting in higher total forest carbon stocks.

The national forest carbon stock biomass showed an overall carbon sink during 2004–2018, with faster growth rates in Yunnan, Shaanxi, Heilongjiang, and Sichuan. Compared with 1999–2013, Heilongjiang and Yunnan showed the same growth trend, the same as the Zhang’ conclusion [43], while Inner Mongolia showed faster growth in 1999–2013 and negative growth in 2004–2018. The highest forest carbon stock density was found in Jilin, followed by Tibet, Yunnan, and Heilongjiang. Both Jilin and Heilongjiang are located in the Northeastern state-owned forest region, which includes the traditional forest areas of Northeastern coniferous and mixed coniferous forests [55]. With good forest quality, larger area, and stock of natural forests in the region, forest carbon stock density is relatively high. From the overall changes during the three inventory periods, the forest carbon stock density did not change much, which is consistent with the changes in forest quality [40].

The average overall efficiency of forest carbon sinks in 31 Chinese provinces was lower [16,24], which was confirmed by this study. The mean values of pure technical efficiency for the two periods were 0.639 and 0.514, respectively, while the differences with the production frontier surface were 0.361 and 0.486, respectively. There was an overall input redundancy or output deficiency. The overall efficiency is the product of pure technical efficiency and scale efficiency. As shown in Table 4, the mean value of pure technical efficiency is lower than the mean value of scale efficiency. As a result, the low comprehensive technical efficiency is mainly caused by the overall low pure technical efficiency [29]. Therefore, it is important to improve the technical efficiency of forest carbon sinks as well as to increase the investment in science and technology in the forestry sector. At the same time, both improving the forestry science and technology system and setting up special science and technology funds accelerate the process of independent research and development while strengthening the linkage with the international technology frontier, which is of great significance and urgency. Compared with the pure technical efficiency, the national forest carbon sink scale efficiency was overall higher and increased by periods, which means that the ratio of the existing technically efficient forest scale carbon sink to the carbon sink at the optimal scale increases gradually for a certain input of forest carbon sink, and a series of afforestation, reforestation, and ecological restoration measures taken to increase forest carbon sink are effective [56].

4.2. Impact Factors

Environmental conditions such as climate change, represented by precipitation and temperature, are interrelated with forest quality [40,57], while some studies have also found insignificant effects on carbon stocks from both temperature and precipitation shocks [34]. The positive effect of precipitation on forest quality is significant [40], but inconsistent with existing studies on the effect of precipitation on carbon stocks [58], where this paper found a significant positive effect of precipitation on FCSE (as shown in Table 7). In addition, regarding the effect of temperature on forest carbon sinks, although some studies suggest that temperature is positively correlated with forest carbon stocks [58]. However, the results show that there is no significant relationship between the two, which is consistent with the results of other studies [34]. In summary, the effect of temperature change on forest quality was obvious [40], but the effect on both forest carbon stock [34] and carbon sink efficiency (as shown in Table 7) was not obvious. Based on the above results, in order to further enhance the FCSE, more efforts are needed to protect the environment and improve the environmental conditions in the region. Enhancing natural precipitation will help the growth of forest trees, increase ecosystem services, and enhance FCSE with certain inputs. Considering the natural conditions of the region, measures to increase forest carbon sinks, such as afforestation, are carried out according to local conditions.

After the 1880s, China’s forest management objectives gradually changed to timber production and ecological construction [59], as evidenced by a massive increase in afforestation area and a significant effect of forest quantity on forest quality [60]. The findings of this paper also showed (Table 7) that afforestation area has a significant effect on FCSE, notably, as the effect it produces was negative. An increase in afforestation area does not necessarily mean an increase in forest carbon sequestration capacity, although an increase in planted forests will change forest productivity, structure, and health [40]. The afforested area was not equivalent to the actual forest increase due to the carbon sequestration characteristics of the trees. The quality of the afforested area needs to be further improved in future forest management to increase the survival rate of forest growth. In addition, it has been shown that forest management, such as ecological protection level and pest control, significantly affects forest quality [61,62]. Consistent with it, this paper found that the effect of environmental management on FCSE was positively significant. Environmental management aims to coordinate the relationship between socioeconomic development and environmental protection, while an increase in the number of regional environmental managers is conducive to improving the environmental quality in the region, providing good natural conditions for the growth of forest organisms, and enhancing the efficiency of forest carbon stocks and forest carbon sink technologies.

The results of this study also highlight the importance of socioeconomic development in improving FCSE. Firstly, economic growth has created a large number of non-farm employment opportunities, thus reducing the pressure on forests [63], which has had an important positive impact on improving forest quality. This study also showed that changes in economic level, represented by GDP per capita, had a positive and significant effect on the improvement of FCSE (Table 7). This means that economic growth was not at the expense of FCSE, and the consumption of forest resources generated by economic growth did not outweigh the positive effects of technological progress and industrial structure upgrading. Secondly, the rate of population urbanization has an important positive impact on improving forest quality [40], where accelerated urbanization reduces the pressure on forests and improves forest quality by reducing the intervention of human activities on forest growth [63]. This study found that, inconsistent with the trend of forest quality change, was that the increase of the population and urbanization rate, that would reduce the comprehensive efficiency of forest carbon sink, leading to complex changes in forest carbon source sink with urbanization process. Intensive and industrialized production under high urbanization rates inevitably increases environmental development pressure, which affects forest growth, forest carbon sequestration capacity, and carbon sink efficiency negatively. Lastly, some studies have argued that social forestry investment can promote the accumulation of forest ecological capital and achieve a balance between economic and ecological effects [49], and the investment efficiency in forest management significantly affects forest carbon sink efficiency [64]. However, the results of this paper showed that total social investment produced a negative effect in enhancing the FCSE (Table 7). This is based on the national context, where the proportion of tertiary industries in China’s industrial structure is still not significant, making the consumption and high dependence on natural resources a “win-win” situation between social development and environmental protection.

4.3. Policy Implications

Firstly, it is necessary to improve the pure technical efficiency. The low overall efficiency of forest carbon sink is caused by the low pure technical efficiency. Improving the comprehensive efficiency needs to enhance the scientific and technological level of FCSE, which requires the forestry departments to increase scientific and technological investment, perfects the forestry science and technology system, and sets up special scientific and technological funds. Both accelerate the process of independent R&D and strengthen the linkage with the international technology frontier. This helps to facilitate the rational allocation of factor resources and avoid the occurrence of input redundancy, which may lead to waste of resources and pure technical inefficiency.

The second necessity is to improve the environmental conditions. At the aspect of natural environmental influencing factors, annual precipitation is one of the main factors to improve the efficiency of forest carbon sinks. Improvement of environmental conditions in the region and enhancement of natural precipitation contribute to the growth of trees, increase ecosystem services, and enhance FCSE with certain inputs.

Finally, the third is to reasonably increase the structural change of land use. Among the influencing factors at the socio-economic development level, the relative increase of forest area can improve FCSE. However, the goal of increasing FCSE cannot be fully achieved only by means of afforestation. Consequently, in the future forest carbon sink management, we should focus on rationally increasing the actual forest area, forest survival rate and, forest quality, through reforestation, and forest operation and management.

4.4. Uncertainty and Limitations

Although this paper measured the forest carbon sink efficiency in Chinese provinces with theoretical and empirical analyses of its influencing factors, there are still some uncertainties and limitations. Firstly, uncertainties in this study mainly arise from the quality of forest area and timber volume data in the forest inventories and the estimation of national biomass stocks using the BEF method, although the precision of forest area and timber volume data is greater than 90% for almost all provinces (greater than 85% for Beijing, Shanghai, and Tianjin). Secondly, the BEF method was used to classify Chinese forest types into 21 categories, which is not a precise estimate of the relationship between BEF and stand timber volume for all tree species. Its R² was greater than 0.8 [65], and the results are credible, but some uncertainty still exists. Finally, although we selected representative natural and non-natural influences, natural disturbances, such as wildfires, storms, and pathogen damage, were not considered in this study due to data and sample size limitations. Although the probability of wildfire and storms is not very high, it does have a certain probability of occurrence. In order to capture more factors influencing the efficiency of forest carbon sinks, it is worthwhile for future research to explore the impact of natural disturbances. We hope that future research can be carried out from this perspective.

5. Conclusions

This paper measures the FCSE of 31 provinces in China from 2004–2018 using the DEA model, which incorporates the Tobit panel regression model to dissect its influencing factors, the conclusion of the study shows that:

(1)

During the period 2004–2018, China’s overall forest carbon stock, carbon sink, and carbon density have all changed to some extent. Specifically, forest carbon stocks increased annually, and by the 9th forest inventory period, the total national carbon stock was 24.021 PgC. However, there are larger differences among regions. The carbon stock in the Northeast, Northwest, and Southwest regions are much higher than that in the Eastern and Central regions. Heilongjiang, Yunnan, Inner Mongolia, Sichuan, and Jilin accounted for 53.69%, 51.23%, and 48.50% of the national carbon stock during the three inventories, respectively. During the period 2004–2018, the overall national forest stand biomass showed carbon sink, with a total sequestration of 2.104 PgC and annual average carbon sink of 0.210 PgC/a. Similarly to the distribution of carbon stocks, the areas with high carbon sinks are also concentrated in the Northeast and Southwest regions such as Yunnan, Heilongjiang, Inner Mongolia, and Sichuan. The national forest carbon stock density exceeds 30 Mg C/hm², the Jilin Province having the highest, being 2.247 times higher than the national average. The Qinghai province has the lowest carbon density, being less than 20% of the national average carbon density level.

(2)

In general, the average comprehensive efficiency of forest carbon sinks in 31 provinces of China is lower. The mean values of overall integrated efficiency for the 7th to 9th forest inventory periods are 0.421 and 0.336, respectively, and the improvement space for the corresponding periods are 57.9% and 66.4%, respectively. The mean values of pure technical efficiency for the two periods are 0.639 and 0.514, respectively, and the differences with the production frontier surface are 0.361 and 0.486, respectively. This means that there is an overall input redundancy or output deficiency in the two periods. Compared with the pure technical efficiency, the national forest carbon sink scale efficiency is higher overall, with the average value above 0.650 in the two inventories, and the average scale efficiency increasing by period. It shows that the ratio of forest-scale carbon sink at the existing technical efficiency to that at the optimal scale gradually increases under certain forest carbon sink inputs, meaning that a series of afforestation, reforestation, and ecological restoration measures taken to increase forest carbon sink are effective. The low comprehensive technical efficiency is mainly caused by the overall low pure technical efficiency, indicating that the current pure technical efficiency of forest carbon sinks is the main factor limiting the development of FCSE.

(3)

The annual total precipitation and economic development level significantly and positively affect the efficiency of forest carbon sink, while the change of temperature, incidence of pests and diseases, afforestation area, total social investment, and urbanization rate significantly and negatively affect the efficiency of forest carbon sink in China. However, there are uncertainties in the effects of land use structure changes and practitioners’ education level on the efficiency of forest carbon sinks. It indicates that improving the comprehensive efficiency of forest carbon sinks in China should improve the environment, reasonably increase irrigation, and promote high-quality economic development. Meanwhile, avoiding excessive temperature changes, reducing the incidence of pests and diseases, and reasonably controlling the total social investment and urbanization process are also conducive to improving the comprehensive efficiency of China’s forest carbon sink.