For the calculation of the efficiency of the new agricultural producers on soybean production, the data envelopment analysis (DEA) of the non-parametric method proposed by Charnes et al. [

19] and the stochastic frontier analysis model (SFA) of the parametric method proposed by Batton and Coeli [

20] are mainly used. The SFA model of the parametric method needs to be based on the specific production function model, which can represent the concrete relation between the input and the output; thus, the unknown parameters can be estimated by the measurement regression method, and the efficiency of new agricultural producers can be calculated. This stochastic model specification not only solves the noise problem associated with deterministic frontiers but also allows the estimation of standard errors and tests of hypotheses, while the DEA model of non-parametric method adopts a linear programming model, which needs no assumption for the specific production function model. Its advantage is to eliminate the necessity of making arbitrary assumptions about the functional form of the frontier and the distributional form of the error terms. Although the SFA model can separate the non-efficiency items from the error items, there is no priori reason for the selection of any particular distributional form for the error items [

21]. Therefore, in order to avoid the deviation of the efficiency calculation caused by the setting errors of error items distribution, the DEA model is used to measure and evaluate the efficiency of new agricultural producers on soybean production. Furtherly, the Tobit model, which is based on the principle of maximum likelihood estimation, is used to analyze the factors that affect the efficiency of new agricultural producers on soybean production.

#### 2.2.1. Data Envelopment Analysis (DEA)

The basic data envelopment analysis (DEA) model is used to calculate the production efficiency of new soybean producers (

TE), which is the technical efficiency under constant scale returns. The technical efficiency (

TE) can be represented by the product of pure technical efficiency (

PTE) and scale efficiency (

SE).

PTE is the technical efficiency under variable scale returns to scale, as shown in Formula (1).

Therefore, when the variable returns are adopted to scale DEA model [

22], it can be formed as shown in Formula (2):

In it, i = 1,2,…, n; j = 1,2,…, m; r = 1,2,…, s. n is the number of DMUs, m the number of input variables, s the number of output variables, x_{ij} the input variable j of DMUi, y_{ir} the output variable r of DMUi, λ_{i} the variables weight of DMUi, S^{+} the relaxation variable of input, S^{−} the relaxation variable of output, εa small number, e (1, 1,…, 1)^{T}, and θ the pure technical efficiency (PTE) to be evaluated.

#### 2.2.3. Selection of Index and Variable

(1) Index selection of data envelopment analysis (DEA)

**① Input index.** In the aspect of the input index, the land scale (N), the productive capital investment (K), and the productive labor input (L) related to the soybean in 2017 as input indexes. The land scale (N) refers to the land area actually used for the soybean production, including the lands of which the producer has acquired the right to produce by means of contract, leasing, and cooperation. Therefore, such lands are selected as indexes for measuring land input, and the measurement unit is ha. The productive capital investment (K) refers to the capital investment in addition to the land and the labor that the agricultural producers must put in for the production of soybeans, including seeds, chemical fertilizers, and pesticides. Therefore, this part of the capital is selected as a measurement index with a unit of 10000 yuan/ha. The productive labor input (L) refers to the quantity of the labor that the agricultural producers must put in with a measurement unit of day/ha. It is calculated by the number of days, and every 10 h per person is taken as 1 day.

**② Output index.** In the aspect of the output index, the annual sales income of soybeans is taken as the output index, of which the unit is 10000 yuan/ha.

In this paper, the data obtained are used to study the soybean production efficiency of the new agricultural producers in the survey area, and the selection of input–output variables and the corresponding explanation are shown in

Table 4.

(2) Index selection of Tobit Model

According to the characteristics of the new soybean producers and the research needs for study, the following factors are selected as the explanatory variables to study the influencing factors of soybean production efficiency, as shown in

Table 5.

**①****The attributes of the household owner.** Three variables are chosen to explain the attributes of the household owner, including age, gender, and level of education. In general, the higher the level of education is, the lower the age is, and the easier it is to accept new technologies and ideas, the higher the efficiency of the resource allocation is. Consequently, higher technical operating efficiency can be obtained in the soybean production process. As a result, the expected influence of age is negative and the expected influence of the level of education is positive.

**②****The attributes of family.** Three explanatory variables are selected to describe the attributes of the family, including soybean planting area (ha.), labor ratio (%) of soybeans, and soybean operating cost (10000 yuan/ha). In general, the larger the area of the soybean planting area is, the higher the labor ratio of soybean is, and the lower the operating cost of the soybean is, the higher the utilization efficiency of the capital and other resources is. Consequently, new soybean producers can have higher technical efficiency. As a result, the expected influence of the soybean planting area and the labor ratio of soybean is positive, and the expected influence of the soybean operating cost is negative.

**③ Production conditions.** Four explanatory variables are selected to describe it, including soil fertility, degree of mechanization, traffic condition, and convenience of water and power access. Agriculture has a strong natural attribute, and the production conditions have a great influence on soybean production efficiency. In general, the better the soil fertility is, the higher the degree of mechanization is, the better the traffic condition is, and the more convenient the access to water and power is, the higher the ability of production and the conversion efficiency of the production factors related to the soybean production are. Consequently, the new agricultural producers can have higher technical operating efficiency in the soybean production process. Therefore, the expected influence directions of the four explanatory variables of soil fertility, degree of mechanization, traffic condition, and convenience of water and power access are all positive.

**④ Market environment.** Three explanatory variables are selected to describe it, including the sales channel of soybeans, the stability of the soybean price, and the difficulty in obtaining soybean market information. The improvement of the technical efficiency in the soybean production process depends on the smooth soybean sales channel, the stability of the soybean price, and the quick acquisition of market information. Therefore, the expected influence of the soybean sales channel of soybean and the stability of the soybean price on the technical efficiency for new agricultural producers are positive, while the difficulty in obtaining soybean market information is negative.

**⑤ External policies.** In this paper, two explanatory variables from external policies are selected to describe the influencing factors, including the implementation of soybean subsidy policy and the promotion and training of soybean planting technology. Soybean subsidy and promotion of soybean planting technology are the two key contents of external policies. Active implementation of soybean subsidies and promotion and training of soybean planting technology are beneficial to improve the overall soybean production efficiency for the new agricultural producers. Therefore, the expected influence of soybean subsidy policy and soybean planting technology promotion and training on the technical efficiency of soybean production are both positive.