**Hypothesis 2 (H2).** *Factors that influence the efficiency of family farms vary by types and regions.*

In summary, most of the research objects in existing literatures are family farms in a certain area or of a certain type; comparative researches on family farms in different regions and of different operating types still need to be supplemented. Furthermore, most articles about the measurement and analysis of family farm efficiency focus on the comprehensive technical efficiency, which seldom decompose it and analyze its influencing factors. Based on the analysis of the literature reviews and their limitations, this paper uses the field survey data of two family farm demonstration bases in China as the research sample, and divides them into three categories, pure planting, pure breeding and mixed family farms, according to the type of operation, so that the family farms in different regions and of different operation types can be compared. In addition, this paper measures and decomposes the efficiency of family farms and analyzes its influencing factors. Through comparisons and analysis, this paper aims to find out the shortcomings of family farms in different regions and types, and put forward targeted policy recommendations to promote the efficiency of various family farms.

#### *1.2. Contributions and Limitations*

The contributions of this paper are as follows:


for it covers as many input and output variables as possible that actually occurred in their agricultural production and operation in 2016.

3. In our paper, we not only analyze the possible influencing factors on full sample family farms' efficiency, but also compare the effect differences on family farms in different regions and of different operation types, which would be very helpful to promote the development of various family farms by applying targeted policies.

However, we admit that this paper has the following limitations:


#### **2. Research Sample and Methods**

#### *2.1. Research Data*

In order to guide the orderly development of local family farms, the Ministry of Agriculture summarized five development modes—Shanghai Songjiang, Zhejiang Ningbo, Hubei Wuhan, Jilin Yanbian, and Anhui Langxi—as typical modes for promotion, among which, the "Hubei Wuhan mode" is the typical example of suburban agriculture serving urban development under the background of the cities' industrialization and urbanization, and the "Anhui Langxi mode" is the representative of agricultural scale transformation in underdeveloped areas after the outflow of laborers, so that they have strong representation across China [22].

The emergence and development of family farms in Hubei Wuhan is closely related to the development of the agricultural product market. As a mega city, Wuhan has had a great and stable demand for agricultural products, resulting in the rise in suburban agriculture. Since the 1990s, under the context of Wuhan's accelerated industrialization and urbanization, some suburban farmers in Wuhan abandoned their farmland and intended to seek well-paid jobs in the urban city. Other farmers took the opportunity to rent contracted land from those farmers who had abandoned farmland, and engaged in vegetable planting and aquaculture; thus, a group of large professional planting and breeding households gradually formed, which is also the prototype of family farms. On the basis of the farms' self-development in the suburbs of Wuhan, the government became involved in time to promote the standardization of the land transfer market. In 2009, the Wuhan government launched a pilot project of developing family farms, and five municipal-level family farms were established. After that, a series of policies were introduced to support the development of family farms, contributing to the formation of the mature Hubei Wuhan family farm development mode. The biggest feature of the Hubei Wuhan mode is that the operating scope of family farms is in line with the needs of urban residents, including vegetables, aquatic products, melons and fruits, livestock and poultry, and other agricultural products, and there is a trend of diversification as people's consumption increases.

The generation of family farms in Anhui Langxi is closely related to industrialization and urbanization. In the early 1990s, with the accelerated development of some industrial cities in the Yangtze River Delta, a growing number of farmers in Langxi chose to work in these cities, leaving their farm land abandoned or for their relatives and friends for farming. In 2001, a farmer in Langxi took the opportunity to rent in more than 100 mu (Mu, a unit of area in China ≈ 0.1647 acre) of abandoned farmland, and established the first family farm in Langxi: "Lvfeng Family Farm". By engaging in the large-scale planting of rice and wheat, "Lvfeng Family Farm" obtained a higher income than traditional farmers, which played an exemplary role for other farmers, and many other farmers started to follow. The Langxi government also played an important role in the development of family farms; it not only

actively guided farmers to transfer their farmland, but also arranged for the availability of special support funds worth CNY 10 million for the development of family farms in the annual budget, and evaluated 15–20 model family farms every year for awards or subsidies. The Family Farm Association is another important driving force for family farms in Langxi. In 2009, some family farms in Langxi with strong representation and obvious radiating effects established the "Langxi Family Farm Association", which is the first family farm association in China, and it has contributed to serving the local family farms as a nongovernmental organization, for example, to coordinate bank loans and organize farmer training. As Langxi is at a distance from big cities, limited by the market capacity and preservation ability, it is unlikely for family farms in Langxi to produce vegetables, aquatic products and other agricultural products with higher economic value on a large scale, so that the most significant feature of the family farms in Langxi is that they maintain the operating pattern dominated by crops.

From July to August 2017, we conducted an on-site investigation of the development situation of all the registered family farms in Wuhan City, Hubei Province, and Langxi County, Anhui Province by using the same set of questionnaires and obtained samples in 2016. The investigation method was face-to-face interviews, and every question was asked by the investigator and answered by the farmer. Then, every answer was recorded by the investigator and immediately confirmed by the farmer, which guaranteed the authenticity and accuracy of the data. The data covered the basic characteristics of the family farms and farmers, land circulation and utilization, fixed assets and investments, farm industry and scale, employment, production and sales, income and expenditure, agricultural technology application, farm operation and management, natural and market risks, agricultural cooperatives and financial support, and a total of 629 questionnaires were distributed. After deleting the questionable questionnaires, such as those that were missing or inconsistent, 584 final samples were obtained and divided by region: 273 in Wuhan and 311 in Langxi. In terms of the operating type, among the final samples, there were 294 for planting family farms, 127 for breeding family farms, and 163 for mixed family farms (the fishery family farms only account for a very small proportion of the total sample and are thus included in the category of breeding (as aquaculture) family farms in this paper). Planting family farms are the family farms that only operate and obtain income from the planting industry, for example, they grow grains, such as rice, wheat, vegetables and fruits. Breeding family farms refer to the family farms that only operate and obtain an income from the breeding industry, for example, they raise livestock, poultry and aquatic products. Mixed family farms are family farms that operate both planting and breeding industries and gain an income from them.

#### *2.2. Empirical Model Setting*

#### 2.2.1. DEA Model

Efficiency usually refers to the relative value of the input and output in production activities. Therefore, the efficiency of family farms can be regarded as the maximum output ratio that can be achieved under certain input constraints [23]. The DEA (Data Envelopment Analysis) method is a common performance evaluation tool in the field of decision analysis. By comparing the distance between the decision-making unit and its production frontier, the production efficiency of the multi-input and multi-output decision-making unit is calculated [24]. If the observation value of the decision-making unit is on the production frontier, the efficiency value of the decision-making unit is the optimal value of 1. If the efficiency value is less than 1, it means that the decision-making unit is inefficient, and the gap between 1 and its efficiency value reflects the inefficiency degree of the decision unit. In this paper, A DEA model that considers multiple inputs and multiple outputs was applied to measure and decompose the operating efficiency of all family farms, as well as to compare the efficiency of family farms in different regions and of different types.

The traditional DEA mainly includes two models: the CCR model and BCC model. Among them, the CCR model was initially proposed by Charnes et al. [24] to obtain the

technical efficiency value of the decision-making unit under the premise of constant return to scale by calculating multiple input and output variables, while the BCC model was put forward by Banker et al. [25]. Under the condition of variable returns to scale, it can not only obtain technical efficiency, but can also decompose the technical efficiency (TE) into pure technical efficiency (PTE) and scale efficiency (SE). Considering that family farms are only able to control and adjust the amount of input rather than the output during the production process, and they follow the premise of variable scale, this paper chose the input-oriented DEA-BCC model [26] as follows:

Suppose there are *n* decision-making units *DMUj*(*j* = 1, 2, 3 ··· *n*), *m* input indicators, and *s* output indicators. Assume *Xij* represents the *i*-th input of the *j*-th decision-making unit, *Yrj* represents the *r*-th output of the *j*-th decision-making unit (1 ≤ *i* ≤ *m*, 1 ≤ *r* ≤ *s*), *S*<sup>−</sup> is the surplus variable, and *S*<sup>+</sup> is the insufficient variable. The CCR model is:

$$\begin{cases} \min \theta\\ \text{s.t.} \sum\_{j=1}^{n} \lambda\_j \mathbf{x}\_{i\bar{j}} + s\_{\bar{i}}^- = \theta \mathbf{x}\_{i0} \\ \sum\_{j=1}^{n} \lambda\_j \mathbf{y}\_{r\bar{j}} - s\_{\bar{i}}^+ = \mathbf{y}\_{i0} \\ \lambda\_{\bar{j}} \ge 0, (j = 1, 2, \dots, n) \\ s\_{\bar{i}}^- \ge 0, s\_{\bar{i}}^+ \ge 0 \end{cases} \quad \text{( $\theta$  unonstrained)}\tag{1}$$

The BCC model considers that the return to scale of the decision-making unit is variable, so it is modified on the basis of the CCR model and shown as follows:

$$\begin{cases} \min \theta\\ \text{s.t.} \sum\_{j=1}^{n} \lambda\_{j} \mathbf{X}\_{j} + \mathbf{S}^{-} = \theta \mathbf{X}\_{0} \\ \quad \sum\_{j=1}^{n} \lambda\_{j} \mathbf{Y}\_{j} - \mathbf{S}^{+} = \mathbf{Y}\_{0} \\ \quad \sum\_{j=1}^{n} \lambda\_{i} = 1 \\ \quad \lambda\_{j} \ge 0, (j = 1, 2, \cdots, n) \\ \quad \mathbf{S}^{+} \ge 0, \mathbf{S}^{-} \ge 0 \end{cases} \quad (\theta \text{ unconstrained}) \tag{2}$$

#### 2.2.2. Tobit Model

Considering that the family farm efficiency values that were calculated by the DEA model range from 0 to 1, which are censored data, the Tobit model with limited dependent variables should be applied for regression. Furthermore, in order to reduce the impact of heteroscedasticity, some agricultural factor input variables with large values are taken to logarithms [27], and a semi-logarithmic model is set as follows:

$$Y\_i = \kappa + \sum \beta\_1 \ln(X\_i) + \sum \beta\_2 Z\_i + \varepsilon\_i \tag{3}$$

In the formula (3), *Yi* is the efficiency of the *i*-th family farm, *Xi* are the variables affecting the efficiency of the family farm that need to take logarithm, *Zi* stands for other factors that affect the efficiency of the family farm, *β* is the coefficient to be estimated, *ε<sup>i</sup>* is the random error term, and the subscript *i* represents every individual family farm.
