Cost Changes and Technical Efficiency of Grain Production in China against a Background of Rising Factor Prices

Abstract

Based on panel data for the inputs and outputs of the three major staple grains (rice, wheat and corn) in China from 2000 to 2020, we calculated the cost efficiency using the stochastic frontier cost function model and examined the effects of cost changes for the three major grains to explore the sources of cost increases for grain production. On this basis, the impact of the input factor structures on the technical efficiency of the three food grains was further analyzed under the conditions of price increases. We found that the labor prices and production costs showed the same trends of changes. Compared to 2000, the labor prices in 2020 increased 7.33-fold and the technical efficiency values for the three grains were all close to 0.9 (0.8689, 0.8912 and 0.8451). An efficiency decomposition showed that the adjustment effect of labor prices was the main factor in cost increases, but the effects of technological progress and efficiency improvement could effectively reduce the costs of grain production (the largest average value for technological progress was for rice at 0.4569). In comparison, the effects of technological progress on cost reduction were more obvious. By analyzing the influence of input factor structures on technical efficiency, it was found that the influence of different input factor structures on technical efficiency was heterogeneous among the different grains. This paper puts forward the following policy recommendations: first, improve the level of mechanization by developing social services to reduce the dependence on labor; secondly, promote the construction of agricultural informatization, such as accelerating the research and development of intelligent agricultural machinery and promoting the transformation of traditional agriculture to intelligent agriculture; finally, promote the marketization of land element price through land trusteeship to reduce the land transfer price.

1. Introduction

At present, China has achieved 18 consecutive harvests for grain output and remarkable results have been achieved in terms of ensuring food security. However, the continuous growth of grain output has been accompanied by increases in input factors and factor prices, which has resulted in rapid rises in the costs of grain production. According to the National Compilation of Agricultural Product Cost and Income Data, from 2000 to 2020, the costs of rice, wheat and corn production in China rose from CNY 6024.75, CNY 5287.2 and CNY 4763.85 per ha, respectively, to CNY 18,802.8, CNY 15,397.5 and CNY 16,199.7 per ha, respectively, which represented 3.12-fold, 2.91-fold and 3.40-fold increases, respectively [1]. It should be noted that inflation was not considered here. If inflation were considered, the increases in actual grain production costs would be lower. The rising costs of grain production constantly reduce profit margins and agricultural income for farmers [2]. The main reason for these high production costs is the distortion of factor allocation, i.e., too many inputs or an unreasonable combination of inputs. Under the conditions of a market economy, the key to ensuring grain production is increasing enthusiasm for grain production among farmers [3], and farmers are mostly concerned with the costs and benefits of growing grains. In order to effectively ensure national food security and stabilize enthusiasm for grain production among farmers, it is necessary to reduce the costs of grain production and increase incomes from grain production. Therefore, why have the costs of grain production risen so rapidly in China over the past decade? What are the main factors that have driven this rapid rise in costs? Understanding the above problems could help us to understand the causes of rising grain production costs and develop targeted cost-reduction strategies, which would be of great significance for improving the quality, efficiency and competitiveness of agriculture, promoting continuous income increases for farmers and ensuring food security.

The increases in the costs of grain production have been accompanied by changes in the combinations of different input factors. In actual agricultural production processes, the combinations of agricultural production factors do not usually reach Pareto optimal states due to constraints from various factors. As the basis of agricultural production, the inputs of production factors have great impacts on the final outputs, and changes within the structures of input factors inevitably bring about changes in the efficiency of grain production [4,5]. Under the influence of rising factor costs and substitutions between factors, what changes have taken place so far in the input factor structures of different types of grain production? What impacts have these changes had on the efficiency of agricultural technology?

Research on the costs of and structural changes in grain factors has mainly focused on the influencing factors of costs, the relationship between costs and benefits and the adjustment effect of factor structures under the influence of costs. The rising costs of grains have become a reality and related studies have suggested that mid-scale agricultural operations could effectively reduce production costs [6,7,8]. Purdy (2019) analyzed the cost efficiency of corn production at 32 typical farms across 12 countries and found an average cost efficiency of 0.720 [9]. Siagian et al. (2020) estimated the cost efficiency of rice production farms in Indonesia and found that the average cost efficiency of rice in 2016 was 0.83, which was higher than that in 2010 [10]. Peng (2021) found that land transfers were more efficient than non-transfer land and could significantly reduce the costs of agricultural production by 0.78 units [11]. Wang et al. (2019) analyzed the costs of grain production in China and found that the adjustment effect of the factor prices was the primary driving factor of cost increases [12]. The empirical results of Lu (2018) showed that the most important factor that affected changes in corn production costs was the labor input [13]. Du (2020) pointed out that against the current background of rising costs and falling prices, the profit margins of grain production have been narrowed further and that the development of agricultural scale and specialization has been accompanied by increases in opportunity costs and declines in the elasticity of production structure adjustments, which could bring about greater production and operational risks for agricultural producers [14]. Using cheaper options to replace more expensive factors is an important consideration in agricultural decision-making and there has been a significant substitution relationship between agricultural machinery and labor [15]. As “rational” producers, farmers gradually decrease the amount of labor in agricultural production processes. In order to reduce the number of laborers and the input of labor time, a large number of machines have gradually been introduced to replace human labor [16,17,18], which has been conducive to improving the allocation efficiency of the labor force and agricultural machinery and improving the production efficiency of the agricultural labor force.

What are the factors that cause the costs of grain production to rise and what are the impacts of input factor structures on the production efficiency of grain production? Previous studies have focused on the analysis of the entire grain production process; however, there are different input factor structures for different grain types. The relative impacts of the various factor costs on changes in the production costs of different grains may vary and the use of factor analysis methods still has certain limitations. Therefore, in this study we analyzed the impacts of cost changes for different staple grain factors on the increases in production costs using the parameter method. In addition, changes in the input factor structures in grain production processes could have greater impacts on the production efficiency of grains. Therefore, we introduced changes in input factor structures in grain production processes into the production efficiency model in order to carefully analyze the relationship between the main input factor structures in China’s grain production processes and grain production efficiency and provide a theoretical reference to effectively guide the allocation of input factors to improve grain production efficiency.

2. Theoretical Framework

2.1. Input Factor Allocation and Grain Cost Changes Driven by Price Factors

Input factors have promoted increases in outputs, but at the same time, they have led to continuous increases in input costs. In particular, increases in input factors have worsened the scarcity of factor resources, pushed up the prices of factors and even increased the costs of agricultural production while maintaining very high grain prices, which has significantly affected farmers’ income from grain production. It is necessary to analyze whether these changes and the allocation of input factors affect production behaviors and cost changes under the influence of price factors.

2.2. Allocation of Grain Production Factors and Efficiency of Grain Production Technology

Technical efficiency is an important measure that is used to reflect the comprehensive production capacity of decision-making entities. From the perspective of production input factors, technical efficiency refers to the ratio between the production factors that are actually used by decision-making entities and the minimum inputs for the optimal state. Technical efficiency not only includes elements such as technology and factor use, but it also reflects non-technical factors in production processes to some extent, such as cost control and production potential.

The endowment structure of grain production factors is one of the important components that determine the development of grain economy. The proportion of grain production factors is the key to determining the efficiency of factor allocation. For example, the capital labor ratio is an input factor for grain production. From the perspective of modern scientific and technological development and improvements in production efficiency, the more capital factors that are invested in a production process, the higher the capital labor ratio and the higher the labor productivity. However, in reality, especially under the influence of various policies and systems, there is often a factor mismatch in which the prices of production factors, such as land and labor, are distorted, resulting in the inclusion of excessive or insufficient input factors in grain production processes [19]. Sui (2022) found that labor structures affect land use efficiency [20]. Mismatches between production factors not only directly cause losses in grain outputs, but also reduce the technical efficiency of grain production.

3. Research Methodology

3.1. Measurement Methods

3.1.1. Stochastic Frontier Cost Function

Cost efficiency refers to the ability to carry out production at the lowest costs for certain outputs. It is also referred to as economic efficiency and it is used to measure the degree to which the real cost of a production process mirrors the effective boundary or minimum theoretical costs. Ever since Aigner and Lovell [21] and Meeusen and Broeck [22] pioneered the stochastic frontier model, it has been widely used for efficiency analyses. According to Battese and Coelli [23,24], the basic form of the stochastic frontier cost function can be expressed as follows:

$$ln{C}_{it}=lnf\left(Y_{it},P_{it},W_{it}\right)+v_{it}+u_{it}$$

(1)

where $C_{it}$ represents the observed actual cost, $f\left(Y_{it},P_{it},W_{it}\right)$ denotes the deterministic frontier costs (which are expressed in the form of a specifically set cost function), $Y_{it}$ is the output, $P_{it}$ is the factor prices, $W_{it}$ represents other factors that may affect costs (e.g., technological progress, efficiency gains, etc.), $v_{it}$ stands for the error term (which can be understood as the possible effects of potential factors on frontier costs) and $u_{it}$ is the non-efficiency term (which is usually used to measure the non-validity of the technique). We assumed that $v_{it}$ was subject to the normal distribution of $N\left(0,{\sigma }_v^2\right)$ and that $u_{it}$ was subject to the semi-normal distribution of $N_{+}\left(0,{\sigma }_u^2\right)$.

By definition, the cost efficiency of the production entity $i$ can be expressed as:

$$C{E}_{it}=E\left(u_{it}|\left(v_{it}-u_{it}\right)\right)=E\left(C^f/C^r\right)=\mathit{exp}\left(-u_{it}\right)$$

(2)

where $C{E}_{it}$ is the cost efficiency, $E$ is the desired condition, $C^f$ is the frontier cost and $C^r$ is the true cost.

The Cobb–Douglas production function and translog function are commonly used in the selection of models for the analysis of relationships between input factors and outputs. The former assumes neutral technological progress and the fixed elasticity of outputs and substitutions, whereas the latter relaxes this assumption and the model form is more flexible, which can avoid the problem of mis-setting functional forms. The translog function has become increasingly widely used in the study of multi-factor production functions. Therefore, for the specific empirical test process, we used the translog cost function to conduct the specific analysis in order to minimize the error. Then, the stochastic frontier cost function could be rewritten as:

$$\begin{gathered} ln{C}_{it}^f={\beta }_0+{\alpha }_{y}lny+0.5{\alpha }_{yy}{\left(lny\right)}^2+{{\displaystyle \sum }}_i{\beta }_{i}ln{p}_i+0.5{{\displaystyle \sum }}_i{{\displaystyle \sum }}_j{\beta }_{ij}ln{p}_{i}ln{p}_j+{{\displaystyle \sum }}_i{\alpha }_{iy}ln{p}_{i}lny+ \\ {\theta }_{t}t+{\theta }_{ty}tlny+0.5{\theta }_{tt}{t}^2+v_{it}+u_{it} \end{gathered}$$

(3)

where $C^f$ represents the frontier costs (which are usually determined by the output level, factor price and technological progress, i.e., $C^f=C\left(y,p,t\right)$); $y$ represents the output level; $p$ represents the factor price; $i$ represents the different production factors (including labor, land, machinery, etc.); $t$ represents technological progress; ${\alpha }_y$, ${\alpha }_{yy}$, ${\alpha }_{iy}$ and ${\theta }_{ty}$ represent the estimated parameters of the relevant variables $lny{\left(lny\right)}^2$, $ln{p}_{i}lny$ and tlny; ${\theta }_t$ and ${\theta }_{tt}$ represent the common effects of technological progress on all individuals and ${\theta }_{ty}$ refers to non-neutral technological progress (which usually reflects the possible heterogeneity in the learning abilities of producers). In order for the above formula to obtain better properties, some other constraints are usually required, including the symmetry, flushness and scale of the unchanged return, which can be specifically described in the following form:

$${\beta }_{ij}={\beta }_{ji};{{\displaystyle \sum }}_i{\beta }_i=1;{{\displaystyle \sum }}_j{\beta }_{ji}=0;{{\displaystyle \sum }}_i{\alpha }_{iy}=0$$

3.1.2. Decomposition of Cost Change Effects

Following on from the research of Kumbhakar and Lovell (2012) [25] and He (2012) [26], we further decomposed the total effects of cost changes into output change effects, factor price adjustment effects, technological progress effects and efficiency improvement effects.

We hypothesized that efficiency changes would be more important than efficiency levels. Even when the initial efficiency level was low, it was possible for us to achieve cost savings and revenue growth through efficiency improvements. Conversely, when the initial efficiency was at a high level, declines in efficiency also reduced returns. For $CE=E\left(\frac{C^f}{C^r}\right)=\frac{C\left(y,p,t\right)}{C^r}$, we took the logarithm of both sides and further derived the time $t$ to obtain:

$$\frac{\partial \ln CE}{\partial t}=\frac{\partial \ln C^f}{\partial t}-\frac{\partial \ln C^r}{\partial t}$$

(4)

$$\frac{\partial \ln C^r}{\partial t}=\frac{\partial \ln C^f}{\partial t}-\frac{\partial \ln CE}{\partial t}$$

(5)

$$\frac{\partial C^r/C^r}{\partial t}=\frac{\partial \ln C^f}{\partial t}-\frac{\partial CE/CE}{\partial t}$$

(6)

$$\frac{\partial C^r/C^r}{\partial t}=\frac{\partial ln{C}^f}{\partial lny}\times \frac{\partial y/y}{\partial t}+\frac{\partial ln{C}^f}{\partial lnp}\times \frac{\partial p/p}{\partial t}+\frac{\partial ln{C}^f}{\partial t}-\frac{\partial CE/CE}{\partial t}$$

(7)

$$\overline{{\dot{C}}^r}=MYC\times \overline{\dot{Y}}+{\displaystyle \sum }_i{S}_i\times \overline{\dot{p}}+CT-\overline{C\dot{E}}$$

(8)

where $\overline{{\dot{C}}^r}$ refers to the actual cost changes, $MYC\times \overline{\dot{Y}}$ refers to the production scale effect (which represents the impacts of output changes on frontier costs), $MYC$ indicates the marginal impacts of output changes on frontier costs, $\overline{\dot{Y}}$ indicates the rate of change in the outputs, ${{\displaystyle \sum }}_i{S}_i\times \overline{\dot{p}}$ refers to the factor price adjustment effect (which represents the changes in frontier costs that are brought about by the factor price adjustment effect), $S_i$ indicates the cost share of the production factor $i$ within the deterministic frontier cost, $\overline{\dot{p}}$ indicates the rate of change in the factor price, $CT$ represents the effect of technological progress and portrays the impacts of technological changes on frontier costs and $\overline{C\dot{E}}$ refers to the efficiency change effect (which represents the impacts of efficiency changes on frontier costs).

3.2. Data Sources

In the process of China’s agricultural policy reform and agricultural economic development, agricultural production costs and technical efficiency have changed dynamically. Cross-sectional data can only represent the state of an individual entity throughout a single year, while panel data can effectively represent the long-term change process of an entity. For this study, we selected panel data from the main rice-, wheat- and corn-producing provinces from 2000 to 2020. The data were mainly derived from the National Compilation of Agricultural Product Cost and Income Data (2000–2020), and primarily represent the changes in the costs of the production of three major staple grains in China since 2000. In addition, these three grains were selected as the specific analysis objects in this study as they are the main food grains in China and have important characteristics, such as wide sowing areas. Other data were sourced from the Yearbook of Chinese Statistics (2000–2020) [27].

According to the basic requirements and data availability of the input and output indicators for the stochastic frontier cost function, the following variables were selected for this study:

• Total cost, which comprised the production costs plus land costs (production costs included labor costs per hectare, direct costs and indirect costs, such as seeds, fertilizers, pesticides, agricultural film, mechanical operations, fuel, etc.);
• Total output, which comprised the average yield of rice, wheat and corn per hectare;
• Labor price, which comprised the labor costs per hectare divided by the labor force investment (which mainly included two types of workers: employees and self-employed laborers);
• Machinery price, which represented the total costs of mechanical services per hectare;
• Land price, which represented the rent per hectare (including the rent of self-owned land per hectare of circulation land and the rent that was converted from the camp per hectare);
• Other input factor prices, which were sourced from the comprehensive price index of agricultural production materials due to the complexity of the other inputs and the fact that the specific quantities of various inputs could not be determined. In addition, in order to maintain the continuity characteristics of the composite production price index, we used 2000 as the base period from which we converted the calendar year index to obtain the final value.

The specific statistics of the relevant variables are shown in

Table 1. The descriptive statistics of the variables in the cost function.

Variable	Variable Description	Rice		Wheat		Corn
		Mean	SD	Mean	SD	Mean	SD
Total Cost	The sum of the cost of each input element (CNY/ha)	13,552.35	444.44	11,168.4	379.22	10,021.35	305.31
Total Output	Average yield per hectare (kg/ha)	7256.25	79.91	6744.6	97.45	5164.2	72.57
Land Price	The price of land (CNY/ha)	2304.9	126.34	1879.65	83.01	1811.1	76.82
Labor Price	The price of labor (CNY/day)	703.8	32.77	670.35	31.27	809.7	78.03
Machinery Price	The total costs of mechanical services (CNY/ha)	22.05	0.37	21.45	0.34	21.6	0.34
Other Input Factor Prices	The price index of agricultural production materials (%)	941.7	37.16	535.05	26.64	856.8	21.73

.

In order to analyze the impact of the input factor structure on the technical efficiency of grain production, we selected the relevant variables. First of all, the explanatory variables included the technical efficiencies of rice, wheat and corn, which were calculated using the above data. Secondly, the explanatory variables comprised the input factor structure of the three grains, which included the land input structure, labor input structure and material capital input structure. The land input structure was calculated as the ratio between the land input level and the total costs over one year. The calculations of the labor and material input structures were the same as above. Finally, the control variables included the proportions of primary industry, human capital level, agricultural disaster area, agricultural mechanization level and regional urbanization level.

The proportion of primary industry was expressed as the proportion of gross agricultural production within the gross domestic product (GDP). Generally, improvements in agricultural economic development levels indicate that the more developed the regional agricultural economy, the higher its production efficiency. However, improvements in agricultural proportion levels may also be caused by the growth of the agricultural economy thanks to high input factors. The level of human capital was expressed as the average education level of the rural labor force. It is generally believed that improvements in human capital levels can improve agricultural production efficiency by promoting the rational allocation of factor resources. The proportion of agricultural disaster areas was calculated as the ratio between the crop disaster area and the cultivated land area in each region. Agricultural disasters adversely affect normal agricultural production, agricultural outputs and thus, agricultural production efficiency. The level of agricultural mechanization was expressed as the total power of agricultural machinery per unit of cultivated land area within the region. Agricultural mechanization is an important tool for agricultural economic growth and improvements in agricultural production efficiency. It refers to the application of modern science and technology to agricultural production processes, which is conducive to improving agricultural production technical efficiency. The level of urbanization was expressed as the proportion of urban population within the total population. Relevant studies have hypothesized that the impact of urbanization on agricultural production efficiency is twofold: on the one hand, the development of urbanization could greatly promote the application of advanced agricultural technology, which would be conducive to the growth of agricultural technology efficiency; on the other hand, the development of urbanization could also promote the transfer of labor and severely restrict cultivated land resources, thus hindering improvements in agricultural production efficiency.

The descriptive statistics of each variable are shown in

Table 2. The descriptive statistics of the variables in the technical efficiency model.

Variable	Variable Description	Rice		Wheat		Corn
		Mean	SD	Mean	SD	Mean	SD
Technical Efficiency	It is measured by the production function	0.87	0.11	0.84	0.07	0.91	0.07
Land Structure	The proportion of land cost in total cost (%)	0.16	0.07	0.17	0.08	0.18	0.08
Workforce Structure	The proportion of labor cost in total cost (%)	0.42	0.12	0.43	0.14	0.33	0.14
Other Material Capital Structures	The proportion of the cost of other inputs in the total cost of input (%)	0.43	0.08	0.33	0.08	0.38	0.08
Proportion of Primary Industry	The proportion of gross agricultural production within the gross domestic product (%)	0.13	0.06	0.13	0.05	0.12	0.04
Human Capital Level	The average education level of the rural labor force (year)	8.05	0.69	7.93	0.67	8.00	0.59
Proportion of Affected Area	The ratio between the crop disaster area and the cultivated land area (%)	0.05	0.05	0.30	0.22	0.05	0.06
Mechanization	Machinery power used per hectare (kw/100ha)	0.81	0.37	0.68	3.70	0.76	0.40
Urbanization	The proportion of urban population within the total population (%)	0.61	17.45	0.45	0.13	0.59	16.97

.

How have the costs of food production changed? In the process of continuous labor transfer, how have the costs of agricultural labor changed? In Figure 1, the changes in grain production costs and labor prices can be seen clearly. The average production costs of the three grains and the labor prices have shown the same trends of change. Before 2008, there was a slow upward trend; from 2008 to 2013, the grain production costs and labor prices showed an obvious upward trend; however, from 2013 to 2020, the total costs of grain production showed fluctuating changes while labor prices evolved into a slow rise around 2017. Throughout this trend of rapid growth, the total costs of grain production and labor prices have risen since 2000. From this trend of convergence, it can be seen that rising labor costs could have a significant impact on the total costs of agricultural production.

What are the proportions of the different input factors within the total costs of China’s grain production and what are their trends of change? In Figure 2, the changes in the input proportions of different elements can be seen clearly. From 2000 to 2008, the proportion of labor costs within the total costs fluctuated and decreased, while from 2008 to 2013, the proportion of labor costs showed a rapid upward trend, rising from 31.12% in 2008 to 41.87% in 2013 (an increase of 10.75%). Meanwhile, the proportion of material service costs showed a significant downward trend during the same period, which showed that the increase in grain production costs during this period mainly came from the increase in labor costs, which was primarily due to the rapid increase in workers’ wages since 2008, the increase in employment costs within grain production and the opportunity costs of family-owned labor. The proportion of land costs within grain production showed a fluctuating upward trend. China’s limited land resources, the scarcity of arable land and price increases all led to the continuous increase in land costs within grain production. The proportion of material service costs showed a declining trend at first but has increased slowly since 2013. With the increasing use of machinery, the proportion of labor costs within production costs has declined as machinery has effectively replaced agricultural laborers, but the proportion of labor costs is still relatively large. In the future, the mechanization of grain production processes should be further promoted to reduce the dependence of grain production on human labor.

3.3. Econometric Models

3.3.1. Cost Efficiency Model

By considering a four-factor cost function based on the inputs of labor, land, machinery and other material costs, combined with the above analysis, we could further describe the cost function as follows:

$$\begin{array}{ll}lnC={\beta }_0+{\alpha }_{y}lny& +0.5{\alpha }_{yy}{\left(lny\right)}^2+{\beta }_{l}ln{p}_l+{\beta }_{t}ln{p}_t+{\beta }_{m}ln{p}_m+{\beta }_{q}ln{p}_q+0.5{\beta }_{ll}{\left(ln{p}_l\right)}^2+0.5{\beta }_{tt}{\left(ln{p}_{tt}\right)}^2\\ & +0.5{\beta }_{mm}{\left(ln{p}_{mm}\right)}^2+0.5{\beta }_{qq}{\left(ln{p}_{qq}\right)}^2+{\beta }_{lt}ln{p}_{l}ln{p}_t+{\beta }_{lm}ln{p}_{l}ln{p}_m\\ & +{\beta }_{lq}ln{p}_{l}ln{p}_q+{\beta }_{tm}ln{p}_{t}ln{p}_m+{\beta }_{tq}ln{p}_{t}ln{p}_q+{\alpha }_{ly}ln{p}_{l}lny+{\alpha }_{ty}ln{p}_{t}lny+{\alpha }_{my}ln{p}_{tm}lny\\ & +{\alpha }_{qy}ln{p}_{q}lny+{\theta }_{t}t+{\theta }_{ty}tlny+0.5{\theta }_{tt}{t}^2+v_{it}+u_{it}\end{array}$$

(9)

In the process of solving the cost function, the constraints of symmetry, homogeneity and constant returns to scale had to be considered at the same time. In order to effectively avoid the homogeneity of the covariance matrix, we used the relative prices of two elements to replace single factor prices. Therefore, the final estimation equation was expressed in the form of the relative price, which was as follows:

$$\begin{array}{ll}ln\frac{C}{p_l}={\beta }_0+{\alpha }_{y}lny& +0.5{\alpha }_{yy}{\left(lny\right)}^2+{\beta }_{t}ln\frac{p_t}{p_l}+{\beta }_{m}ln\frac{p_m}{p_l}+{\beta }_{q}ln\frac{p_q}{p_l}-0.5p_{tl}{\left(ln\frac{p_t}{p_l}\right)}^2-0.5p_{ml}{\left(ln\frac{p_m}{p_l}\right)}^2\\ & -0.5p_{ql}{\left(ln\frac{p_q}{p_l}\right)}^2-0.5p_{tm}{\left(ln\frac{p_t}{p_m}\right)}^2-0.5p_{tq}{\left(ln\frac{p_t}{p_q}\right)}^2-0.5p_{mq}{\left(ln\frac{p_m}{p_q}\right)}^2+{\alpha }_{ty}ln\frac{p_t}{p_l}lny\\ & +{\alpha }_{my}ln\frac{p_m}{p_l}lny+{\alpha }_{qy}ln\frac{p_q}{p_l}lny+{\theta }_{t}t+{\theta }_{ty}tlny+0.5{\theta }_{tt}{t}^2+v_{it}+u_{it}\end{array}$$

(10)

where $C$represents the costs of grain production, $y$ represents the grain outputs, $p_l$ represents the costs of labor, $p_t$ represents the land costs, $p_m$ represents the machinery costs, $p_q$ represents the costs of other material expenses and $t$ represents time.

3.3.2. Technical Efficiency Model

The measurement methods for agricultural technical efficiency are becoming increasingly mature. Most scholars use the stochastic frontier production function model in the form of the transcendental logarithmic production function to estimate technical efficiency [28,29]. This method has the advantages of simplicity, easy decomposition and obvious economic meaning, which is why it is favored by many economic researchers. Therefore, when using the stochastic frontier production function (SFA) method to estimate the technical efficiency of agricultural production, we also chose to estimate the technical efficiency of Chinese grain production using the logarithmic production function. Based on the transcendental logarithmic production function, we selected the grain yield $Y_{it}$ as the explanatory variable and the indicators of labor input $L_{it}$, land input $F_{it}$, agricultural machinery input $M_{it}$ and grain sown area $A_{it}$ as the independent variables and we added the time trend variable $t$ to reflect the impacts of technological changes on grain yields. We then constructed a grain production function model in the form of a logarithmic function, which was as follows:

$$\begin{array}{ll}ln{Y}_{it}={\beta }_0+{\beta }_{l}ln{L}_{it}& +{\beta }_{f}ln{F}_{it}+{\beta }_{m}ln{M}_{it}+{\beta }_{a}ln{A}_{it}+\frac{1}{2}{\beta }_{ll}{\left(ln{L}_{it}\right)}^2+\frac{1}{2}{\beta }_{ff}{\left(ln{F}_{it}\right)}^2+\frac{1}{2}{\beta }_{mm}{\left(ln{M}_{it}\right)}^2\\ & +\frac{1}{2}{\beta }_{aa}{\left(ln{A}_{it}\right)}^2+{\beta }_{lf}ln{L}_{it}ln{F}_{it}+{\beta }_{lm}ln{L}_{it}ln{M}_{it}+{\beta }_{la}ln{L}_{it}ln{A}_{it}+{\beta }_{fm}ln{F}_{it}ln{M}_{it}\\ & +{\beta }_{fa}ln{F}_{it}ln{A}_{it}+{\beta }_{ma}ln{M}_{it}ln{A}_{it}+{\beta }_{t}t+\frac{1}{2}{\beta }_{tt}{t}^2+{\beta }_{lt}tln{L}_{it}+{\beta }_{mt}tln{M}_{it}+{\beta }_{at}tln{A}_{it}+{\nu }_{it}\\ & -u_{it}\end{array}$$

(11)

where the square term represents the effects of input factors on agricultural yields over time, the second-order cross term represents the interactions between the factors, $v_{it}$ represents a random error term that follows a normal distribution and $u_{it}$ represents a technical inefficiency term that follows a normal distribution. Additionally, $v_{it}$ and $u_{it}$ are independent from each other.

The technical efficiency levels of grain production were expressed as:

$$T{E}_{it}=\mathit{exp}\left(-u_{it}\right)$$

(12)

In order to test the influences of input factor structure changes on the efficiency of grain production, we established a panel data regression model in the following form:

$$T{E}_{it}=\alpha +\beta St{r}_{it}+\sum {\gamma }_i{Z}_{it}+{\mu }_i+{\epsilon }_{it}$$

(13)

where ${\mu }_i$ is the individual effect, ${\epsilon }_{it}$ is the perturbation term, $\alpha$ is the constant term, $T{E}_{it}$ indicates the technical efficiency of grain production, $St{r}_{it}$ indicates the changes in the input factor structure of grain production and $Z_{it}$ represents the other factors that can affect the efficiency of grain production.

4. Model Results and Analysis

4.1. Model Estimation and the Decomposition of Grain Cost Change Effects

The maximum likelihood estimation method was used to estimate the stochastic frontier cost functions of the production of three major grains in China: rice, wheat and corn. The estimation results are shown in

Table 3. The estimations of the stochastic frontier cost function model.

	Rice	Wheat	Corn
$lny$	0.1978 (1.9840)	−1.2806 (1.7085)	−0.3117 *** (0.0987)
${\left(lny\right)}^2$	0.1589 (0.3486)	−0.3651 (0.4061)	0.0580 *** (0.0180)
$ln\frac{p_t}{p_l}$	1.1244 ** (0.4542)	−2.5052 *** (0.6195)	0.0643 (0.0511)
$ln\frac{p_h}{p_l}$	3.5918 (2.6550)	5.6602 ** (2.4489)	0.1953 (0.3420)
$ln\frac{p_q}{p_l}$	−3.4064 (2.5912)	2.5367 (0.0000)	−0.3347 (0.3517)
${\left(ln\frac{p_t}{p_l}\right)}^2$	0.0096 (0.0318)	−0.2308 *** (0.0631)	0.0076 (0.0048)
${\left(ln\frac{p_h}{p_l}\right)}^2$	−0.2579 * (0.1446)	0.3083 (0.2202)	−0.0284 (0.0252)
${\left(ln\frac{p_q}{p_l}\right)}^2$	0.2217 (0.1455)	−0.0463 (0.2174)	0.0991 *** (0.0260)
${\left(ln\frac{p_t}{p_h}\right)}^2$	0.1331 (0.1474)	−0.5971 ** (0.2891)	0.0556 ** (0.0266)
${\left(ln\frac{p_t}{p_q}\right)}^2$	−0.2766 * (0.1458)	0.5232 * (0.3087)	−0.0571 ** (0.0271)
${\left(ln\frac{p_h}{p_q}\right)}^2$	0.0920 (1.2245)	0.7006 (1.5783)	0.0812 (0.2143)
$ln\frac{p_t}{p_l}lny$	−0.2689 *** (0.0814)	0.3580 *** (0.1197)	−0.0106 (0.0090)
$ln\frac{p_h}{p_l}lny$	−0.5484 (0.4565)	−0.6443 * (0.3489)	−0.0495 (0.0617)
$ln\frac{p_q}{p_l}lny$	0.7136 (0.4492)	−0.7603 *** (0.1981)	0.0441 (0.0640)
$t$	0.2057 *** (0.0715)	0.7183 *** (0.2202)	−0.0057 (0.0094)
$tlny$	−0.0322 *** (0.0119)	−0.1269 *** (0.0376)	0.0013 (0.0016)
$t^2$	−0.0007 * (0.0004)	0.0020 *** (0.0005)	0.0001 (0.0001)
Sigma	−3.0964 *** (0.3081)	−2.2379 *** (0.7402)	−7.3041 *** (0.3934)
Gamma	2.2760 *** (0.3473)	2.7050 *** (0.8384)	1.7444 *** (0.4691)
Mu	0.5489 *** (0.0978)	0.2288 (0.2313)	0.0433 *** (0.0122)
Eta	−0.0194 *** (0.0038)	−0.0333 *** (0.0079)	−0.0742 *** (0.0078)
Constant	−7.0135 (5.8367)	17.8953 *** (4.7820)	0.7299 ** (0.3334)
Observations	462	294	420

Note: *** p < 0.01; ** p < 0.05; * p < 0.1.

. It can be seen from Table 3 that the variance parameters $\gamma$ of rice, wheat and corn all rejected the null hypothesis of zero, which indicated that the cost inefficiency term $\mu$ existed and that there was a cost inefficiency in grain production in China, so a stochastic frontier cost model was necessary.

Specifically, the relative costs of land and labor had positive impacts on the costs of rice and corn production, the relative costs of machinery and labor had positive impacts on the costs of the production of all three grains, and the relative costs of other physical capital and labor had negative impacts on the costs of rice and wheat production but positive impacts on the costs of corn production. By estimating the results in Table 3, the parameter values of each variable within the cost function could be obtained, which was convenient for analyzing the decomposition of the cost change effects.

According to the estimation coefficient of the stochastic frontier cost function and the cost effect decomposition model, the cost change effects of rice, wheat and corn were decomposed into production scale effects, factor price adjustment effects, technological progress effects and efficiency improvement effects. The specific results are shown in

Table 4. The decomposition of the cost change effects on the production of the three main grains.

	Year	Rate of Cost Change	Production Scale Effect	Factor Price Adjustment Effect				Technological Progress Effect	Efficiency Improvement Effect
				Labor	Land	Machinery	Other
Rice	2000–2005	0.0692	0.0024	0.0460	0.0009	0.0027	0.0616	−0.0273	−0.0171
	2006–2010	0.1076	0.0004	0.0836	0.0093	0.0024	0.0292	−0.0012	−0.0161
	2011–2015	0.0717	0.0013	0.0858	0.0051	−0.0014	0.0315	−0.0405	−0.0101
	2016–2020	0.0062	0.0007	0.0111	0.0028	−0.0036	0.0057	−0.0094	−0.0011
Wheat	2000–2005	0.0422	0.0036	0.0557	0.0028	0.0042	0.3022	−0.3057	−0.0206
	2006–2010	0.1003	0.0001	0.1004	0.0316	0.0098	0.173	−0.1951	−0.0195
	2011–2015	0.0716	0.0003	0.0520	0.0148	0.0044	0.2629	−0.2433	−0.0195
	2016–2020	0.0047	0.0006	0.0311	0.0065	0.0111	0.0405	−0.0619	−0.0232
Corn	2000–2005	0.0495	0.0401	0.0485	0.0027	−0.0006	−0.0101	−0.0215	−0.0096
	2006–2010	0.1145	0.0267	0.0918	0.0293	0.0068	0.1028	−0.1367	−0.0062
	2011–2015	0.0862	0.0473	0.1072	0.013	0.0007	0.2937	−0.3706	−0.0051
	2016–2020	0.0025	0.0201	0.0140	0.0024	0.0013	0.2731	−0.3047	−0.0037

.

Overall, the production scale effects and factor price adjustment effects on the cost changes within the production of the three grains increased the total production costs, but the factor price adjustment effects were the primary factors that drove the rise in production costs; in particular, the labor price performance was the strongest and the production scale effects on the cost changes were relatively small. This study also found that the effects of technological progress and efficiency improvements were negative, which indicated that both cutting-edge technological progress and improvements in production efficiency could reduce the cost of rice production, but cutting-edge technological progress had the greatest impact on reducing production costs. Four effects were explored further:

• Production scale effects. These effects were calculated as the product of the marginal impacts of output changes on frontier costs and the output growth rate. The production scale effects of the three grains were positive, which was largely due to the growth in grain production. Comparatively speaking, the production scale effect of corn had a higher impact on cost changes than those of rice and wheat.
• Factor price adjustment effects. In general, the factor price adjustment effect of wheat had a higher impact on the cost change rate than those of rice and corn. In the price adjustment for the labor, land and mechanical factors, the impact of the labor price adjustment on cost changes was the most obvious, so this paper considered that rises in labor prices were the primary factors that promoted rises in grain production costs.
• Technological progress effects. For the production processes of rice, wheat and corn, this paper found that the means of technological progress were 0.4569, 0.2575 and 0.4305, respectively, and that the contribution of technological progress to production costs was negative, i.e., technological progress could promote reductions in production costs. Comparatively, the technological progress effects of corn and wheat contributed more to lowering production costs than that of rice.
• Efficiency improvement effects. Efficiency improvement effects refer to the growth rate of cost efficiency (CE). This paper found that efficiency improvements could reduce production costs to a certain extent, but they had small impacts. For the three kinds of grain production, the efficiency improvement effects generally showed downward trends, which indicated that the cost efficiency of China’s grain production still has room for improvement.

4.2. Technical Efficiency of the Three Grains

This study found that the average technical efficiencies of rice, wheat and corn were 0.8689, 0.8912 and 0.8451, respectively, and that the highest technical efficiency level was that of wheat. Before the regression, the correlation variables were tested collinearly. The results show that there were no significant collinear relationships between the variables for rice, wheat and corn and that the mean values of the variance inflation factors were 1.40, 1.44 and 1.40, respectively. Further, we used a fixed-effects model for the specific regression analysis.

Labor, land and physical capital were important input factors that affected the efficiency of grain production.

Table 5. The analysis of the effects of input factor structures on the technical efficiency of grain production.

	Rice	Wheat	Corn
Land Structure	−0.0190 *	−0.31360	−0.0080 ***
	(0.0111)	(0.21030)	(0.0030)
Workforce Structure	−0.0021	−0.33750 ***	0.0020
	(0.0090)	(0.08699)	(0.0017)
Physical Capital Structures	0.0322 ***	−0.12816	−0.0146 ***
	(0.0054)	(0.32454)	(0.0023)
Proportion of Primary Industry	0.0113	0.01704	−0.0014
	(0.0156)	(0.02351)	(0.0039)
Human Capital Level	0.0001	0.00201 ***	0.0002 ***
	(0.0009)	(0.00011)	(0.0000)
Proportion of Affected Area	−0.0040	−0.00377 **	−0.0079 ***
	(0.0101)	(0.00231)	(0.0022)
Mechanization	0.0006	−0.00027	−0.0000
	(0.0026)	(0.00032)	(0.0007)
Urbanization	−0.0002 ***	−0.01233 *	0.0000
	(0.0000)	(0.00725)	(0.0000)
Constant	0.8652 ***	0.85951 ***	0.8993 ***
	(0.0097)	(0.00628)	(0.0018)
Observations	462	420	294
R-squared	0.2679	0.5305	0.6011

Note: *** p < 0.01; ** p < 0.05; * p < 0.1.

shows the results for the impacts of different input factor structures on the efficiency of the production of the three grains. It can be seen that the land input structure had a negative impact on the technical efficiency of the production of the three grains and that its impacts on rice and wheat passed the statistical levels of 10% and 1%, respectively. The structure of labor inputs had a significant negative impact on the technical efficiency of corn production and the current dependence of agricultural production on the human labor force gradually decreased, which showed that increases in labor inputs could bring about labor redundancy and adversely affect technical efficiency. In addition, the structure of physical capital inputs had a negative impact on the technical efficiency of corn and wheat production, but it improved the efficiency of rice production.

From the perspective of the control variables, improvements in the levels of human capital within the labor force generally promoted increases in the levels of technological efficiency. Improvements in the levels of human capital were also conducive to agricultural producers mastering more agricultural production technologies and the effective allocation of agricultural production factors. Improvements in human capital levels could encourage agricultural producers to apply modern agricultural science and technology to production practices, which was conducive to the technological progress of agriculture. Improvements in the levels of human capital within the labor force could also effectively promote improvements in agricultural production efficiency by improving factor allocation and the application of modern agricultural science and technology.

The agricultural disaster areas had significant negative impacts on improvements in technical efficiency as agricultural disasters adversely affect agricultural production: on the one hand, natural disasters affect the levels of agricultural outputs; on the other hand, remediation and other measures could cause the misallocation of resource elements, which would not be conducive to improvements in technological efficiency.

In addition, the levels of urbanization as a whole showed negative impacts on the technical efficiency of the three kinds of grain production. The transfer of the agricultural labor force during the process of urbanization and the loss of resources, such as arable land, were not conducive to the development of regional agriculture. With improvements in the levels of urbanization, the squeeze of the secondary and tertiary industries on the primary production could become an obstacle to agricultural development, which could result in a decline in agricultural technology efficiency.

5. Discussion

This paper uses the method of cost-efficiency decomposition to analyze the factors that affect the cost increases for the production of different grains in China. Considering that the cost increases have been accompanied by changes in input factor structures, this paper further analyzed the impacts of input factor structures on the technical efficiency of grain production. The innovations and contributions of this study are mainly reflected by the following two aspects: first, using panel data in translog form in the stochastic frontier production function and the cost efficiency decomposition method, this paper explored the factors that influence the cost changes in grain production, including the effects of price adjustment, technological progress and efficiency improvements on the costs of four aspects of effective decomposition. Previous studies have mostly used cross-sectional data or have only used influencing factor analysis methods [30,31], which could not explain long-term cost changes or the impacts of different factor changes on cost increases. Second, this paper explored the reasons for the rise in the costs of different types of grains. Previous studies have mostly analyzed the average costs of certain types of grains [32] and the differences between the input factors of different types of grains have not been taken into account, which could cause certain deviations.

Whether in Europe, the United States or developing countries, the rising costs of grains is a common problem. Li (2020) compared the production costs of wheat in China to those in the United States and found that the input costs per unit area in 2020 increased by CNY 1589 per ha compared to those in 2016 [33]. The rising prices of chemical inputs and labor can have important impacts on food costs [34] and agricultural costs. Under the conditions of high food prices, the profit margins for producers are further reduced, which could have adverse effects on their welfare [35] and could change the structure of agricultural production to a certain extent [36]. In turn, this could affect global food security. It is of great significance to clarify the causes of rising grain costs and seek targeted cost reduction policies to improve farmers’ income and ensure food security.

Our study found that the rising cost of grain production in China is mainly due to the rapid rise in labor prices, which is consistent with the research of Huang et al. (2000) [37] and Zhong et al. (2016) [38], Wang et al. (2016) found that labor costs in corn production contributed 48.5% to the total cost increase [39]. It can be considered that the promotion of rising labor costs on grain production costs has become the consensus of most scholars, and agricultural socialization services can effectively reduce the dependence of agricultural production on labor [40]; thus, in order to reduce agricultural costs, it is necessary to further improve the level of farmers’ participation in the social division of labor, so as to achieve an effective replacement of labor. In addition, this study also found that the effect of technological progress and efficiency improvement can effectively reduce the cost of food production, which is consistent with the research of Wang et al. (2017) [12]. In order to promote the progress of agricultural technology, we can further improve agricultural infrastructure, promote operating at an appropriate scale and improve the efficiency of factor allocation.

This paper analyzes the impact of factor input structure on agricultural technical efficiency and finds that the land factor structure reduces the technical efficiency of rice and corn, which is similar to the research of Wang et al. (2018) [41], who found that rising land costs had a negative impact on the technical efficiency of rice cultivation. Therefore, in order to solve the problem of high land prices, land costs can be internalized through land trusteeship and land ownership. In addition, the research in this paper also found that the impact of labor structure on the technical efficiency of corn is significantly negative; that is, the increase in labor costs is not conducive to the improvement in technical efficiency. Yi et al. (2021) found a significant “inverted U-shaped” relationship between labor prices and rice production technical efficiency [42]. The increase in the proportion of labor costs to total costs will squeeze the technical input, making it difficult for some agricultural producers to improve technical efficiency through technological innovation. Therefore, strengthening the division of labor in agriculture and improving the level of optimal allocation of resources are important ways to improve the technical efficiency of grain production.

Of course, this study also had some shortcomings. Due to the difficulty of data collection, this paper only analyzed the reasons for the rising costs of grain production and the impacts of changes in different input factor structures on technical efficiency in China, without comparing the situations in different countries. Due to the differences in agricultural production processes in different countries, the results and policy recommendations in this paper would only be applicable to some developing countries that have relatively poor cultivated land resources per capita. However, as China is an important global economy, this study could be of great significance to China’s agricultural production.

6. Conclusions

Using panel data for the costs and revenues of grain production in China from 2000 to 2020, this paper explored the reasons for the rising costs of grain production and analyzed the impacts of input factor structures on agricultural technical efficiency. This study found that (1) within the reality of the rising costs of grain production, the adjustment effect of labor prices was key to promoting increases in grain production costs, but the effects of technological progress and efficiency improvement could effectively reduce the costs of grain production. The effect of technological progress on reducing costs was more prominent. The rates of change for the costs of rice and corn production were larger and the production scale effect of corn had a greater impact on costs than those of rice and wheat. Additionally, this paper found that (2) the factor price adjustment effects, labor prices, land prices and the prices of the other factors all showed positive effects, although labor prices and the prices of the other material inputs had greater impacts. Finally, (3) the continuous increases in the levels of labor inputs were not conducive to improvements in the technical efficiency of grain production. There was heterogeneity in the impacts of land and material capital inputs on the technical efficiency of different grain production, which indicated that the traditional patterns of grain production that rely on labor and material inputs have been changing gradually and that modern production technologies, such as high-quality seed production, suitable agricultural machinery and agricultural technology, could be key to promoting improvements in grain production efficiency.

In order to effectively curb increases in grain production costs and improve agricultural technical efficiency, this paper puts forward the following policy suggestions. Firstly, in view of the fact that the rise in labor costs has promoted increases in agricultural production costs, it is necessary to further improve the mechanization levels of agriculture to effectively replace human labor, especially in weak areas of mechanization, such as rice transplanting and disease and pest control. It is also necessary to intensify the promotion of mechanization through subsidies and other forms. Secondly, it is necessary to further enhance innovations within agricultural technology, strengthen the digital aspects of grain production, rely more on the application of modern and digital agricultural technologies to reduce the inputs of traditional factors and effectively improve the efficiency of agricultural technologies.