Modernization and Elasticity of Substitution in China’s Grain Production: Evidence from 1991 to 2023

Abstract

The intensive utilization of agricultural inputs is key to agricultural modernization. This study analyzed the elasticity of substitution among inputs in Chinese grain production (1991–2023) using a Translog production function, controlling for price disturbances. The key findings are as follows: (1) Complementary relationships exist between capital–fertilizer, capital–land, fertilizer–land, pesticide–land, and fertilizer–labor, while capital–pesticide, fertilizer–pesticide, pesticide–labor, and land–labor are substitutive. (2) The elasticity of substitution among agricultural inputs stabilizes over time, with substitutive and complementary relationships among most factors weakening after 2004. (3) Eastern and northeastern regions tend to substitute labor with capital more significantly, while central and western regions show a balanced interplay. (4) Nationwide trends in agricultural input shares indicate increasing mechanization, land-use efficiency, fertilizer use, and reduced labor input. These results provide insights for optimizing input allocation and enhancing food security.

1. Introduction

Developing modern agriculture and enhancing grain production are essential for fostering economic growth and ensuring stability (Bustos et al., 2018) [1]. Developed countries initiated agricultural modernization earlier and have achieved notable success (Neumann et al., 2010) [2]. Through the rational allocation of resources and the precise application of agricultural technology, these countries have enhanced their grain production (Tey & Brindal, 2012) [3]. In contrast, grain production in China faces significant challenges, including limited per capita arable land, insufficient capital investment, and inadequate infrastructure. Since the 1990s, China has made substantial efforts to transition from traditional to modern agriculture, successfully ensuring a stable food supply and maintaining a relatively high level of self-sufficiency through agricultural reforms and modernization (Cao & Birchenall, 2013) [4]. Despite these advancements, sustainability challenges and uncertainties in optimal resource allocation persist (Singh, 2012; Brandt et al., 2013; Knickel et al., 2013) [5,6,7]. First, the increase in food supply has not fully reflected the shift in development models, particularly the urgent need to move away from extensive production methods (Xu & Jeffrey, 1998; Munton, 2014) [8,9]. Second, there are significant differences across provinces in terms of agricultural technology application, production efficiency, and resource utilization efficiency (Wang et al., 2020) [10].

Enhancing grain production efficiency through the rational and technologically advanced allocation of key inputs has become a critical imperative for China to ensure food security and advance agricultural modernization. This process involves significantly improving the allocation efficiency and utilization of key production factors, such as land, labor, capital, and technology, in agricultural production. The efficient and rational use of modern production inputs, including mechanization, fertilizers, and pesticides, can reduce agricultural costs and enhance production efficiency, representing a key pathway for increasing grain yields (Reddy, 2022) [11]. Critical significance remains in our understanding of the substitutability and complementarity of these inputs. Addressing these challenges requires a deeper understanding of factor allocation, and the elasticity of substitution is key to this understanding (Blackorby & Russell, 1989) [12]. Accurately estimating the elasticity of substitution among grain production inputs, quantifying their substitutive or complementary relationships, and exploring strategies to enhance input efficiency based on factor substitution elasticity and biased technological progress are essential not only for theoretical advancement but also for safeguarding food security and promoting high-quality agricultural development. This study aims to provide empirical evidence by estimating the elasticity of substitution among agricultural inputs in Chinese grain production, thereby providing a foundation for optimizing input allocation and enhancing productivity in the process of deepening agricultural modernization in China. Considering that the Translog production function model is more suitable for analyzing the complex dynamics of grain production in China than others, we use panel data from 28 Chinese provinces covering the period from 1991 to 2023 to estimate the elasticity of substitution among agricultural inputs in grain production by employing a Translog production function model that controls for price disturbances.

This study makes several key contributions. First, measuring the substitution elasticity of factors is an important basic work for the study of output growth and resource utilization efficiency (Vissing-Jørgensen, 2002; León-Ledesma, 2010; Bellocchi & Travaglini, 2023; Jo & Miftakhova, 2024) [13,14,15,16], specialized empirical research explicitly focused on grain production remains limited. We estimate the elasticity of substitution among agricultural inputs in grain production, quantify the substitutive and complementary relationships among these inputs, and analyze their trends over time (Liu et al., 2022) [17], thus addressing a critical gap in research on substitution elasticity within grain production. Second, by measuring regional and provincial differences in input substitution elasticity and production patterns in China’s grain production, we provide important insights into the efficiency and adaptability of agricultural processes across different regions. Third, to address the difficulties in calculating input prices and production costs noted in previous studies (Lee, 2023) [18], we use output and input measures derived from a transcendental logarithmic production function to effectively eliminate the interference of price factors in the estimation of substitution elasticities. By comprehensively considering key production inputs—including labor, land, capital, fertilizer, and pesticides—our study fills a gap in the literature where the roles of fertilizer and pesticides have been overlooked. By clarifying the complementarities and substitution relationships among various production inputs in grain production, as well as the direction of technological progress, we provide a scientific basis for formulating policies to boost grain production.

2. Literature Review

2.1. Agricultural Modernization and Grain Production

Agricultural modernization is a systematic transformation of the traditional agricultural production system into a modern industrial system. Through the establishment of a mechanized, large-scale, and intensive production system, the effectiveness of agricultural production and the ability to achieve sustainable development are fundamentally improved. Among the various facets of agricultural modernization, the advancement of grain production holds particular significance. Grain production serves as a fundamental pillar for economic development and social stability. Modernizing grain production is key to boosting capacity and efficiency, making it a growing focus in China’s agricultural development research. Motoki (2004) [19] examines the transformation of China’s grain production and explores changes in production levels and patterns across Southern, Northern, and Northeastern China. Additionally, he extrapolates structural changes between these regions. Lohmar et al. (2009) [20] indicate that China’s reform and opening-up policy resulted in farm households shifting land and labor from grain production to cash crops and livestock. Nevertheless, grain production increased, which they explain by the more efficient resource allocation by farmers than by central planners. At present, there is a trend of rising labor prices in China’s grain production, so it is necessary to change the structure of agricultural production to maximize profits (Tian et al., 2020) [21]. However, there is still a lack of systematic examination of the modernization of food production from the perspective of the structure and relationship of factor inputs. Jetté-Nantel et al. (2020) [22] identify a deceleration in the growth rate of agricultural productivity in China during the 2000–2010 period, which has consequently elevated the modernization of agriculture to a principal concern for the Chinese government. With a specific focus on the potential contributions of mechanization and land/farm consolidation, the findings indicate that the potential for efficiency improvements from mechanization and land reforms, when considered in isolation, is constrained. He & Chen (2021) [23] point out that China needs to strengthen its own grain production capacity and reserves to ensure the stability and security of food supply.

Some scholars have already conducted specific measurements on the status of grain production in China (Song & Wu, 2013; Li et al., 2014) [24,25]. Although previous studies have provided valuable insights into agricultural modernization, systematic, multi-year, and multi-province investigations with standardized measurements and unified estimates are still needed. Therefore, using a unified theoretical framework to analyze the issue of agricultural modernization has become a key element for further study. Studying the elasticity of substitution of factors in agriculture provides a strong grip on this issue.

2.2. Measurement Method and Key Conclusions

Reflecting on the evolution of measurement research, the significant advancements in microeconomics since the 1960s and 1970s, particularly the exploration of the duality between production and cost functions along the expansion path, have greatly facilitated empirical estimation processes. The accuracy of the results of factor elasticity of substitution depends on the accurate characterization of the form of the production function. Representative methodologies in the literature include those by Klump et al. (2007) [26] and Henningsen & Henningsen (2012) [27], among others, which provide methods such as the Kmenta method, the standardized supply-side equation method based on the CES production function, and the VES production function measurement method. However, the Kmenta method is limited to production functions involving two factors, and the standardized supply-side equation and VES estimation method become more complex when addressing multi-factor scenarios. Considering a nested CES production function further complicates the definition of relationships between factors, and different equation forms can lead to varying regression results, making these methods less practical compared to the Translog production function (Önalan & Başmez, 2022) [28].

In terms of measuring agricultural factor elasticity of substitution, researchers have studied production organization forms and factor combinations, considered various agricultural inputs, and distinguished the production processes of different types of agricultural products to derive more realistic Translog production function forms (Thirsk, 1974; Vincent, 1977; Ray, 1982) [29,30,31]. This approach allows for an exploration of the interrelationships between factors and their joint effects based on the production function (Uri, 1988; Van & Groenewald, 1988; Erickson et al., 2003; Wijetunga, 2023; Safari et al., 2024) [32,33,34,35,36]. Numerically, Sharma (1991) [37], based on the estimation of Korean agriculture using the Translog production function, found that the substitution elasticity of land and labor is roughly around 1.1; land and capital, labor and capital are basically between 0 and 1. Debertin et al. (1990) [38] estimated that the Allen substitution elasticity of land, labor, fertilizer, energy, and machinery in the United States from 1950 to 1979 varies widely, but most of the estimates are concentrated in the range of −1 to 1. Little research has been done on the factor relationships of food production in China. Zhu et al. (2016) [39] estimated the long-term substitution elasticity of labor and capital in wheat production based on the cost function, around 0.9, and found that urbanization and manufacturing development lead to an increase in labor costs, and labor and capital have substitution relationships. Due to differences in the methodology used, the form of the production function, and the definition of the elasticity of substitution, the results of the factor elasticity of substitution are not the same. Their study provides us with valuable numerical references.

3. Theoretical Base

3.1. Factor Elasticity of Substitution and Biased Technological Change

The elasticity of substitution between factors refers to the extent to which they can substitute for each other in the production process. Specifically, it quantifies the percentage change in the ratio of two inputs resulting from a percentage change in their marginal rate of technical substitution while keeping output constant. This concept reflects the substitutive relationships between factors, indicating how readily one factor can replace another to maintain production levels. At the macro level, the elasticity of substitution characterizes the aggregate production function, thereby representing the overall effects of output and factor characteristics at the industry or regional level. The concept was first introduced by Hicks (1932) [40] and is known as the direct elasticity of substitution between two input factors, or the Hicks-neutral elasticity of substitution:

$$\sigma ={\displaystyle \frac{dln\left(\frac{I}{J}\right)}{\mathit{dln}\left(\frac{p_J}{p_I}\right)}}$$

(1)

where I and J represent the inputs of two production factors, and p_I and p_J represent the prices of these two factors. Subsequently, Hicks and Allen extended this concept to production functions involving more than two factors. The resulting elasticity of substitution is known as the Hicks–Allen partial direct elasticity of substitution and follows a similar form to the equation above (Allen, 1938) [41]. Building on this foundational research, scholars such as Morishima (1966) [42] and Acemoglu (1998) [43] have further expanded the concept and application of the elasticity of substitution. The elasticity of substitution has become crucial for studying the output effects of production inputs within the neoclassical framework, attracting increasing empirical investigation. Moreover, some researchers have broadened their definition and applicability by incorporating technological progress parameters.

Biased technological progress refers to advancements that disproportionately enhance the productivity of specific production inputs, such as labor or capital, rather than uniformly affecting all inputs. This phenomenon alters the input efficiency within production functions, leading to changes in factor intensity or conservation. Understanding the interplay between input substitution elasticity and the direction of technological bias provides empirical guidance for producers aiming to optimize resource allocation. The generalized expression of technological progress is as follows:

$$A_I=A_{I0}{e}^{{\gamma }_i\left(t-t_0\right)},A_J=A_{J0}{e}^{{\gamma }_j\left(t-t_0\right)}$$

(2)

Hence, the difference between ${\gamma }_i$ and ${\gamma }_j$, namely ${\gamma }_i-{\gamma }_j$, is widely defined as the biased technological change. Based on biased technological progress, the definitions of elasticity of substitution are as follows:

$$\sigma ={\displaystyle \frac{dln\left(\frac{A_{I}I}{A_{J}J}\right)}{\mathit{dln}\left(\frac{p_J}{p_I}\right)}}$$

(3)

In this context, parameter A signifies technological progress. The distinct technological progress parameters associated with each element are central to the theory of biased technological progress. The primary goal of examining the elasticity of substitution is to understand how changes in relative prices influence the input quantities of factors while maintaining a constant output level. However, accurately estimating factor prices in grain production is challenging, as price fluctuations can distort estimation results. To articulate this problem more clearly, we introduce the cost function in Van & Groenewald (1988) [33] and Sharma (1991) [37], and so on. We employ an alternative approach: utilizing the cost function definition to integrate factor income shares into the expression for factor substitution elasticity, thereby highlighting its potential impact. Assuming two factors, I and J, the total production cost calculated by the cost method is as follows:

$$C=p_{I}I+p_{j}J$$

(4)

In a perfectly competitive grain market, we can assume that the total cost (C) equals total output (Y), and that the marginal cost of each production factor equals its marginal product. Consequently, the factor income share (S) can be defined as follows:

$$S_I={\displaystyle \frac{p_{I}I}{Y}}, S_J={\displaystyle \frac{p_{J}J}{Y}}$$

(5)

By substituting (5) into (3) and simplifying it, we can derive the following expression:

$$\sigma ={\displaystyle \frac{\left(\frac{S_I}{S_J}\right)dln\left(\frac{I}{J}\right)}{\frac{I}{J}d\left(\frac{S_I}{S_J}\right)+\left(\frac{S_I}{S_J}\right)d\left(\frac{I}{J}\right)}}$$

(6)

Through the derivation above, we observe that the factor substitution elasticity (σ) can be estimated using the coefficients of the Translog production function and factor shares without direct knowledge of factor prices. This approach allows us to utilize changes in factor shares to estimate substitution elasticity, thereby avoiding potential errors associated with direct price estimation. Due to diminishing marginal returns, producers tend to substitute expensive inputs with cheaper alternatives to maintain efficiency. When the cost of an input rises, producers respond by adjusting their input mix. Substitutability exists when a producer can reduce the usage of the more expensive input and increase the usage of a cheaper alternative while maintaining output. This is characterized by an absolute elasticity of substitution exceeding 1. Complementarity exists when increasing the usage of one input requires increasing the usage of another input to maintain output, characterized by an absolute elasticity of substitution less than 1. An elasticity of 1 indicates neither relationship. Thus, by analyzing the magnitude of the factor elasticity of substitution and technological change, we can assess the interrelationships between factors and achieve the optimal utilization of factor resources.

3.2. Transcendental Logarithmic Production Function

The selected form of a production function significantly influences the accuracy of elasticity of substitution estimates. Different production functions are suited to various production environments and analytical requirements. Considering the common forms, the Cobb–Douglas function does not reflect the real change in the degree of substitution or complementarity between factors. The Constant Elasticity of Substitution (CES) function has a constant elasticity of substitution, which is more flexible, but the model is complex, and the estimation method is cumbersome in multi-factor estimation. The Variable Elasticity of Substitution (VES) function adds time-varying features to capture more details, but it is relatively difficult to interpret the economic meaning of the results. The Translog production function, introduced by Christensen et al. (1973) [44], offers a flexible second-order approximation capable of capturing varying elasticities of substitution between inputs, including how these elasticities change with input ratios and time. This ability to reflect the dynamic adjustment of factor allocation makes it particularly suited for analyzing the multifaceted nature of agricultural production, which is significantly influenced by temporal and spatial effects. Consequently, the Translog production function is commonly used in regression analyses within grain production. In grain production, common factors include labor, land, capital, and other inputs such as pesticides, fertilizers, and other production materials. Estimating the factor elasticity of substitution in agricultural grain production functions allows for a clearer understanding of agricultural production efficiency, optimal resource allocation, and food security. Therefore, after considering various analytical methods while maintaining general applicability, this paper selects the empirical method based on the Translog production function for calculation. Our generalized Translog production function with two factors is expressed as follows:

$$lnY=\alpha +{\beta }_{I}lnI+{\beta }_{J}lnJ+{\beta }_{IJ}lnI\times lnJ+{\beta }_{II}{\left(lnI\right)}^2+{\beta }_{JJ}{\left(lnJ\right)}^2$$

(7)

Based on Equation (7), we can solve the specific expression of Equation (6). By employing the calculation method based on the Translog production function referring to Wang & Xie (2014) [45], Lin & Ahmad (2016) [46], we can derive the elasticity of substitution formula:

$${\sigma }_{ij}={\left\{1+{\displaystyle \frac{-{\beta }_{ij}+2\frac{{\epsilon }_i}{{\epsilon }_j}{\beta }_{jj}}{{\epsilon }_j-{\epsilon }_i}}\right\}}^{-1}$$

(8)

Thereinto,

$${\epsilon }_i={\displaystyle \frac{\frac{dY}{Y}}{\frac{dI}{I}}}={\beta }_i+{\sum }_j{\beta }_{ij}lnJ+2{\beta }_{ii}lnI$$

(9)

where i and j represent two arbitrary, distinct factors in the Translog regression coefficients, and ${\epsilon }_i$ represents the output elasticity of the factor i. Moreover, biased technological change in the Translog function can be written as follows:

$${Bias}_{ij}={\displaystyle \frac{{\beta }_{it}}{{\epsilon }_i}}-{\displaystyle \frac{{\beta }_{jt}}{{\epsilon }_j}}$$

(10)

The elasticity of factor substitution and biased technological progress significantly influence decisions regarding the intensive or conservative use of production factors, which holds substantial importance in agricultural policy implementation. When two factors are substitutes, an increase in the input of one factor, typically associated with rapid technological advancement, leads to a decrease in the use of the other factor, assuming constant output levels. Conversely, for complementary factors, an increase in the input of one factor results in a corresponding increase in the use of the other. This analysis completes the quantitative characterization of substitution elasticity within the Translog production function framework.

4. Empirical Analysis

4.1. Regression Results of the Translog Production Function

The data utilized in this paper are sourced from the China Agricultural Statistical Yearbook, National Agricultural Product Cost and Benefit Data Compilation, National Major Agricultural Product Cost and Benefit Data Compilation since the Founding of the People’s Republic of China, and other relevant materials, forming a panel dataset for 28 provinces and cities from 1991 to 2023. Among them, we have merged Guangdong with Hainan and Sichuan with Chongqing to exclude the interference caused by the adjustment of administrative divisions. In this analysis, total grain output is quantified by the aggregate tonnage of all grain crops. Capital input is represented by the total horsepower of agricultural machinery. Pesticide usage is measured in metric tons, as is fertilizer application. These proxies are commonly employed in agricultural studies to assess the impact of various inputs on production outcomes. As Dong et al. (2021) [47] pointed out, a major reason for the lack of empirical research in this field is the difficulty in obtaining data on factor prices, especially the price of capital inputs in agricultural production in developing countries. Sicular (1988) [48] also noted that grain prices are an important external factor influencing food production. We follow the approach of Önalan and Başmez (2022) [28] by employing output and usage quantities to eliminate the influence of price factors. Descriptive statistics indicate that the data are of high quality. After applying a logarithmic transformation to address skewness and stabilize variance, the data were utilized in the subsequent regression analysis. In the following text, we use Y to represent grain output, K for agricultural capital, L for labor, F for fertilizer, D for pesticides, and Z for land. The descriptive statistics of the data are shown in

Table 1. Descriptive statistics.

Variable Name	Unit	Obs.	Mean	S. D.	Min.	Max.
Grain Output	Thousand tons	917	19,382.3	15,336.4	280.6	78,677.2
Agricultural Capital	Thousand kW	917	26,614.7	25,904.8	939.7	133,530.2
Labor	Ten thousand people	917	1061.5	823.8	0.0	4321.3
Fertilizer	Thousand tons	917	1707.3	1327.4	45.4	7160.9
Pesticide	Ten thousand tons	917	4.9	4.2	0.08	19.9
Land	Thousand hectares	917	3953.3	2850.9	46.5	14,743.1

.

According to the descriptive statistics, the variables have good values and are easy to use in the next regression analysis and measurement. Our Translog production function takes the following form:

$$\begin{array}{l}lnY=\alpha +{\beta }_{1}ln{Y}_{-1}+{\beta }_{2}lnk+{\beta }_{3}lnf+{\beta }_{4}lnd+{\beta }_{5}lnz+{\beta }_{6}lnl+{\beta }_{7}lnk\times lnf+{\beta }_{8}lnk\times lnd\\ +{\beta }_{9}lnk\times lnz+{\beta }_{10}lnk\times lnl+{\beta }_{11}lnf\times lnd+{\beta }_{12}lnf\times lnz+{\beta }_{13}lnf\times lnl\\ +{\beta }_{14}lnd\times lnz+{\beta }_{15}lnd\times lnl+{\beta }_{16}lnz\times lnl+{\beta }_{17}{\left(lnk\right)}^2+{\beta }_{18}{\left(lnf\right)}^2\\ +{\beta }_{19}{\left(lnd\right)}^2+{\beta }_{20}{\left(lnz\right)}^2+{\beta }_{21}{\left(lnl\right)}^2+{\beta }_{22}t+{\beta }_{23}{t}^2+{\beta }_{24}lnk\times t+{\beta }_{25}lnf\times t\\ +{\beta }_{26}lnd\times t+{\beta }_{27}lnz\times t+{\beta }_{28}lnl\times t\end{array}$$

where the superscript ² refers to the square of the variable. To address potential multicollinearity inherent in the Translog production function, we incorporated lagged dependent variables into our panel regression model to mitigate endogeneity concerns. Additionally, we employed ridge regression to enhance the robustness of our polynomial regression findings, as this technique effectively addresses multicollinearity issues by introducing a biased term to stabilize coefficient estimates. The regression results of the Translog model are presented in

Table 2. Regression results.

Variables	Coef.	Std.	t	p Value	95% Conf. Interval
lnk	0.213	0.001	396.79	<0.001	0.212	0.214
lnf	−0.060	0.001	−60.43	<0.001	−0.062	−0.058
lnd	−0.170	0.002	−83.49	<0.001	−0.174	−0.166
lnz	−0.096	0.003	−27.46	<0.001	−0.102	−0.089
lnl	−0.202	0.004	−50.26	<0.001	−0.210	−0.195
lnklnf	0.346	0.005	65.08	<0.001	0.336	0.356
lnklnd	0.083	0.005	15.23	<0.001	0.072	0.093
lnklnz	−0.055	0.007	−8.46	<0.001	−0.683	−0.043
lnklnl	−0.024	0.011	−2.13	0.033	−0.047	−0.002
lnflnd	0.470	0.018	26.38	<0.001	0.435	0.505
lnflnz	−0.300	0.022	−13.57	<0.001	−0.343	−0.257
lnflnl	0.066	0.036	1.86	0.064	−0.004	0.136
lndlnz	−0.028	0.041	−0.68	0.500	−0.108	0.053
lndlnl	0.020	0.047	0.43	0.666	−0.072	0.113
lnzlnl	−0.038	0.050	−0.76	0.446	−0.137	−0.060
(lnk)2	0.200	0.065	3.06	0.002	0.072	0.328
(lnf)2	0.161	0.077	2.09	0.037	0.010	0.313
(lnd)2	−0.130	0.090	−1.45	0.148	−0.306	0.046
(lnz)2	0.191	0.109	1.75	0.081	−0.024	0.406
(lnl)2	−0.913	0.153	−5.98	<0.001	−1.213	−0.613
lny (−1)	−0.310	0.213	−1.45	0.147	−0.728	0.109
t	−0.030	0.243	−0.12	0.901	−0.507	0.446
t2	−0.044	0.340	−0.13	0.897	−0.712	0.624
lnkt	−0.342	0.371	−0.92	0.357	−1.070	0.387
lnft	−0.979	0.501	−1.95	0.051	−1.963	0.004
lndt	1.151	0.526	2.19	0.029	0.119	2.184
lnzt	1.526	0.619	2.46	0.014	0.311	2.742
lnlt	−1.856	0.779	−2.38	0.017	−3.384	−0.328

.

4.2. Factor Elasticity of Substitution Calculation Results

4.2.1. Analysis of Overall Estimation Results

The regression results presented in Table 2 indicate that the model is statistically significant and suitable for estimating the elasticity of substitution.

Table 3. Estimation results of factor elasticity of substitution.

${\mathit{\sigma }}_{\mathit{K}\mathit{F}}$	${\mathit{\sigma }}_{\mathit{K}\mathit{D}}$	${\mathit{\sigma }}_{\mathit{K}\mathit{Z}}$	${\mathit{\sigma }}_{\mathit{K}\mathit{L}}$	${\mathit{\sigma }}_{\mathit{F}\mathit{D}}$	${\mathit{\sigma }}_{\mathit{F}\mathit{Z}}$	${\mathit{\sigma }}_{\mathit{F}\mathit{L}}$	${\mathit{\sigma }}_{\mathit{D}\mathit{Z}}$	${\mathit{\sigma }}_{\mathit{D}\mathit{L}}$	${\mathit{\sigma }}_{\mathit{Z}\mathit{L}}$
0.973	1.011	0.969	1.007	1.030	0.927	0.987	0.920	1.017	1.017

presents the calculated elasticities of substitution for the factors under consideration.

Analysis of data from 1991 to 2023 reveals distinct relationships among China’s agricultural production factors. The following factor pairs exhibit clear complementarity, indicating that an increase in one factor’s input leads to an increase in the other’s usage: capital and fertilizer, capital and land, fertilizer and land, fertilizer and labor, and pesticide and land. These factor pairs demonstrate substitution characteristics, where an increase in one factor’s input results in a decrease in the other’s usage: capital and pesticide, fertilizer and pesticide, pesticide and labor, and land and labor. The substitution relationship between capital and labor is relatively weak. From a national perspective, in the context of agricultural modernization and green ecological agriculture, the allocation of agricultural factors involves trade-offs. Estimating factor substitution elasticity provides valuable guidance for optimizing these allocations.

According to the results of σ_KF (capital and fertilizer), integrating agricultural machinery with fertilizers enhances operational efficiency, leading to significant improvements in crop yield and quality. Fertilizers, essential for crop nutrition, work synergistically with machinery to boost grain production. The use of agricultural machinery increases the efficiency, precision, and accuracy of fertilizer application, optimizing nutrient delivery and promoting sustainable agricultural practices.

According to the results of σ_KD (capital and pesticides), the substitutability between capital and pesticides is notably evident in the interplay between agricultural machinery and pesticide inputs. Enhancing mechanization can reduce pesticide usage, thereby diminishing chemical pollution risks in farmland, safeguarding soil and water purity, and preserving the balance of farmland ecosystems.

According to the results of σ_KZ (capital and land), while capital investment can drive agricultural mechanization, in China, the substitution effect between capital and land is not pronounced. This may be due to abundant, low-cost rural labor, which reduces the incentive to replace labor with machinery. Additionally, certain agricultural tasks, such as planting and harvesting, remain labor-intensive and pose challenges to full mechanization, hindering the mechanization process. Land serves as the fundamental production factor in agriculture, while machinery enhances land productivity. The synergy between capital investment in machinery and land use significantly boosts agricultural productivity. Modern agriculture benefits from economies of scale; expanding land holdings improves machinery efficiency and reduces costs, leading to increased output.

According to the results of σ_KL (capital and labor), while capital investment can enhance agricultural mechanization, in China, the substitution effect between capital and land remains limited. This is likely due to the availability of abundant, low-cost rural labor, which reduces the incentive to replace land with capital. Additionally, certain agricultural tasks, such as planting and harvesting, are labor-intensive and pose challenges to full mechanization, further hindering significant labor substitution. On this point, our conclusions are much more moderate than those of Zhu et al. (2016) [39].

According to the results of σ_FD (fertilizer and pesticides), fertilizers and pesticides can, to some extent, serve as substitutes for each other. However, modern agricultural practices necessitate environmentally sustainable approaches. This finding underscores the need to balance two distinct negative environmental impacts: water eutrophication resulting from fertilizer usage and the bioaccumulation risks associated with excessive pesticide application.

According to the results of σ_FZ (fertilizer and land), fertilizers and land are complementary factors in agricultural production. Land serves as the fundamental resource for farming, providing physical space and a medium for crops to grow. Fertilizers supply essential nutrients, such as nitrogen, phosphorus, and potassium, that may be deficient in the soil, enhancing plant growth and productivity. The combined use of fertilizers and land supports food production by increasing crop yields per unit area. Moreover, the judicious and sustained application of fertilizers can improve soil structure and fertility, further enhancing land productivity.

According to the results of σ_FL (fertilizer and labor), while fertilizers and labor are generally considered complementary in agricultural production, studies suggest that in China, the relationship between fertilizer use and labor input is less pronounced. This is largely because fertilizer application continues to depend heavily on manual labor. Therefore, optimizing the coordination between fertilizer application and labor can lead to significant production cost savings and support the expansion of grain production.

According to the results of σ_DZ (pesticides and land), the strong complementary relationship between pesticides and land primarily arises from the fact that land serves as the direct medium for pesticide application. Utilizing pesticides enables more efficient and effective use of land resources by preventing and controlling pests and diseases, thereby enhancing land productivity and preserving its economic value. However, with the advancement of modern ecological agriculture, there is a growing emphasis on environmental protection and sustainability. This shift has led to a reduction in the practice of heavily applying pesticides per unit area to boost production, promoting more balanced and eco-friendly agricultural methods.

According to the results of σ_DL (pesticides and labor), in terms of the substitution relationship between pesticides and labor, pesticides are predominantly used over manual labor for pest and disease control. The high efficacy of pesticides has simplified tasks that previously required significant labor input. A key reason for this shift is that, in many instances, the cost of purchasing and applying pesticides is lower than hiring labor to achieve the same results. Additionally, utilizing pesticides allows labor to be redirected from intensive pest control activities to other, more productive agricultural tasks, thereby enhancing overall labor productivity.

According to the results of σ_ZL (labor and land), Land and labor are mutually substitutable throughout China. As agricultural modernization progresses and agricultural labor costs rise, farmers face decisions between land rental expenses and labor costs, leading to a substitutive relationship between these factors.

4.2.2. Analysis of Estimation Results by Province

The calculations presented in

Table 4. Estimation results of provincial factor elasticity of substitution.

Province	${\mathit{\sigma }}_{\mathit{K}\mathit{F}}$	${\mathit{\sigma }}_{\mathit{K}\mathit{D}}$	${\mathit{\sigma }}_{\mathit{K}\mathit{Z}}$	${\mathit{\sigma }}_{\mathit{K}\mathit{L}}$	${\mathit{\sigma }}_{\mathit{F}\mathit{D}}$	${\mathit{\sigma }}_{\mathit{F}\mathit{Z}}$	${\mathit{\sigma }}_{\mathit{F}\mathit{L}}$	${\mathit{\sigma }}_{\mathit{D}\mathit{Z}}$	${\mathit{\sigma }}_{\mathit{D}\mathit{L}}$	${\mathit{\sigma }}_{\mathit{Z}\mathit{L}}$
Anhui	0.993	1.055	0.954	1.006	1.025	0.984	0.990	0.934	1.016	1.015
Beijing	1.002	0.993	0.995	1.010	0.984	0.912	0.980	0.951	1.024	1.022
Fujian	0.839	1.020	0.943	1.006	1.024	1.028	0.988	0.917	1.017	1.016
Gansu	0.966	0.996	1.032	1.006	1.132	0.962	0.986	0.956	1.017	1.017
Hainan, Guangdong	0.970	0.932	1.041	1.006	1.090	0.971	0.990	0.907	1.016	1.015
Guangxi	0.922	1.015	0.930	1.006	1.013	0.926	0.989	0.923	1.016	1.016
Guizhou	0.964	0.935	1.037	1.005	1.070	0.854	0.986	0.949	1.016	1.016
Hebei	0.949	1.004	0.995	1.007	1.042	0.965	0.991	0.911	1.016	1.016
Henan	0.947	1.061	1.003	1.006	1.028	0.969	0.991	0.980	1.015	1.015
Heilongjiang	1.020	1.013	1.141	1.008	1.033	0.927	0.988	1.034	1.018	1.018
Hubei	0.980	1.043	0.971	1.006	1.035	0.983	0.990	0.831	1.016	1.015
Hunan	0.997	1.099	0.965	1.006	1.047	0.976	0.990	0.910	1.016	1.015
Jilin	0.911	0.995	0.924	1.007	1.027	0.865	0.987	0.901	1.018	1.017
Jiangsu	0.953	1.002	1.020	1.006	1.052	0.973	0.990	0.935	1.016	1.015
Jiangxi	0.956	1.015	0.941	1.006	1.020	0.923	0.988	0.903	1.017	1.016
Liaoning	0.968	1.014	0.929	1.007	1.008	0.924	0.988	0.938	1.018	1.017
Inner Mongolia	0.980	0.995	1.133	1.007	1.127	0.973	0.985	1.003	1.018	1.018
Ningxia	0.985	1.004	0.965	1.007	1.037	0.895	0.979	1.051	1.021	1.020
Qinghai	0.961	1.075	0.998	1.006	1.054	0.896	0.977	0.927	1.020	1.020
Shandong	0.977	0.935	0.997	1.007	1.060	0.956	0.991	1.005	1.015	1.015
Shanxi	1.057	1.006	0.863	1.007	0.858	0.821	0.987	0.869	1.018	1.017
Shaanxi	0.974	1.000	0.843	1.006	0.949	0.813	0.987	0.869	1.017	1.016
Shanghai	0.976	0.994	1.022	1.008	1.004	0.918	0.980	0.748	1.023	1.022
Chongqing, Sichuan	1.020	1.033	0.801	1.006	1.023	0.969	0.990	0.867	1.015	1.015
Tianjin	0.939	0.988	1.007	1.009	1.025	0.872	0.979	1.015	1.023	1.022
Xinjiang	0.973	0.988	0.950	1.008	1.027	0.886	0.986	0.938	1.020	1.018
Yunnan	1.050	1.000	0.862	1.006	0.954	0.810	0.988	0.685	1.016	1.016
Chekiang	1.022	1.112	0.899	1.007	1.056	0.990	0.988	0.924	1.017	1.017

lead to several key conclusions. First, regional consistency with distinct patterns matters. While the overall results across regions are similar, differences emerge in the patterns of factor substitution and complementarity. The eastern and northeastern regions exhibit stronger substitution characteristics among factors, indicating a higher degree of substitutability between inputs. In contrast, the central and western regions display more balanced relationships, suggesting a more equal interplay between substitution and complementarity among factors. Second, from a factor-specific insight, analyzing each factor individually provides more nuanced information. For instance, agricultural machinery and fertilizers often complement land usage, while pesticides tend to substitute for labor. Additionally, fertilizers can both complement and substitute for land and labor, depending on regional practices. These insights are crucial for understanding regional agricultural dynamics and informing targeted policy interventions. Our findings underscore the importance of considering regional and factor-specific contexts when analyzing agricultural production relationships, as they reveal significant variations that can inform more effective and tailored agricultural policies.

According to the results of σ_KF (capital and fertilizer), in China, capital and fertilizer generally exhibit a complementary relationship across most provinces. Specifically, changes in the prices of capital and fertilizer, while holding food production constant, lead to simultaneous changes in the usage of both factors. The stronger the complementarity, the tighter the integration between capital and fertilizer, and the greater the dependency on either input. Fujian Province has the strongest factor complementarity, indicating a close relationship between agricultural machinery and fertilizers. In contrast, provinces such as Sichuan-Chongqing, Heilongjiang, Zhejiang, Yunnan, and Shanxi exhibit characteristics of factor substitution, where an increase in the input of one factor leads to a decrease in the use of the other. Considering the trends in agricultural development, it is advisable to invest in agricultural machinery at appropriate times and apply fertilizers according to local conditions to promote the scale efficiency of output.

According to the results of σ_KD (capital and pesticides), regional variations exist in the relationship between machinery and pesticide inputs across Chinese provinces, with notable differences observed. Provinces such as Zhejiang, Hunan, Qinghai, and Henan have demonstrated that increased pesticide inputs can reduce the necessity for certain agricultural machinery inputs. In contrast, provinces like Sichuan-Chongqing, Guizhou, and Shandong exhibit a complementary relationship between these inputs, indicating that both are utilized together. Provinces such as Shaanxi, Yunnan, and Jiangsu show minimal substitution effects between machinery and pesticide inputs. Overall, the substitution effect primarily stems from the ability of pesticide inputs to decrease the reliance on agricultural machinery. Pesticides play a vital role in preventing and controlling pests and diseases, enhancing yields, and reducing dependence on machinery. However, geographical factors mean that some regions utilize both pesticides and agricultural machinery simultaneously, resulting in a complementary relationship between these inputs. These findings align with studies indicating that regional economic development and agricultural practices significantly influence the intensity and efficiency of pesticide and machinery use across different regions in China.

According to the results of σ_KZ (capital and land), significant provincial variations exist in the relationships between agricultural machinery and pesticide inputs. While most provinces exhibit complementary interactions among these factors, regions such as Heilongjiang, Inner Mongolia, and Guangdong-Hainan demonstrate mutual substitution effects. This suggests that in these areas, increased investment in pesticides can reduce the need for certain agricultural machinery inputs. Overall, the adoption of agricultural machinery enhances planting and harvesting efficiency, leading to an increase in per-unit yields. This improvement allows for expanded cultivation areas and can contribute to reduced land rental costs. However, it is important to note that the impact of agricultural machinery on production efficiency can vary based on regional factors, including terrain and the availability of suitable infrastructure.

According to the results of σ_KL (capital and labor), the data across provinces exhibit minimal variation, with values clustering around 1, indicating an absence of substitution or complementary relationships between the two factors. This observation aligns with classical economic theory, which posits the independence of capital and labor, a concept that has been extensively validated. Current evidence suggests that China’s grain production remains heavily reliant on labor inputs. Studies have found that the transfer of agricultural labor does not significantly negatively impact grain output and may even promote production through increased use of machinery and fertilizers. However, as rural labor costs rise, there is a discernible shift in land use patterns, with reductions in areas devoted to labor-intensive crops and expansions in those requiring less labor. Additionally, the adoption of agricultural machinery services has been linked to a decreased likelihood of relative poverty among farmers, primarily by enhancing their human capital through skills training. These findings underscore the necessity for further research into the systematic benefits of replacing manual labor with agricultural machinery. Such studies are essential to fully comprehend the mechanization and labor dynamics, and overall productivity within China’s agricultural sector.

According to the results of σ_FD (fertilizer and pesticides), most provinces show a mutual substitution relationship. The elasticity of substitution between fertilizers and pesticides varies across China’s provinces, reflecting diverse agricultural practices and regional conditions. Only Shanxi, Shaanxi, Yunnan, and Beijing showed complementary characteristics, while Gansu, Inner Mongolia, Guangdong-Hainan, and Guizhou showed obvious characteristics of mutual substitution. This pattern aligns with the expectation that farmers often adjust input combinations to optimize productivity and cost-effectiveness. The variations underscore the importance of tailoring agricultural input strategies to regional contexts, considering factors like local climate, soil fertility, crop types, and pest pressures.

According to the results of σ_FZ (fertilizer and land), in most provinces, fertilizers and land exhibit a pronounced complementary relationship, significantly enhancing grain yields per unit area and ensuring stable production. This synergy arises because fertilizers supply essential nutrients that bolster soil fertility, leading to increased crop productivity. However, Fujian province stands as an exception to this trend. Understanding these provincial dynamics is crucial for developing tailored agricultural strategies that align with regional characteristics and challenges.

According to the results of σ_FL (fertilizer and labor), in all provinces, fertilizer and labor inputs exhibit complementary characteristics. Increasing fertilizer application alongside labor input enhances grain production efficiency. This shift supports the transition from relying solely on labor to adopting multifaceted input strategies in agricultural modernization.

According to the results of σ_DZ (pesticides and land), in most provinces, agricultural inputs exhibit complementary relationships; however, provinces such as Heilongjiang, Ningxia, and Tianjin display substitution effects between certain inputs. Similar to fertilizers, pesticides directly affect land by promoting increased grain production per unit area. Our observations substantiate this relationship.

According to the results of σ_DL (pesticides and labor), pesticides and labor are mutually substitutable, indicating that there is a trend of pesticides replacing labor in grain production across the country. The use of pesticides can improve the efficiency of pest control and reduce the need for manual spraying and field management, thereby reducing agricultural production costs and increasing grain crop yields and quality. However, we should not rely too much on pesticide inputs, not only because of the diminishing rate of return of factors, but also because of the pollution of pesticides to the environment. Therefore, enhancing scientific pesticide application and adopting ecological pest management practices are essential to achieve a balance between food security and environmental protection.

According to the results of σ_ZL (labor and land), land and labor exhibit mutual substitutability influenced by economic and policy factors. Rising labor costs, driven by urban migration and reduced agricultural labor supply, encourage farmers to expand land holdings to achieve economies of scale, thereby substituting labor with land. Conversely, land finance mechanisms that increase land prices compel farmers to intensify labor use to maintain output per unit area, leading to complementary land–labor relationships. This dynamic interplay underscores the complex substitution and complementarity between land and labor in agricultural production.

4.2.3. Analysis of Time-Based Estimation Results

As is shown in

Table 5. Estimation results of annual factor elasticity of substitution.

Year	${\mathit{\sigma }}_{\mathit{K}\mathit{F}}$	${\mathit{\sigma }}_{\mathit{K}\mathit{D}}$	${\mathit{\sigma }}_{\mathit{K}\mathit{Z}}$	${\mathit{\sigma }}_{\mathit{K}\mathit{L}}$	${\mathit{\sigma }}_{\mathit{F}\mathit{D}}$	${\mathit{\sigma }}_{\mathit{F}\mathit{Z}}$	${\mathit{\sigma }}_{\mathit{F}\mathit{L}}$	${\mathit{\sigma }}_{\mathit{D}\mathit{Z}}$	${\mathit{\sigma }}_{\mathit{D}\mathit{L}}$	${\mathit{\sigma }}_{\mathit{Z}\mathit{L}}$
1991	1.104	0.800	−0.625	1.050	0.572	−1.072	1.028	−1.023	1.033	1.006
1992	1.176	0.610	1.559	1.037	1.646	1.128	1.014	1.580	1.032	1.017
1993	1.230	1.592	1.561	1.028	1.156	0.682	1.005	1.396	1.031	1.022
1994	1.172	1.131	0.599	1.022	1.088	0.912	0.998	1.374	1.029	1.024
1995	0.840	1.064	0.832	1.018	1.060	0.955	0.994	1.415	1.027	1.025
1996	0.602	1.039	0.932	1.014	1.045	0.972	0.991	1.552	1.026	1.025
1997	0.833	1.027	0.962	1.012	1.035	0.981	0.989	1.313	1.024	1.024
1998	0.891	1.020	0.976	1.009	1.029	0.986	0.987	2.072	1.023	1.023
1999	0.917	1.016	0.983	1.008	1.024	0.989	0.985	0.654	1.021	1.023
2000	0.933	1.012	0.988	1.006	1.021	0.991	0.984	−0.138	1.020	1.022
2001	0.943	1.010	0.991	1.005	1.018	0.993	0.983	0.190	1.019	1.021
2002	0.951	1.008	0.993	1.004	1.016	0.994	0.983	0.526	1.018	1.020
2003	0.957	1.007	0.994	1.003	1.014	0.995	0.982	0.676	1.018	1.019
2004	0.961	1.006	0.995	1.003	1.013	0.995	0.982	0.754	1.017	1.019
2005	0.965	1.005	0.996	1.002	1.012	0.996	0.982	0.804	1.016	1.018
2006	0.968	1.005	0.997	1.002	1.011	0.996	0.982	0.836	1.016	1.018
2007	0.970	1.004	0.997	1.001	1.010	0.997	0.981	0.860	1.015	1.017
2008	0.973	1.004	0.998	1.001	1.010	0.997	0.981	0.878	1.014	1.016
2009	0.975	1.003	0.998	1.001	1.009	0.997	0.981	0.892	1.014	1.016
2010	0.976	1.003	0.998	1.000	1.008	0.997	0.982	0.903	1.013	1.015
2011	0.978	1.003	0.999	1.000	1.008	0.998	0.981	0.911	1.013	1.015
2012	0.979	1.003	0.999	1.000	1.007	0.998	0.982	0.919	1.013	1.015
2013	0.980	1.002	0.999	1.000	1.007	0.998	0.982	0.925	1.012	1.014
2014	0.981	1.002	0.999	0.999	1.007	0.998	0.982	0.931	1.012	1.014
2015	0.982	1.002	0.999	0.999	1.006	0.998	0.982	0.936	1.011	1.013
2016	0.983	1.002	0.999	0.999	1.006	0.998	0.982	0.940	1.011	1.013
2017	0.984	1.002	0.999	0.999	1.006	0.998	0.982	0.944	1.011	1.013
2018	0.984	1.002	0.999	0.999	1.005	0.999	0.982	0.947	1.011	1.012
2019	0.985	1.002	0.999	0.999	1.005	0.999	0.982	0.950	1.010	1.012
2020	0.986	1.001	1.000	0.999	1.005	0.999	0.982	0.953	1.010	1.012
2021	0.986	1.001	1.000	0.999	1.005	0.999	0.982	0.956	1.010	1.012
2022	0.987	1.001	1.000	0.999	1.005	0.999	0.982	0.958	1.010	1.011
2023	0.987	1.001	1.000	0.998	1.004	0.999	0.982	0.961	1.010	1.011

above, we mainly use annual estimation results to determine whether there are significant changes in the time series. It is obvious that σ_KL, σ_FL, σ_DL, and σ_ZL do not change much over time, and their values remain near 1 from 1991 to 2023 and are relatively stable. In contrast, the elasticity of substitution of other factors showed more volatility in the first few years and eventually converged to a low volatility state, reflecting the improvement of the integration of modern agricultural factors.

We also assessed the heterogeneous impact of China’s agricultural and food policies on the elasticity of factor substitution, as shown in

Table 6. Estimation results of factor elasticity of substitution: before and after policy.

	${\mathit{\sigma }}_{\mathit{K}\mathit{F}}$	${\mathit{\sigma }}_{\mathit{K}\mathit{D}}$	${\mathit{\sigma }}_{\mathit{K}\mathit{Z}}$	${\mathit{\sigma }}_{\mathit{K}\mathit{L}}$	${\mathit{\sigma }}_{\mathit{F}\mathit{D}}$	${\mathit{\sigma }}_{\mathit{F}\mathit{Z}}$	${\mathit{\sigma }}_{\mathit{F}\mathit{L}}$	${\mathit{\sigma }}_{\mathit{D}\mathit{Z}}$	${\mathit{\sigma }}_{\mathit{D}\mathit{L}}$	${\mathit{\sigma }}_{\mathit{Z}\mathit{L}}$
Before 2004	0.891	0.939	0.545	1.017	−0.563	0.837	0.994	−1.887	1.025	1.021
After 2004	0.978	1.003	0.998	1.000	1.007	0.998	0.982	0.908	1.012	1.014

. Notably, in 2004, the State Council of China issued the “Opinions of the State Council on Further Deepening the Reform of the Grain Circulation System”, which aimed to promote market-oriented reforms in the grain circulation system, protect farmers’ interests, and facilitate adjustments in agricultural production structure as well as grain production and circulation. Increasing evidence suggests that this reform has been a crucial factor in boosting production income. According to the regression results for factor substitution elasticity, the most significant change observed after 2004 is that, except for the relationship between fertilizers and labor, the substitution or complementary relationships between most factors have weakened, and the relationship between pesticides and land has even reversed. Following the policy’s implementation, agricultural production has shifted toward marketization and increased competition, leading to more effective use of various factors within the framework of agricultural modernization. This shift has contributed to improvements in agricultural production efficiency.

4.3. Biased Technological Change and Optimal Factor Use Efficiency Trend

By analyzing Table 4 and

Table 7. Estimation results of biased technological change.

Province	bKF	bKD	bKZ	bKL	bFD	bFZ	bFL	bDZ	bDL	bZL
Anhui	−0.267	−0.181	−0.462	−0.155	0.086	−0.195	0.112	−0.282	0.026	0.307
Beijing	0.069	0.130	−0.231	0.149	0.061	−0.299	0.080	−0.361	0.019	0.380
Fujian	0.038	−0.075	−1.101	−0.049	−0.112	−1.139	−0.087	−1.027	0.025	1.052
Gansu	−0.484	−0.126	−0.265	−0.101	0.357	0.219	0.383	−0.138	0.025	0.163
Hainan, Guangdong	−0.357	−0.097	1.670	−0.071	0.259	2.027	0.286	1.768	0.026	−1.741
Guangxi	−0.277	−0.471	−0.795	−0.445	−0.194	−0.518	−0.168	−0.324	0.027	0.350
Guizhou	−11.951	0.690	0.534	0.715	12.641	12.485	12.666	−0.156	0.026	0.182
Hebei	0.762	0.374	0.044	0.399	−0.389	−0.718	−0.363	−0.330	0.025	0.355
Henan	0.307	−0.017	−0.359	0.008	−0.323	−0.665	−0.299	−0.342	0.025	0.367
Heilongjiang	−0.344	−0.343	−0.477	−0.319	0.001	−0.133	0.025	−0.134	0.024	0.158
Hubei	0.170	0.274	−0.143	0.300	0.105	−0.313	0.131	−0.418	0.026	0.444
Hunan	0.052	0.086	−0.271	0.114	0.035	−0.322	0.063	−0.357	0.028	0.385
Jilin	0.000	−0.149	−0.359	−0.128	−0.149	−0.359	−0.128	−0.210	0.021	0.231
Jiangsu	0.740	0.237	−3.392	0.262	−0.502	−4.131	−0.478	−3.629	0.025	3.654
Jiangxi	0.551	−0.953	−1.241	−0.926	−1.504	−1.792	−1.477	−0.288	0.027	0.315
Liaoning	−0.636	−0.217	−0.533	−0.193	0.419	0.103	0.443	−0.316	0.024	0.341
Inner Mongolia	−0.174	−0.073	−0.185	−0.051	0.102	−0.011	0.124	−0.112	0.022	0.134
Ningxia	0.006	0.026	−0.120	0.044	0.020	−0.126	0.039	−0.146	0.018	0.164
Qinghai	0.019	−0.034	−0.169	−0.010	−0.053	−0.188	−0.029	−0.136	0.024	0.160
Shandong	−0.022	−0.068	−1.173	−0.043	−0.046	−1.151	−0.021	−1.105	0.025	1.130
Shanxi	−0.958	−0.971	−1.159	−0.948	−0.013	−0.201	0.010	−0.188	0.023	0.211
Shaanxi	1.461	1.390	1.2149	1.413	−0.071	−0.246	−0.048	−0.176	0.023	0.198
Shanghai	−0.083	−0.022	−5.073	−0.002	0.062	−4.990	0.082	−5.052	0.020	5.072
Chongqing, Sichuan	0.213	0.211	−0.020	0.239	−0.002	−0.232	0.026	−0.231	0.028	0.258
Tianjin	1.204	0.211	0.047	0.231	−0.992	−1.156	−0.973	−0.164	0.020	0.184
Xinjiang	−0.014	0.031	−0.247	0.053	0.045	−0.233	0.067	−0.278	0.022	0.300
Yunnan	−0.120	−0.136	−0.321	−0.109	−0.016	−0.201	0.011	−0.185	0.027	0.212
Chekiang	−0.244	−0.260	−0.835	−0.233	−0.016	−0.592	0.011	−0.575	0.027	0.603

, we can compare the technological progress biases and factor substitution elasticities across various factor combinations. The overall trend results for the period 1991–2003 are shown in

Table 8. The moving tendency about pairs of factors.

Pairs	K-F	K-D	K-Z	K-L	F-D	F-Z	F-L	D-Z	D-L	Z-L
Outcome	F↑	K↑	Z↑	K↑	D↑	F↑	L↑	D↑	D↑	Z↑
	K↓	D↓	K↓	L↓	F↓	Z↓	F↓	Z↓	L↓	L↓

The ↑ and ↓ arrows in the table indicate the upward and downward trends in factor shares resulting from the nature of the technological progress bias and factor elasticity of substitution. In general, this trend is spontaneous if production is organized according to the optimal level of production presumed by the model.

, and detailed charts are provided in Appendix A. This comparison reveals the trends in factor input changes within each province, offering valuable insights for the real economy. Observing the patterns across most provinces, we can draw the following conclusions.

Where b refers to the technological progress bias, or Bias in Equation (10). Judging from the estimated results of Table 8, the relative shares of factors such as fertilizers, agricultural machinery, pesticides, land, and labor have increased and decreased between 1991 and 2023, showing a specific development trend. First, rural labor shortages, decreasing mechanization costs, and modernization requirements have collectively increased the relative share of agricultural machinery, indicating that agricultural production is developing in the direction of mechanization and automation, reducing dependence on manual labor and pesticides. In particular, the increase in the share of agricultural machinery relative to pesticides reflects the development of precision agriculture and environmentally friendly agriculture, which helps to save pesticide inputs through mechanized equipment and protects rural natural resources and the environment. The increase in the relative share of land means that expanding the planting area has become one of the important ways to increase grain production. It reflects the improvement of unit land productivity under the blessing of modern agriculture, which has increased the importance of land input. The increase in the relative share of chemical fertilizers suggests that farmers can use chemical fertilizers to replenish soil nutrients when seeking to increase output per unit area, which is more efficient than increasing mechanization or expanding cultivated land. The decline in the relative share of labor indicates that the importance of agricultural labor is declining. Due to the trend of China’s rural population migrating to cities, the scarcity of agricultural labor has gradually emerged, and the price of agricultural labor has risen. Driven by this factor, China has gradually reduced its investment in traditional labor in grain production. Overall, these changes reflect that China’s agricultural production is transforming towards mechanization, scale, intensification, and technology.

5. Conclusions and Discussion

This study systematically estimates the elasticity of substitution among production inputs in China’s grain production from 1991 to 2023, filling a critical gap in the literature. By providing robust numerical simulations, the research offers valuable insights into optimizing factor allocation and improving input utilization efficiency. It is also an empirical explanation for the grain productivity in China in Zheng et al. (2023) [49] and Wang et al. (2025) [50]. The analysis reveals that agricultural modernization is increasingly reliant on the coordinated use of diverse inputs and the optimal allocation of resources to enhance production efficiency.

Traditional agriculture, which heavily depends on labor, faces significant constraints due to labor shortages and technological limitations. Unlike wheat farming in Zhu et al. (2016) [39], the contribution of food crops to output through machine substitution alone is somewhat weak. The complex relationships of substitution and complementarity among various inputs must be effectively managed to optimize input utilization and mitigate the adverse effects of diminishing returns to scale, ensuring stable agricultural output in large-scale operations. Moreover, the law of diminishing marginal returns suggests that continuous investment in a single input can result in declining marginal productivity, thereby reducing overall production efficiency. These findings underscore Pingali (2012) [51] and Liu (2022) [17], with the conclusion that relying solely on traditional inputs such as labor and land is insufficient for achieving sustainable agricultural development.

The study also highlights significant regional disparities in the modernization process. In eastern regions, characterized by limited land, agricultural development depends more on capital and technological investments, which enhance land productivity. Conversely, in central and western regions, abundant land resources lead to a continued reliance on traditional input combinations, such as labor and land, which delays the pace of modernization. Northwestern regions face unique challenges, including severe water scarcity and fragile ecosystems, which limit agricultural development. Meanwhile, southwestern mountainous areas, with their complex terrain and low mechanization, experience high dependence on labor, compounded by rural labor migration.

To address these structural disparities, region-specific agricultural policies must be developed to reflect the diverse factor endowments and production conditions across the country. In view of the shortage of labor and arable land in the eastern region, the use of agricultural machinery should be rationally promoted so as to replace the higher labor costs and achieve higher production efficiency, while accelerating the construction of high-standard farmland to improve the efficiency of arable land use. It responded forcefully to Tian et al. (2020) [21] and Hao et al. (2024) [52]. As a traditional grain-producing area, the central region should introduce policies to regulate and control the use of chemicals to prevent the decline of soil quality and improve production efficiency. At the same time, farmers should be trained to improve their ability to operate machinery to realize better synergy of elements. The sparsely populated and ecologically fragile characteristics of the Northwest region require that food production must prioritize arable land protection, green development orientation, and efficient allocation of resources as a prerequisite for guiding the development of an ecologically friendly mode of agricultural development. The mountainous characteristics of the southwest region should also adopt new production tools, such as drones, to replace manual labor, while strengthening the integrated land supervision and centralized management. The northeastern region, with its concentrated and sparsely populated arable land, is suitable for the development of large-scale mechanized production, and farmers should be encouraged to purchase advanced and suitable agricultural machinery to improve production efficiency. While optimizing the management of fertilizer and pesticide input, use should also be strengthened, only by considering the interplay of these inputs and building regional agricultural support systems oriented toward mechanization, scale, greening, and technological advancement can China achieve high-quality, sustainable agricultural development.

After the policy in 2004, it is also necessary to continue to pay attention to the rational allocation of factors. Continuing to deepen market-oriented reform and optimize resource allocation, we should continue to promote the marketization process of land, labor, fertilizers, pesticides and other production factors, so that market mechanisms can play a greater role in resource allocation. At the same time, to promote agricultural competition, it is necessary to break down local protectionism, encourage cross-regional competition, and promote fair competition in all links of the grain industry chain.

The research in this paper is still slightly deficient. First of all, the empirical process is based on estimation, and the discussion of endogeneity based on the form of the model is not sufficient, and the robustness of the conclusions of the elasticity of substitution measured in this paper still needs to be verified by subsequent scholars who have researched in related aspects, due to the small number of estimation conclusions that can be used as comparisons. Second, this paper only discusses a shorter time span and does not further analyze the longer-term trend findings. A more comprehensive analysis that stretches the time span is also a direction for further research that could be considered. Finally, some international comparative analyses can be introduced based on different geographical locations and different industrial characteristics.