1. Introduction

2. Theoretical Analysis and Research Hypotheses

2.1. Theoretical Analysis

2.1.1. The ""Rational Man"" Hypothesis and Cropland Abandonment

The "rational man" assumption is one of the most basic assumptions of economics, which is the cornerstone of the entire economic theory [70], and can effectively explain why farmers choose to abandon their farmland.

According to the "rational man" hypothesis, every individual is a "rational man", and farmers are no exception, whose biggest goal is to maximize their own interests, with the same motivation as that of the micro subjects of the market economy [28]. As a "rational person", farmers weigh the long-term and short-term interests and risk factors to make decisions in order to maximize the benefits [71]. Therefore, when the benefits of agricultural production cannot be maximized, farmers will gradually leave the field. The damage of maximizing the benefits of agricultural production is closely related to the impact of urbanization and industrialization, changes in market demand, fluctuations in agricultural prices, adjustments in agricultural policies and systems, and advances in agricultural technology [3]. Among them, the promotion of urbanization and industrialization plays the most obvious role, and its various impacts can effectively explain the phenomenon of farmland abandonment.

On the one hand, the advancement of urbanization and industrialization will lead to the marginalization of cropland, which is the root cause of cropland abandonment and an important driving force for farmers to choose cropland abandonment. The so-called marginalization of cropland, that is, when a piece of cropland has only one alternative use, due to changes in production costs and income, the profit of the cropland falls to zero or negative, that is, the cropland is outside the no-rent margin; and no matter how the farmers adjust the inputs of factors of production of the cropland is outside the no-rent margin, then as a "rational person", the farmers will choose not to operate this cropland. Then the farmer as a "rational person" chooses not to operate this piece of farmland, resulting in the abandonment of farmland [3]. The advancement of urbanization and industrialization will mainly bring changes in labor factors, which provide non-farm employment opportunities and increase non-farm income, making the price of agricultural labor rise rapidly, resulting in the increase of the cost of farming, thus compressing the profitability of agricultural production, so that farmers can not continue to maximize the benefits of engaging in agricultural production, and turn to the non-farm employment field.

On the other hand, the process of urbanization and industrialization provides the possibility and opportunity for farmers to maximize their benefits in non-farm employment, which further exerts a pull on farmers to choose to leave their farmland abandoned. With the massive influx of rural population into the cities, the livelihood strategy of farm households has gradually changed to part-time employment and non-farming, and the maximized benefits they can obtain are specifically manifested in both economic and non-economic gains [70]. From the point of view of economic gain, generally speaking, the part-time and non-farming livelihood strategy has higher economic gain compared with traditional agriculture, and can realize the maximization of economic gain; from the point of view of non-economic gain, due to the long-term existence of the urban-rural dichotomous structure, there is a big difference between urban and rural areas in terms of the social security system, health care conditions, and educational resources, etc. [72], the rural households from the countryside to the city, and they also can enjoy the more superior living conditions in the city and maximize non-economic gains.

2.1.2. The Sustainable Livelihoods Analytical Framework and the Cropland Desertification Phenomenon

The sustainable livelihood analysis method has been widely used in related research in many fields as well as deriving diversified sustainable livelihood analysis frameworks, among which, the Sustainable Livelihoods Framework (SLA) proposed by the UK Department for International Development (DFID) is used relatively frequently [73,74].

Figure 1. DFID Sustainable Livelihoods Analytical Framework.

Figure 1. DFID Sustainable Livelihoods Analytical Framework.

The framework consists of five components: vulnerability background, structural and institutional change, livelihood capital, livelihood strategy and livelihood output [75,76,77,78], which provides a theoretical basis for exploring the influencing factors that farmers consider when choosing to abandon their farmland.

From the analysis of the "rational man" hypothesis, it can be seen that, as one of the livelihood strategies of farmers, there is a motivation to maximize the benefits behind the choice of farmland abandonment. However, from the perspective of the sustainable livelihood analysis framework, the adjustment of the livelihood strategy of farmers cannot be arbitrary, but is determined by the status of their livelihood capital [74]. The advancement of urbanization and industrialization, changes in market demand, and fluctuations in agricultural prices are essentially part of the vulnerability background and structural and institutional shifts in the framework of sustainable livelihoods, which are uniformly defined in this study as exogenous shocks, which, while leading to the failure to maximize the returns from agricultural production, also have an impact on various types of livelihood capitals of the farm households, and thus affect the choices of their livelihood strategies.

At the meanwhile, the choice of farmland abandonment is not only stimulated by their own livelihood capital, but also by the influence of external natural and socio-economic factors [74]. Nevertheless, most of the existing studies based on the framework of sustainable livelihood analysis to explore the factors influencing livelihood strategies have ignored the external environmental context or confused it with livelihood capital [73], and the conclusions obtained are not comprehensive and accurate. In view of this, this study extends and improves the status quo sustainable livelihood analysis framework by analyzing the external environmental background faced by farmers when choosing whether to leave their farmland abandoned or not, which can be categorized into two types: first, the external shocks consisting of the vulnerability background and the structural and institutional shifts; and second, the characteristics of the village that have the most direct and close relationship with the farmers. China is the world's largest developing country, in order to ensure food security and achieve long-term sustainable development, cropland protection and agricultural production have always been highly valued by the party and the state, the vulnerability background and structural and institutional changes faced by farmers in the process of agricultural production are basically the same in all regions [79]; and villages, due to the relatively microscopic spatial scale, have obvious differences in the natural geographic features and socio-economic features and are easy to recognize. Therefore, this study analyzes village characteristics as specific variables, and the purpose of exploring external shocks is mainly to make the theoretical analysis relatively complete.

In summary, when choosing whether or not to leave farmland abandoned, farmers should consider their own livelihood capital and village characteristics comprehensively. It has been shown that farmers are nested within villages, and the data on cropland abandonment has a nested structure, therefore, the impacts of farmers' livelihood capital and village characteristics on farmers' choice of cropland abandonment have both individual and background effects, and it is necessary to pay attention to the independent impacts of the factors at each level as well as analyze the interactions of the factors at different levels, and in this study, we focus on the moderating effect of the village-level factors on the impacts of the factors at the farmer level on the cropland abandonment. This study focuses on the moderating effect of village-level factors on the impact of farm household-level factors on cropland abandonment.

2.1.3. Theoretical Analysis Framework

By integrating the "rational man" hypothesis and the sustainable livelihood analysis framework with the relevant content of farmland abandonment, the theoretical analysis framework is constructed by focusing on the individual and background effects of factors at the household and village levels that farmers consider when choosing whether or not to abandon their farmland.

Figure 2. Theoretical analysis framework.

Figure 2. Theoretical analysis framework.

The analytical framework shows that in the face of external shocks that prevent agricultural production from continuing to maximize benefits, farmers, as "rational beings", will adjust their livelihood strategies and shift from traditional agriculture to part-time farming and off-farming, in order to achieve the expected livelihood outcomes and continue to maximize their benefits. However, the process by which farmers adjust their livelihood strategies in order to continue to maximize their benefits is not random; on the one hand, it is influenced by their own livelihood capital, which changes as a result of external shocks; on the other hand, it is also important to take into account the role of external factors, and this study focuses on analyzing the relevant factors at the village level, which is the level that is the most closely related to the farmers. Finally, whether farmers choose to abandon their farmland or not is the result of the nested structure of influencing factors at the farmer and village levels, and when considering the specific influence of factors at each level, it is not possible to analyze them at the same level, and it is necessary to fully identify their individual and background effects, and to explore the moderating effect of village-level factors on the influence of farmer-level factors on cropland abandonment on the basis of clarifying the influence of factors at each level on cropland abandonment.

3. Data Sources and Research Methodology

3.2. Variable Identification and Indicator System

3.2.1. Explained Variables

To measure cropland abandonment, there are two types of variables commonly used in academia, discrete and continuous, of which the discrete variable is whether or not to abandon the cropland; and the continuous variable is the area of abandonment and the rate of abandonment of cropland. In this study, we believe that the use of the dummy variable of whether to abandon or not to abandon reflects the abandonment behavior of farm households, which will lose a lot of important information [32]; at the same time, there is a significant difference in the size of the cultivated area in each region, and the abandonment area ignores the positive correlation between the number of abandoned areas and the total area of cropland, which is also insufficient for this measurement. In light of this, in order to more accurately measure the phenomenon of cropland abandonment, the abandonment rate, i.e., the ratio of the area of cropland left abandoned by households to the total area of cropland in the household, was selected as the explanatory variable in this study.

3.2.2. Explanatory Variables

(1) Farm household level (Level-1) explanatory variables

Based on the livelihood capital in the sustainable livelihood analysis framework, this study selects farm household level explanatory variables from the five aspects of human, natural, physical, financial and social capital, taking into account existing research and data availability. ①Human capital: covering the quantity and quality of labor, this study selects the size of the household to characterize the quantity of labor; the head of the household, as the head of the family, has an important influence on the choice of household livelihood strategies, and selects whether the head of the household has a high school education or higher and whether the head of the household is physically healthier to characterize the quality of labor. ②Natural capital: the focus is on tangible productive capital, mainly cropland resources, which is the objective object of abandonment. This study analyzes the quantity and quality of cropland, of which the per capita area of cropland and the ratio of transferred cropland characterize the quantity of cropland, and whether there is pollution of cropland characterizes the quality of cropland. ③Physical capital: This includes infrastructure and public services and means of production. In China, the government sector, as the main provider of infrastructure and public services, strongly guarantees that farmers can enjoy basically the same infrastructure and public services in each region. Therefore, this study focuses on the means of production of farm households, which are characterized by whether they own large-scale agricultural production machinery used for agricultural production or whether the number of livestock and household durable goods reaches five or more types. ④Financial capital: mainly examining the inflow of funds, in order to more accurately and comprehensively reflect the inflow of funds to the farm household, this study from the per capita and the proportion of the two dimensions, the total annual income of the family per capita, agricultural income and non-agricultural income of the three aspects of the logarithm of the total annual income of the family per capita, the share of agricultural income and non-agricultural income accounted for the proportion of the three indicators were selected. ⑤Social capital: mainly derived from social organizations and social networks, in this study, the participation in social organizations is characterized by whether or not there is a village in the ministry, and the logarithm of annual human expenditure and whether or not they use the Internet are selected to characterize social networks.

(2) Village level (Level-2) explanatory variables

In this study, village-level explanatory variables were selected from the aspects of natural geographic characteristics and socio-economic characteristics. ①Physical geographic characteristics: mainly reflecting the topography and location of the village, covering three indicators: commuting distance, whether it is a suburb of a large or medium-sized city, and the topography of the village. ②Socio-economic characteristics: emphasize the industrial development and policy implementation of the village, including the ratio of the number of agricultural producers in the village, the presence of non-agricultural enterprises, whether the implementation of agricultural services and whether the village has experienced land expropriation.

3.2.3. Indicator System

Based on the results of variable identification, the indicator system of the causes of cropland abandonment is constructed. At the same time, according to the existing research in the academic world, combined with its own data characteristics and the actual situation, this study predicts the direction of the role of the variables.

Table 1. Indicator system of causes of cropland abandonment.

Table 1. Indicator system of causes of cropland abandonment.

Level	Variable Type	Variable Group	Variable Name and Symbol	Variable Definition and Assignment	Intended Effect
	Explained variable		Abandonment rate (QGZB)	Proportion of land abandoned by farmers to total cultivated area(%)
Farm household level	Explanatory variable	Human capital	Do household heads have a high school diploma or higher (EDU)	No = 0; Yes = 1	+
			Whether the head of household is in relatively good health (HEAL)	No = 0; Yes = 1	-
			Household size (JTRKGM)	Sum of persons living with the family and persons away from the family (person)	-
		Natural capital	Cropland area per capita (RJGDMJ)	Ratio of area of cropland owned by households to total population size (acre/person)	-
			Ratio of transferred cropland (ZRGDB)	Proportion of area of cropland transferred by households to total area of cropland (%)	-
			Presence of contaminated cropland (TRWR)	No = 0; Yes = 1	-
		Physical capital	Ownership of large agricultural production machinery or livestock for agricultural production (SCGJ)	No = 0; Yes = 1	-
			Whether the number of types of durable goods in the household is five or more (NYZL)	No = 0; Yes = 1	+
		Financial capital	Total log annual household income per capita (LNRJSR)	Logarithm of the ratio of the sum of all types of household income in a year to the size of the household (yuan)	+
			Agricultural income ratio (NYSRB)	Share of annual household income from agriculture in total annual household income (%)	-
			Non-farm income ratio (FNSRB)	Household annual non-farm income as a share of total annual household income (%)	+
		Social capital	Availability of village cadres (CGB)	No = 0; Yes = 1	-
			Log of annual expenditure on favours (LNRQZC)	Total household expenditure on gifts and gratuities in a year (yuan)	±
			Use of the Internet or not (HLWQK)	No = 0; Yes = 1	±
Village level	Explanatory variable	Physical geographic characteristics	Commute distance (TQJL)	Distance of villages from township offices (kilometers)	-
			Whether it is a suburb of a medium-sized city (DLWZ)	No = 0; Yes = 1	+
			Topography of the village is plain or not (CZDX)	No = 0; Yes = 1	-
		Socio-economic characteristics	Number of village agricultural producers (CZNYSCB)	Percentage of people engaged in agriculture in villages compared to the total number of people in villages (%)	-
			Availability of non-farm enterprises (FNQY)	No = 0; Yes = 1	+
			Whether or not to implement agricultural services (HNFW)	No = 0; Yes = 1	-
			Experiencing land expropriation or not (TDZY)	No = 0; Yes = 1	+

3.2.4. Descriptive Statistics of Variables

Descriptive statistics of the selected explained and explanatory variables were performed using HLM 6.08 software.

Table 2. Results of descriptive statistics of variables.

Table 2. Results of descriptive statistics of variables.

Variable Type	Variable Name	Sample Size	Mean	Standard Deviation	Min	Max
Explained variable	QGZB	13120	8.75	24.92	0.00	100.00
Farm household level explanatory variables	EDU	13120	0.09	0.29	0.00	1.00
	HEAL	13120	0.54	0.50	0.00	1.00
	JTRKGM	13120	5.17	2.75	1.00	15.00
	RJGDMJ	13120	1.68	2.58	0.02	50.00
	ZRGDB	13120	5.58	18.65	0.00	100.00
	TRWR	13120	0.49	0.50	0.00	1.00
	SCGJ	13120	0.12	0.32	0.00	1.00
	NYZL	13120	0.39	0.49	0.00	1.00
	LNRJSR	13120	8.39	1.21	0.18	12.21
	NYSRB	13120	36.85	42.70	0.00	100.00
	FNSRB	13120	39.77	44.09	0.00	100.00
	CGB	13120	0.01	0.10	0.00	1.00
	LNRQZC	13120	5.39	3.65	0.00	9.90
	HLWQK	13120	0.41	0.49	0.00	1.00
Village level explanatory variables	TQJL	645	5.68	5.22	0.00	30.00
	DLWZ	645	0.07	0.26	0.00	1.00
	CZDX	645	0.41	0.49	0.00	1.00
	CZNYSCB	645	64.51	34.09	0.00	100.00
	FNQY	645	0.27	0.45	0.00	1.00
	HNFW	645	0.84	0.37	0.00	1.00
	TDZY	645	0.47	0.50	0.00	1.00

4. Analysis of Empirical Results

4.1. Normality Test of the Explanatory Variables

The hierarchical linear model requires that the explained variables must satisfy the condition of obeying normal distribution, which is loosely approximated to satisfy the condition of obeying normal distribution [83]. Therefore, in this study, the skewness and kurtosis tests were chosen to test the normality of the abandonment rate with the help of SPSS 22.0 software.

Table 3 shows that the skewness value of 2.953 (standard error 0.021), Z-score = 2.953/0.021 = 140.619 and the kurtosis value of 7.420 (standard error 0.043), Z-score = 7.420/0.043 = 172.558. The skewness and kurtosis values are both >0 and the Z-score is not in the range of ±1.96, which indicates that the that the explanatory variables do not obey normal distribution. However, some studies in academia have shown that when the kurtosis is 7.420 less than 10 and the skewness is 2.953 less than 3, this indicates that the data is not absolutely normally distributed but basically acceptable as normal distribution [84], therefore the data is capable of stratification study.

Table 3. Results of normality test for explained variables.

Table 3. Results of normality test for explained variables.

Variable Name	Sample Size	Mean	Standard Deviation	Skewness		Kurtosis
				Skewness value	standard error	Kurtosis value	standard error
QGZB	13120	8.751	24.924	2.953	0.021	7.420	0.043

4.2. Null Model

The so-called null model, which is a model with no explanatory variables in each level of the model, is the first step in the analysis of the hierarchical model, aiming to decompose the overall variance of the abandonment rate at the levels of farmers and villages, and to judge the necessity of the Level-2 model. The specific form of the model is shown below:

Level-1 model:

$${QGZB}_{ij}={\beta }_{0j}+{\gamma }_{ij}$$

(2)

Level-2 model:

$${\beta }_{0j}={\gamma }_{00}+{\mu }_{0j}$$

In Equation (2), the variables have the same meaning as in equation (1).

The results of model confidence estimation showed that the confidence of Level-1 intercept was estimated to be 0.765, and the higher the confidence, the smaller the variance of the error, and the closer the estimated farm abandonment rate fitted by the model was to the actual abandonment rate. In general, if the model estimated confidence > 0.5, the model can be considered to basically meet the requirements [85]. Fixed effects showed that the overall mean of the abandonment rate for all villages was 9.0206%. The chi-square test for random effects showed that there was an extremely significant difference in the rate of farm abandonment at the village level (P=0.000), i.e., the village level factors had an important influence on the rate of farm abandonment, and it was necessary to add some explanatory variables in the Level-2 model. Using the intragroup correlation coefficient (ICC) formula, the intragroup correlation coefficient of the model can be calculated as 101.9664/(101.9664+521.0150)=0.1637. Generally speaking, this value is greater than 0.059, which belongs to the medium degree of intragroup correlation, and it can be applied to the HLM analysis [86,87]. This value indicates that 16.37% of the variance in farm abandonment rate is village variance and the remaining 83.63% is farm household variance. This shows that although farm household differences are the main cause of differences in abandonment rates, the effect of village differences on them should not be underestimated.

Table 4. Null model estimation results.

Table 4. Null model estimation results.

Fixed Effects and Significance test				Random effects and significance test
Parameters	Regression coefficient	T-test	P-value	Parameters	Standard Deviation	Variance component	Chi-square test	P-value
γ00	9.0206	19.8610	0.000	μ0	10.0978	101.9664	3164.5207	0.000
				r	22.8258	521.0150

4.3. Random Effects Regression Model

The random effects regression model, which included only Level-1 variables and did not include village-level variables in the equation, was used to determine the effect of Level-1 variables on the explanatory variables and to determine whether the intercept and regression coefficients of Level-1 variables had significant variation at the village level. In order to improve the accuracy of the full model, this study first used a one-factor random effects regression model to investigate the influence of individual explanatory variables of Level-1 on the abandonment rate [87]; after that, we screened the factors with significant influence in the one-factor model and constructed a multifactor random effects regression model.

4.3.1. One-factor Random Effects Regression Model

Taking the abandonment rate as the explained variable, Level-1 variables were introduced one by one in a non-centralized way to construct a one-factor random effects regression model, and no variables were introduced in the Level-2 model. The effect of farmer-level variables on abandonment rate was tested by the fixed effects statistics of the model. The specific form of the model is shown below:

Level-1 model:

$$\begin{gathered} {QGZB}_{ij}={\beta }_{0j}+{\beta }_{1j}\left[{EDU}_{ij}/{HEAL}_{ij}/{JTRKGM}_{ij}/{RJGDMJ}_{ij}/{ZRGDB}_{ij}/{TRWR}_{ij}/{SCGJ}_{ij}/{NYZL}_{ij}/ \\ {LNRJSR}_{ij}/{NYSRB}_{ij}/{FNSRB}_{ij}/{CGB}_{ij}/{LNRQZC}_{ij}/{HLWQK}_{ij}\right]+{\gamma }_{ij} \end{gathered}$$

(3)

Level-2 model:

$$\begin{gathered} {\beta }_{0j}={\gamma }_{00}+{\mu }_{0j} \\ {\beta }_{1j}={\gamma }_{10}+{\mu }_{1j} \end{gathered}$$

In Equation (3), EDU_ij is the education level of the head of the household of the i_th farm household in the j_th village, and the rest of the Level-1 explanatory variables have similar meanings and represent the livelihood capital situation of each farm household in each village; the other variables have the same meanings as in equation (1).

Table 5. Fixed effects estimates of one-factor random effects regression models.

Table 5. Fixed effects estimates of one-factor random effects regression models.

Variable Name	Regression coefficient	standard error	T-test	P-value
EDU	-0.5046	0.6864	-0.735	0.462
HEAL	-1.6655	0.4355	-3.824	0.000***
JTRKGM	-0.0124	0.1004	-0.124	0.902
RJGDMJ	-0.5925	0.0523	-11.341	0.000***
ZRGDB	-0.0617	0.0086	-7.213	0.000***
TRWR	-0.4463	0.5051	-0.884	0.378
SCGJ	-4.3581	0.5950	-7.325	0.000***
NYZL	-0.6327	0.4236	-1.494	0.136
LNRJSR	-0.3407	0.2185	-1.559	0.119
NYSRB	-0.0872	0.0061	-14.313	0.000***
FNSRB	0.0431	0.0061	7.078	0.000***
CGB	-2.7299	1.2966	-2.105	0.035**
LNRQZC	-0.0250	0.0641	-0.390	0.697
HLWQK	-0.2000	0.4305	-0.465	0.642

Note: P < 0.01, extremely significant, labeled ***; P<0.05, significant, labeled **; P<0.1, generally significant, labeled *.

The fixed effects estimation results of the one-factor random effects regression model show that the human capital, natural capital, physical capital, financial capital and social capital of farmers have different degrees of influence on the abandonment rate.

(1) Among human capital, whether the head of household is relatively healthy has an extremely significant negative effect on the abandonment rate of farm households, which is consistent with the expected direction of the effect, indicating that the healthier the head of household is, the lower the abandonment rate of farm households. This may be because the head of household plays a major role in determining the direction and content of household production and management activities, and the healthier the head of household is, the more energy and stamina he or she will have to engage in a variety of production activities, including agricultural production, and the farmland will not be easily abandoned [88,89]. (2) In natural capital, the per capita cropland area and the ratio of transferred cropland have extremely significant negative impacts on the abandonment rate of farm households, which is consistent with the expected direction of action, indicating that the larger the per capita cropland area and the higher the ratio of transferred cropland, the lower the abandonment rate of farm households. This may be because the number of cropland is an important guarantee of cropland yield, the larger the per capita cropland area, the better the cropland resource endowment of the farmers, the more convenient the scale and mechanization of production and operation, the cropland yield and agricultural income are guaranteed, and the cropland is not easy to be abandoned [89,90]; the purpose of the farmers transferring to other people's cropland is the same in order to realize the scale of operation, and to seek a higher agricultural income, so when the total cropland area has a larger area of transferred cropland, in order to obtain agricultural income that is greater than the cost of land parcels, farmers tend to continue to engage in agricultural production [91]. (3) Among the physical capital, whether or not to own large agricultural production machinery or livestock used for agricultural production has an extremely significant negative effect on the abandonment rate of farm households, which is consistent with the expected direction of the effect, which indicates that the abandonment rate of farm households who own agricultural production machinery or livestock is lower. This may be because agricultural production equipment or livestock as a supporting facility for agricultural production, not only can make farmers operate a larger area of farmland, improve yields and increase agricultural income; and enough to reduce the input of agricultural labor, prompting farmers to have the opportunity to engage in a variety of production and management activities, the abandonment rate of farmland is not easy to be abandoned [92,93]. (4) In financial capital, the agricultural income ratio has an extremely significant negative effect on the abandonment rate of farm households, while the non-farm income ratio has an extremely significant positive effect on the abandonment rate of farm households, which is consistent with the expected direction of action, which indicates that the higher the agricultural income ratio, the lower the rate of abandonment of farm households [35,42]; the higher the non-farm income ratio, the higher the rate of abandonment of farm households, which may be due to the fact that the agricultural income ratio and the non-farm income ratio reflect the differences in the main sources of income of farm households, farm households relying on agricultural income may be less prone to abandonment of cropland, while farm households with predominantly non-farm income are more prone to abandonment of cropland [22,39]. (5) In social capital, the presence of village cadres has a significant negative effect on the abandonment rate of farm households, which is consistent with the expected direction of the effect. This may be because the village cadres in the farm household are more likely to understand the requirements of farmland protection policies, have a higher degree of awareness of the serious situation and importance of farmland protection, and need to play a good role as a model for farmland protection, so that the rate of abandonment of farmland is lower [89,94].

4.3.2. Multi-factor Random Effects Regression Model

Based on the statistical results of the one-factor model, a multi-factor random effects regression model is constructed. Taking the abandonment rate as the explained variable, the Level-1 variables in the one-factor model, which have a significant effect on the abandonment rate, are added to the Level-1 model in a non-centralized way, and no variables are added to the Level-2 model. The specific form of the model is shown below:

Level-1 model:

$$\begin{gathered} {QGZB}_{ij}={\beta }_{0j}+{\beta }_{1j}{HEAL}_{ij}+{\beta }_{2j}{RJGDMJ}_{ij}+{\beta }_{3j}{ZRGDB}_{ij}+{\beta }_{4j}{SCGJ}_{ij} \\ +{\beta }_{5j}{NYSRB}_{ij}+{\beta }_{6j}{FNSRB}_{ij}+{\beta }_{7j}{CGB}_{ij}+{\gamma }_{ij} \end{gathered}$$

(4)

Level-2 model:

$$\begin{gathered} {\beta }_{0j}={\gamma }_{00}+{\mu }_{0j} \\ {\beta }_{1j}={\gamma }_{10}+{\mu }_{1j} \\ {\beta }_{2j}={\gamma }_{20}+{\mu }_{2j} \\ {\beta }_{3j}={\gamma }_{30}+{\mu }_{3j} \\ {\beta }_{4j}={\gamma }_{40}+{\mu }_{4j} \\ {\beta }_{5j}={\gamma }_{50}+{\mu }_{5j} \\ {\beta }_{6j}={\gamma }_{60}+{\mu }_{6j} \\ {\beta }_{7j}={\gamma }_{70}+{\mu }_{7j} \end{gathered}$$

In Equation (4), the variables have the same meaning as in equations (1) and (3).

Comparing the fixed effects estimation results of one-factor and multi-factor random effects regression models, it can be found that the overall impact trend of the regression coefficients of most of the indicators remains the same, and there are only different degrees of weak changes in the coefficient size, which may be due to the existence of multiple covariates among multiple variables in the multi-factor model [87]; among them, the impact of the non-farm income ratio on the abandonment of farmland rate is changed from a significant positive impact to a non-significant impact, and the probable reason is that the multicollinearity of this indicator is relatively large, which affects the regression results [87], in view of this, this study considered to exclude the non-farm income ratio in the full model in order to improve the reliability of the model regression results. Meanwhile, the fixed-effects estimation results show that the overall average of the abandonment rate of all villages is 13.2053%; the abandonment rate will decrease by 1.9220% if the head of the household is healthier; the abandonment rate will decrease by 0.1843% for every increase in per capita cropland area; the abandonment rate will decrease by 0.0374% for every increase in the ratio of transferred cropland by 1%; and for every increase in the ratio of transferred cropland by 1%; and for every increase in the ratio of households owning large agricultural production for agricultural The abandonment rate decreases by 2.3390% for households owning large agricultural machinery or livestock used for agricultural production; the abandonment rate decreases by 0.0792% for every 1% increase in the ratio of agricultural income; and the abandonment rate decreases by 3.8157% for households owning village cadres.

The results of the random effects estimates are used to characterize whether there is significant two-level variation in the regression coefficients of the intercept term and Level-1 variables. As can be seen from Table 6, (1) the chi-square test result of the intercept term is significant, with a p-value of 0.000, indicating that there are significant village differences in the mean value of farm abandonment rate among villages, and it is necessary to add the village-level variables in the subsequent analysis for the analysis of background effects; (2) the chi-square test results of the regression coefficients of the ratio of the transferred to cropland, the possession of large-scale agricultural production machinery or livestock used for agricultural production, and the ratio of the farm income on the abandonment rate of the farmers are significant, with p-values of 0.085, 0.040 and 0.000 respectively, that is, among different villages, there are significant inter-group differences in the negative impacts of the ratio of transferred cropland, the possession of large-scale agricultural production machinery or livestock used for agricultural production, and the ratio of agricultural income on the rate of abandonment of farming by farm households, and it is necessary to add village-level explanatory variables in the full model, to clarify the moderating effect of their effects on the impacts of household-level variables on the rate of abandonment; (3) the negative effects of other variables are relatively consistent across villages.

Table 6. Estimates of multifactor random effects regression models.

Table 6. Estimates of multifactor random effects regression models.

Variable Name	Fixed effects regression results			Random effects regression results
	Regression coefficient	standard error	T-test	Variance component	Chi-square test
γ00	13.2053	0.8196	16.112***	222.4776	141.8825***
HEAL	-1.9220	0.4144	-4.638***	3.3173	45.7651
RJGDMJ	-0.1843	0.0460	-4.006***	0.0344	47.4904
ZRGDB	-0.0374	0.0087	-4.300***	0.0022	55.0921*
SCGJ	-2.3390	0.5426	-4.310***	21.1288	59.3682**
NYSRB	-0.0792	0.0075	-10.522***	0.0124	84.2431***
FNSRB	0.0003	0.0078	0.036	0.0108	57.9672*
CGB	-3.8157	1.2928	-2.951***	22.7815	38.7926

Note: P < 0.01, extremely significant, labeled ***; P<0.05, significant, labeled **; P<0.1, generally significant, labeled *.

Comparing the Level-1 random effects estimation results of the multifactor random effects regression model and the null model [85], this study calculated the overall explanatory power of the Level-1 explanatory variables on the explained variables, and obtained that the variance shrinkage ratio of the Level-1 random term was (521.0150-484.4892)/ 521.0150=0.0701, which indicated that the head of household being relatively healthy, per capita area of cropland, ratio of transferred cropland, ownership of large agricultural production machinery or livestock for agricultural production, ratio of agricultural income, ratio of non-farm income, and presence of village cadres can explain 7.01% of the within-group variance in the rate of abandonment of farming by farm households.

4.4. Intercept Model

The intercept term in the Level-1 model was used as an explained variable, and the Level-2 variables were added to the Level-2 model in a non-centered manner to construct an intercept model in order to test whether the village level variables have a significant effect on the abandonment rate. The specific form of the model is shown below:

Level-1 model:

$${QGZB}_{ij}={\beta }_{0j}+{\gamma }_{ij}$$

(5)

Level-2 model:

$$\begin{gathered} {\beta }_{0j}={\gamma }_{00}+{\gamma }_{01}{TQJL}_j+{\gamma }_{02}{DLWZ}_j+{\gamma }_{03}{CZDX}_j+{\gamma }_{04}{CZNYSCB}_j+{\gamma }_{05}{FNQY}_j \\ +{\gamma }_{06}{HNFW}_j+{\gamma }_{07}{TDZY}_j{+\mu }_{0j} \end{gathered}$$

In Equation (5), TQJL_j is the commuting distance to the j_th village, and the rest of the Level-2 explanatory variables have similar meanings, which represent the physical geography and socio-economic situation of each village; the meanings of all other variables are the same as in equation (1).

The fixed effects estimation results show that the abandonment rates are all affected to varying degrees by the physical geographic and socio-economic characteristics of the villages.

Table 7 shows that the regression coefficients of five variables, namely, commuting distance, whether it is a suburb of a large or medium-sized city, whether the topography of the village is a plain or not, the ratio of the number of people in agricultural production in the village, and whether it has experienced land expropriation, passed the significance test for the intercept term β₀. Among them, commuting distance, whether the terrain of the village is plain or not, and the ratio of the number of agricultural producers in the village have extremely significant negative effects on the abandonment rate of farm households, which is consistent with the expected direction of effect; whether it is a suburb of a large or medium-sized city has a generally significant negative effect on the abandonment rate of farm households, which is opposite to the expected direction of effect; and whether it is experiencing land expropriation has a significant positive effect on the abandonment rate of farm households, which is consistent with the expected direction of effect. direction. An increase in commuting distance reduces the abandonment rate, probably because in villages with a long commuting distance, the farmers in the village have a heavier "land-loving plot", and the convenience of engaging in non-agricultural employment is relatively lower, which makes them more inclined to engage in agricultural production activities [95,96]. The flatter the topography of the village, the lower the rate of abandonment of farming, which may be due to the flat topography, more conducive to the scale of cultivated land and mechanized management, to improve agricultural income, and to maintain the incentive of agricultural production of farmers [21,25]. The higher the ratio of the number of people engaged in agricultural production in the village, the lower the abandonment rate, which may be due to the fact that farmers are prone to herd behavior and continue to operate cropland in such a production environment; at the same time, a large number of farmers engaged in agricultural production in the village also provides a relatively broad market for the transfer of agricultural land, which also reduces the abandonment rate of cropland [32,97]. The fact that villages are on the outskirts of large and medium-sized cities reduces the rate of cropland abandonment may be due to the fact that proximity to large and medium-sized cities, on the one hand, provides a relatively broad market for farmers' agricultural production activities and facilitates the sale of agricultural products; on the other hand, the convenient location provides the possibility for farmers to operate both agricultural and non-agricultural production activities at the same time. In villages that have experienced land expropriation, the abandonment rate will increase, probably because land expropriation will lead to the fragmentation of some farmers' farmland, resulting in the reduction of the area of farmland available for production and operation, which is not conducive to the realization of large-scale management and the transfer and trusteeship of farmland, reducing the incentive of farmers' agricultural production [21,32], and contributing to the increase in the rate of abandonment of farmland.

Table 7. Intercept model fixed effects estimation results.

Table 7. Intercept model fixed effects estimation results.

Variable Name	Regression coefficient	Standard error	T-test
γ00	15.3173	1.7085	8.965***
TQJL	-0.2571	0.0682	-3.771***
DLWZ	-2.5563	1.3533	-1.889*
CZDX	-4.7083	0.8881	-5.302***
CZNYSCB	-0.0586	0.0147	-3.993***
FNQY	0.0227	1.0449	0.022
HNFW	0.2797	1.3159	0.213
TDZY	1.9319	0.9553	2.022**

Note: P < 0.01, extremely significant, labeled ***; P<0.05, significant, labeled **; P<0.1, generally significant, labeled *.

Comparing the Level-2 random effect estimates of the intercept model and the null model [85], the variance shrinkage ratio of the Level-2 random term was calculated to be 0.0956, indicating that the village-level variables could explain 9.56% of the between-group variation in abandonment rate. The within-group conditional correlation coefficient was further calculated to be 15.04%, indicating that the proportion of inter-village variance to the total variance was reduced with the inclusion of the five village variables mentioned above.

4.5. Full Model

The full model was constructed based on the results of the multifactor random effects regression model and intercept model analysis. Variables with significant effects on abandonment rate at the farm household level were included in the Level-1 model, in which continuous variables for moderating effect test were added with group mean centering. Variables with significant effects of village level on abandonment rate were included in Level-2 model with intercept as explained variable; at the same time, these significant variables were included in Level-2 model with slope of farm level variables with significant group differences as explained variable, where continuous type variables for the test of moderating effect were added by centering the total mean to verify the effect of village level factors on the effect of farm level factors on the moderating effect of the effect of abandonment rate. The specific form of the model is shown below:

Level-1 model:

$$\begin{gathered} {QGZB}_{ij}={\beta }_{0j}+{\beta }_{1j}{HEAL}_{ij}+{\beta }_{2j}{RJGDMJ}_{ij}+{\beta }_{3j}\left({ZRGDB}_{ij}-{\overline{ZRGDB}}_{.j}\right) \\ +{\beta }_{4j}{SCGJ}_{ij}+{\beta }_{5j}\left({NYSRB}_{ij}-{\overline{NYSRB}}_{.j}\right)+{\beta }_{6j}{CGB}_{ij}+{\gamma }_{ij} \end{gathered}$$

(6)

Level-2 model:

$$\begin{gathered} {\beta }_{0j}={\gamma }_{00}+{\gamma }_{01}{TQJL}_j+{\gamma }_{02}{DLWZ}_j+{\gamma }_{03}{CZDX}_j+{\gamma }_{04}{CZNYSCB}_j+{\gamma }_{05}{TDZY}_j{+\mu }_{0j} \\ {\beta }_{1j}={\gamma }_{10}+{\mu }_{1j} \\ {\beta }_{2j}={\gamma }_{20}+{\mu }_{2j} \\ {\beta }_{3j}={\gamma }_{30}+{\gamma }_{31}\left({TQJL}_j-\overline{{TQJL}_{.}}\right)+{\gamma }_{32}{DLWZ}_j+{\gamma }_{33}{CZDX}_j \\ +{\gamma }_{34}\left({CZNYSCB}_j-\overline{{CZNYSCB}_{.}}\right)+{\gamma }_{35}{TDZY}_j{+\mu }_{3j} \\ {\beta }_{4j}={\gamma }_{40}+{\gamma }_{41}\left({TQJL}_j-\overline{{TQJL}_{.}}\right)+{\gamma }_{42}{DLWZ}_j+{\gamma }_{43}{CZDX}_j+{\gamma }_{44}\left({CZNYSCB}_j-\overline{{CZNYSCB}_{.}}\right)+{\gamma }_{45}{TDZY}_j{+\mu }_{4j} \\ {\beta }_{5j}={\gamma }_{50}+{\gamma }_{51}\left({TQJL}_j-\overline{{TQJL}_{.}}\right)+{\gamma }_{52}{DLWZ}_j+{\gamma }_{53}{CZDX}_j+{\gamma }_{54}\left({CZNYSCB}_j-\overline{{CZNYSCB}_{.}}\right)+{\gamma }_{55}{TDZY}_j{+\mu }_{5j} \\ {\beta }_{6j}={\gamma }_{60}+{\mu }_{6j} \end{gathered}$$

In Equation (6), the variables have the same meaning as in Equations (1), (4) and (5).

As can be seen from Table 8, the effects of significant variables at the farm household level and village level on the abandonment rate are similar to those estimated by the multifactor random effects regression model as well as the intercept model. In terms of village-level variables, commuting distance, whether the village terrain is plain or not, and the ratio of the number of people in agricultural production in the village still have extremely significant negative effects on the abandonment rate of farm households, whether it is a suburb of a large or medium-sized city still has a generally significant negative effect on the abandonment rate of farm households, while whether one has experienced land expropriation or not has a significant positive effect on the abandonment rate of farm households, with only slight differences in the size of the regression coefficients, which may be due to the introduction of village-level significant variables in the full model. The possible reason for this is that there is a certain moderating effect of the village-level variables introduced by the full model [87]. Based on the estimation results of the full model, this study focuses on analyzing the moderating effect of village-level variables on the effect of farm household-level variables on abandonment rate. When the regression coefficients of the village-level variables have the same sign as the regression coefficients of the farm household-level variables, it means that the village-level variables strengthen the influence of the farm household-level variables on the abandonment rate; when the regression coefficients of the village-level variables have the opposite sign of the regression coefficients of the farm household-level variables, it means that the village-level variables weaken the influence of the farm household-level variables on the abandonment rate [86].

Table 8. Full model fixed effects estimation results.

Table 8. Full model fixed effects estimation results.

	Variable Name	Regression coefficient	Standard error	T-test	P-value
β0	Intercept term γ00	12.0579	0.7842	15.377	0.000
	TQJL γ01	-0.2528	0.0677	-3.735	0.000
	DLWZ γ02	-2.4540	1.3157	-1.865	0.062
	CZDX γ03	-4.7223	0.8827	-5.350	0.000
	CZNYSCB γ04	-0.0548	0.0148	-3.690	0.000
	TDZY γ05	1.8234	0.9293	1.962	0.050
β1	HEAL γ10	-1.9073	0.4164	-4.581	0.000
β2	RJGDMJ γ20	-0.1975	0.0503	-3.927	0.000
β3	ZRGDB γ30	-0.0541	0.0125	-4.338	0.000
	ZRGDB*TQJL γ31	0.0028	0.0015	1.820	0.069
	ZRGDB*DLWZ γ32	-0.0387	0.0290	-1.337	0.182
	ZRGDB*CZDX γ33	0.0058	0.0164	0.354	0.723
	ZRGDB*CZNYSCB γ34	0.0007	0.0003	2.440	0.015
	ZRGDB*TDZY γ35	0.0111	0.0188	0.592	0.554
β4	SCGJ γ40	-3.5314	0.8546	-4.132	0.000
	SCGJ*TQJL γ41	0.0038	0.0879	0.044	0.966
	SCGJ*DLWZ γ42	-2.3175	1.3835	-1.675	0.094
	SCGJ*CZDX γ43	3.0912	1.2162	2.542	0.012
	SCGJ*CZNYSCB γ44	0.0071	0.0201	0.352	0.725
	SCGJ*TDZY γ45	-1.1113	1.2374	-0.898	0.370
β5	NYSRB γ50	-0.0685	0.0097	-7.093	0.000
	NYSRB*TQJL γ51	0.0020	0.0011	1.849	0.064
	NYSRB*DLWZ γ52	0.0026	0.0224	0.116	0.908
	NYSRB*CZDX γ53	0.0251	0.0120	2.092	0.037
	NYSRB*CZNYSCB γ54	-0.0000	0.0002	-0.018	0.985
	NYSRB*TDZY γ55	-0.0364	0.0127	-2.862	0.005
β6	CGB γ60	-3.6382	1.2818	-2.838	0.005

The significant moderating effects of the estimation results are as follows: (1) the slope of the commuting distance and the ratio of transferred farmland is generally significantly positively correlated with a regression coefficient of 0.0028, and the ratio of transferred farmland is extremely significantly negatively correlated with the abandonment rate, so the further the commuting distance is from the village, the weaker the negative correlation relationship will be between the ratio of transferred farmland and the abandonment rate. The slope of the ratio of the number of people in agricultural production in villages and the ratio of transferred farmland is generally significantly positively correlated, with a regression coefficient of 0.0007, whereas the ratio of transferred farmland is extremely significantly negatively correlated with the rate of abandoning farmland, therefore, the higher the ratio of the number of people in agricultural production in villages is, the weaker the negative correlation between the ratio of transferred farmland and the rate of abandoning farmland is. (2) The slope of the relationship of whether the village is a suburb of a large or medium-sized city and the ownership of large agricultural production machinery or livestock for agricultural production is generally significantly negatively correlated, with a regression coefficient of -2.3175, thus, the villages in the suburbs of a large or medium-sized city are extremely significantly negatively correlated with the rate of abandonment of cropland. The negative correlation between the availability of large agricultural production equipment or livestock and the abandonment rate is stronger in villages that are suburbs of large and medium-sized cities. There is a significant positive correlation between the topography of the village and the slope of the ownership of large agricultural production machinery or livestock for agricultural production, with a regression coefficient of 3.0912, whereas there is a highly significant negative correlation with the abandonment rate of the village, therefore, if the topography of the village is plain, the negative correlation between the slope of the ownership of large agricultural production machinery or livestock for agricultural production and the abandonment rate of the village is weaker. The weaker is the negative correlation between the ownership of large agricultural production machinery or livestock and the abandonment rate. (3) The slope of commuting distance and agricultural income ratio is generally significantly positively correlated, with a regression coefficient of 0.0020, and the agricultural income ratio is extremely significantly negatively correlated with the abandonment rate, so the further the commuting distance, the weaker the negative correlation of agricultural income ratio and abandonment rate. The slope of the agricultural income ratio is significantly positively correlated with village topography, with a regression coefficient of 0.0251, and a highly significant negative correlation with abandonment rate, so the weaker the negative correlation between the agricultural income ratio and abandonment rate, the more the village topography is plain. There is a highly significant negative correlation with the slope of the agricultural income ratio, with a regression coefficient of -0.0364, and a highly significant negative correlation with the abandonment rate, so that the villages that have experienced land acquisition have a stronger negative correlation between the agricultural income ratio and the abandonment rate.

From Table 9, it can be seen that after the introduction of the five Level-2 variables of commuting distance, whether it is a suburb of a large or medium-sized city, whether the village is a plain, the ratio of the number of people in agricultural production in the village, and whether it has experienced land expropriation, the random effects of the ratio of the cropland that was transferred to cropland, the ratio of the number of people in agricultural production that owns a large-scale agricultural production machine or livestock used for agricultural production and the ratio of the agricultural income are still significant, which indicates that the introduction of Level-2 variables to the Level-1 variables needs to be enhanced, and further village-level related variables or higher-level variables need to be added for analysis [85]. Meanwhile, after further comparing the random effect estimation results of the full model random effect regression results and the multifactor random effect regression model, and calculating the variance reduction ratio, it was found that: (222.4776-130.3265)/222.4776=0.4142, that is to say, 41.42% of the difference in the mean value of abandonment of farmland rate in villages could be explained by the above five Level-2 variables.

Table 9. Full model random effects regression results.

Table 9. Full model random effects regression results.

Variable Name	Random effects regression results
	Variance component	Chi-square test
γ00	130.3265	116.5629***
HEAL	2.7051	49.5024
RJGDMJ	0.0773	43.2623
ZRGDB	0.0027	52.8242*
SCGJ	35.0686	59.8170**
LNRJSR	8.7962	98.1779
NYSRB	0.0080	86.9579***
CGB	19.6672	34.9425

5. Conclusion and Discussion

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