*2.2. Study Area*

Since the reform and opening up, the industrialization and urbanization level has continued to improve in 30 provinces in China, and rural areas have undergone many changes in the rural land system and household registration management system, which have significantly promoted the farmland transfer and labor migration. As recorded by China Rural Management Statistical Annual Report, there is a total of area of 3.70 million hectares of farmland transfer, with a total of 254 million people of labor migration in 2019 in China, and the level of farmland transfer or labor migration had a large increase compared with 2018. However, the improvement of farmland transfer level and labor migration level brings about changes in the extent of farmland use, and problems such as the contradiction between rural labor and farmland are gradually highlighted. At the same time, as China's farmland transfer and labor migration expand, the level of them varies significantly between provinces. Specifically, only a few provinces such as Inner Mongolia and Liaoning in China have reached the equilibrium state of farmland transfer level and labor migration level. Other provinces have failed to achieve the trend of balanced development, which means that the two have not reached coupled and coordinated development. For details, see Figure 1. Therefore, the evaluation of the CCD of FT and LM is not only significant to improve of the use efficiency of land resource elements and labor resource elements, but also beneficial for the development of agriculture, rural areas, and farmers in China.

**Figure 1.** The rate of farmland transfer (FT) and labor migration (LM) in 2019 in China.

#### *2.3. Methods*

2.3.1. The Evaluation Index System

The study referred to previous studies [48] and the index system was built according to scientificalness, integrity, and operability to measure the development levels of FT and LM. In this study, we selected 14 indexes from three aspects to represent the degree of FT development, and 13 indexes from three aspects to represent the degree of LM development (Table 1).

**Table 1.** Evaluation index system and weight of farmland transfer (FT) and labor migration (LM) in China.



**Table 1.** *Cont.*

Before calculating the CCD of FT and LM, the study determined each index's weight used the mean variance decision method. The specific steps are as follows: Firstly, to find a solution to the issue of significant differences in evaluation indicators, the extreme method is used to standardize the original indexes in the evaluation index system of FT and LM. The formula can be described by Equations (1) and (2):

$$\text{Benefit Indicator}: X'\_{i\bar{j}} = \frac{X\_{i\bar{j}} - X\_{\text{min}}}{X\_{\text{max}} - X\_{\text{min}}} \tag{1}$$

$$\text{Coat Indicator}: X'\_{ij} = \frac{X\_{\text{max}} - X\_{ij}}{X\_{\text{max}} - X\_{\text{min}}} \tag{2}$$

The *Xij*, *X ij* represent the original and standardized values of the index, and the j index's maximum and minimum values are respectively represented by *Xmax* and *Xmin.*

The determination of the index weight has an important influence on the accuracy and objectivity of the evaluation results. We select the mean variance decision method in the objective empowerment method to determine the index weight and obtain the weight of each criterion layer and each index. The formula can be described by Equations (3)–(6):

$$E(s) = \frac{1}{n} \sum\_{i=1}^{n} Z\_{ij} \tag{3}$$

$$\sigma(\mathcal{S}\_i) = \sqrt{\sum\_{i=1}^n Z\_{i\bar{j}} - E(\mathcal{S}\_i^2)} \tag{4}$$

$$w\_i = \sigma(S\_i) / \sum\_{j=1}^{m} \sigma(S\_j) \tag{5}$$

$$D\_i(w) = \sum\_{j=1}^{m} Z\_{ij} w\_i \tag{6}$$

In the formula, *E(s)* is the mean of a random variable, *σ(Si)* is the mean variance of *Si*, *wi* is the weight factor of *Si*, and *Di (w)* is the multi-indicator decision and ranking.

#### 2.3.2. Linear Weighting Method

Based on the standardized weight and value of each index, drawing on the relevant research results [49], the evaluation index of FT and LM is calculated by linear weighting method. The formula can be described by Equations (7) and (8):

$$f(\mathbf{x}) = \sum\_{i=1}^{m} w\_i \mathbf{x}\_{ij} \tag{7}$$

$$\mathbf{g}(\mathbf{x}) = \sum\_{j=1}^{n} w\_j \mathbf{x}\_{ij} \tag{8}$$

The *f(x)* and *g(x)* indicate the evaluation index of FT and LM, *wi* and *wj* represent the index weights of FT and LM, respectively, and the index value following standardization is *xij*.

#### 2.3.3. CCDM

In order to study the level of CCD between FT and LM, the study referred to relevant research [50], and constructed the coupling coordination degree model (CCDM). The formula can be described by Equations (9)–(11):

$$\mathcal{C} = \left\{ \frac{f(\mathbf{x}) \times g(\mathbf{x})}{\left[\frac{f(\mathbf{x}) + g(\mathbf{x})}{2}\right]^2} \right\}^{\frac{1}{2}} \tag{9}$$

$$D = \sqrt{\mathbb{C} \times T} \tag{10}$$

$$T = \mathfrak{a}f(\mathfrak{x}) + \mathfrak{z}\mathfrak{g}(\mathfrak{x})\tag{11}$$

where *C* is the coupling degree (CD) of FT and LM, *D* is the CCD of FT and LM, and *T* is the comprehensive evaluation index of them. *α* and *β* are the pending coefficients of FT and LM, respectively. The study accepts that the two subsystems of FT and LM are similarly significant, so the pending coefficient is α = β = 0.5.

Referring to the correlation study [51], the CCD between FT and LM was divided into 10 grades by using the uniform function distribution method (Table 2).


**Table 2.** Classification standards for coupling and coordination degree.

#### 2.3.4. ESDA Method

When carrying out the overall research on the provinces in China, we ought to follow a mix of overall and local development, propose a top-level design based on the strategic height, and formulate the coordinated development strategy of spatial linkage. Therefore, spatial analysis should also be introduced when analyzing the relevant problems of the provinces in China. According to the relevant literature [52,53], the study used the ESDA method to analyze the CCD, and studied the spatial agglomeration, dispersion, and interaction mechanism by describing and visualizing their spatial layout, which is typically divided into global and local spatial autocorrelations. A global *Moran's I* was used to calculate global spatial autocorrelation in order to show how the CCD of FT and LM were distributed across the entire space. The formula is as follows:

$$\mathbf{I} = \frac{\mathbf{M}}{\mathbf{S}\_0} \times \frac{\sum\_{i=1}^{M} \sum\_{j=1}^{M} w\_{ij} \left( \mathbf{X}\_i - \overline{\mathbf{X}} \right) \left( \mathbf{X}\_j - \overline{\mathbf{X}} \right)}{\sum\_{j=1}^{M} \left( \mathbf{X}\_i - \overline{\mathbf{X}} \right)^2} \tag{12}$$

where *M* is the number of the study regions, and *Xi* and *X* represent the observed value and average value, respectively. The study regions *i* and *j* are weighted spatially as *wij*, and the space adjacent is 1 and space non-adjacent is 0. the range of the *Moran's I* values is [−1,1], where a value larger than 0 indicates a positive correlation and a value lower than 0 indicates a negative correlation.

To determine the degree of spatial correlation and difference between the CCD of FT and LM in neighboring provinces, the local spatial autocorrelation test was calculated using local *Moran's I.* The formula is as follows:

$$I\_i = Z\_i \sum\_{i=1}^{M} W\_{ij} Z\_j \tag{13}$$

where *Wij* are the spatial weights, while *Zi* and *Zj* are the normalized values of the observed values in the study regions *i* and *j*, respectively.

#### 2.3.5. GRA Model

The driving factors of CCD of FT and LM were examined using the GRA model in 30 provinces in China [54]. The following is the workflow: Find out the feature sequence and the factor sequence. The characteristic sequence, which is denoted by *Y0(m,t)*, is the CCD of FT and LM. Each driver was selected as the factor sequence and represented by *Xi(m,t)*. Next, the grey correlation coefficients were determined. The formula can be described by Equation (14):

$$r\_i(m, t) = \frac{\min\_{i, m, t} \left| Y\_0'(m, t) - X\_i'(m, t) \right| + \rho \times \max\_{i, m, t} \left| Y\_0'(m, t) - X\_i'(m, t) \right|}{\left| Y\_0'(m, t) - X\_i'(m, t) \right| + \rho \times \max\_{i, m, t} \left| Y\_0'(m, t) - X\_i'(m, t) \right|} \tag{14}$$

Among them, *Y 0(m,t)* and *X i(m,t)* represent the feature and factor sequences after standardized treatment, respectively, and the coefficient of resolution is *ρ* (*ρ* = 0.5).

Finally, we calculated the grey correlation degree of the panel data by Equation (15):

$$r\_i = \frac{1}{M \times T} \sum\_{m=1}^{M} \sum\_{t=1}^{N} r\_i(m, t) \tag{15}$$

In the formula, *ri* represents the gray correlation degree, where the larger the *ri* value, the stronger the correlation between the feature sequence and the factor sequence and the weaker the correlation.

#### **3. Results**

#### *3.1. The Integrated Level of FT and LM Has Changed over Time in a Time Series*

The level of China's LM evaluation index was relatively high from 2015 to 2019, with an overall slight upward trend but obvious fluctuations, soaring to 0.5082 in 2019, up from 0.4958 in 2015, representing an average annual growth rate of 0.50%. While the index level showed a small decline from 2016 to 2017 and started to rise after reaching a minimum value in 2017. The evaluation index of FT fluctuated from 0.3798 in 2015 to 0.4009 in 2019, with an annual growth rate of 1.11% on average, and showed a good upward trend in all years except for a short decline in 2016. It benefited from the improvement of the level of FT and LM, the comprehensive evaluation index of them in China increased from 0.4378 in 2015 to 0.4546 in 2019, with an annual growth rate of 0.76% on average, and the comprehensive evaluation index during the study period showed a stable upward trend without obvious differences in the rate of change. For details, see Figure 2.

**Figure 2.** Farmland transfer (FT) and labor migration (LM) evaluation index and comprehensive evaluation index in China (2015–2019).

There are great differences in provincial FT, LM, and comprehensive evaluation index levels in China. The national average values of FT and LM evaluation indexes were only 0.3750 and 0.4882, respectively, from 2015 to 2019, whereas the comprehensive evaluation index only had an average value of 0.4316 (Figure 3). Among them, 21 provinces had the evaluation indexes of FT higher than the national average value, showing the spatial distribution characteristics of northeast region > central region > eastern region > western region. In total, 11 provinces had the evaluation indexes of LM higher than the national average value, showing the spatial distribution characteristics of central region > eastern region > western region > northeast region. Under the interaction of FT index and LM index in 30 provinces, there were 16 provinces with comprehensive evaluation index higher than the national average value, forming the spatial distribution characteristics of central region > eastern region > northeast region > western region.

**Figure 3.** Average evaluation index of farmland transfer (FT) and labor migration (LM) and comprehensive evaluation index in China (2015–2019).

#### *3.2. Spatio-Temporal Evolution of the CCD between FT and LM*

The CDs of FT and LM in China from 2015 to 2019 were all higher than 0.970, indicating that the CD of FT and LM reached a high level of coupling and tends to be stable. While the CCD between FT and LM in China showed a tendency of upward and fluctuate, from 2015 to 2019, the CCD increased from 0.6558 to 0.6695, reaching the overall primary coupling coordination; however, the average annual growth rate was only 0.42%, which was relatively slow. The CCD of FT and LM had a large difference among regions, showing a distribution pattern of central region > eastern region > northeast region > western region. Among them, the central region had the highest level of coupling coordination between FT and LM, with an excellent upward trend, and the CCD fluctuated between 0.6692 and 0.6917, with an annual growth rate of 0.67% on average, which was at the middle and late stage of primary coupling coordination. Followed by the eastern region, the CCD decreased from 0.6654 to 0.6599, with an annual growth rate of −0.17% on average, and the CCD showed a slight downward trend. The northeast region ranked the third, with the CCD rising from 0.6420 to 0.6427, with an average annual growth rate of 0.02% and a relatively slow upward trend. The western region had the lowest coupling coordination level, rising from 0.6292 to 0.6346, with an annual growth rate of only 0.17% on average. For details, see Figure 4.

**Figure 4.** The development trend of coupling and coordination of farmland transfer (FT) and labor migration (LM) in China (2015–2019).

The CD of FT and LM of provinces in China from 2015 to 2019 was consistent with the overall national coupling degree and reached a high level of coupling. Except for Guangdong (0.942), the coupling degrees of FT and LM in all other provinces were above 0.950. In contrast, the CCDs of FT and LM in provinces of China were not high. The national average value was 0.6542, while most provinces had CCDs between 0.60 and 0.70, which was at a primary coupling coordination level (Table 3). Particularly, there were 15 provinces with CCD of FT and LM higher than the national average value, accounting for 50.00%, among which five provinces, including Shanghai (0.7450), Jiangsu (0.7361), Heilongjiang (0.7155), Anhui (0.7107), and Chongqing (0.7003) had the highest level of coupling coordination, with the average value higher than 0.70, which was at the early stage of the middle coupling coordination, accounting for 16.67% over the country. The CCDs of 10 provinces, including Zhejiang, Henan, and Hubei, were between 0.6578 and 0.6916, which were at the middle and late stage of primary coupling coordination, accounting for 33.33% of the country. There were 15 provinces with the CCD of FT and LM lower than the national average, accounting for 50.00% nationwide, among which 12 provinces, including Shandong, Inner Mongolia, and Guangdong, had the CCD between 0.6047 and 0.6502, and were at the middle and early stage of primary coupling coordination, accounting for 40.00% nationwide. Three provinces including Liaoning, Yunnan, and Hainan, had the CCD between 0.5411 and 0.5913 and were at the level of barely coupling coordination, accounting for 10.00% nationwide. Therefore, at this stage, there are still obvious regional differences in the CCD between FT and LM in 30 provinces in China. Although all of them have reached the coupling coordination, the coordination levels of most provinces are relatively low, and there is still large room for growth.


**Table 3.** The mean degree of the coupling and coupled coordination of farmland transfer (FT) and labor migration (LM) in China (2015–2019).
