2.3.2. Tobit Variables

Table 2 shows the Tobit regression variables and their descriptive statistics. The variables include four aspects:


family farms. Similarly, using new agricultural technologies can not only improve the productivity of family farms [36], but also increase the intellectual content of agricultural products and their derivatives, thus it is expected to positively influence family farm efficiency. Additionally, as the use of fertilizers is conducive to cultivating land fertility and increasing yields; it is projected to have a positive impact on the efficiency of family farms.

4. Environmental factors. The environmental factors mainly include government subsidies, financial credit, and natural disasters. Government subsidies may encourage family farms to invest in production, but they may also enable farmers to form the idea of "getting something for nothing" and reduce their production enthusiasm [13]. Therefore, the impact of government subsidies on family farm efficiency is uncertain. Financial credit is conducive to the production expansion of family farms, thus it is expected to be positively correlated with the performance of the family farm. Family farms that suffer from natural disasters face the plights of reduced or no harvest, so it is predicted that natural disasters negatively affect the performance of family farms.


**Table 2.** Tobit regression variables and descriptive statistics.

Note: the total sample size is 584, 273 from the Wuhan area, and 311 from the Langxi area.

#### **3. Results and Analysis**

#### *3.1. Efficiency Measurement of Family Farms: Based on the DEA Model*

Table 3 presents the results of the variance inflation factor (VIF) of the input indicators and the results of the Pearson test on the input and output indicators. The results show that the VIF values of the input indicators are all less than 10, indicating no multicollinearity, and the Pearson correlation coefficients of the input and output indicators are significantly positive at the level of over 5%, indicating that the land input, labor input and capital input are all positively correlated with the output indicator, with the significant coefficients at 0.9078, 1.9938 and 1.6773, respectively. Therefore, the input and output indicators selected for this study satisfy the assumption of the same direction, so that the DEA model can be used for the analysis.

**Table 3.** Multicollinearity and Pearson test results.


Note: \*\*\*, \*\* are their significance at the levels of 1% and 5%, respectively.

Table 4 shows the results of the efficiency value of the family farms. The average value of the technical efficiency (TE) of all the family farms is low (0.3058), verifying that H1 is true. From the decomposition of the technical efficiency (TE) into pure technical efficiency (PTE) and scale efficiency (SE), it is shown that the average value of the family farms either in SE or PTE is not high (0.5779 and 0.5213, respectively), contributing to the low TE. Although the PTE is slightly higher than the SE, both of them still have much room for improvement. Therefore, family farms should further improve their technical skills, while focusing on scale operations. A further analysis of the returns to scale shows that, among all the family farm samples, as many as 516 family farms are in a state of increasing their returns to scale, only 31 are in a state of decreasing their returns to scale, and the other 37 family farms are in a state of constant returns to scale.


**Table 4.** The efficiency of all the family farms of different types and in different regions.

Note: the efficiency values of the technical efficiency (TE), pure technical efficiency (PTE), and scale efficiency (SE) are the calculated average efficiencies; TE = PTE × SE.

Table 4 also presents the results of the efficiency values of the family farms of different types and in different regions. In terms of family farms of different types, the TE, PTE and SE of breeding family farms are the highest, with values reaching 0.4104, 0.7102, and 0.5547, respectively, while the efficiency values of the planting family farms and mixed family farms are relatively lower. The SE of the mixed family farms is the lowest (0.4874), and it is also confirmed by the fact that among the 163 mixed family farms, 150 households are in a state of increasing returns to scale. Hence, the mixed family farms need to pay more attention to adjusting the scale of operation to improve their TE. The PTE of the planting family farms is lower than their SE, indicating that the planting family farms should focus more on the improvement of technology and management skills.

From a regional perspective, the TE of the family farms in Wuhan is higher than that of Langxi (0.3734 and 0.2464, respectively). A similar pattern can be observed in the figure for the PTE and SE in Wuhan and Langxi, indicating that the family farms in Wuhan have more advantages in technology, management and scale operation, which contributes to a TE that is relatively higher.

#### *3.2. Factors Affecting the Efficiency of the Family Farms: Based on the Tobit Model*

This paper used stata11 to process and analyze the data. On the basis of estimating the total sample, regression estimations were also carried out by region and operation type, and the estimated value of each variable coefficient and its significance were obtained. The results are shown in Table 5.


**Table 5.** Tobit regression results of the variables affecting family farm efficiency.

Note: *t*-values are in brackets, \*\*\*, \*\*, and \* are their significance at the levels of 1%, 5%, and 10%, respectively.

Model 1-1 and 1-2 show the results of the efficiency influencing factors of all the family farm samples and those obtained after gradually eliminating the insignificant variables, respectively. From the perspective of considering the agricultural input variables, land input

[ln(land)] is negatively correlated with the family farms' efficiency at the 1% level, while its square term shows an opposite trend, forming a U-shaped relationship between the farm efficiency and land operating area. In fact, there is an almost globally inverse relationship between the farm size and productivity within developing countries [37], including India, the Philippines, Latin America [38–41], China, Nigeria, Mexico, and Bangladesh [30]. In other words, in these developing countries, both small and large farmers are more productive than the intermediate-sized farmers, and this can be explained by the more efficient hiring labor utilization of small farmers and the machine scale economies of large farmers [30]. To be more specific, intermediate-sized farmers are most likely to employ part-time workers, which proves to be costly and less efficient than small farmers, while the full mechanization in large farms saves on labor-related costs [42], of which the increase in the scale capacity can explain for the upper tail of the U shape. The capital input (ln(cap)) of the family farm is significantly positive at the level of 1%, indicating that the efficiency of the family farms increases with the input of capital. To our knowledge, the more capital invested in the family farm, the easier it is for the family farms to purchase equipment, achieve mechanized production and economies of scale, which can promote the productivity of family farms. Among the farmers' characteristic variables, only the farmers' education level (Edu) has a significant impact on the efficiency of the family farm at a 5% level, proving that the farmers with a higher education degree have better skills relating to farming operations, which is beneficial in the making of smart decisions and enhancing the productivity of the farm. In terms of the family farm characteristic variables, the market channels (Market), brand trademark registration (Brand), and use of fertilizer (Fer) are all significantly positively correlated with the family farms' efficiency at a 1% level. Unblocked market channels contribute to the increase in product sales, registered brand trademarks enable the family farms to achieve a better publicity effect, and the use of fertilizer increases the fertility of the land and improves the unit output. Therefore, the three variables are conducive to the improvement of family farm efficiency. From the perspective of environmental factors, government subsidies (Aid) negatively affect the efficiency of the family farms at a 5% level; a possible explanation for this is that government subsidies may induce farmers to form the idea of "getting something for nothing", thereby reducing their enthusiasm for production. Financial credit (Credit) shows a positive correlation with family farm efficiency at the level of 1%. External credits can expand the budget constraint of the family farms and allow them to invest more funds for production, thus improving the efficiency of the family farms. When family farms suffer as a consequence of natural disasters (Dis), this significantly influences the efficiency of the family farm, because the natural disasters directly result in plights, such as a reduction in or no harvest, which poses a threat to the efficiency of the family farms.

Models 2, 3, and 4 present the results of the efficiency influencing factors of family farms of different operation types, while Models 5 and 6 show this for different regions. The heterogeneity of the results verify that H2 is true, and the analyses of each model are as follows:

Model 2 presents the result of regression on the factors affecting the efficiency of planting family farms. The land scale (ln(land)) shows a significantly negative correlation with the efficiency at a 10% level, with which the labor input (labor) is significantly positively correlated at the level of 5%, indicating that, for a planting type family farm, a smaller operating scale and a greater labor force can improve the production efficiency of the family farms. The education level (Edu) of the farmer positively affects the efficiency of the family farms at the level of 5%, proving that the higher the education level of the family farmer, the more possible it is for them to make decisions that are beneficial to the development of the planting family farm. The brand trademark registration (Brand) and use of fertilizer (Fer) both significantly and positively influence the efficiency of the family farm, indicating that brand promotion is conducive to the sale of planting products, and the use of fertilizer can boost the yield of agricultural products, thereby improving the efficiency of the family farms. As a consequence of suffering from natural disasters (Dis), the efficiency of family farms can lower, as the planting agricultural operations are weak and high risk, and therefore suffering from natural disasters may result in family farms having no income for the entire year.

Model 3 presents the result of regression on the factors affecting the efficiency of the breeding family farms. The land scale (ln(land)) and its square term show a U-shaped relationship with the efficiency of the family farm, where their coefficient values are significantly at −0.2049 and 0.0264, respectively, verifying that the smallest and largest breeding family farms are more efficient than the intermediated-sized farms. Capital input (ln(cap)) and new technology application (Tec) are both significantly positively correlated with efficiency at the 1% level; similarly, financial credit (Credit) presents a positive correlation with breeding family farms' efficiency at a 10% level, as the capital input and financial credit they obtain make it possible for breeding family farms to purchase advanced machinery and apply new technologies, such as cultivating new varieties and applying assembly lines, which contributes to the improvement of farm productivity. Brand trademark registration (Brand) is negatively related to the efficiency of the family farm at a 10% level. A possible explanation for this is that the breeding industry already has wellknown brands, such as Hairy Crab of a famous Lake or Local Pork of a Mountain. Brands registered by single family farms find it difficult to compete with the more well-known trademarks in the market with a higher price, and, as a result, agricultural products with family farms' registered trademark brands may not be as popular as the original sales.

Model 4 shows the result of the factors that affect the efficiency of the mixed family farms. The land scale (ln(land)) negatively affects the family farm efficiency at the level of 5%, while the capital input (ln(cap)) presents an opposite influencing direction, indicating that the mixed family farms are not suitable for an excessively large scale of operation, and the capital input is proved to be helpful in building a good circular agricultural mixed model, such as the recycling of pig manure and urine, and rice–duck symbiosis, so as to improve the efficiency of the farm. In addition, the market channels (Market) and brand trademark registration (Brand) are significantly positively correlated with the farm efficiency at the levels of 5% and 1%, respectively, indicating that the smooth market channels and brand promotion can improve the efficiency of the mixed family farms by broadening the market. The adoption of new technology (Tec) shows a significantly negative correlation with farm efficiency at the 5% level, and it is probably because the new technologies are not yet mature in this field, which leads to a lower efficiency at this stage. Financial credit (Credit) positively influences the efficiency of the farm, since it can provide a sufficient source of external funds for the mixed family farms, which is conducive to their expansion in terms of production.

Models 5 and 6 are the regression results of the factors affecting the efficiency of the family farms in Wuhan and Langxi, respectively. From the perspective of the common points, firstly, among the agricultural input variables, the land operating area (ln(land)) in two regions is significantly negatively correlated with the family farm efficiency, while the capital input (ln(cap)) in the two regions is significantly positively correlated with this at a 5% level, showing that the family farms in both regions are more efficient at a smaller scale and with more capital investment. Capital investment contributes to the expansion of the production of the family farms, thereby increasing the productivity and efficiency of the family farms, and since family farms in Wuhan are located in the provincial capital city, the efficiency improvement affected by the capital input is better than that in Langxi. Secondly, among the other influencing factors, the market channels (Market) both in Wuhan and Langxi have positive impacts on the efficiency of the family farms. This is due to the fact that unblocked sales channels can increase the choice of markets at which family farms can sell more goods.

From the perspective of differences, in Langxi, the square term of the land operating area [ln(land)]<sup>2</sup> shows a positive relationship with the efficiency of the farm, thus the U-shaped relationship between the land area and farm efficiency is obvious in Langxi. The farmer's years of farming (Exp) shows a significantly negative relationship with the

efficiency of the farm at the 10% level. Farmers who have spent more years in the practice of farming may have a richer farming experience, but they are also less likely to accept new technology and modernized methods, which is not conducive to improving the efficiency of the family farms. The regulation (Regu), the brand trademark registration (Brand), and the use of fertilizer (Fer) in the family farms in Langxi are all significantly positively correlated with the farms' efficiency, indicating that a complete internal regulation system, brand publicity, and fertilizer use will improve the farms' operating efficiency through an improvement of the management efficiency, the sale of more products, and the increase in yields, respectively. Among the environmental factors, financial credit (Credit) in Wuhan presents a significantly positive impact on farm efficiency, while that in Langxi is nonsignificant. This situation may be due to the relatively standardized development of the financial market in Wuhan, as Wuhan is a provincial capital city, so financial credit enables the family farms to expand their production and improve productivity through financing, while the development of the financial market in Langxi is relatively lagged. The efficiency of the family farms in the Langxi area is negatively affected at a 1% level, as a consequence of suffering from natural disasters (Dis). Since many family farms in the Langxi area suffered from natural disasters in 2016, they were affected by the disaster and their income was reduced. Therefore, this has a significantly negative impact on the efficiency of the local family farms.

#### **4. Discussion**

#### *4.1. Discussion about the Efficiency of the Family Farms*

In order to present family farm efficiency more specifically and elaborate on the discussion, this paper presents the decomposition of the DEA results of the family farms, according to the level of their ineffectiveness by types in Table 6.


**Table 6.** The decomposition of the efficiency of the family farms measured by the DEA.

Note: the inefficiency of the DEA is divided into three levels: low, medium and high; θ is the efficiency value; TE = PTE × SE.

#### 4.1.1. Full Sample Discussion

The results show that the TE (technical efficiency), PTE (pure technical efficiency) and SE (scale efficiency) of the family farms are low. The mean value of the TE of all the family farms is as low as 0.3058, and among all the family farms, only 5.99% have the status of DEA effectiveness, while up to 75.66% are at a high level of ineffectiveness. The TE reflects the distance between the actual output of each decision-making unit (family farm) and the optimal output (production frontier) under the premise that the inputs of the production factors, such as labor, capital, and land, remain unchanged. The higher the TE, the better the production capacity. The result implies that the TE of family farms is low, indicating that the resources have not been used reasonably and effectively by the family farms, so the family farms are still in the primary stage of development and have much room for improvement.

By decomposing the TE into PTE and SE, it can be observed that the PTE value of all family farms is similar to that of the SE (0.5779 and 0.5213, respectively). Although the PTE and SE values of all the family farms are both higher than the TE, only 19.52% and 6.68% of family farms are in an effective status in terms of the PTE and SE, respectively. According to the equation of "TE = PTE × SE", the values of the PTE and SE that are not high enough resulted in the low value of the TE. As the PTE refers to the management ability and technical level of the family farms when other conditions remain unchanged, and the SE reflects the effectiveness of farm specialization and moderate scale operation, in order to improve the TE of family farms, it is not only necessary for family farms to improve the PTE by improving their management ability and technical level, but also to improve the SE by forming a moderate operation scale.

#### 4.1.2. Discussion of the Family Farm Efficiency in Different Regions and of Different Types

From the perspective that considers the different regions, the TE of family farms in Wuhan (0.3734) is slightly higher than that in Langxi (0.2464), and it is mainly attributed to the relatively higher SE in Wuhan (0.5994) than that in Langxi (0.4527), since the PTE values of Wuhan (0.5994) and Langxi (0.5590) are similar. Additionally, there are up to 50.8% of family farms in Langxi that are highly inefficient in terms of the SE, while the proportion for that in Wuhan is 28.94%, verifying that family farms in Wuhan are better at performing moderate scale operations to achieve higher efficiency.

From the perspective of different operation types, the TE of breeding family farms (0.4104) is higher than that of planting family farms (0.2605) and mixed family farms (0.3060). A possible explanation for this is that, given the similar SEs of the three types of family farms (0.5256, 0.5547 and 0.4874), breeding family farms have a higher PTE at 0.7102, while the PTE of planting and mixed family farms are 0.4997 and 0.6160, respectively. The values imply that the planting, breeding and mixed family farms all experience a similar condition of scale operation, whereas the breeding family farms benefit more from technical improvements rather than the expansion of scale, for breeding family farms do not require a scale as large as planting or mixed family farms, but rather require new technology to achieve intensive production.

#### *4.2. Discussion about the U-Shaped Relationship between Farm Efficiency and Land Scale*

The results of this paper show that the land scale has a U-shaped relationship with family farm efficiency. With the expansion of land scale, the efficiency of family farms first decreased then increased after a threshold, forming a U-shape.

However, many people are convinced that the land scale of family farms ought to have an inverted U relationship with their efficiency because of the achievement of optimal scale. In fact, the two views are not contradictory, because the U-shaped relationship between the land scale and farm efficiency is mostly observed in low-income developing countries, while the inverted U relationship is usually found in high-income developed countries.

Foster and Rosenzweig [30] explained the U-curve relationship very thoroughly. The Ucurve relationship between land scale and farm efficiency is driven by two factors: the cost of hiring laborers and the scale economies of machine capacities. In low-income countries, such as India, Indonesia and China, family farms are, on average, much smaller than those in developed countries, such as the U.S. For very small family farms in low-income countries, limited by the land scale, it is unlikely to implement mechanized production, and only family members work the land and operate their own farms efficiently. As the farm size increases, the family members work harder until they are unable to afford operating larger farmland by themselves and begin to hire additional labor, which comes with additional transaction costs and thus lowers their net income. The family continues to work the land as the farm size increases until the point that the benefit of hiring additional laborers outweighs the cost, and productivity starts to increase—which is where we observed the bottom of the curve. After this point, productivity rises with the farm size, as larger farms can take advantage of machines that have a greater capacity at larger scales and lower labor use, mirroring the economies of scale that are well-observed in developed countries. The inverted U-shaped relationship that many other scholars observed appears after the optimal scale achieved by the larger family farms, as after this optimal size point, the overlarge scale of family farms may exceed the management ability of family farmers and lead to diminishing farm efficiency. Hence, small farms in developing countries are more productive than those that are slightly bigger, but far less productive than the larger farms observed in high-income countries, as shown in Figure 1.

**Figure 1.** Relationship between farm efficiency and land scale.

The result of the U-shaped relationship between farm efficiency and land scale addressed in this paper indicates the left side of Figure 1, as the farm land scale is too small in China compared to that in developed countries, and family farms in China have to experience initial decreasing returns to increasing farm size to acquire a higher efficiency.

#### **5. Research Conclusions and Suggestions**

In recent years, in order to realize agriculture modernization and rural revitalization, the Chinese government has been focusing on the cultivation of new types of agricultural operating entities, among which family farms are promoted as typical representatives. Therefore, it is of great significance to study the efficiency of family farms and their influencing factors. This paper used the field survey data of 584 family farms in 2 national family farm demonstration bases in Wuhan City, Hubei Province and Langxi County, Anhui Province in 2016, and applied the DEA model to measure the efficiency of family farms. Then, the Tobit model was used to examine the key factors affecting the efficiency of family farms from four perspectives, agricultural factor input, characteristics of farmers, characteristics of family farms, and environmental factors, and further compared the family farms in different regions and of different types.

The research results show that the TE of all family farms is not high, and both the PTE and SE obtained by decomposing the efficiency can be improved. Breeding family farms have the highest efficiency, while planting family farms and mixed family farms have relatively lower efficiencies. The SE of mixed family farms is lower than their PTE, and it is the lowest among all types of family farms. The TE, PTE and SE of family farms in Wuhan are higher than that in Langxi.

Among the factors affecting the efficiency of family farms, capital input, farmer's education level, market channels, brand registration, the use of fertilizer and financial credit have positive impacts on the efficiency of family farms, while government subsidies and natural disasters negatively affect the efficiency of family farms. More specifically, the land operating area shows a U-shaped relationship with farm efficiency.

For planting family farms, labor input, farmer's education level, brand registration, and the use of fertilizer positively affect their efficiency, while land operating scale and natural disasters negatively affect it. For breeding family farms, capital input, new technology, and financial credit positively affect their efficiency, while brand registration negatively affects it. More specifically, the land operating area shows a U-shaped relationship with farm efficiency. As for the mixed family farms, capital input, market channels, brand registration, and financial credit positively affect their efficiency, while land operating scale and new technology negatively affect their efficiency.

From a regional perspective, the key factors affecting the efficiency of family farms in Wuhan mainly include the land operating scale, capital input, market channels and financial credit, and the key factors that affect the efficiency of family farms in Langxi include the land operating scale, capital input, farmer's years of farming, regulations, market channels, brand registration, fertilizer use, financial credit and natural disasters. More specifically, the land operating area negatively influences the farm efficiency in Wuhan, while it shows an obvious U-shaped relationship with farm efficiency in Langxi.

According to the research conclusions, it can be seen that although the family farms in the Wuhan and Langxi regions have been supported by the government for many years, the efficiencies of family farms in the two regions are still low, so it is of great significance to improve the family farms' efficiency. The factors affecting the efficiency of family farms in different types and regions vary. Therefore, family farms in each region and of different types needs to choose appropriate measures based on the actual situation and different types of local family farms, paying particular attention to the following points:

First, the local government should attach importance to the accumulation of agricultural input factors on family farms, especially encouraging the labor input of planting family farms and capital input of breeding and mixed family farms, to help improve the efficiency of family farms more precisely.

Second, the operating scale of family farms should be reasonably determined and family farms need to pay attention to moderate scale operations and not blindly expand their land scale. At the present stage, family farms in China should either stick to moderate scale operation, or transfer in a great amount of land under the support of the government to move beyond the bottom of the U-shape, to obtain a higher efficiency.

Third, family farms should be stimulated to optimize the internal operating environment, such as smooth their market channels, register brands and trademarks, and use fertilizer, so as to improve the productivity and market competitiveness of family farms.

Fourth, it is necessary for the government to create a favorable external environment for family farms, for example, build a standardized and multi-level rural financial market; increase support for financial credit; rationally plan government subsidies; and focus on the prevention and control of natural disasters.

**Author Contributions:** Conceptualization, Q.M.; methodology, Q.M.; software, Q.M.; validation, Z.C.; formal analysis, Q.M.; investigation, Z.C.; resources, Z.C.; data curation, Q.M.; writing—original draft preparation, Q.M.; writing—review and editing, Q.M., K.Y. and Z.C.; visualization, R.X. and K.Y.; supervision, Z.C.; project administration, Z.C.; funding acquisition, Z.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Humanities and Social Science Foundation of the Ministry of Education of China, grant number 17JJD790017; and the National Social Science Foundation of China, grant number 18ZDA040.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to restrictions.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

