Qualitative Comparative Analysis (QCA) is a case-oriented method that lies somewhere between statistical analysis and single-case analysis. QCA combines case-based research with Boolean algebra and set theory, and observes the relationship between conditions and results from the perspective of set theory. By using Boolean algebra algorithms to formally analyze the logical process of a problem, QCA conducts systematic and formal cross-case comparisons (Ragin, 2008). QCA can excavate multiple paths with equivalent results, which is particularly suitable for studying complex causality and multiple interactions (Fiss, 2011). The QCA method denies any form of constant causality and believes that causality is dependent on specific situations and configurations. The “multiple concurrent causality” developed by QCA focuses on how multiple different condition variables can affect the outcome variable in the form of a combination. While the traditional empirical research can only deal with the symmetric relationship between A→B, then ~A→~B^①(^① The relationship between variables is represented by formal mathematical operation symbols (“→” means “cause or derived”; and “~” means “not”, which means that the condition does not appear).), QCA solves the problem of asymmetric causality. Whether there is a sufficient and necessary relationship between conditional variables and outcome variables is determined by consistency and coverage (Ragin, 2006a). The QCA formulas are shown below. Equation (1) and Equation (2) are used to calculate the consistency and coverage of X as a necessary condition for Y. Equation (3) and Equation (4) are used to calculate the consistency and coverage of X as a sufficient condition for Y.

where, “i” represents the cases or samples, i.e., each village in this study; and “I” represents the number of cases or samples. “X_i” refers to the membership score of sample i in the condition combination X. “Y_i” refers to the membership score of sample i in the outcome Y. The membership score is the degree to which a given case belongs to a set. “min(X_i, Y_i)” refers to the minimum values across the membership scores in X_i and Y_i. “X_i≥Y_i ” means that for a condition to be necessary for outcome Y, the membership score of each case in the condition X must be equal to or greater than its membership in score Y; while “Xi ≤ Y_i” means that for a condition to be sufficient for outcome Y, the membership score of each case in the condition X must be equal to or smaller than its membership score in Y.

Equation (1) indicates that the consistency of set Y as a subset of set X is their intersection expressed as a proportion of set Y. Similarly, other formulas can be obtained, and the consistency measures the degree to which the attribution of each solution is a subset of the result set. The range of values in the consistency index is 0-1. If the consistency is greater than or equal to 0.9, then this condition variable (combinations) X is considered a necessary condition for the outcome variable Y (Ragin, 2006b). If the consistency index is met, the explanatory power of the condition (combination) X to the result Y can be described by the coverage. That is, the coverage can measure the extent to which each solution and the whole solution explain the results. The coverage index has a value range of 0-1, and it can be considered as similar to the goodness of fit in regression analysis. If the coverage value is closer to 1, then condition (combination) X will have greater explanatory power for result Y (Huang et al., 2019).

QCA generally requires 10 to 60 samples (Bennett and Elman, 2006), which is suitable for the case analysis of small and medium sample sizes. At present, four derivative analytical techniques have been developed in academic circles, namely, csQCA (crisp-set Qualitative Comparative Analysis), fsQCA (fuzzy-set Qualitative Comparative Analysis), mvQCA (multi-value Qualitative Comparative Analysis) and tsQCA (time-series Qualitative Comparative Analysis) (Caren and Panofsky, 2005; Rihoux and Ragin, 2009). This paper uses the first developed and most widely used technique of csQCA. The binary-coded data were used in the assignment of the cause condition and the result condition, where 0 indicates full non-membership, and 1 indicates full membership. The formed set has a clear correspondence relationship. The choice of csQCA in this paper is mainly based on two considerations. The first is whether abandonment is a binary problem. The second is that our interviewees are village cadres, who may conceal or understate the amount of abandoned farmland. The adoption of csQCA can reduce the errors caused by the concealing or under-reporting to some extent.

Based on the existing research and questionnaire data, the factors influencing farmland abandonment are selected from the two aspects of agricultural production conditions and socio-economic factors. The list of factors mainly includes traffic conditions, agricultural facilities, agricultural mechanization, land circulation, agricultural labor force, and industrial policy support, which are determined as condition variables. QCA is based on the set relationship. Therefore, it is necessary to assign a set membership degree to the case, and calibrate the variables to a set based on theoretical knowledge and the actual situation (Schneider and Wagemann, 2012). According to the above variable assignment criteria, combined with the survey questionnaire, the outcome variables and condition variables of the cases are assigned (Table 1).

3.2.1 Condition variables

Traffic Conditions (TC): Road traffic conditions are one of the vital factors affecting agricultural production, and the distance from the county will also affect the agricultural production behavior of the households. In the questionnaire, if the respondent selects good traffic, and the distance between the village and the market town is lower than the sample mean, the value is “1”, otherwise it is assigned “0”.

Agricultural Facilities (AF): Agricultural infrastructure is an important foundation for the development of rural productivity, and lagging construction of agricultural infrastructure is the main factor restricting agricultural production. In the questionnaire, if the respondent selects poor farmland water conservancy facilities or poor agricultural infrastructure, the value is “0”, otherwise it is assigned “1”.

Agricultural Mechanization (AM): The level of agricultural mechanical equipment is a significant indicator of the developmental level of agricultural production and the comprehensive agricultural production capacity. In this paper, the ratio of small agricultural machinery to the number of permanent households (i.e., small farm machinery ownership rate) in a village is used to represent the mechanization degree of the village (Yang et al., 2019). With the average value as the boundary, a value greater than or equal to the average value of the small agricultural machinery ownership rate is assigned 1, otherwise it is 0.

Land Circulation (LC): The establishment and improvement of the land circulation market will promote the circulation and reuse of abandoned farmland to a certain extent, and reduce or even avoid the occurrence of abandonment. In this paper, the circulation rate of land management rights in Ganzhou^②(^② The data come from the Ganzhou Statistical Yearbook and Department of Agriculture and Rural Affairs of Jiangxi Province. The circulation rate of land management rights in Ganzhou is equal to the circulation area of land management rights divided by the total area of farmland in Ganzhou in 2018.) is used as the standard for measuring the convenience of farmland circulation. If the circulation rate of cultivated land in the case is higher than that of Ganzhou, the value is 1, otherwise, the value is 0.

Agricultural Labor Force (AL): Labor migration is one of the main factors affecting the abandonment of farmland. Based on the availability of the data, this paper takes the proportion of people engaged in agriculture in Jiangxi^③(^③ The data come from the 2018 Statistical Yearbook of Jiangxi Province. The ratio of agricultural labor in Jiangxi Province is equal to the number of agricultural laborers divided by the total labor force in Jiangxi in 2018.) as the standard for measuring the degree of rural labor abundance. In the cases where the ratio of the people engaged in agriculture is higher than that of Jiangxi, the value is “1”, otherwise, the value is “0”.

Industrial Policy Support (PS): The optimization and adjustment of agricultural policies can effectively stimulate the enthusiasm of farmers for production and planting, and promote the rational use of rural land resources. According to the questionnaire survey data, if the village has industry support policies or other favorable policies, the value is “1”, otherwise, the value is “0”.

3.2.2 Outcome variables

Since the abandonment of farmland is a sensitive topic, it is difficult to obtain comprehensive and true data on the amount of farmland that is abandoned, whether it is from official statistics or household surveys. Therefore, this paper focuses on the binary classification problem of whether farmland is abandoned (Zhang et al., 2014a). In the outcome variable, the abandonment of farmland is assigned a value of 1, and no abandonment is assigned a value of 0.

3.3.1 Truth table construction

The truth table contains information about outcome variables, condition variables and cases, and is one of the core elements of QCA. The truth table can reflect how the combination relationships between the appearance or non-appearance of various conditions causes a certain phenomenon to either occur or not occur. The QCA usually summarizes the data for each indicator in the unit of a case, and presents the obtained condition variables combination in the form of a matrix to produce the truth table. This paper inputs the assigned variable data into fs/QCA3.0 software to generate the truth table (Table 2).

3.3.2 The verification and correction of contradictory configurations

The truth table shows that there are combinations which yield factual contradiction cases (as shown in Table 3), that is, two completely contradictory results which appear in the same combination of conditions. According to the contradictory configuration resolution strategies of either “Orient the result according to the frequency standard” or “Recode the result value of all contradictory configurations to 0” (Rihoux and Ragin, 2009), this paper eliminates or reduces the contradictory configurations as much as possible. That is to say, the result value is assigned according to the standard of high frequency. For example, the codes of nine groups of combinations are all (1, 1, 0, 0, 1, 0). Among them, six sets of results are displayed as “1” and three sets are displayed as “0”, so then the higher frequency result of “1” is regarded as the revised common result of all nine sets. In the same way, the result of Case 45 is amended to “0”. If the number of result values of “1” and “0” in a given case each account for half, then the result will be uniformly revised to “0”, which means “low degree, poor result” or “unclear”. After these corrections, the revised truth table is obtained (Table 4).

Necessity analysis refers to exploring the extent to which the result set constitutes a subset of the condition set (Rihoux and Ragin, 2009). Consistency is an important indicator for measuring necessary conditions, that is, to what extent a certain result requires the variable to exist (Crilly et al., 2012). This article sets the threshold of the necessary condition to 0.9.

Table 5 shows that the consistency of low-level agricultural mechanization (~AM) exceeds 0.9, so it can be regarded as a necessary condition for the abandonment of farmland. The low-level agricultural mechanization (~AM) has a coverage rate of 0.8, indicating that in the process of farmland abandonment in Ganzhou, 80% of the cases of farmland abandonment are affected by the agricultural mechanization level. Since the explanatory power is strong, it can be explained independently. This is because Ganzhou is located in hilly and mountainous areas, and the farmland is generally distributed among scattered areas with steep slopes. Thus, these farmers had to give up farming because of the hindrance of limited mechanization development and the high labor intensity of farming. Among other variables, the consistency of convenient traffic conditions (TC), perfect agricultural facilities (AF), and sufficient agricultural labor force (AL) are all higher than 0.8, and the consistency of low-level land circulation (~LC) is close to 0.8, so it can be considered to have a greater impact on the farmland abandonment. The table shows that the individual factors include only a low-level of agricultural mechanization (~AM), which is a necessary condition for farmland abandonment. Moreover, the coverage of each single antecedent condition is low, which indicates that the explanatory power of each one to farmland abandonment is weak. In other words, whether farmland is abandoned or not is the result of multiple factors, rather than any single reason. Therefore, it is necessary to carry out configuration analysis on these condition variables. These antecedent conditions were incorporated into fsQCA3.0 Software to further explore the configuration that leads to the farmland abandonment.

Using the fs/QCA3.0 software, a Boolean minimization algorithm is applied to simplify the truth table, the revised truth table is imported into the software, and the consistency threshold is set to 0.8 (Fiss, 2011). Meanwhile, in order to avoid the impact of low-quality data on the results and cover at least 75% of the samples (Ragin et al., 2008), this paper sets the case frequency threshold to 2. After selecting the standard analysis, the results will have three kinds of solutions of varying complexity: parsimonious solution, intermediate solution and complex solution. The three solutions differ in how many logical remainders they contain, that is, the condition combination of counterfactuals which is logically possible but does not appear in the case studied. Among them, the complex solution excludes all counterfactual combinations, but the result is too complicated and has poor universality. While the parsimonious solution contains a large number of counterfactual combinations, the result is often too simple, and the conclusion may be quite different from the actual situation, so its revelation is the worst. The intermediate solution lies between these two and contains some counterfactual combinations, but there are fewer than in the parsimonious solutions. Previous research has shown it to be close to the theoretical reality and moderate in complexity, and it does not permit the elimination of the necessary conditions. Therefore, the intermediate solution has become the first choice for reporting and interpretation by most researchers who use QCA (Rihoux and Ragin, 2009; Crilly et al., 2012; Ragin et al., 2014), and, the intermediate solution is used in this paper.

In order to better explore the causal process, Fiss (2011) divided the causal conditions into core conditions and peripheral conditions. There is a strong causal relationship between the core conditions and the result. The core conditions appear in both the parsimonious solution and the intermediate solution, and they have an important impact on the result. The causal relationship between the peripheral conditions and the result is weak, and while it appears in the intermediate solution, it is excluded by the parsimonious solution, playing only an auxiliary role in the result. According to the operational results, the analysis of the intermediate solution shows that there are five condition combinations, and the results are shown in Table 6.

Generally, the closer the overall solution coverage is to 1, the higher the degree to which the combination of condition variables can explain the result variable. When the overall solution consistency is close to 1 and not less than 0.75, this indicates a better relationship between the calculated condition variables combination and the condition variables combination presented by the case data itself.

Table 6 shows that the overall solution consistency in this case is 1, and the overall solution coverage is 0.82, indicating that the calculated condition variables combination has passed the test, and that it has certain convincing power for the outcome variable, which can be used to explain whether farmland is abandoned. The consistency of all path combinations in this paper is 1, which proves that these combinations have a good subset relationship with farmland abandonment. That is, antecedent conditions have a good explanatory power for the outcome variable. According to the parsimonious solution consistency logic, the combinations with the same core conditions are merged to form the following two scenarios to explain the path combination.

Scenario 1: Including two combinations of A1 and A4, their core conditions are convenient traffic, low-level agricultural mechanization, and low-level land circulation. Combination A1 (TC * AF * ~AM * ~LC * ~PS)^④(^④ “*” means “and”, which indicates a parallel relationship; “~” means “not”, which means that the condition does not appear.) shows that even for villages with convenient traffic and complete production facilities, the conditions of low-level agricultural mechanization, low land circulation rate, and insufficient industrial policy support can also cause abandonment. The possibility of such a combination is 1, and this path can explain 35% of the farmland abandonment. This outcome may be due to the difficulty of large-scale farming in some villages in the mountainous and hilly areas of Ganzhou. In addition, the adjustment of agricultural-related policies is lagging and the land transfer system is not perfect. Therefore, the scale of farmland cannot reach the required level, and the operation of scale and mechanization are difficult, so farmland abandonment occurs. The raw coverage of combination A4 (TC * ~AM * ~LC * AL * PS) is 0.24, and its unique coverage is the largest, indicating that A4 aligns with the situation of farmland abandonment in many villages. There are conditions of convenient external transportation, sufficient agricultural labor and industry support policies in these villages. However, due to the difficulty of agricultural mechanization and the high cost of hired labor, it was difficult to attract farmers, enterprises, cooperatives and other agricultural organizations to transfer the land. The single-family farming income was low, so farmland was abandoned.

Scenario 2: There are three combinations of A2, A3 and A5 in scenario 2. The core conditions are sound agricultural facilities, low-level agricultural mechanization, and a sufficient labor force engaged in agriculture. Combination A2 (AF * ~AM * ~LC * AL * ~PS) shows that when the rural production facilities are perfect and the agriculture labor is sufficient, regardless of whether the external transportation is convenient or not, the village is without industrial policy support, and where the level of agricultural mechanization and the land circulation are low, the land would also be abandoned. The possibility of such a combination is 1, and this path can explain 32% of the farmland abandonment phenomenon. Although such villages have sufficient labor for agriculture, because Ganzhou is close to the economically developed areas of Fujian and Guangzhou, there are many opportunities for migrant workers, so many farmers have part-time jobs. Research showed that the average area of farmland abandoned by rural families increases by 5% for every 10% increase in part-time employment (Xu et al., 2019). Coupled with the imperfect circulation policy and industrial policy support, the influence of the endowment effect and the “land complex”, farmers are reluctant to transfer and contract the land. Therefore, large-scale mechanized operations cannot be carried out, and the possibility of abandonment is increased. Combination A3 (TC * AF * ~AM * AL * ~PS) shows that under the conditions of convenient external transportation, complete production facilities, and sufficient agriculture labor, regardless of the level of land circulation, where the level of agricultural mechanization is low and without policy support, the village would also be affected by the abandonment phenomenon. The possibility of this combination is 1, which can explain 38% of cultivated land abandonment. The prices of agricultural production materials such as seeds, pesticides, and fertilizers have remained high for a long time, which not only pushes up the cost of agricultural production, but also weakens the effect of subsidies that benefit farmers. Moreover, the current land circulation policy is not perfect, and there is no additional authoritative national or local governance policy to alleviate the abandonment of farmland. The scattered land is difficult to operate on a large scale, resulting in the abandonment of cultivated land. Combination A5 (~TC * AF * ~ AM * LC * AL * PS) shows that even with complete agricultural production facilities, high-level land circulation, sufficient agricultural labor and policy support, where the agricultural mechanization rate of the villages is not high and traffic is inconvenient, the farmland would be abandoned. This is because the land circulation system can slow down the abandonment of farmland to a certain extent, but it only has a certain effect on the farmland that is forced to be abandoned due to lack of labor. There is no weakening effect on the abandonment of low-quality farmland that cannot be worked using agricultural machinery and has an extremely low efficiency of input-output. Combined with the inconvenience of transportation, the increased cost of commuting has discouraged the farmers from farming in this combination.

In addition, as shown in Table 6, the conditions of external traffic conditions, land circulation degree and industrial policy support are contradictory in different combinations, indicating they have no significant influence on the outcome variable. They can work together with other factors in the form of auxiliary conditions in different combinations to produce different results because these external factors will gradually improve with the development of favorable agricultural policies such as precise poverty alleviation, land circulation, and social-economic development. The low-level agricultural mechanization appears in the form of a core condition in different combinations, which again indicates that it has a significant impact on the farmland abandonment. However, the high rate of agricultural labor appears in the combination of multiple variables at the same time and is not contradictory. Although it has a great influence on the abandonment of cultivated land, it is not a limiting factor because the use of agricultural machinery can (to a certain extent) alleviate the impact of the loss of rural labor on farming. In the context of a rapid increase in farming opportunity costs, mechanical replacement is the most effective way to increase labor productivity. He et al. (2020) also pointed out that improving the efficiency of mechanical farming can indeed make up for a shortage of labor, thus achieving the purpose of reducing abandonment. By adopting agricultural machinery to save farming time, farmers can increase their time for outside work.

This paper abandoned the traditional statistical quantitative analysis perspective. Instead, it used the configuration perspective to discuss the farmland abandonment, and studied the sufficiency and necessity of individual antecedent conditions and antecedent condition combinations, which provided a new research perspective for the study of farmland abandonment in terms of research methods. Farmland abandonment is a dynamic process, which is driven by a combination of socio-economic, political, and environmental factors (Ustaoglu and Collier, 2018). Traditional statistics assume that the functions of individual factors are independent of each other, focusing instead on analyzing the “net effects” of various factors. However, this oversimplified assumption often fails to fully reflect the complexity of causality in the real world, and the "net effect" of a single factor may be masked or offset by other related factors. Although some scholars have tried to address the configuration effect, cases with more than three interacting variables have been difficult to explain (Du and Jia, 2017). For example, Müller et al. (2013) used the Boosted Regression Trees to explain the nonlinearities and interactions between the factors influencing farmland abandonment, but this approach only allowed for two-variable interaction effects.

Unlike the traditional regression method that emphasizes causal symmetry, the factors that cause the outcomes in the real world are often different. The asymmetry of causality and conditional effects emphasized by QCA precisely explains the opposite conclusions of the same factors in reality. For example, Shao et al. (2016) found that the amount of farmland abandoned is not entirely determined by the quality of the farming conditions, while Lin and Zhu (2014) reached the contrary conclusion, which also confirms the asymmetric nature of the abandonment of farmland.

In addition, the research cases in this paper come from different villages in different counties, so they consider the potential impacts of different sets of conditions in different counties and villages. Parcels within the same homogeneous geographic area tend to have more similarities in the degree of abandonment and time trends (Han and Song, 2019). There have been few studies of farmland abandonment on the village scale. Although Yang et al. (2019) have conducted research at the village scale, all their samples were concentrated in one county, so the potential impact of differences in county conditions were not considered.

There are still some problems that need to be further improved.

(1) The framework system of factors influencing farmland abandonment needs to be improved. Taking into account the availability and operability of the data, this paper mainly analyzes the agricultural production conditions and socio-economic factors that affect the abandoned farmland, but the analysis of natural factors such as farming distance and slope is insufficient. In addition, this paper uses csQCA, which can only be used to analyze dichotomous variables, so the division of variables is not detailed enough. In the future, the fuzzy-set Qualitative Comparative Analysis can be used to assign more detailed values to the variables to improve the accuracy of the results.

(2) It is necessary to accurately judge whether the farmland is abandoned and the amount of the abandoned land to reduce the errors. This paper directly judges whether the farmland is abandoned based on the area of abandoned farmland in the survey questionnaire. However, as the The Rural Land Contract Law and other relevant laws and regulations clearly stipulate that the abandonment of farmland is strictly prohibited, farmland abandonment has become a sensitive issue, so the data obtained through questionnaires on abandoned farmland may not be true. Therefore, combining high-resolution remote sensing images, deep learning and other methods to extract more accurate data on abandoned farmland and determine whether there is abandonment of farmland is the next crucial step in future research work.

(3) The research area and sample size need to be further expanded to make the research conclusions more broadly applicable. Although this paper has considered the potential impact of the differences in conditions between the counties and villages, all the samples are still concentrated in Ganzhou. The potential impact of the differences in the conditions of different cities and provinces has not been considered. Therefore, the explanatory power of this conclusion for other regions is still uncertain, and further research is needed.

Based on the above conclusions, this paper puts forward the following corresponding policy implications.

(1) Give full play to the role of agricultural machinery. A low-level of agricultural mechanization is not only a necessary factor but also a sufficient and core factor for the abandonment of farmland. Therefore, the key issue of mechanization must be handled well. The survey found that most farmers are affected by economic conditions, lengthy idle time of agricultural machinery, a low survival rate due to mechanical planting, and the variety of agricultural machinery needed, so their willingness to purchase agricultural machinery is not strong. Therefore, the promotion of small machinery usage should be combined with technical services. First, the R&D Department must accurately grasp the actual demand of farmers to ensure that agricultural machinery meets the needs of local industries. The boundaries between villages need to be broken, and large agricultural machinery households and specialized agricultural machinery service organizations should be jointly cultivated and developed to reduce the costs and realize large-scale and mechanized operations. Furthermore, for areas that cannot be concentrated into contiguous land, subsidies need to be increased and implemented to allow ordinary farmers with weak economic power to purchase agricultural machinery or technical services.

(2) Pay attention to the interactions between measures, and implement multiple measures to alleviate the abandonment of farmland. In the process of farmland abandonment, a single factor does not work alone. It must work with other factors for the abandonment of farmland to occur. This paper shows that there are five condition combinations which can result in the abandonment of farmland in the hilly and mountainous areas of Ganzhou, which provide a variety of perspectives for government managers to target in order to prevent the abandonment of farmland. Moreover, when farmland is abandoned, the measures to resolve the abandoned land should be formulated according to local conditions.

(3) Manage the abandonment of farmland systematically, and explore and promote the management strategies of the farmland abandonment in depth. The reasons affecting the abandonment of farmland are asymmetric. The reasons why the abandonment of farmland does not occur cannot be deduced backwards based on the reasons for the abandonment of farmland. This fact inspires us to treat the abandonment of cultivated land rationally, and it is not necessarily true that the phenomenon of farmland abandonment will not occur if the factors leading to farmland abandonment are changed completely. Therefore, it is necessary to treat the abandonment of farmland as a long-term systematic project. The government should effectively integrate various forces such as agricultural scientific research units, universities, agricultural enterprises, and cooperatives to conduct research on the management strategies for farmland abandonment.