Which Scale Is Appropriate for the Sustainable Management of Paddy Field?—A Case Study of Jiaxing, China

Abstract

This article aims to explore the appropriate scale for the cultivation of paddy field and its influencing factors in Jiaxing. The stochastic frontier production function and binary logit method were used to calculate the appropriate scale. The results showed: (1) The appropriate management scale of the paddy field in Jiaxing is 10–30 ha. (2) The farmers’ willingness to cultivate paddy field on a large scale was positively correlated with land quality, and their number of years engaged in agriculture. (3) It was negatively correlated with the difficulty of obtaining a loan and the age of the farmers. This research proposed that the government should continue to support the appropriate scale management of paddy field, and promote agricultural modernisation. At the same time, the government should also attach importance to promoting the role of science and technology in agriculture by actively training new generations of professional farmers, promoting land transfer, and implementing the subsidy policy for larger-scale cultivation to create a good environment for farmers to work on an appropriate scale.

1. Introduction

The term “appropriate scale management of paddy field” refers to the best use of land and other inputs to maximise agricultural income, while avoiding changes in the technical and economic environment. The theory of appropriate scale management of paddy field was first proposed by Arthur Young [1], a classical British economist in the 18th century. Since then, scholars have experienced a long period of exploration and research. At present, the study of appropriate scale management of paddy field mainly focuses on the standard calculation of moderate-scale operation, the factors affecting scale management [2], the relationship between scale management and productivity, and the relationship between scale management and economic benefits and technical efficiency [3,4].

The “appropriate” moderate-scale management of agricultural land varies in different regions. Koltun takes the Polish family farm as the background and obtains the result that the moderate management scale of a Polish family farm is more than 30 ha [5]. According to research by Jayne and other academics, which examined changes in farm size distribution in Ghana, Kenya, Tanzania, and Zambia over the past ten years, the number of medium-sized farms with a size of 5 to 100 ha is growing quickly throughout much of sub-Saharan Africa [6].

Scholars gradually realize that the management of small farmers has the characteristics of intensive farming and the advantage of low cost under family supervision, which have contributed to the improvement of production efficiency. As early as the 1990s, Russian scholar Chayanov discovered and proposed that there is an inverse relationship between farmland management scale and agricultural production efficiency (IR) [7]. Empirical research on developing nations in Asia, Africa, and South America has also confirmed this inverse relationship. For instance, Maina’s study of small farms in Kenya revealed that increased land size had a negative impact on economic efficiency [8]; Shete and Rutten discovered that large-scale agricultural operations in densely populated areas of central Ethiopia’s highlands resulted in a decrease in farmers’ incomes [9]. Researchers have also examined the causes of IR in farmland-scale operation. Due to the imperfect nature of the labour market, large-scale operations are more likely to generate transaction risks, such as information asymmetry and land transfer disputes. On the other hand, small-scale household management is more conducive to maximising farmers’ enthusiasm and reducing supervision costs and risks. Foster et al., for instance, use labour market transaction costs to explain why small farms are more efficient than large farms in the majority of low-income countries [10]; the constant rate of return on land-level data from Ali in Rwanda demonstrates a negative correlation between farm size and crop productivity, a key factor of which is the imperfect labour market [11].

In addition, the primary focus of the study of appropriate scale is the research on the influencing factors of farmland’s appropriate scale, which includes socioeconomic and natural environmental factors. For illustration, between 2005 and 2016, Ambros analysed statistical data on agricultural land development in ten European Union (EU) member states surrounding the Baltic Sea. The results show that the transformation from small farms to large farms is due to production mechanisation and agricultural policy tendencies [12]. Gorton found that factors affecting the scale of family farm management include the education of the labour force and the level of agro-technical training [13]. According to Ogundaril, the number of parcels, the degree of dispersion, the area of farmland, the level of education, and the availability of credit funds all affect agricultural production in Africa [2].

Despite the fact that scale management research in China began later than in other countries, numerous theoretical and practical research methods have accumulated in recent years. In 1987, the Chinese government raised the issue of agricultural production’s appropriate scope for the first time. Several documents have since addressed the issue of paddy field management’s appropriate scope. China has investigated the concepts of connotation, scale size, path mode, factors influencing the appropriate scale management, and practical concerns [14,15,16,17,18,19,20,21]. The appropriate scale of paddy field management varies with different regions. For agricultural development, it is crucial to determine the optimal scope of management based on local conditions. Wang Rou developed an evaluation criterion based on the dimensions of land management efficacy and income [22], while Duan Lufeng conducted research from the standpoint of the marketisation of land management rights [23].

With regard to research methods, in addition to the parameter method of SFA random analysis [24,25,26] and the non-parameter method of DEA data envelopment analysis [27], several methods commonly used in the academic circle also include the production function method of the linear programming model [28]. As an example, Wu Fang utilised the trans logarithmic stochastic frontier model to analyse the technical efficiency of grain production in family farms [29], Li Ruihao chose the DEA data envelopment method to study the optimal management mode of the tea industry [30], and Hu Yanni et al. utilised the C-D production function to quantitatively calculate the appropriate scale of farmers’ operations in Longxi Count [31]. For the most part, parametric and nonparametric methods are utilised by scholars to investigate technical efficacy. Unlike existing studies based on non-parametric methods [32,33,34] that are susceptible to random factors, the stochastic frontier production function model can distinguish between random and technically inefficient items. As rice production is susceptible to the external environment and has randomness, it is preferable to use the SFA stochastic frontier production function, which can effectively eliminate data noise for technical efficiency analysis, to investigate the appropriate scale of paddy field management. For instance, Ajibefun used the stochastic frontier production function model to estimate what kind of total land area has the highest average technical efficiency of farmers and found that the appropriate agricultural management scale in Nigeria is 1–1.49 ha [35].

Research on the appropriate scope of paddy field management in China has been conducted primarily in grain-producing regions of the northeast or central China, with very few studies conducted in east China. In addition, the study of paddy field scale management must be combined with the reality of economic system transformation and social service renewal. Current research on the specific circumstance of China’s rural areas within the context of agricultural development in the new era is insufficient. Therefore, the purpose of this study is to determine the optimal paddy field management scale in Jiaxing, East China, utilising the stochastic frontier production function and a survey of 94 peasant households in order to provide references for promoting the efficient and intensive use of paddy field in the water net plain area. The purpose of this study includes the following points: 1. To understand the rice management status of rice farmers in Jiaxing. 2. Calculating the scope of appropriate scale operation of farmland in Jiaxing. 3. Exploring the realistic factors that affect farmers’ expansion of management scale, and putting forward the ways to achieve appropriate scale management. On the basis of a comprehensive analysis of the moderate-scale operation scope and influencing factors of each region, we conclude that each region’s operation scale is dependent on its own conditions. Due to the favourable natural and socioeconomic conditions of rice cultivation in Jiaxing City and the context of China’s agricultural modernisation, this study proposes two hypotheses.

Hypothesis 1.

Compared with other regions, the scope of moderate-scale operation in Jiaxing is larger.

Hypothesis 2.

Land factors and policy factors play an important role in influencing the moderate-scale management of farmers in Jiaxing.

2. Study Area and Data Source

2.1. Study Area

The reasons for choosing Jiaxing City, Zhejiang Province as the study area in this study include the following points: (1). Jiaxing is an important grain production base in China, and its rice output ranks first in Zhejiang Province for many years. (2). As an economically developed water network plain, Jiaxing is representative in the study of appropriate scale in China. (3). Jiaxing City has implemented global land renovation and promoted the development of agricultural production conditions conducive to the development of appropriate scale operation.

Jiaxing is located in the north of Zhejiang Province, East China. It is in the center of the Yangtze River Delta urban agglomeration, with convenient transportation. It is under the control of the subtropical monsoon climate. Because of its excellent natural conditions, i.e.,a plain topography, plenty of light and water, it is suitable for rice planting, being an important commodity grain base, and has the laudatory name “granary in northern Zhejiang”. In 2021, the sown area of grain crops in Jiaxing was 150,900 ha, accounting for 14.98% of the sown area of Zhejiang Province, and the grain output amounted to 977,900 tons, accounting for 15.75% of the whole province. At the same time, Jiaxing has achieved good results in rural governance. Therefore, it is representative and beneficial to choose Jiaxing to study the appropriate scale management of rice planting against the background of rural revitalisation in the new era.

In recent years, the cost of rice production has been rising year by year, the prices of land rent and labour have remained high, and the threshold for applying for agricultural loans is high. In addition, the situation of agricultural production and operation is strongly dependent on natural conditions, and it is still difficult for agricultural insurance to fully play the role of protection. The above problems have become concerns for farmers to expand their business scale.

2.2. Data Sources

The data used in this paper were based on a questionnaire survey of rice growers in Xiuzhou, Haining, Jiashan, and Tongxiang countries in Jiaxing in June 2022. A total of 94 valid questionnaires were obtained by telephone interview. The questionnaire items include the basic information of the farmers’ families, the input of rice planting factors, costs and benefits, influencing factors, and so on. Other data were obtained from the Statistical Yearbook of Jiaxing, the Statistical Yearbooks of Xiuzhou, Tongxiang, and Jiashan, and the Statistical Bulletin of National Economic and Social Development of the above counties and districts in recent years.

The descriptive statistical information is shown in

Table 1. Descriptive statistical information on input and output factors of rice farmers in Jiaxing in 2021.

Variable	Average Value	Standard Deviation	Minimum	Maximum	Coefficient of Variation
$\mathrm{Y}$	546,029.36	460,109.42	45,353	2,526,826.5	0.84
$\mathrm{H}$	309,731.21	271,717.93	21,700	1,531,410	0.88
$\mathrm{C}$	302,088.93	310,431.52	18,600	1,725,000	1.03
$\mathrm{L}$	430.85	209.88	180	1260	0.49
$\mathrm{X}$	25.08	20.88	2.07	120.91	0.83

. $\mathrm{Y}$ denotes rice output value per household; $\mathrm{H}$ denotes land input per household; $\mathrm{C}$ denotes capital investment per household; L denotes labour input per household; and X denotes rice area. According to the survey, the average output value of rice among farmers in the study area in 2021 was CNY 546,000 per household, the maximum value amounted to CNY 2.5268 million, and the minimum value was only CNY 45,400, indicating that there was a large gap between farmers. From the perspective of the rice sown area, the maximum operating area was 120.91 ha, the minimum was 2.07 ha, and the average operating area of farmers was 25.08 ha. From the perspective of input factors, the average input land cost, capital cost, and labour cost of farmers in the sample area in 2021 were CNY 309,700, CNY 302,100, and 430.85 working days, respectively. The coefficient of variation reflects the discrete degree of labour, capital, and land input factors, and the total output of rice. According to the table below, the coefficient variation of agricultural capital input is the largest, while that of labour input is small. Generally speaking, there is a big difference between the input data and output data of rice farmers in Jiaxing, indicating that the moderate-scale development of agriculture in the study area is not balanced, and the household capital investment of farmers with larger operation scales is also higher. On the other hand, small-scale farmers cannot enjoy the benefits of scale returns. Therefore, it is necessary to explore the best rice business scope. In the following, the selection of research methods takes into account the dispersion of the data, uses the stochastic frontier production function method to separate the technical invalidity term, and also significantly eliminates the impact of statistical errors on the results.

3. Methodology

To test the aforementioned hypothesis, the stochastic frontier production function was used to investigate the optimal scale of paddy field management. This model’s distinguishing feature is that it can estimate the studied production unit with the highest probability and derive the only effective theoretical frontier function. Simultaneously, the error effects and technical efficiency losses caused by random factors that may exist in agricultural production activities are incorporated into the process of building the model so that the research results can to a certain extent eliminate interference, thereby ensuring the accuracy and stability of the research results. In the past, numerous existing studies employed the non-parametric method and DEA data envelopment method and were conducted from a provincial perspective or comparative analysis of provinces. Using the parameter method of the stochastic frontier production function model and a survey of family farms in the water network plain area, the appropriate scale of paddy field management is investigated in this paper. In addition to considering objective factors such as farmers’ satisfaction with subsidies and the difficulty of loans, this study also considers objective factors such as farmers’ age and level of education.

3.1. Stochastic Frontier Production Function Model

In this paper, the stochastic frontier production function model was selected to analyse the technical efficiency of rice-growing family farms in Jiaxing. This method was put forward by Aigneret in 1977 [36]. In agricultural production, it can also examine the relationship between multiple inputs and a singular output. This method has the ability to account for the impact of technical inefficiencies, resulting in more accurate and comprehensive results.

Referring to the research on the technical efficiency of the main grain-producing areas by Zeng Yating et al. [37], the model is set as follows:

$$Y_i=f\left({{\rm X}}_i,\beta \right)\exp \left(V_i-U_i\right)$$

(1)

Taking the logarithm of both sides gives:

$$\ln Y_i=\ln f\left({{\rm X}}_i,\beta \right)+V_i-U_i$$

(2)

In Formulas (1) and (2), $i=1\sim n$, $Y_i$ represents the output of the farmer numbered $i$; $f\left(\cdot \right)$ represents the best output under the current technical conditions; and ${\mathrm{{\rm X}}}_i$ represents the input of production factors of the household numbered $i$, including land input, agricultural capital input, and labour input. $\beta$ denotes the parameter vector to be estimated; $V_i$ denotes the random error term, which means uncontrollable influence; and $U_i$ denotes the management error item, representing the difference between the actual output and the expected output of the farmer household.

The formula of farmers’ production technical efficiency is

$$\mathrm{{\rm T}}\mathrm{{\rm E}}=\frac{\mathrm{{\rm E}}\left(Y_i|u_i,{\mathrm{{\rm X}}}_i\right)}{\mathrm{{\rm E}}\left(Y_i^{\ast }|u_i=0,{\mathrm{{\rm X}}}_i\right)}=\exp \left(-u_i\right)$$

(3)

In the Formula (3), $Y_i$ denotes the actual output of the farmer; $Y_i^{\ast }$ denotes the expected output. When the value of $\mathrm{{\rm T}}{\mathrm{{\rm E}}}_i$ is between 0 and 1, the technical efficiency reaches the highest point when the value is 1, and there is no loss of efficiency.

In the practical application of the stochastic frontier production function, the transcendental logarithmic production function is selected according to the actual situation, which has the advantages of flexibility and good inclusiveness. The research formula is set as follows:

$$\begin{gathered} \ln Y_i={\beta }_0+{\beta }_1\ln L_i+{\beta }_2\ln C_i+{\beta }_3\ln H_i+{{\beta }_4\left(\ln L_i\right)}^2+{{\beta }_5\left(\ln C_i\right)}^2+{{\beta }_6\left(\ln H_i\right)}^2 \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+{\beta }_7\ln L_i\times \ln C_i+{\beta }_8\ln L_i\times \ln H_i+{\beta }_9\ln C_i\times \ln H_i+{\nu }_i-{\mu }_i \end{gathered}$$

(4)

In the above formula, $Y_i$ denotes the total output value of rice peasant household; $L_i$ denotes the number of labour force of peasant household; $C_i$ denotes the capital input value of peasant household, including the costs of agricultural materials, such as seeds, fertiliser, medicine, machinery, water, electricity and oil; and $H_i$ denotes the operating area of paddy field per household, including the area of contracted land transfer. ${\beta }_i$ denotes unknown parameters; ${\nu }_i$ denotes random error terms; and ${\mu }_i$ denotes technical inefficiency terms.

3.2. Binary Logit Regression Model

The binary logit regression model is mainly aimed at the situation where the dependent variable is dichotomous, that is, the 01 variable. In this study, whether farmers are willing to expand the scale of management is selected as the dependent variable for regression analysis, so combined with the actual requirements, the farmers who are willing to expand the scale of management are selected to choose $\mathrm{Y}=1$, otherwise $\mathrm{Y}=0$. In order to minimise the sum of squares of the error term, maximum likelihood estimation (maximum likelihood estimation) is chosen to solve. The formula is set as follows:

$${\log }_{i}t\left(\frac{p}{1-p}\right)=\alpha +{\beta }_1\times x_1+{\beta }_2\times x_2+\cdots +{\beta }_i\times x_i+\epsilon$$

(5)

In Equation (5), $\alpha$ denotes the intercept of the regression model, $\beta$ denotes the unknown parameter, $x_i$ denotes the explanatory variable, and $\epsilon$ denotes the error term. $p$ denotes the probability of the event of expanding the management scale for rice growers: the farmers expand the management scale when the set value is 1, and when the value is 0, the farmers do not choose to expand the management scale.

4. Results

4.1. Appropriate Scale

4.1.1. Input and Output Data

When measuring the technical efficiency of agricultural production, most scholars choose the total output value, or total output, as the output variable. This paper examines the scale of land management, and since it is inappropriate to use yield per unit area, the total output value of rice managed by farmers is chosen as the output factor, and the rice price for the year is multiplied by the total output of rice managed by farmers. There are three input factors: land, capital, and labour force.

The most essential element in agricultural production is land. The quantity of capital and labour farmers invest will be influenced by the quality of the land and the agricultural infrastructure. A paddy field that is too small is not conducive to mechanised production, while a paddy field that is too large may squander resources. In addition to issues such as land transfer and the determination of paddy field rights, farmers’ business expectations will also consider land transfer and the determination of paddy field rights. The land input factor is expressed as the product of the total rice management area and the land rent price, with yuan serving as the unit.

The cost of agricultural means of production and agricultural apparatus is included in the capital input. A vital link in agricultural production is the input of means of production. The key is high-quality rice, and chemical fertilisers and pesticides compensate for soil fertility deficiencies and natural disasters. The use of agricultural machinery for rice planting and harvesting significantly reduces labour requirements and increases production efficiency. This paper’s method for calculating capital input factors is the sum of the costs of seeds, pesticides, and fertilisers; agricultural apparatus purchased by peasant households; and labour, water, electricity, and oil used in the production process.

Even though Jiaxing has a high level of agricultural mechanisation in the process of rice production, labourers are still required for manual input from a cost and convenience perspective. The labour input is proportional to the number and duration of employees. It is calculated by multiplying the number of employees engaged in rice production by the number of working days.

4.1.2. The Suitability of Stochastic Frontier Production Function

Considering the convenience of data acquisition and the accuracy of the research results, the cross-sectional data of input and output of rice farmers in four counties of Jiaxing in 2021 were mainly selected, and the input and output data obtained from the questionnaire were input into the model by using FRONTIER4.1 software to measure the technical efficiency of rice planting and production. The running results can be seen in the following

Table 2. Parameter estimation of stochastic frontier production function.

Parameters	Estimated Result	Standard Deviation	t-Test Value
${\beta }_0$	0.4362	0.0941	4.6344
${\beta }_1$	0.8489	0.0525	16.1633
${\beta }_2$	0.1067	0.0410	2.6057
${\beta }_3$	0.0836	0.0237	3.5229
${\sigma }^2$	0.0334	0.0120	2.7781
$\gamma$	0.9712	0.0019	516.0858
$\mu$	0.1819	0.1046	1.7400

:

It can be seen that there was a significant positive correlation between land, capital, and labour input and rice management output value in the study area. The elasticity coefficients of land input, capital input coefficient, and labour input coefficient were 0.8489, 0.1067, and 0.08359, respectively. A value of 0.9712 indicated that 97.12% of the technical inefficiency came from management errors rather than observation errors, and only 2.98% stemmed from random errors, which verified the accuracy of parameter estimation, indicating the feasibility of using the stochastic frontier production function to study. In addition, the logarithmic likelihood function was 59.7083 and the LR test of unilateral error was 12.664. It showed that the fitting result of the function was good and passed the LR one-sided test. All the above showed that it is suitable to use the stochastic frontier production function method to explore the technical efficiency of rice production.

4.1.3. Appropriate Scale Size

According to the regional management situation and investigation in Jiaxing, farmers with technical efficiencies of less than 0.7 were defined as inefficient production households, those with technical efficiencies between 0.7 and 0.8 as low-efficiency households, those with technical efficiencies between 0.8 and 0.9 as higher-efficiency production households, and those with technical efficiencies between 0.9 and 1 as the most efficient households. Thirteen households were inefficient producers, with a technical efficiency of 0.6841 on average. The average efficacy of the 32 low-efficiency households was 0.7499. There were 26 more efficient households, resulting in a mean efficiency value of 0.8461. The average efficiency value of the 23 most effective households was 0.9490. It revealed that the overall technical efficacy of rice cultivation in Jiaxing was high, but that some inputs and outputs were inefficient. Therefore, it is necessary to investigate the precise connection between technical efficacy and management scale.

The technical efficiency of paddy field management scale varies with the business scale: as scale that is too large often leads to extensive waste of resources, while an operation scale that is too small is not conducive to agricultural mechanisation. Therefore, we must choose an appropriate scale operation according to local conditions. Liu Ying [38], Qu Xiaobo [39], and other scholars confirmed that there was an inverted U-shaped relationship between operation scale and technical efficiency through empirical research, and showed a trend that the technical efficiency of agricultural production increased first and then decreased with the expansion of management scale. With reference to the existing research classification standards and combined with the basic situation of rice management in Jiaxing City, the household management scale is divided into four groups: less than 10 ha, 10–30 has, 30–50 ha, and more than 50 ha. The survey showed that 55.3% of households grew their rice crop in the range of 10–30 ha, 20.2% in the range of 30–50 ha, and 17% in the range of fewer than 10 ha, while those in the range of 50 ha or more accounted for only 8.5%. The scale of rice management in Jiaxing was mainly medium-sized. From a technical efficiency standpoint, the optimal management scale was between 10 and 30 ha.

As shown in

Table 3. Comparison of annual input-output and technical efficiency of rice planting at different scale sizes in Jiaxing.

Scale Grade/ha	H ≤ 10	10 < H ≤ 30	30 < H ≤ 50	H > 50
Average scale size/ha	6.35	18.96	36.09	80.34
Average land input/yuan	72,651.94	230,094.1	421,422.32	1,026,309.94
Average capital investment/yuan	72,339.65	216,181.00	411,487.37	915,976.70
Average labour input/yuan	74,250.00	84,000.00	98,526.32	94,500.00
Average output value/yuan	138,605.26	417,168.26	735,300.51	1,732,848.11
Average technical efficiency	80.55%	82.04%	81.23%	79.09%

, the expansion of the management scale increased producers’ land and capital investment in rice management, as well as the output value of rice. In contrast, the level of labour input initially increased and then decreased, and when the operating scale exceeded 50 ha, labour input decreased relatively. This indicates that the maximum consumption of artificial input occurred between 30 and 50 ha. Depending on the extent, farmers’ investment in production and operations varied. When the scale of rice cultivation was less than 10 ha, the average value of land capital and labour input was low, as was the output value, and the technical efficacy was low. The greatest level of paddy field management efficiency at a scale of 10–30 ha was 82.04%. The farmers’ land, capital, and labour inputs were more reasonable at this magnitude, resulting in an efficient allocation of resources. When the management scale was greater than 30 ha but less than 50 ha, the technical efficiency of rice production was relatively high; however, when the management scale exceeded 50 ha, the technical efficiency of rice production dropped to its lowest level, and the input-output level was the most unreasonable.

4.2. Farmers’ Willingness to Operate on a Large Scale

4.2.1. Influencing Factors

There found four categories of variables affecting the scale operation willingness of rice farmers in Jiaxing.

(1)

Peasant household and personal characteristics

Three factors are mainly considered: the age of farmers, the level of education, and the number of the family labour force. The average age of rice farmers surveyed was about 52 years old, and 80% of them were under 60 years old, indicating that the labour force age structure was slightly aging. The education level of farmers was mostly concentrated in primary and junior high school, of which junior high school education and below accounted for nearly 2/3. The number of labour forces per household was usually two, accounting for 58.51%.

(2)

Agricultural management characteristics

The results showed that 54.26% of the respondents rated their paddy field as of average quality. In addition, the average number of years of farming of sample farmers was 20.51 years, and their overall farming experience was rich.

(3)

Land transfer characteristics

The number of years of land transfer and land rent was considered. The average transfer duration of the contracted land was 4.19 years, and actually, the length of land transfer was mostly only one year, reaching a proportion of 45.74%. Annual land transfer rent per mu under the contract ranged from CNY 700 to CNY 1030, with an average of CNY 808.4.

(4)

External environment characteristics

The farmers’ satisfaction degree for policy subsidies reached 71.28%, while agricultural loans were difficult for 52% of farmers.

Table 4. Factors influencing the scale management willingness of rice farmers in Jiaxing.

Index Variable	Assignment Description	Mean Value	Standard Deviation	Expected Direction
Scale management behaviour of rice growers ($Y$)	Whether there is a willingness to expand the scale of operation; if so, then $Y=1$, otherwise $Y=0$
1. Peasant household and personal characteristics
Age (${\chi }_1$)	Farmers’ age/year.	52.45	9.08	-
Education level (${\chi }_2$)	1 = primary school and below, 2 = junior high school, 3 = senior high school and above.	1.76	0.66	+
The labour number per household (${\chi }_3$)	Labour forces per household	2.39	1.16	+
2. Agricultural management characteristics
paddy field quality (${\chi }_4$)	1 = poor, 2 = average, 3 = good	1.73	0.62	+
Number of years of farming (${\chi }_5$)	Years engaged in rice planting	20.51	11.15	-
3. Land transfer characteristics
The number of years of land transfer (${\chi }_6$)	The duration of land transfer under contract/year	4.19	4.28	+
Land transfer rent per mu (${\chi }_7$)	Annual land transfer rent per mu under the contract/yuan	808.40	72.98	-
4. External environment characteristics
The satisfaction degree for subsidy policy (${\chi }_8$)	Satisfied = 1, not satisfied = 0	0.71	0.45	+
Difficulty degree of agricultural loan (${\chi }_9$)	1 = easy, 2 = difficult, 3 = not clear	2.01	0.69	-

reflects the data statistics of nine variables for the four categories of indicators selected above, as shown below:

4.2.2. Collinearity Test and Binary Logit Regression of Influencing Factors

To determine whether or not the variables were independent of one another, the variance expansion factor was employed. The specific step is to insert the explanatory variables into the model for multiple collinearity tests in order to calculate the variance expansion factor (VIF) via regression. If the VIF value is less than 10, multicollinearity does not exist. In this study, the variance expansion factor ranged from a maximum of 2.25 to a minimum of 1.04, indicating that the studied influence factors were independent and passed the multiple collinearity test. The sample data were processed by SPSS 26.0 software, and the likelihood ratio test results are shown in

Table 5. Likelihood ratio test results of bivariate logistics regression model.

Model	−2 Times Logarithmic Likelihood	Wald	df	p
Final model	91.167	29.401	12	0.003

, p less than 0.05, indicating that the model is effective.

The fitting degree of the logit regression model, the coefficient of the logit regression model, and the significance of the coefficient were calculated by the software. The significance of the model tested by Hosmer–Lemeshow was 0.496; p > 0.05 means the fitting effect of the model and real data is good.

$x_1$ denotes the age of farmers; $x_2$ denotes the education level of farmers; $x_3$ denotes the labour number per household; $x_4$ denotes the quality of paddy field; $x_5$ denotes the number of years engaged in rice planting; $x_6$ denotes the duration of land transfer under contract; $x_7$ denotes land transfer rent per mu; $x_8$ denotes the satisfaction degree of farmers with the subsidy policy; and $x_9$ denotes the difficulty degree of agricultural loans.

The results of binary logit regression are shown in

Table 6. Hosmer–Lemeshow fit test.

χ2	df	p
7.432	8	0.496

, and the binary logit regression function for predicting the selection of rice farmers is obtained.

$$\begin{gathered} \ln \left(\frac{p}{1-p}\right)=10.297-0.169\times x_1+0.001\times x_2+0.275\times x_3+1.243\times x_4 \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+0.080\times x_5-0.024\times x_6-0.004\times x_7+0.762\times x_8-0.813x_9 \end{gathered}$$

(6)

The formula represents the probability of choosing $p$ to expand the management scale of paddy field, the probability of choosing $1-p$ not to expand the scale. The meanings of $x_1$ to $x_9$ are the same as those in

Table 7. Results of binary logit regression analysis.

Variable	B	Standard Error	Wald	Significance	OR Value	95% Confidence Interval of OR Value
$x_1$	−0.169	0.051	10.867	0.001 ***	0.844	0.763~0.934
$x_2$	0.001	0.471	0.000	0.999	1.001	0.398~2.517
$x_3$	0.275	0.239	1.322	0.250	1.317	0.824~2.106
$x_4$	1.243	0.458	7.375	0.007 ***	0.289	0.118~0.708
$x_5$	0.080	0.032	6.370	0.012 **	1.084	1.018~1.153
$x_6$	−0.024	0.072	0.105	0.745	0.977	0.847~1.126
$x_7$	−0.004	0.004	0.779	0.377	0.996	0.988~1.005
$x_8$	0.762	0.622	1.500	0.221	2.143	0.633~7.259
$x_9$	−0.813	0.411	3.920	0.048 **	2.254	1.008~5.040
Constant	10.279	4.594	5.007	0.025	29124.165	3.580~236,912,134.622
−2 Log likelihood = 91.17
Cox and Snell R square: 0.269
Nagelkerke R square: 0.372

Note: *** p < 0.01; ** p < 0.05.

.

5. Discussion

The appropriate scale of paddy field management is jointly influenced by natural resources and the social economy and varies with regions. Compared with the research results of other regions, the optimal operation scale of this study is relatively larger. This may be attributed to the fact that, in Jiaxing, the terrain is flat, the economy is developed, the level of agricultural science and technology is high, and the conditions for agricultural mechanisation are superior. In addition, the perfect agricultural land transfer policy and transfer transaction platform are also conducive to the centralised and large-scale development of land.

The analysis of the coefficient of elasticity of land, labour, and capital in the study area shows that farmers’ land input has a positive impact on agricultural technical efficiency. The main reason is that the increase of land investment and the expansion of operation scale help to realise the scale effect of agricultural production and management. The expansion of rice scale creates flat and continuous land conditions for agricultural mechanisation production.

Inputs of capital and labour have a positive effect on the technical effectiveness of rice management. This is due to the fact that capital investment is not only an essential factor affecting rice yield, but also helps to solve the problem of nutrition absorption and reduce diseases and insect pests during rice growth, thereby increasing farmland production and income. The use of agricultural machinery can simplify the traditional rice production process, reduce labour input, and increase production efficacy. The larger the operation’s scope, the more conducive it is to economies of scale as the number of employees rises. Jiaxing is an economically developed coastal city; the cost of youthful labour is higher, and the greater the number of household labourers, the greater the labour cost savings for farmers, which increases the rice production’s technical efficiency.

In term of the regression results from Table 6, the farmers’ willingness to cultivate paddy field on a large scale were positively correlated with land quality and their number of years engaged in agriculture, while it was negatively correlated with the difficulty of the loan and the age of farmers. First of all, the land quality affected the willingness of farmers to expand their management scale. The regression coefficient of land quality was 1.243, which indicated that land quality had a significant positive effect on farmers’ willingness. Land quality is the integration of land smoothness and soil fertility, including paddy field infrastructure. The higher the land quality, the higher the output of agricultural production, and the higher the agricultural technical efficiency. Therefore, farmers with better-quality land were more willing to expand their management scale to increase the output value.

Second, the number of years farmers had planted rice influenced their propensity to increase the scale of management. The longer the producers planted rice, the more eager they were to increase the cultivation area. Agricultural produce is highly dependent on farmers’ management skills. In general, the longer producers have managed rice, the greater their rice planting expertise. Farmers with more experience understand the growth and development of crops better and are frequently more inclined to expand their operations.

Third, age had a negative impact on the producers’ willingness. Although agricultural mechanisation has become commonplace, rice cultivation still requires a significant amount of manual labour. It is normal to work lengthy hours under difficult circumstances. Due to physical limitations, older farmers are unable to manage larger plots of land; consequently, as farmers age, their desire to expand their cultivation area progressively wanes.

At last, the loan difficulty had a substantial negative effect on farmers’ willingness to increase the scope of their cultivation. In addition to the costs associated with purchasing agricultural production materials such as seeds, pesticides, and chemical fertilisers, there are also costs associated with employing harvest labour and purchasing agricultural machinery. These must invest a large sum of money in a brief period of time. A government loan is an effective means of resolving a lack of funds, but agricultural loans frequently have complex procedures and stringent terms. When the difficulty of the loan increases, producers lack the funds necessary to increase their scale, so they are forced to maintain the original size.

Despite the fact that this study is limited to a specific rice management area in Jiaxing, it can be used to explain the appropriate scale and influencing factors of rice in other water network plain areas. The factors influencing the appropriate magnitude of paddy field management in Jiaxing shared similarities with other studies. It is also influenced by agricultural modernisation and market-driven growth. In this case, farmers must not only consider the environmental endowment of the region during production and management but also give greater attention to policy adaptation. Considering the uniqueness of the crop-sowing industry, this paper’s findings also pertain to international research. For instance, Xiong Zhichao put forward that the important factors affecting the willingness of farmers in Qiyang County include age, land rent and time limit, the area of contracted land, and so on [40]. Sun Tong’s exploration of the tea industry in Anhui Province confirmed that the degree of mechanisation and regional circulation were correlated with farmers’ willingness [41]. Ambros found that the reason for the transformation from small farms to large farms in the Baltic Sea lies in the change of agricultural policy tendency [12]. Yagi et al. found that the government’s policy of promoting leasing improves land mobility and helps to increase the size of family rice farms in Fukui Prefecture, Japan [42]. Hoang et al. put forward that government intervention is an important factor in promoting agricultural specialisation in the study of the rice scale in Vietnam [43]. This study has its limitations in terms of the different relationships that may exist in different backgrounds of the influencing factors of agricultural production. Comparatively, developed regions have more agricultural production resources and greater agricultural technical efficacy than China, which explains why European government regulation and farmer education may play a larger role in the agricultural upgrading process [44]. As this study concentrates on the rice planting industry, although its results can serve as a reference for other policy-oriented and labour-intensive production and management, the diversity of industrial characteristics necessitates additional empirical research to validate our conclusions. Omotilewa et al. also have found that agricultural policy can promote the growth of agricultural productivity, agricultural commercialisation, and food security in Nigeria [45]. Kusz et al. discussed the impact of macro factors and agricultural subsidies on the scale change of grain farms in Poland [46]. This is because geography and policy support may continue to influence the business decision-making behaviour of farmers in other nations, as evidenced by studies on the agricultural scale and efficacy of the dairy industry in Western Europe and the grape industry in Western Cape, South Africa [47].

The novelty of this paper resides in the beneficial investigation of the content model of moderate-scale agricultural land management in conjunction with the new era’s Chinese characteristics. The study examines the issue of agricultural land management on a moderate scale from the standpoint of farmer income and concludes that the optimal rice management scale in Jiaxing is between 10 and 30 ha. Moreover, it is concluded that the quality of farmland, the age of farmers, the number of years of rice planting, and the difficulty of obtaining agricultural loans are the primary factors influencing the propensity of rice farmers in Jiaxing to expand their operations.

6. Conclusions and Countermeasures

6.1. Research Conclusions

This study examined the agro-technical efficacy of rice producers in Jiaxing’s water network plain using the stochastic frontier production function. The following conclusions were reached after using the binary logit technique for the analysis of the variables influencing rice farmers’ desire to increase their management scale:

(1)

From the perspective of technical efficiency per household, paddy field management scale which is too large or too small does not have advantages; only moderate-scale operation can achieve the goal of increasing farmers’ income, and resource allocation under a reasonable scale can achieve the best operating profits. A moderate-scale operation had a significant positive impact on technical efficiency. To realise the moderate-scale operation of rice for farmers, we must realise the optimal allocation of land, capital, and labour force. The development conditions of moderate-scale operation in Jiaxing are good, and most farmers also have the will to continue to transfer land and expand the scale of operation in the future.

(2)

The overall technical efficiency of rice farmers in Jiaxing was higher: the average technical efficiency was 0.8072. The condition of paddy field scale management was better: the average management scale reached 25.08 ha, and the optimal range of scale management was 10–30 ha. There are still some farmers whose rice management scale is too small or too large. In order to realise the appropriate scale operation with the best technical efficiency of rice production, it is necessary to promote land transfer and optimise the scale of rice management per household in Jiaxing.

(3)

From the perspective of technical efficiency, the land input coefficient, capital input coefficient, and labour input coefficient of Jiaxing are 0.8489, 0.1067, and 0.0835, respectively, indicating that the returns of grain production scale of rice farmers in Jiaxing are increasing and the effect of economies of scale is significant. Land input factors have the most significant impact on the technical efficiency of management, indicating that the scale of agricultural land management is an important factor affecting agricultural production. The calculation results of the stochastic frontier production function show that when resources are allocated reasonably and effectively, farmers in Jiaxing have 19.28% of potential output under given input-output conditions.

(4)

According to the regression analysis of whether rice farmers in Jiaxing are willing to expand their management scale in the future, we know that the factors that affect farmers’ decision-making willingness mainly include farmland quality, the number of years of rice management, the age of interviewed farmers, and the difficulty of agricultural loans. The quality of farmland and the number of years in which farmers operate rice play a positive role, while the age of farmers interviewed and the difficulty of agricultural loans have a negative impact. This is determined by the endowment characteristics of agricultural production and the personal quality of farmers. Farmers’ rice planting is affected by the quality of farmland and the level of their management. The better the quality of farmland is and the more experienced farmers are, the higher the income of rice planting is. Therefore, the production enthusiasm of expanding operation and increasing agricultural income is higher. On the other hand, the older farmers interviewed and those who have difficulties with agricultural loans do not have more time, energy, and capital investment. In addition, compared with the young peasant households, the anti-risk ability of the aged labour force is poor, and the farmers pay more attention to the social security function of land rather than the function of operating income.

6.2. Countermeasures and Suggestions

In the future, the government must stick to the strategy of prioritising agricultural development, first by reforming the agricultural production and management model, encouraging the development of modern agriculture in Jiaxing in accordance with local conditions, actively guiding and promoting appropriate scale cultivation, and figuring out the rational distribution of human and land resources.

(1)

Promoting moderate-scale agricultural management and enhancing agricultural quality and productivity. The government should construct, convert, and upgrade agricultural infrastructure and increase the impetus for mechanising grain production. In the production process, they should optimise the input structure of factors, improve the allocation efficiency, increase investment in agricultural scientific and technological innovation, maximise the contribution of scientific and technological personnel to the development of agriculture, and implement high-level processing technology. The construction of the rice industrial chain must be actively improved throughout the entire process, and production and marketing must be merged to create rice brands of superior quality and attract consumers with high-quality regional characteristics. Additionally, they must encourage the integrated development of the primary, secondary, and tertiary industries in rice-producing regions, as well as the development of the agricultural production system towards specialisation, standardisation, and modernisation.

(2)

Farmers’ age and knowledge structure should be optimised, as should the training of agricultural personnel of a new type. In light of the ageing of farmers and their lower levels of education, it is necessary to maximise policy advantages to encourage young and middle-aged workers with a higher level of knowledge to return to their hometowns and start businesses, as well as to guide middle-aged workers to actively engage in agricultural professional and technical training. Additionally, the rural old-age insurance system should be enhanced to provide land transfer security for ageing farmers.

(3)

In order to inject vitality into rural development, it is vital to maximise the government’s leadership and policy support. Additionally, the government should invest special funds and actively support the improvement of cultivated land, the scale of rice cultivation, and the acquisition of agricultural apparatus and agricultural supplies. The rural financial loan system will be enhanced by the formulation of reasonable agricultural insurance compensation standards designed to increase farmers’ risk resistance, to address the issues of numerous restrictive conditions and stringent requirements for the review and approval of agricultural loans, and to assist producers in putting their desire to operate on a larger scale into action. Through policy guidance, it should be encouraged to train technical personnel and transform the results of scientific research into the propelling force of agricultural production practise. The government may promote professional agricultural technology training for large-scale operation and implement diverse guidance programmes based on the needs of different types of farmers, such as breeding and fertiliser cultivation and agricultural machinery operation, in order to increase farmers’ willingness and capacity to operate at an appropriate scale.

Although this study is only based on the moderate scale of rice in Jiaxing, the results of this paper can provide experience sharing and a reference for other countries to develop appropriate scale operation in the plain area of water networks similar to Jiaxing. The research of other crops can use this research method to calculate the appropriate scale of this crop. The conclusion of this study can be used as a reference for the study of rice planting regions related to similar resource and environmental conditions and socio-economic conditions. Due to the influence of subjective and objective factors of investigation ability and social environment, the study has some limitations.

Further research is still needed in the future, and the following research can be considered from the following aspects: first, by increasing the number of samples to carry out empirical research on the appropriate scale management of farmland of rice farmers in Zhejiang Province or other areas, in order to enhance the universality of the study. Secondly, in the future, we can increase the sample research objects, such as increasing the research content of other food crops and even cash crops. Finally, in the future, we need to continue to track the problem of appropriate scale management of rice planting in Jiaxing based on the global dynamic perspective and use the time series and spatial series data of Jiaxing to study the problem of appropriate scale management of rice planting farmland in China.