The data used in this paper are derived from the Agricultural Microeconomic Survey Database of the Institute of Agricultural Economics and Development, Chinese Academy of Agricultural Sciences. Based on the economic development level, rank the provinces in each region according to the average per capita net income of farmers, and select the provinces with the middle average from each region. A stratified random sampling method was adopted to select three counties (cities or districts) in each province, three towns in each county (city or district), three villages in each town, and about 20 households in each village for questionnaire survey. Data are collected by filling out a questionnaire on the spot.

This paper selects the micro-survey data of grain farmers in 2019 and 2020, including Heilongjiang Province, Hebei Province, Henan Province, Fujian Province, Jilin Province, Sichuan Province, Anhui Province, Hunan Province, Shaanxi Province, Yunnan Province, Shandong Province, and Xinjiang Autonomous Region. In 2020, Guangdong Province and Zhejiang Province were added, involving 42 cities and counties and 126 administrative villages. After removing samples with outliers and missing values, the valid samples are 3,927. The questionnaire mainly includes basic household information, production status, income and expenses, and adoption of agricultural socialized services, involving 344 data indicators. Select the survey data of grain farmers, mainly including farmers planting wheat, rice, and corn. The selection of grain farmers as the research object is mainly based on the following three reasons: first, food security is the important content and basis of the overall national security. As wheat, rice and corn are the three major grain crops, it is of great significance to study the impact of agricultural socialized services on food production; Second, food crops belong to field crops, and agricultural socialized service is the most widely used, representative and typical. Third, we can better explore and summarize the promotion experience and model from food crops, and promote the introduction of successful experience into other crop varieties.

The benchmark regression analysis uses ordinary least squares (OLS) to construct the benchmark regression model.

In Equation 1, the dependent variable Y_i is the farmers' economic income, the core independent variable Service_i is the farmers' adoption of agricultural socialized services, Controls is the control variable, β is the coefficient to be estimated, β₀ is the constant term, and ε_i is a random disturbance term.

Whether farmers choose to use agricultural socialized services is affected by their own resource endowments, and there is a sample selectivity bias problem. The propensity score matching method (PSM) can well deal with the sample self-selection problem, and eliminate the effect of selectivity bias by matching individuals with the same endowment conditions. It is divided into the following steps:

The sample farmers were divided into two groups according to whether to adopt agricultural socialized service, in which the farmers who adopted agricultural socialized service were the treatment group and the farmers who did not adopt agricultural socialized service were the control group.

First, a tendency score PS_i is calculated, and the tendency score can be estimated using a Logit model or a Probit model,

In Equation 2, it indicates that farmers use agricultural socialized services, while it indicates that farmers do not use agricultural socialized services, which is a covariate, indicating the probability that farmers use agricultural socialized services.

Use the Logit model to estimate the propensity score:

Secondly, matching is performed. The observable variables are controlled by matching samples with the same covariate characteristics, so that the result variables are only affected by the process variables. The selected matching methods are K-nearest neighbor matching, radius matching and kernel matching. Different matching methods are selected to verify the robustness of the results.

The average processing effect (ATT) is then estimated:

In Equation 4, Y_1i and Y_0i represent the income of farmers who use agricultural socialized services and those who do not, respectively, p(X_i) representing the probability that farmers will use agricultural socialized services, calculated by the logit model. E[Y_0i | D_i = 1, p(X_i)] indicates the economic income of the farmers who use agricultural socialized services when they do not use agricultural socialized services. However, this cannot be known from the observation. This is a counterfactual estimate. Therefore, suppose:

The explained variable is the economic effect brought by farmers' adoption of agricultural socialized service, which is measured by farmers' agricultural operational income, operating cost, and net operating income. Net operating income is obtained by calculating the difference between farmers' agricultural operational income and operating costs. Amounts are logarithmic to eliminate numerical effects, however, net gains is not logarithmic when they have negative values.

The core explanatory variable is the adoption of agricultural socialized services, which is assigned to 1 if farmers adopt agricultural socialized services in any production link and 0 if they do not adopt agricultural socialized services in any link.

Referring to the related researches, the control variables selected in Li and Li (2019), Tang et al. (2021) and Yang et al. (2022) include the characteristics of farmers and families. The characteristics of farmers include gender, age, education level, health status, technical training, and whether they are party member of the Communist Party of China. The characteristics of families include the number of labor force in the family, whether farming is the main income, whether to join cooperatives, and whether to purchase agricultural insurance.

See Table 1 for the specific variable definition and descriptive statistics.

After the benchmark regression, the question of whether there is multicollinearity among variables is tested. The results show that the distribution interval of VIF values of variables is [1.01, 1.24], and the average VIF value is 1.11, all < 10, indicating that there is no multicollinearity among variables.

As shown in the benchmark regression results in Table 2, on the whole, agricultural socialized service has a significant positive impact on farmers' agricultural production operational income, operating costs and net income at the level of 1%, indicating that agricultural service has positive economic benefits for agricultural production and can promote farmers' income.

From the regression results of model (1), agricultural socialized service has a significant positive impact on farmers' agricultural production operational income at the level of 1%, indicating that farmers' adoption of agricultural socialized service can bring about an increase in agricultural production income. Among the control variables, gender has a significant positive impact, indicating that men can obtain higher agricultural income than women, because women are significantly weaker than men in physical strength and labor intensity, and have disadvantages in mechanical work and social communication ability. Age has a significant negative impact on agricultural income, indicating that with the growth of age, the decline in technical level and physical ability affects agricultural production. Agricultural technology, labor force, major sources of income, joining cooperatives, and purchasing agricultural insurance all have significant positive effects on farmers' agricultural income. Farmers trained in agricultural technology can master advanced technology and apply it to agricultural production, thus promoting the improvement of production level. The larger the number of household labor force, the more labor force is put into agricultural production, and the more refined production can be realized. If the family's main source of income is farming, the higher the level of specialization in agricultural production, the more experienced and skilled the farmers will be in agricultural production in order to obtain agricultural income. Farmers joining the cooperatives can obtain economies of scale in the process of purchasing agricultural materials and selling agricultural products, thus achieving the effect of saving money and increasing income. The purchase of agricultural insurance can increase the risk of farmers to resist natural disasters and reduce the economic losses caused by production reduction.

From the regression results of model (2), agricultural socialized service has a significant positive impact on agricultural production and operation costs at 1%, indicating that farmers' adoption of agricultural socialized service will increase production costs. Among the control variables, gender, party member, household labor force, joining cooperatives, taking farming as the main source of income and purchasing agricultural insurance variables will significantly increase the production cost of farmers, while age, length of education, and health status have significant negative impact on operating cost.

From the regression results of model (3), the agricultural socialized service has a significant positive impact on the net income of agricultural production at the level of 1%, indicating that the adoption of agricultural socialized service by farmers can bring about the improvement of agricultural benefits. Among the control variables, age and health status have significant negative effects, while farmers as party member and families with farming as the main source of income have significant positive effects.

The Logit model is used to estimate the probability of farmers adopting agricultural socialized services, and the tendency score is obtained. The estimation results of Logit model are shown in Table 3. Age, agricultural technology training, joining cooperatives, and agricultural insurance have significant positive effects on farmers' adoption of agricultural socialized services, while health status has significant negative effects.

In order to ensure the validity of the PSM estimation, the common support hypothesis test was performed. Taking K-nearest neighbor matching as an example, as shown in Figure 1, the tendency scores of the control group and the processing group overlap in a large range, the sample size outside the common support domain is small, and the vast majority of samples are in the common support domain, indicating that the matching effect is good and the common support hypothesis is satisfied.

The covariates are checked for balance to check whether the matching results better balance the data. The standard deviations of the variables after matching are all reduced to < 10%. Comparing the results before matching, the standardized deviations of the variables are all significantly reduced, indicating that the matching effect is good. After matching, the difference of covariates between the control group and the treatment group is eliminated.

In order to test whether the balance of PSM regression results is satisfied, K-nearest neighbor matching is taken as an example to compare the normalized deviation, B-value and R-value before and after variable matching. From Table 4, it can be found that after matching, Pseudo R² is significantly reduced to below 0.005, the mean deviation and median deviation are both reduced from above 10% to below 5%, the B-value is also significantly reduced from above 38% to below 17%, and the range of R-value is [0.86, 1.27]. The above index changes indicate that the matching result is good. After matching, the difference of covariates between the processing group and the control group is eliminated, and the data is well balanced.

In order to eliminate the interference of other relevant characteristics of farmers on the research results, the propensity score matching method (PSM) was used to further verify the robustness of the impact of agricultural socialized services on farmers' income. When estimating the average processing effect (ATT) of agricultural socialized services, three matching methods, namely, K-nearest neighbor matching method, caliper matching method and kernel matching method, were used to perform regression to test the robustness of the model estimation results. As shown in Table 5, the estimation results of the three matching methods are consistent, the average processing effect is significant at the level of 1%, and the ATT values and significance levels of the corresponding variables in PSM regression are consistent, indicating that the model results have certain reliability. The average level of operational income, operating cost and net income of the farmers group using agricultural socialized services are significantly higher than the average level of the farmers group not using agricultural socialized services.

Farmers who use agricultural socialized services have higher agricultural production operational income than those who do not use agricultural socialized services, while farmers who use agricultural socialized services have higher production costs, indicating that farmers need to pay for agricultural socialized services and spend more on mechanized fuel costs. Compared with farmers who did not use agricultural socialized services, although the use of agricultural socialized services increased production costs, but the net income did not decrease. It is worth noting that the average net income of farmers who do not use agricultural socialized services is negative. After removing various production costs, the income from selling agricultural products is difficult to sustain agricultural production.

According to the difference of the varieties planted by the farmers, the varieties of grain planted by the farmers are paddy, wheat and corn. The regression is carried out according to the kinds of crops to test the income-increasing effect of socialized agricultural services on the farmers' production. The regression results are shown in Table 6. The results showed that from the significance of the regression coefficient, rice farmers and corn farmers increased the farmers' agricultural income after using agricultural socialized services, while wheat farmers did not have a significant increase in income after using agricultural socialized services. Judging from the size of the regression coefficient, agricultural socialized service has a greater effect on increasing the income of farmers who plant corn than those who plant rice. From the perspective of the crops' own characteristics, the production process of rice involves multiple complex links such as seedling raising, transplanting, irrigation, and pest control, with each link having high requirements for technology and management, which is difficult for individual farmers to complete efficiently on their own. Corn planting, on the other hand, is highly dependent on large machinery in links like sowing and harvesting, and large-scale operations can significantly reduce costs. Therefore, rice and corn growers have a more urgent demand for agricultural socialized services. When they adopt these services, such as professional seedling raising services and mechanized harvesting services, they can effectively improve production efficiency, thereby bringing about significant income growth. However, the production process of wheat is relatively standardized. Farmers have formed a relatively mature traditional planting model through long-term practice in all links from sowing to harvesting, resulting in a low elasticity of demand for external socialized services. This makes the effect of income increase after adopting the services less significant.