Convergence Analysis of the Overall Benefits of Returning Farmland into Forest in the Upper Yangtze River Basin, China

Abstract

Returning farmland to the forest (RFTF) in the upper Yangtze River basin is a strategic measure to promote the sustainable development of ecological protection. The convergence analysis of the overall benefits of the upper Yangtze River basin provides a basis for a scientific and reasonable understanding of the improvement in the comprehensive benefits of RFTF in the basin. It provides policy suggestions for basin governance and sustainable development. Therefore, the convergence analysis and its spatial effect decomposition are carried out based on the entropy weight method to calculate the overall benefits of RFTF in the upper Yangtze River basin. The results indicate that there is no σ convergence in the overall benefits of RFTF in the upper Yangtze River basin, but there is significant absolute β convergence and significant conditional β convergence, and the overall development trend is stable. After thoroughly considering certain economic and social factors, especially the traffic infrastructure and the intensity of economic activities, the convergence rate of the overall benefits of RFTF in the upper reaches of the Yangtze River is accelerated. From the perspective of the spacing effect, the overall benefits of RFTF in this region and surrounding areas in the previous period significantly affected this region. As a result, sustainable development of the upper Yangtze River basin needs to include coordinated regional action to ensure ecological benefits, to improve transportation infrastructure, to scientifically recognize economic activities, and to guard against food security risks.

1. Introduction

Due to the development of the economy and society, human activities have caused land use changes, resulting in a series of serious ecological and environmental problems such as soil erosion, floods, droughts, sandstorms, etc. [1]. To improve this situation, the Chinese government launched the first round of a project aimed at returning farmland to the forest (RFTF) in 1999 [2]. RFTF mainly refers to converting sloping farmland and sandy farmland with serious soil erosion and low and unstable yields into forest land. The core objective of RFTF is to improve the ecology and environment, which will also have a certain economic and social impact.

In recent studies conducted on the ecological benefits of RFTF, it has been demonstrated that the ecological environment has been greatly restored as a result of the project [3,4,5,6]. In addition to providing a positive impact on the climate and the ecosystem, RFTF improves the level of stability and sustainability of ecosystem vitality, organization, and function [7,8]. For different ecosystems, RFTF benefits both ecological restoration in arid and semi-arid regions [9] and the stability and diversity of ecosystems in alpine areas [10]. It has been demonstrated that RFTF improves soil conservation and carbon sequestration [11,12] and reduces the net primary productivity and water yield within the sub-watershed [13]. In terms of the economy, RFTF encourages income diversification and prevents poverty [14], boosts farmers’ incomes [15,16], increases industrial and agricultural output values [17], and improves the local economic environment [18]. The second phase of RFTF advocates for farmers to organize cooperatives, cooperate with investors, and plant fruit trees to generate sustainable income [19]. However, there is the possibility that RFTF has slowed down China’s economic growth [20]. In addition, RFTF also causes changes in labor force employment structures [21], agriculture and animal husbandry systems [22], agricultural industry, planting and animal husbandry [23], and urbanization [24,25]. However, through the improvement of agricultural production conditions, RFTF leads to an increase in grain output [26] and does not affect food security [27].

Some scholars used the NUFER model to assess the impact of RFTF on the green development of Ningxia [22]. Some scholars use the market approach, income approach, and cost approach to calculate the overall benefits of RFTF [28]. In combination with the above related research on the benefits of RFTF and its calculation methods, it is possible to establish an indicator system regarding ecological, economic, and social dimensions to calculate the comprehensive benefits. However, there is little convergence analysis on the comprehensive benefits of RFTF in the existing literature.

In the long run, the ecological benefits of RFTF show a certain convergence trend. A series of key ecological protection projects implemented by the government, including RFTF, impacted the convergence mode of the environmental sensitivity index in Korla City from 1994 to 2018 [29]. As precipitation increases in Costa Rica, Ecuador, Chile, and Argentina, the flood peak area shows a relative or absolute convergence trend in response to land use [30]. However, it is unknown whether the comprehensive benefits of RFTF will converge. By studying whether the growth rate of the overall benefits of RFTF (including ecological benefits, economic benefits, and social benefits) is faster in low benefit areas than in high benefit areas, and then gradually narrowing the gap between regions, we can explain its convergence characteristics. Therefore, it can be judged whether the overall benefit of RFTF in the upper reaches of the Yangtze River displays a stable development trend. This will help to provide countermeasures and suggestions for the coordinated development of the region and the harmonious coexistence of man and nature.

As a key area for the implementation of the project aimed at returning farmland to forests in China, this paper takes the upper reaches of the Yangtze River as the research area, establishes an indicator system for the calculation of the comprehensive benefits of RFTF, uses the entropy weight method to calculate the comprehensive benefits of RFTF in various regions, and conducts convergence analysis and spatial effect decomposition. Finally, countermeasures and suggestions to improve the comprehensive benefits are put forward (Figure 1).

2. Materials

2.1. Study Area

The Yangtze River’s upper reaches begin at the river’s source in Yichang, Hubei Province, and flow across nine provinces including Qinghai, Tibet, Yunnan, Guizhou, Sichuan, Chongqing, Shaanxi, Gansu, and Hubei. There are a variety of terrains in the basin: its altitude rises sharply from the southeast to the northwest; its rivers are both vertical and horizontal; its canyons are numerous; its water flow differences are substantial, and its hydropower resources are significant. Additionally, the basin exhibits the distinctive characteristics of the East Asian subtropical climate, making it an important part of the extensive development of China’s western region. The continuous development of urbanization, industry, agriculture, and animal husbandry in the upper Yangtze River basin will continue to aggravate the deterioration of the ecological environment in this region. Then, RFTF in the upper reaches of the Yangtze River will play a role in improving the problem. This study consists of 33 cities and states divided into five sub-basins [31]. Panzhihua, Yibin, Ganzi, Liangshan, Kunming, Qujing, Zhaotong, Lijiang, Dali, and Yushu are part of the Jinsha River basin. In the Mintuo River basin (Mintuo River basin refers to the general name of Minjiang River basin and Tuojiang River basin), Chengdu, Zigong, Deyang, Neijiang, Leshan, Meishan, Ya’an, and Aba are located. Guiyang, Zunyi, and Bijie are included as part of the Wujiang River basin. The main channel area of the upper Yangtze River basin encompasses Yichang, Enshi, and Chongqing. The Jialing River basin includes Mianyang, Guangyuan, Suining, Guang’an, Dazhou, Bazhong, Hanzhong, and Longnan (Figure 2).

2.2. Data and Processing

2.2.1. Socio-Economic Data

This information is taken from China’s Social and Economic Big Data Research Platform (https://data.cnki.net/HomeNew/index (accessed on 18 March 2022)) and China’s Statistical Information Network (http://www.tjcn.org/tjgb/ (accessed on 20 February 2022)). In 2015 and 2018, the cultivated land area of cities and states in Yunnan Province was calculated using an interpolation method. In 2000 and 2005, the urban household registration population was replaced by the non-agricultural population to calculate the urbanization rate of the household registration population, since the statistical caliber of the urban household registration population was inconsistent around 2005. Since 2003, the classification standard of the gross output value of agriculture, forestry, animal husbandry, and fishery has changed. In order to increase the sample size, the output value of agriculture, forestry, animal husbandry, and fishery services in 2000 was filled with interpolation. Additionally, to eliminate the interference of price factors, all value-measured index data were subtracted from the consumer price index, using the year 2000 as the base period. The total population referred to in this paper refers to the total registered people, and in some years, the primary business income of postal and telecommunication services in Sichuan province represents the total post and telecommunication industry.

2.2.2. Ecological Statistics

China’s policy of RFTF involves returning farmland to forests and grassland. Throughout this study, the term “RFTF” refers to both conversions of farmland to forests and the conversion of farmland to grassland. The ecological benefit index was calculated using ArcGIS software and Landsat TM/ETM remote sensing images from the Resources and Environmental Science and Data Center of the Chinese Academy of Sciences (https://www.resdc.cn/Default.aspx (accessed on 3 December 2021)). The China Multiperiod Land Use and Land Cover Remote Sensing Monitoring Data Set (CNLUCC) was obtained through manual visual interpretation using Landsat remote sensing image data from the United States as the main information source. According to the land use types laid out by the Resource and Environmental Science and Data Center of the Chinese Academy of Sciences, the index is divided into cultivated land, forest land, grassland, water area, construction land, and unused land. The data set used in this paper comprises 1 km grid data of seven periods in total from 1995, 2000, 2005, 2010, 2013, 2015, and 2018. According to the division of China’s terrestrial ecosystem and the land use characteristics of the study area, the land area of cultivated land converted into forest land or grassland in the upper Yangtze River basin in each year was calculated [32]. The calculation results are shown in Appendix A. On this basis, according to reference [33], various ecological benefit indicators can be calculated. Among them, the grain output, grain sown area, and grain price data are taken from the statistical yearbooks of provinces and cities in the upper reaches of the Yangtze River basin as well as from national agricultural product price survey yearbooks. The data of adjacent years are used to fill in the missing data of individual regions.

2.3. Methods

2.3.1. Construction of the Index System

It can be concluded from the introduction that the conversion of farmland to the forest has a variety of effects on farmers’ income [15,16], local GDP [17], grain output [26], employment patterns [21], industrial structure [23], and urbanization [24], in addition to producing ecological benefits. Referring to the “National Report on Monitoring the Overall Benefits of Farmland Return to Forestry Projects” and the choice of pertinent indicators in the body of previous research, thorough understanding of what it means to return farmland to forest is required. Therefore, an indicator system for calculating the comprehensive benefits of returning farmland to forests in the upper reaches of the Yangtze River basin is established, as shown in Appendix B.

The entropy weight method is a very common objective weighting method [34,35]. The smaller the degree of variation of the indicator, the less information it reflects and the lower its corresponding weight. As seen in

Table A2. Calculation system for determining the benefits of RFTF in the upper Yangtze River basin.

Object Evaluation	System Evaluation	Indicator Evaluation	Weight
Calculation of the overall benefits of RFTF in the upper Yangtze River basin	Ecological benefits	Production of food	0.0786
		Production of raw materials	0.0810
		Regulation of gases	0.0804
		Regulation of climate	0.0802
		Regulation of hydrology	0.0803
		Disposal of waste	0.0794
		Conservation of soil	0.0800
		Biodiversity preservation	0.0803
		Supply of aesthetic landscapes	0.0803
	Economic benefits	Forestry output value	0.0331
		Animal husbandry output value	0.0284
		Per capita GDP	0.0297
		Gross agricultural product per labor	0.0169
		Yield of grains per unit area	0.0181
		The gross value of agricultural production	0.0167
		The proportion of cash crop sown areas to total sown areas	0.0091
	Social benefits	Arable area	0.0392
		The number of rural employees	0.0324
		Rate of urbanization of residents with household registrations	0.0204
		A significant portion of the total output value is accounted for by secondary and tertiary industries	0.0047
		A significant portion of the value of agricultural output comes from forestry and animal husbandry	0.0058
		Output value of agricultural service industries accounts for the portion of total agricultural output	0.0197
		Intensity of application of agricultural chemical fertilizers	0.0053

, the comprehensive benefits of RFTF in the upper reaches of the Yangtze River basin were calculated by using the entropy weight method. Due to space constraints, the calculation results are not presented. The calculation results of the comprehensive benefits of RFTF in cities (and states) in the upper reaches of the Yangtze River are shown in Appendix C.

2.3.2. Convergence Analysis Model

Baumol used the convergence analysis to study economic problems for the first time [36]. Convergence means that the economic indicators of the two individuals gradually approach each other and move towards a stable state. This study aims to further investigate whether the development and evolution of the overall benefits of RFTF in the upper Yangtze River basin show this trend. σ convergence and β convergence are used for empirical analysis.

• σ convergence

σ convergence verifies the extent to which the divergence between overall benefits in different areas decreases over time. In order to measure convergence, standard deviations (SD) [37,38,39,40] and coefficients of variation (CV) [41,42,43] are commonly used. In this paper, standard deviation and the coefficient of variation are used for comprehensive analysis and are expressed as follows:

$$S{D}_t=\sqrt{{\displaystyle \sum _{i=1}^n{\left(com{b}_{it}-\overline{com{b}_t}\right)}^2/n}}$$

(1)

$$C{V}_t=\frac{{\sigma }_t}{\overline{com{b}_t}}$$

(2)

In Equations (1) and (2), $S{D}_t$ represents the standard deviation of the difference in benefits from RFTF in year $t$. In year $t$, $C{V}_t$ represents the coefficient of variation of the overall benefit development differences from RFTF. In year $t$, $com{b}_{it}$ represents the overall benefits of RFTF in an area $i$. The value $com{b}_{it}$ represents the mean value of the overall benefits of RFTF in year $t$, while $n$ represents the number of regions. There is $\sigma$ convergence in the overall benefits of RFTF if the standard deviation and coefficient of variation decrease over time.

2.

$\beta$ convergence

According to the growth theory of neoclassical economics, $\beta$ convergence means that certain economic indicators in poor areas have improved faster than those in rich areas, thus gradually narrowing the gap between regions. The application of $\beta$ convergence has become increasingly popular in recent years [44,45,46]. It can be classified as classical $\beta$ convergence or spatial $\beta$ convergence depending on whether the spatial factor is taken into account. Based on whether control variables are considered, it is divided into absolute $\beta$ convergence and conditional $\beta$ convergence. Overall, this paper analyzes $\beta$ convergence in four ways: classical absolute $\beta$ convergence, spatial absolute $\beta$ convergence, classical conditional $\beta$ convergence, and spatial conditional $\beta$ convergence.

Classical absolute $\beta$ convergence mainly considers the convergence characteristics of the overall benefits of RFTF in terms of time. Its expression is:

$$\ln (com{b}_{i,t+1}/com{b}_{it})=\alpha +\beta \ln (com{b}_i)+{\epsilon }_{it}$$

(3)

In Formula (3), $\beta$ represents the convergence coefficient, and all other symbols represent the same values as in previous equations.

Regional development is not independent, and there are constantly varying degrees of spatial dependence, so modeling must consider the potential effects of spatial dependence. The spatial weight matrix is one of the differences between spatial econometrics and traditional econometrics. The construction of the spatial weight matrix is mainly based on adjacent criteria or distance criteria. The 0–1 space weight matrix based on the adjacency criterion is the simplest and most common type of space weight matrix. If the region $i$ and region $j$ have a common boundary, then $w_{ij}=1$. On the other hand, $w_{ij}=0$. According to recent geographical economics research, spatial distance plays a significant role in regional economic relations. Several systematic activities are involved in the implementation of the project of returning farmland to forest. It is important to note that the process of generating comprehensive benefits is not only influenced by social and economic factors but also by geographical environmental factors. Accordingly, a spatial weight matrix $W$ is constructed based on the adjacency effect, as shown in Equation (4). Practically, normalizing the row elements of a spatial weight matrix is often necessary, and the diagonal elements are all zero.

$$W_{ij}=\left\{\begin{array}{l}1,\mathrm{When} \mathrm{the} \mathrm{area} i \mathrm{is} \mathrm{adjacent} \mathrm{to} \mathrm{the} \mathrm{area} j\\ 0,\mathrm{When} \mathrm{the} \mathrm{area} i \mathrm{is} \mathrm{not} \mathrm{adjacent} \mathrm{to} \mathrm{the} \mathrm{area} j\end{array}\right.$$

(4)

Considering spatial correlation, absolute $\beta$ convergence models of spatial lag model (SLM), spatial error model (SEM), and spatial Durbin model (SDM) are constructed.

The absolute $\beta$ convergence model of SLM can be expressed as follows:

$$\ln (com{b}_{i,t+1}/com{b}_{it})=\alpha +\beta \ln com{b}_{it}+\xi {\displaystyle \sum _{j=1}^n{w}_{ij}}\ln (com{b}_{j,t+1}/com{b}_{jt})+{\epsilon }_{it}$$

(5)

The absolute $\beta$ convergence model of SEM can be expressed as follows:

$$\ln (com{b}_{i,t+1}/com{b}_{it})=\alpha +\beta \ln com{b}_{it}+{\mu }_{it} {\mu }_{it}=\rho {\displaystyle \sum _{j=1}^n{w}_{ij}{\mu }_{jt}+{\epsilon }_{it}}$$

(6)

The absolute $\beta$ convergence model of SDM can be expressed as follows:

$$\begin{array}{l}\ln \left(com{b}_{i,t+1}/com{b}_{it}\right)=\alpha +\beta \ln (com{b}_{it})\\ +\xi {\displaystyle \sum _{j=1}^n{w}_{ij}}\ln \left(com{b}_{j,t+1}/com{b}_{jt}\right)+\gamma {\displaystyle \sum _{j=1}^n{w}_{ij}}\ln com{b}_{jt}+{\epsilon }_{it}\end{array}$$

(7)

To analyze $\beta$ convergence, a series of control variables are added to take into account the differences in economic, technical, financial, and policy development levels in different regions. Therefore, the control variables are introduced based on the above to establish the conditional $\beta$ convergence model. Classical conditional $\beta$ convergence is expressed as follows:

$$\ln (Com{b}_{i,t+1}/Com{b}_{it})=\alpha +\beta \ln (Com{b}_i)+{\displaystyle \sum _{k=1}^n{\lambda }_k{X}_{i,t,k}}+{\epsilon }_{it}$$

(8)

In Formula (8), $X_{i,t,k}$ represents the $k-th$ control variable of $i$ region in $t$ year and $m$ represents the number of control variables, which is the same as below.

The conditional $\beta$ convergence models of SLM, SEM, and SDM are, respectively, expressed as follows:

$$\ln (com{b}_{i,t+1}/com{b}_{it})=\alpha +\beta \ln com{b}_{it}+\xi {\displaystyle \sum _{j=1}^n{w}_{ij}}\ln (com{b}_{j,t+1}/com{b}_{jt})+{\displaystyle \sum _{k=1}^m{\lambda }_k{X}_{i,t,k}}+{\epsilon }_{it}$$

(9)

$$\ln (com{b}_{i,t+1}/com{b}_{it})=\alpha +\beta \ln com{b}_{it}+{\displaystyle \sum _{k=1}^m{\lambda }_k{X}_{i,t,k}}+{\mu }_{it} {\mu }_{it}=\rho {\displaystyle \sum _{j=1}^n{w}_{ij}{\mu }_{jt}+{\epsilon }_{it}}$$

(10)

$$\begin{array}{l}\ln \left(com{b}_{i,t+1}/com{b}_{it}\right)=\alpha +\beta \ln (com{b}_{it})+\xi {\displaystyle \sum _{j=1}^n{w}_{ij}}\ln \left(com{b}_{j,t+1}/com{b}_{jt}\right)\\ +\gamma {\displaystyle \sum _{j=1}^n{w}_{ij}}\ln com{b}_{jt}+{\displaystyle \sum _{k=1}^m{\lambda }_k{X}_{i,t,k}}+{\displaystyle \sum _{j=1,k=1}^n{w}_{ij}{\theta }_k{X}_{j,t,k}}+{\epsilon }_{it}\end{array}$$

(11)

If $\beta$ is negative, then the overall benefits of RFTF tend to converge, and if $\beta$ is positive, then the overall benefits of RFTF tend to diverge. Accordingly, the convergence rate and the half-life cycle of convergence for the investigation period can be calculated, and the calculation formula is as follows: $\eta =-\ln (1-\left|\beta \right|)/T$, $\tau =\left(\ln 2\right)/\eta$ where $\eta$ represents the convergence rate within the time sequence length $T$ of the investigation period, while $\tau$ is the half-life cycle of convergence.

2.4. Variables

Based on the data available, the variables used in this study are as follows.

Explained variable: the overall benefits of RFTF.

Explanatory variables: government intervention, education development, transportation infrastructure, human capital, population density, economic activity, business activity level, investment in fixed assets of society as a whole, agricultural mechanization, financial development level, and informatization.

Due to the obvious differences in the economic size and fiscal scale of different cities, “gov” means that government intervention is reflected by the logarithm of fiscal expenditure as a percentage of GDP. By taking the logarithm of the ratio of education expenditure to GDP, we can determine the level of education expenditure. By measuring road density and calculating road mileage, “highways” represent transportation infrastructure. Considering the uneven distribution of resources in urban higher education, “stu” means that human capital can be measured by the proportion of ordinary middle school students in the total population. There is no doubt that the population is an essential indicator of the impact of human activities on the natural environment, and it is often used to indicate how closely human activities interact with the natural environment. “pop” represents population density, which can be calculated by dividing the total population by the land area. There is no question that both densities of the people and the intensity of economic activity can reflect the spatial carrying function and represent the pressure of population and economy on cultivated land. “econ” represents the intensity of economic activity, calculated by dividing GDP by land area. Retail sales of consumer goods can be used to assess residents’ level of commercial activity and purchasing power, and their role in driving economic growth is prominent. Furthermore, there is a strong circulation of commercial activities, a spatial effect which, to a certain extent, can reflect the level of economic prosperity. Therefore, using the retail sales of consumer goods in each region as an indicator of commercial activity has some explanatory power. It is calculated by taking the logarithm of per capita retail sales of consumer goods and dividing the total retail sales by the total number of people in order to estimate the level of business activity. A key factor in promoting regional economic development is the investment in fixed assets of the entire society. “ass” is the logarithm of the investment in fixed assets of the whole of society. In modern agriculture, agricultural machinery is indispensable material equipment. As an investment for agricultural growth, it promotes the improvement of comprehensive benefits of returning farmland to forest. There is also an increase in the number of interregional agricultural machinery service operations. By taking the logarithm of the total power of agricultural machinery, “agrm” represents the level of agricultural mechanization. Improvements in financial development can improve the business environment and alleviate some of the economic and employment pressures brought about by returning farmland to the forest. Therefore, “Fin” represents the level of financial development that can be measured by taking the logarithm of the deposit balances in financial institutions at the end of the year. In addition to being an essential factor of regional economic and social development, information mobility and influence are also important factors for improving the benefits of converting farmland into forests. “tele” represents informatization, which is indicated by the average number of post and telecommunications services in the country, taken as a logarithm.

3. Results

3.1. Results of σ Convergence Analysis

In Figure 3, the standard deviation of overall benefits of RFTF in the Jinsha River basin and Mintuo River basin did not change much, showing a small rebound and increase, whereas in the Jialing River basin and Wu River basin, the standard deviation of the overall benefits of RFTF slightly decreased, following the same trend. In recent years, the benefits of RFTF in the upper Yangtze River main channel area increased steadily, and the standard deviation does not appear to be rising. Generally, the standard deviation of the overall benefits of RFTF increased in the upper Yangtze River basin. Based on the trend of coefficient of variation shown in Figure 4, the Mintuo River basin displays a fluctuating trend, while the Jinsha River basin, Jialing River basin, Wu River basin, and upper Yangtze River main channel area show a decreasing trend. There was no obvious upward or downward trend in the coefficient of variation of the overall benefits of RFTF in the upper Yangtze River basin. The specific $\sigma$ convergence analysis results are shown in Appendix D.

The overall benefits of RFTF in the Jialing River basin and the Wu River basin display a significant $\sigma$ convergence. In the Mintuo River basin and the upper Yangtze River basin, there is no $\sigma$ convergence in the overall benefits of RFTF.

3.2. Results of $\beta$ Convergence Analysis

Since the random effects of spatial econometric models are still controversial in the application process and do not apply to small samples, for example, the upper Yangtze basin study, the fixed-effects model was selected based on Hausman test results when testing the $\beta$ convergence analysis of the overall benefits of RFTF.

In the absence of $\beta$ convergence, the regions with high overall benefits are predicted to grow faster than those with low overall benefits, resulting in an infinite expansion of the overall benefit gap between them. However, a gradual reduction in the overall benefits gap between regions demonstrates the presence of $\beta$ convergence, which indicates that the region with the low overall benefits is growing faster than the region with the high overall benefits.

For the purpose of comparison, the spatial lag model (SLM), the spatial error model (SEM), and the spatial Durbin model (SDM) with $\beta$ convergence are presented in this paper. As seen in

Table 1. Regression results of $\beta$ convergence for the overall benefits of RFTF.

Variables	Classic Absolute β Convergence	Spatial Absolute β Convergence			Classic Conditional β Convergence	Spatial Conditional β Convergence
		SLM	SEM	SDM		SLM	SEM	SDM
comb	−0.31 ***	−0.108 ***	−0.414 ***	−0.43 ***	−0.988 ***	−0.548 ***	−0.548 ***	−0.571 ***
	(−5.21)	(−3.5)	(−6.48)	(−6.52)	(−14.22)	(−9.33)	(−8.18)	(−8.99)
					0.1	−0.81	−0.091	−0.202
					(0.68)	(−0.87)	(−0.85)	(−1.8)
edu					−0.44	−0.41	−0.009	−0.086
					(−0.3)	(−0.44)	(−0.09)	(−0.84)
highway					0.746 ***	0.364 ***	0.178	0.16
					(4.37)	(3.25)	(1.37)	(1.22)
stu					0.046	0.337	0.069 *	0.062 *
					(0.67)	(0.86)	(1.73)	(1.39)
pop					24.624 ***	17.5 ***	15.45 ***	18.129 ***
					(2.69)	(3.05)	(2.72)	(3)
eco					−0.000 ***	−0.000 **	−0.000	−0.000
					(−2.95)	(−2.37)	(−1.48)	(−1.98)
pcon					0.48 ***	0.307 ***	0.235 ***	0.202 ***
					(3.55)	(3.59)	(2.67)	(1.96)
ass					−0.12	−0.087	−0.076	−0.132
					(−1.04)	(−1.2)	(−1.05)	(−1.46)
agrm					0.175 *	0.147 **	0.151 **	0.162 **
					(1.7)	(2.3)	(2.38)	(2.48)
fin					0.224 *	0.137 *	0.142 *	0.115 *
					(1.96)	(1.91)	(1.9)	(1.43)
tele					0.045	0.073 *	0.084 **	0.05 **
					(0.74)	(1.92)	(2.48)	(1.27)
W × comb				0.359 ***				0.053
				(5.44)				(0.49)
W × highway								0.469 **
								(2.18)
W × gov								0.134
								(0.74)
W × edu								−0.127
								(−0.59)
W × stu								−0.043
								(−0.74)
W × pop								3.642
								(0.29)
W × eco								−0.000
								(−1.31)
W × pcon								0.105
								(0.55)
W × ass								0.125
								(1.01)
W × agrm								0.01
								(0.07)
W × fin								−0.067
								(−0.55)
W × tele								−0.127 **
								(−0.99)
C	−1.515 ***				−13.634 ***
	(−4.25)				(−6.65)
ρ		0.73 ***		0.739 ***		0.526 ***		0.482 ***
		(19.08)		(22.31)		(11.13)		(6.64)
λ			0.783 ***				0.725 ***
			(22.48)				(15.29)
R2	0.18	0.158	0.18	0.18	0.686	0.759	0.581	0.809
Log-likelihood		−35.439	−22.673	−22.284		1.286	−6.063	8.72
sigma2		0.076 ***	0.062 ***	0.062 ***		0.053 ***	0.052 ***	0.049 ***
		(8.57)	(8.53)	(8.53)		(8.7)	(8.46)	(8.62)
AIC		76.877	51.346	52.568		25.429	40.127	34.56
BIC		86.008	60.476	64.742		68.037	82.735	113.689
η	0.025	0.008	0.036	0.037	0.295	0.053	0.053	0.056
τ	28.020	90.973	19.455	18.496	2.351	13.094	13.094	12.286

Note: *, **, and *** represent significance at the 10%, 5%, and 1% levels, respectively. Data in classical convergence brackets are t-test values, and data in spatial convergence brackets are z-test values. Data processing was performed by stata16.0.

, both SLM and SEM have significant p-values at the 1% level, so we chose the SDM, as it incorporates both. Based on the criterion of basic pool information, the lower the AIC value, the higher the explanatory power, and the model with the highest explanatory power was selected. Statistically, the higher the Log-likelihood and R², the lower the Sigma2, and the higher the degree of model fit, the better the model fit. To determine the best estimation model for $\beta$ convergence, the above principles were integrated. Among the three spatial econometric models for absolute $\beta$ convergence and conditional $\beta$ convergence, the estimation results of SDM were also better, and the spatial effect coefficients $\rho$ were all significantly greater than 0 at the 1% level, indicating that there was significant spatial spillover from returning farmland to forest between regions. Accordingly, increasing the overall benefits of RFTF in neighboring regions positively impacted the rate of growth of comprehensive benefits in this region, as there is a significant spatial spillover effect. To analyze the results and to conduct empirical research, SDM was be used.

As shown in Table 1, no matter which $\beta$ convergence model is used, all of them pass the 1% significance level test, and the classical condition $\beta$ convergence model has the fastest convergence rate at 0.295. Accordingly, the following convergence characteristics of RFTF in the upper Yangtze River basin are observed: (1) all $\beta$ convergence models demonstrate negative coefficients of lnxy and pass the 1% significance level test, which indicates significant $\beta$ convergence in the overall benefits of RFTF. Therefore, there is a likelihood that areas with low overall benefits of the fallow forest will gradually catch up with those with high overall benefits, resulting in a gradual reduction of regional differences in comprehensive benefits. (2) The convergence speed of the condition $\beta$ is significantly greater than the absolute $\beta$ convergence and is more than twice as fast than the absolute $\beta$ convergence. There is no doubt that the conditional $\beta$ convergence takes into account regional differences in economic and social conditions, accelerating the convergence of the overall benefits of RFTF and shortening the convergence period. (3) In the case of absolute $\beta$ convergence, spatial spillovers can also accelerate convergence speed. The reason may be that the mobility and spatial interaction effects of socioeconomic factors in neighboring regions will slow the convergence speed of the overall benefits of RFTF, eventually resulting in a significant $\beta$ convergence of the overall benefits of RFTF.

Based on the empirical results, the SDM with $\beta$ convergence has a higher explanatory power and better goodness of fit, which can be used to analyze the coefficients of control variables. Several of the estimated coefficients for human capital, population density, commercial activity level, agricultural mechanization level, financial development level, and information level passed the significance level test, and all of the estimated coefficients are positive. In particular, the density of the population and the level of commercial activity passed the 1% significance level test. Improving human capital, population density, retail activity level, agricultural mechanization level, financial development level, and information level is conducive to enhancing the benefits of RFTF, in which population density and commercial activity level play a greater role. The other variables are not significant.

This section is divided into subheadings. It provides a concise and precise description of the experimental results, their interpretation, and the experimental conclusions that can be drawn.

3.3. Results of the Spatial Spillover Effect Analysis

The spatial Durbin model includes spatially lagged independent variables. Therefore, estimation results cannot directly reflect the marginal effects of the independent variables on the dependent variable, and it is difficult to determine their direct effects. The change of an independent variable will not only affect the dependent variable in this region but also affect the dependent variable in adjacent regions, which leads to a series of changes and adjustments through circular feedback. It is therefore necessary to decompose the total spatial effect and partially differentiate the SDM to examine the direct and indirect effects of the independent variable. A direct effect can be observed when the independent variable in the region influences the dependent variable in the region, and an indirect effect can be observed when the independent variable in the region influences the dependent variable in neighboring regions (spatial spillovers). Total effects are the sum of direct and indirect effects.

Table 2. Decomposition of effects based on spatial conditions $\beta$ convergence.

Variables	Direct Effect	Indirect Effects	Total Effect
comb	−0.605 ***	−0.395 ***	−1 ***
	(−9.64)	(−3.53)	(−8.19)
gov	−0.188 *	0.033	−0.155
	(−1.76)	(0.11)	(−0.49)
edu	−0.107	−0.3	−0.407
	(−0.94)	(−0.77)	(−0.9)
highway	0.243 *	0.977 ***	1.22 ***
	(1.93)	(2.97)	(3.35)
stu	0.062	−0.008	0.053
	(1.3)	(−0.07)	(0.37)
pop	20.458 ***	21.177	41.635
	(3.1)	(0.93)	(1.59)
eco	−0.000 **	−0.000 *	−0.001 **
	(−2.37)	(−1.71)	(−2.05)
pcon	0.234 **	0.348	0.582
	(2.14)	(1.03)	(1.51)
ass	−0.113	0.107	−0.006
	(−1.21)	(0.5)	(−0.02)
agrm	0.18 **	0.175	0.355
	(2.47)	(0.69)	(1.2)
fin	0.106	−0.02	0.086
	(1.33)	(−0.1)	(0.36)
tele	0.035	−0.182	−0.147
	(0.74)	(−1.48)	(−0.95)

Note: *, **, and *** represent significance at the 10%, 5%, and 1% levels, respectively. Data in parentheses are t-test values. Data processing was carried out by stata16.0.

shows the decomposition results of the full effect.

The direct and indirect effect coefficients of the overall benefits of RFTF on its convergence were −0.605 and −0.395, respectively. They were both significant at the 1% level, suggesting that the convergence of the overall benefits of RFTF in this region is significantly affected by the overall benefits of RFTF in the region and adjacent areas in the previous period.

Government intervention has a direct effect coefficient of −0.188 and an indirect effect coefficient of 0.033. The direct impact is negative and passes the significance test. The indirect effect is positive but does not pass the significance test. Government intervention in this region is not conducive to improving the overall benefits of RFTF.

Transportation infrastructure and economic activity intensity can both be seen to have significant direct and indirect effects. In this region or adjacent regions, the direct and indirect effects of transportation infrastructure are 0.243 and 0.977, respectively, indicating that the transportation infrastructure is conducive to improving the benefits of RFTF. The spatial spillover effect of transportation infrastructure is greater from the perspective of the coefficient value and significance, which results in a weakening of the convergence of its overall benefits. In this region or adjacent regions, the direct and indirect effect coefficients of the intensity of economic activities are negative, which indicates that the intensity of economic activities is not conducive to improving the overall benefits of RFTF in this region.

In this region, the direct effect coefficient is significant at the 1% level, while the indirect effect coefficient is not significant, indicating that the increase in population density is conducive to improving the overall benefits of RFTF.

The direct effect of commercial activities and agricultural mechanization is significant at 1%, while the indirect impact is insignificant, based on the estimated coefficients of 0.234 and 0.18, respectively. This demonstrates that the level of commercial activities and agricultural mechanization is conducive to improving the overall benefits of RFTF.

4. Discussion

Many scholars have studied the convergence of rural or agricultural green development [47,48]. However, there is no specific study on RFTF. Some scholars evaluated the nutrient cycle and green development change of RFTF in Ningxia, China, but did not apply econometrics to further analyze whether it was convergent [22]. Some scholars analyzed the impact of RFTF on rural economy but did not consider the impact on ecology and society [49]. This study systematically analyzed the convergence of the comprehensive benefits of RFTF. The conclusion is scientific and reliable.

4.1. Discussion of Convergence Analysis

With the expansion of the scale of converting farmland to forests, the land that can be converted to farmland is gradually reduced, and the resulting ecological, economic, and social benefits also converge. Some studies have shown that the increase in population pressure will lead to the convergence of forest value and delays in returning farmland to forests [50]. The convergence of the overall benefits of RFTF will lead to the gradual reduction of the differences in the overall benefits of RFTF between regions.

The empirical results of absolute $\beta$ convergence and conditional $\beta$ convergence show that whether economic and social factors are considered or not, the overall benefits of RFTF in the upper Yangtze River basin show a convergence trend, indicating that the convergence characteristic of RFTF in the upper Yangtze River basin is its essential attribute. The conditional $\beta$ convergence takes into account the heterogeneity of economic and social development conditions, further accelerating the convergence rate of the overall benefits of RFTF in the upper Yangtze River basin and shortening the convergence period. This conclusion is consistent with the conclusion that human activities affect the convergence mode of land degradation sensitivity mentioned in reference [29]. Therefore, the adjustment of economic and social factors will help give full play to the overall benefits of RFTF in the region and promote the coordinated development of the region.

4.2. Discussion of the Spatial Effect Decomposition

The overall benefits of RFTF should consider the spatial links between regions. Whether in this region or adjacent areas, the transportation infrastructure is conducive to improving the overall benefits of RFTF in this region. From the coefficient value and significance of spatial effect decomposition, the spatial spillover effect of transportation infrastructure is greater, resulting in greater improvement of its overall benefits. This is because transportation not only strengthens the links between regions but also promotes the free flow of production factors [51]. Therefore, vigorously developing transportation can improve the overall benefits of RFTF in this region and adjacent regions. The direct effect and indirect effect coefficients of the intensity of economic activities are significantly negative, indicating that the intensity of economic activities in both this region and adjacent areas is not conducive to improving the overall benefits of RFTF in this region. The possible reason for this is that the excessive intensity of economic activities and the increased demand for natural resources, leading to a series of ecological and environmental problems [52,53,54], which is contrary to the original intention of RFTF. We need to scientifically understand the role of economic activities in improving the overall benefits of RFTF.

In the future, we will conduct in-depth investigation and research to understand the specific reasons for the convergence of overall benefits of RFTF from departments to grassroots level and put forward insights for the follow-up industry and sustainable development of RFTF. In a practical sense, the sustainable development of RFTF should be truly solved.

5. Conclusions

Research on the overall benefits of RFTF primarily examines how people and nature can coexist harmoniously. To maximize the comprehensive benefits of RFTF, it is essential to develop ecological, economic, and social systems within and between regions in a synergistic manner, as outlined in the “root” and “soul” of the new development concept of seeking happiness for people and rejuvenation for nations. To promote the high-quality development of RFTF, an essential topic in the construction of ecological civilization will be the coordinated improvement and convergence of the overall benefits of RFTF.

Using a calculation of the overall benefits of RFTF in the upper Yangtze River basin from 2000 to 2018, this study empirically tested the convergence of the benefits and their spatial spillover effects. An overview of the relevant statistical models and methods was first presented. Based on the empirical results, we examined the convergence characteristics and spatial impact of RFTF in the upper Yangtze River basin. Our main conclusions are as follows:

• To improve the overall benefits of RFTF, it is necessary to strengthen the financial support and management of RFTF in slow-growing areas, give full play to regional advantages, improve the radiation capacity of regions with high overall benefits of RFTF, and improve the comprehensive benefit monitoring system of RFTF. According to the objectives and tasks of ecological construction and the needs of industrial development, in combination with the local climate, hydrology, and geographical conditions, scientific and reasonable planning must be carried out to ensure the full range of ecological benefits.
• Regions should continuously improve transportation infrastructure, strengthen the inter-regional links, promote the free flow of factors, ensure the effective development of economic activities in the area of RFTF, and play a significant role in promoting the coordinated development of the regional economy. At the same time, it is necessary to scientifically understand the impact of economic activities on the overall benefits of RFTF.
• China’s farmland accounts for about 8% of the world’s farmland but feeds more than 21% of the world’s population. In the decision-making and management of RFTF, special attention should be paid to how to protect surplus farmland, carefully managing for long-term agricultural production and guarding against potential food security risks caused by the excessive conversion of farmland.