Does Marketization Promote High-Quality Agricultural Development in China?

Abstract

Over the past 40 years of reform and opening, the enhancement in marketization has greatly promoted the development of the Chinese economy. At present, China’s economic development model has shifted from a focus on speed to a focus on quality. Against this background, it is necessary to further promote marketization reform to promote high-quality development in China. This paper begins with an introduction to high-quality agricultural development and the degree of marketization. According to the definitions of high-quality development and marketization, we constructed an index of high-quality agricultural development and an index of marketization degree, respectively. First, we determined the characteristics of high-quality agricultural development in China. There are large regional differences in agriculture development, but these disparities are improving simultaneously, and regional differences are showing a narrowing trend, except for the western region. Then, we measured the impact of marketization reforms on high-quality agricultural development using the Quadratic Assignment Procedure. Based on sample data from 2009 to 2019, this paper found that marketization reform has played a significant role in promoting high-quality agricultural development. The three sub-indicators of non-state-owned economy, factor market, and the market’s level of order, which represent the marketization degree, had significant impacts on reducing regional differences in high-quality agricultural development. Additionally, the effects of these three variables gradually increased, narrowing the regional differences in high-quality agricultural development. Finally, we suggested that promoting the development of a non-state-owned economy, factor market, and the market’s level of order would be an important path to boosting the high-quality development of agriculture.

1. Introduction

Since the reform and opening, increased marketization has greatly improved economic growth. Given the high-speed development of China’s economy, it is worth considering whether further improvement in the degree of marketization can boost high-quality development of the economy. This paper uses high-quality agricultural development as an example to sort out the mechanism behind the marketization degree affecting high-quality agricultural development, explore and analyze the relationship between the marketization degree and high-quality agricultural development, and explain how the marketization degree promotes high-quality agricultural development.

Agricultural development is closely related to the level of economic development [1]. With the rapid development of the economy, China’s agricultural development has made great achievements. How these achievements were made is worth exploring. China created some subsidies to support agriculture, just like some developed countries have implemented the policy of supporting agriculture with industrial accumulation. The other develo** countries in Asia, such as Indonesia, the Philippines, and Vietnam, have also increased investment in agricultural support, including subsidies and insurance, promoting the industrialization and modernization of agriculture [2,3]. The government subsidies for agriculture in China increased from USD 450 million in 1995 to USD 65.5 billion in 2019; in Vietnam, from USD 100 million in 2000 to USD 400 million in 2019; in the Philippines, from USD 100 million in 2000 to USD 300 million in 2019, and in Indonesia, from USD 300 million in 1995 to USD 2.8 billion in 2019. In 2020, China spent USD 11.5 billion on agriculture insurance, becoming the largest investor in agriculture insurance in the world. Are these policies enough to support high-quality agricultural development? Many scholars have confirmed that China’s industrial structure optimization and industrial agglomeration have promoted the development of agriculture [4]. Based on the history of agricultural development in China, we found that marketization is another powerful force.

Marketization means the market plays a key role in resource allocation and means less government interference, which has greatly contributed to the economic growth of Chinese cities [5]. Since the opening and reform, marketization has become the fundamental driving force for the development of the urban economy. Gang et al. provided quantitative evidence that marketization contributed an average of 1.3 percentage points to China’s economic growth rate [6]. In 2017, the Chinese government announced an ambitious statement of high-quality development (HQD), which is an important guarantee for sustainable development. In general, HQD is efficient, fair, and sustainable development [7]. In this context, we are very interested in whether marketization has contributed to high-quality agricultural development in China.

High-quality agricultural development is a complex, systematic project. Agricultural development shows different characteristics at different stages of economic development. With increased marketization, China’s agricultural development displays the following characteristics. First, it has significant development potential. With the development of the market, agriculture-related service industries have been derived successively. These industries gradually become new elements that play a vital role in promoting the expansion of the agricultural production scale, optimizing the agricultural production modes, and more [8]. Second, the agricultural development mode is relatively extensive. Agricultural production is characterized by a long production period, significant investment in land and other capital, the need for large amounts of agricultural chemicals in the production process, and so on. The rapid growth of agricultural production has also resulted in environmental pollution, unbalanced product structure, overproduction of certain crops, and other issues [9]. Third, there is spatial–temporal heterogeneity in agricultural development. Due to constraints in natural conditions, agricultural production has significant regional and seasonal characteristics, which lead to significant regional imbalances in agricultural development in China. Although agricultural production has greatly developed, traditional development modes are no longer sufficient to meet the needs of economic development at the present stage. Agricultural development also needs to shift from an orientation toward speed to an orientation toward quality. Currently, few studies have investigated high-quality agricultural development. In the context of the new normal of economic development, further research is necessary to promote high-quality agricultural development.

Marketization is an important power that can be used to promote the economy [10,11]. In order to answer the question of how marketization contributed to the high-quality development of Chinese agriculture, we first constructed a system of indicators for the high-quality development of agriculture and constructed an index for the high-quality development of agriculture in China with principal component analysis. Secondly, this paper analyzed the spatial variation in and dynamic evolution of high-quality development of agriculture using the Gini coefficient and kernel density methods. Finally, on the basis of evaluating the high-quality development of Chinese agriculture, we used the QAP method to analyze the impact of marketization reform on the high-quality development of agriculture.

The remainder of this paper is organized as follows: Section 2 summarizes the existing research and puts forward the hypotheses, Section 3 outlines the research methodologies and the source of data, Section 4 presents the empirical results, including the spatial and temporal patterns as well as the evolution process and influential factors for high-quality agricultural development in China, Section 5 concludes and provides policy implications, and Section 6 discusses the limitations and future research.

2. Literature Review

2.1. Marketization

Marketization has been seen as a phenomenon that occurs in economic system reforms in transition countries. Many researchers have found that marketization reforms usually have a positive effect on economic growth in the process of marketization reform. The European Bank for Reconstruction and Development (EBRD) constructed a system of indicators to measure the effect of marketization reforms on economic growth in its annual transition report, which scores 27 transition countries on various aspects of reform. In an earlier study, Havrylyshyn found a significant explanatory power of marketization reforms on economic growth using the EBRD transition indicators [12]. Demelo used the internal market, external market, and privatization as detailed marketization indicators and found a positive relationship between marketization and economic growth [13].

After reaching a common understanding of the relationship between marketization and economic development, many scholars further studied the pathways through which marketization affects the economy. Marketization can improve the efficiency of resource allocation. This improvement will be necessary for industrialization. Yang proved that marketization could promote industrialization and urbanization, which support the performance of economic development [14]. Mwangi and Kariuki found that marketization could also increase food crop yields, proving that marketization can promote agricultural development [15]. Fan, Aghion, and Iradian proposed that agricultural marketization could promote agricultural technology and thus economic development [16,17,18]. Meanwhile, Fu further discovered that market openness, which is part of marketization, has a negative impact on agricultural technical efficiency in the short term but a positive impact in the long term [19,20,21]. Wan and Van uncovered that the marketization of land markets could reduce the efficiency losses associated with land market fragmentation, increasing the development quality of the economy [22,23].

2.2. High-Quality Development

A growing number of scholars around the world are focusing on development quality rather than only on the production of agriculture. Martinez defined high-quality agricultural development as strong, stable, and sustainable growth; he stated that it is important to promote the quality of agricultural development to improve people’s lives and reduce poverty [24]. Many scholars stressed the importance of the development quality of agriculture. Brown stated that the government should enhance agricultural technology, which could not only boost agricultural productivity but also promote agricultural development quality [25]. King showed that technological innovation in agriculture is an important reason why there is a huge difference in agricultural productivity between developed and develo** countries; he also stated that improving the development quality of agriculture is an important path to reducing the gap in agricultural development [26]. Because agricultural production needs chemical inputs, Shumin highlighted that environmental degradation leads to a deterioration in the quality of agricultural development in China’s reform and opening, hindering its economic and cultural development [27].

The pathway by which marketization affects high-quality agricultural development is characterized by agriculture production. Many scholars further determined the agricultural factors influenced by marketization, with some articles pointing out that the education level of farmers could be influenced by agriculture marketization, which would further affect the yield of crops [28,29]. Zhong identified that land marketization could improve the efficiency of resource allocation by giving more effective play to the land price signal and guiding the combination of production factors to create matches more effectively [30]. Yao also conducted relevant research on the land market; he found that land marketization would also increase the green TFP significantly [31]. Additionally, the marketization of agricultural land could reduce the land price, thus improving the average land productivity by improving land allocation efficiency [32].

In addition to the elements previously mentioned, such as technology, the environment, farmers’ living quality, and the rural government, we speculate that marketization will also affect agriculture through the following several elements. The development of marketization will promote not only the domestic trading of agricultural products but also their exportation to the world; therefore, the external trade of agriculture will also increase. The development of agriculture marketization could promote the development of agriculture on a larger scale, and the demand for agricultural expansion could promote the emergence of the agricultural finance industry and infrastructure development.

The high-quality development of agriculture and marketization has been well-researched, giving us a good basis for our study. Thus, based on the connotations of high-quality development, we further analyzed the promotion of agriculture development by different regional levels of marketization in China. Then, we analyzed the impact of marketization on high-quality agricultural development in detail to find the concrete factors influencing high-quality agricultural development. We also determined the impact of marketization on agricultural development trends.

3. Research Hypotheses

3.1. The Mechanism by Which Marketization Promotes High-Quality Agricultural Development

In China’s economic transition, the market competition mechanism plays an important role in economic development. Market competition means the survival of the fittest. In economic development, the efficiency of resource allocation is an important factor in determining the rate of economic growth and the income gap [33]. Optimizing resource allocation is the basic characteristic of the market economy. The change in resource allocation will induce a change in the production mode. Resources flow into the more efficient sector, which causes industrialization.

Additionally, marketization is the process of price formation with market competition and further adjusts the relationship between supply and demand. Compared with the planned economy, marketization leads to flexible prices under which high-quality products may be sold at a higher price. This flexible price mechanism will encourage producers to focus more resources on the R&D of high-quality products in order to make a profit, thus obtaining advantages in price and competition. The process of market competition may lead to better commodity quality, more patterns, and a more reasonable price. Economic development in various countries has demonstrated the role of marketization in promoting the economy [34] with product innovation.

High-quality agricultural development is a new development mode based on the development of the agricultural industry. High-quality agricultural development cannot be separated from industrialization and high-quality products. In order to promote high-quality agricultural development, optimized resource allocation and flexible prices are needed first. Based on the above relationship, this paper proposes the following:

Hypothesis 1.

The increase in marketization may promote high-quality agricultural development.

3.2. The Mechanism by Which the Degree of Governmental Regulation of the Economy Influences High-Quality Agricultural Development

There have been many classic discussions on government and economic development [35,36,37,38]. Some studies have shown the promotional effect of governmental regulations on economic development [39,40,41,42,43]. However, some studies have proved a negative relationship between them [44,45,46]. Before the reform and opening, the planned economic system was implemented in China. Although it has played a role in promoting economic development, its hindering effect on economic development has also been gradually exposed. After the reform and opening, market-oriented reforms were advocated in China to give full play to the advantages of the market mechanism. Meanwhile, the negative aspects of the markets have been restrained by governmental regulation of the economy.

The market plays an important role in promoting economic development. However, relevant evidence proves that governments also affect economic growth at different stages of the marketization process [47,48,49,50]. At the initial stage of marketization, demand for agricultural products exceeded supply. It was a seller’s market. It was difficult to maintain the balance between supply and demand based solely on the regulatory function of the market, and market failure appeared. At this stage, a good market system and economic functioning system established by governments could regulate the behaviors of market players, which played important roles in resource allocation. Governments avoided the disadvantages of the market mechanism that failed to effectively regulate the supply of public goods with the provision of public goods, particularly agricultural infrastructure. Government policies on agricultural product price protection and agricultural subsidies ensured farmers’ income. After the degree of marketization gradually improves, under the regulation of the market, the concentration of the main production factors in agricultural production, such as technologies, funds, and lands, can promote technical innovation and product development.

Overall, at the initial stage of the marketization process, governments participated extensively in economic operations, which alleviated the misallocation of resources, market failures, and other phenomena caused by the undeveloped market mechanism and effectively boosted economic growth. After the middle stage of the marketization process, the market plays a major role in resource allocation, which promotes the effective circulation of the means of production and improves economic efficiency. The functions of governments and markets are relevant to different economic development situations, and both have great significance for high-quality agricultural development. Therefore, this paper proposes the following:

Hypothesis 2.

In the relationship between the government and the market, the government’s regulatory degree may promote or hinder high-quality agricultural development.

3.3. The Mechanism by Which the Development of the Non-State-Owned Economy Influences High-Quality Agricultural Development

Enterprises of all forms of ownership coexist in transition economies [51,52]. Among them, state-owned enterprises and non-state-owned enterprises are the leading force of national economic development, competing with each other in all industries. In China’s economic reform, the non-state-owned economy has played an important role [53]. It accounts for 75 percent of China’s total output. The rapid development of the non-state-owned economy has prompted the rural population to migrate to cities. The total labor force engaged in agricultural production has declined, which has led to an increase in agricultural productivity. The labor force flowing into the non-state-owned economy lowers the labor price and thus promotes the development of the labor market. The development of the labor market has improved the efficiency of labor factor allocation. Additionally, this further boosts the development of the non-state-owned economy, forming a virtuous cycle. High-quality agricultural development requires continuous improvement in the efficiency of agricultural production. It can be seen from the facts of agricultural development in China, that the development of the non-state-owned economy is closely related to the improvement in agricultural production efficiency. Therefore, this paper proposes the following:

Hypothesis 3.

The development of the non-state-owned economy may boost high-quality agricultural development.

3.4. The Mechanism by Which the Degree of Product Market Development Influences High-Quality Agricultural Development

The development of product markets is the basis for exercising the market’s ability to allocate resources. Additionally, the price regulatory mechanism formed by product marketization is the necessary condition to achieve effective resource allocation. A great deal of classic literature discusses the impact of marketization on economic development [54,55]. In recent years, studies on product marketization have gradually extended to agriculture. The impacts of agricultural product marketization on output, input, technologies, etc., can be found everywhere in the literature [56]. These studies consider the marketization of agricultural products as one of the driving forces for the transformation of subsistence production agriculture into maximization-oriented and market-based production. Such transformation affects not only the yield of agricultural products but also the choice of input factors [57]. There are many theories supporting the promotion of agricultural product marketization [58]. The main reason for this is that the development of agricultural product marketization provides more possibilities for applying new technologies in agricultural production. High-quality agricultural development needs to be driven by innovation. The development of the agricultural product market determines the innovative capabilities of agricultural production. Innovation is related to the promotion of high-quality agriculture development. Therefore, this paper proposes the following:

Hypothesis 4.

The degree of product market development may promote high-quality agricultural development.

3.5. The Mechanism by Which the Degree of Factor Market Development Influences High-Quality Agricultural Development

A well-developed agricultural factor market is a prerequisite for agricultural development [59]. Agriculture is a labor-intensive industry, which means laborers’ skills are the main elements determining production. In an under-developed factor market, it is hard for laborers to improve frequently, and most of them lack the opportunities to improve their skills. In this situation, the productivity of agriculture would not be high because the techniques used remain at a low level. Additionally, it is hard to have technical innovation in agriculture with lower labor skills. In the agricultural goods market, lower productivity represents lower prices; thus, it is hard for the producers to input more capital to improve laborer skills.

Compared with the product market, marketization development of the factor market is relatively slow, and one of the main reasons is the constraint of local governments. Under a planned economy, the local government has the right to order agricultural products with locked prices. However, such interventions distort the factor price and thus distort the resource allocation in factor markets [60]. Much evidence suggests that the distorted factor price makes the production factor price fail to reflect the true factor market supply and demand, and thus causes a mismatch between factor supply and demand in agricultural production [61]. A lower price reduces the motivation for laborers to improve their skills and thus hinders agricultural development.

High-quality agricultural development is green and developmentally friendly to the environment. To solve the pollution problem of current agricultural production, technical improvement is required. Thus, skilled labor is a necessary input for agriculture. To improve labor skills, giving full play to the regulatory role of the factor market to enhance the accuracy of price regulation in the factor market is needed. Therefore, this paper proposes the following:

Hypothesis 5.

The degree of factor market development may positively affect high-quality agricultural development.

3.6. The Mechanism by Which the Level of Market Order Influences High-Quality Agricultural Development

It is necessary to give full play to the price regulation role of the agricultural product market for high-quality agricultural development, and price regulation depends on the continuous improvement in market order. A good market order can prevent monopolies and vicious competition to protect the interests of both consumers and producers, thus promoting the effective operation of the price mechanism and the reasonable distribution of production elements as well as the level of market order, which further increases production efficiency [62,63]. High-quality agricultural development is a kind of sustainable development that needs a stable and healthy development environment. Additionally, based on the important role of the level of market order in the developmental environment, this paper proposes the following:

Hypothesis 6.

The level of market order may promote high-quality agricultural development.

4. Research Methods and Data Source

This paper sets up an evaluation index system for high-quality agricultural development based on the connotation of high-quality development and obtains indexes for high-quality agricultural development from 2009 to 2019 by measuring using principal component analysis. Then, this paper measures and decomposes regional differences in China’s high-quality agricultural development using the Dagum Gini coefficient, describes the dynamic evolution process of the differences using kernel density estimation, and analyzes their influencing factors using the Quadratic Assignment Procedure (QAP) method. All the methods and data used and involved will be explained in this section.

4.1. Measurement Indicators

Understanding the connotation of high-quality development accurately is the basis for setting up a scientific and reasonable measurement system for high-quality development. This paper ascertains that high-quality development is an inevitable requirement for economic development to a certain extent, is a development mode beyond the economic category, and is a mode emphasizing quality. Therefore, the measurement system for high-quality development should not only include costs and benefits according to economics but also should take the internal impetus, regional coordination, sustainability, inclusiveness, regional differences, and other aspects of development into consideration. High-quality development is based on growth, and high-quality agricultural development also needs to ensure the stable growth of agriculture. From the perspective of new development philosophy, this paper sets up a measurement system for high-quality agricultural development (see

Table 1. Agricultural quality development index.

Guidelines	Elements	Indicators	Indicator Calculation	Properties	Weight
Innovation	Innovation foundation	Education level of residents	Number of years of education per inhabitant over 15 years old	+	0.063
		Percentage of highly knowledgeable personnel	Percentage of population aged 15 and above with college education	+	0.042
		Mechanized density	Total machinery power/sown crop area	+	0.053
		Mechanization development	Total mechanical power/number of people employed in the primary sector	+	0.071
	Innovation performance	Economic growth rate	Annual growth rate of added value from agriculture, forestry, animal husbandry, and fishery	+	0.038
		Labor productivity	Value added from agriculture, forestry, animal husbandry, and fishery/total rural population	+	0.065
		Land output rate	Value added from agriculture, forestry, animal husbandry, and fishery/ sown crop area	+	0.053
		Irrigation area ratio	Irrigated area/sown crop area	+	0.031
Coordination	People’s livelihood	Urban–rural income ratio	Urban per capita income/rural per capita income	−	0.096
		Urban–rural consumption ratio	Urban per capita consumption/rural per capita consumption	−	0.113
		Degree of income balance	Rural per capita income /GDP per capita	+	0.010
		Degree of consumption balance	Rural per capita consumption/GDP per capita	+	0.024
	Industry development	Employment level	Number of people employed in primary industry	+	0.020
		Industry structure	Value added from agriculture, forestry, animal husbandry, and fishery/GDP	+	0.034
Greenness	Environmental protection	Fertilizer application intensity	Fertilizer application/sown crop area	−	0.018
		Pesticide application intensity	Pesticide application/sown crop area	−	0.036
		Film usage intensity	Amount of agricultural film used/sown crop area	−	0.002
		Carbon emission intensity	Carbon emissions from the agricultural sector	−	0.016
	Resource conservation	Forest resources	Forest cover	+	0.040
		Arable land resources	Sown crop area/total area of the region	+	0.018
Opening	Infrastructure	Road density	Number of road miles/total area of the region	+	0.031
	Market development	Foreign trade level	Total import and export of agricultural products/GDP	+	0.001
Sharing	Standard of living	Electricity use per capita	Rural electricity consumption/rural population	+	0.005
	Public services	Medical resources distribution	Average number of staff per village health office	+	0.043
		Scale of medical resources	Average number of rural doctors and health care workers per 1000 people in the agricultural population	+	0.020

Note: A positive sign in the attribute column indicates that the indicator value is positively correlated with the value of the agricultural quality development index, and the higher the indicator value, the higher the level of agricultural quality development; a negative sign indicates that the indicator value is negatively correlated with the value of agricultural quality development index, and the higher the indicator value, the lower the level of agricultural quality development. The last column is the weight coefficients from the principal component analysis in Section 4.1, which can measure the correlation between a sub-indicator and the agricultural high-quality index, and the greater the weight, the stronger the correlation.

for the indication system in detail) in five dimensions, including innovation, coordination, greenness, opening, and sharing. After selecting the indexes, we determine the weight of each index using principal component analysis.

In this paper, all inverse indexes are positively processed using reciprocal forms, and the basic indexes are standardized using the equalization method. This paper first obtains the basic index data on the high-quality agricultural development of 30 provinces (the Tibet Autonomous Region is not included as it has a significant amount of missing data) in China from 2009 to 2019 and then uses the factor analysis process in the statistical software SPSS to perform a global principal component analysis on the indicator data for the high-quality agricultural development index. The results of both the KMO Test and Bartlett’s Test of Sphericity reached critical values, indicating that the variables are suitable for principal component analysis. When performing global principal component analysis, the covariance matrix is applied, and six principal components are extracted according to the principle of the variance cumulative contribution rate Qm ≥ 85%. Using the proportion of the eigenvalues for each principal component to the total eigenvalue as the weight, weighing and summarizing the scores of the 6 principal components for all the provinces over the years, this paper finally works out the high-quality agricultural development index of the 30 provinces in China.

4.2. Source of Data and Explanation

The basic data used in this paper come from the China Statistical Yearbook, China rural statistical yearbook, and China Agricultural Statistical Yearbook published by China Statistics Press from 2009 to 2019. The data on agricultural carbon emissions come from the China Emission Accounts and Datasets (CEADs).

The marketization index data refer to the methods used to set up Chinese marketization indexes mentioned in the article by Wang ** effect among different regions. This paper divides the 30 provinces (except Tibet) in China’s mainland into 3 regions: the east, the center, and the west (note: they are divided according to the economic development status. The eastern region includes Bei**g, Tian**, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan. The central region includes Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, and Hunan. The western region includes Guangxi, Inner Mongolia, Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, and **njiang).

First, we calculate the overall Gini coefficient G, the intra-regional Gini coefficient G_j, and the inter-regional Gini coefficient G_jh using the respective calculation equations as follows:

$$G=\frac{{\displaystyle \sum _{j=1}^k{\displaystyle \sum _{h=1}^k{\displaystyle \sum _{i=1}^{n_j}{\displaystyle \sum _{r=1}^{n_h}\left|Y_{ji}-Y_{hr}\right|}}}}}{2n^2\overline{Y}}$$

(1)

$$G_{jj}=\frac{\frac{1}{2{\overline{Y}}_j}{\displaystyle \sum _{i=1}^{n_j}{\displaystyle \sum _{r=1}^{n_j}\left|Y_{ji}-Y_{jr}\right|}}}{n^2}$$

(2)

$$G_{jh}=\frac{{\displaystyle \sum _{i=1}^{n_j}{\displaystyle \sum _{r=1}^{n_k}\left|Y_{ji}-Y_{hr}\right|}}}{n_j{n}_h({\overline{Y}}_j+{\overline{Y}}_h)}$$

(3)

In these equations, k = 3 represents the number of regions, n = 30 represents the number of provinces, Y represents the average value of the high-quality agricultural development indexes for all provinces, Y_j(Y_h) represents the average value of the high-quality agricultural development indexes for the region j(h), and Y_ji(Y_hr) represents the level of high-quality agricultural development in the province i(r) in the region j(h).

Second, we define the relevant variables. $P_j=n_j/n$, $S_j=n_j{\overline{Y}}_j/n\overline{Y}$, and $D_{jh}=\frac{M_{jh}-N_{jh}}{M_{jh}+N_{jh}}$ represent the relative influences of the high-quality agricultural development indexes between two regions; $M_{jh}={\displaystyle {\int }_0^{\infty }\mathrm{d}{F}_j(Y)}{\displaystyle {\int }_0^Y(Y-x)\mathrm{d}{F}_h(x)}$ represents the difference in the high-quality agricultural development indexes between the regions, and when ${\overline{Y}}_j>{\overline{Y}}_h$, M_jh represents the weighted average of all the difference values for the high-quality agricultural development indexes $Y_{ji}-Y_{hr}$ under the condition $Y_{ji}-Y_{hr}>0$. $N_{jh}={\displaystyle {\int }_0^{\infty }\mathrm{d}{F}_h(Y)}{\displaystyle {\int }_0^Y(Y-x)\mathrm{d}{F}_j(x)}$ is the hypervariable first moment, and when ${\overline{Y}}_j>{\overline{Y}}_h$, N_jh represents the weighted average of all $Y_{hr}-Y_{ji}$ under the condition $Y_{hr}-Y_{ji}>0$.

Finally, we calculate the contribution of the intra-regional differences G_w, the contribution of inter-regional differences G_nb, and the hypervariable density contribution G_t using the respective calculation equations as follows:

$$G_w={\displaystyle \sum _{j=1}^k{G}_{jj}{P}_j{S}_j}$$

(4)

$$G_{nb}={\displaystyle \sum _{j=2}^k{\displaystyle \sum _{h=1}^{j-1}{G}_{jh}{D}_{jh}}}(P_j{S}_h+P_h{S}_j)$$

(5)

$$G_t={\displaystyle \sum _{j=2}^k{\displaystyle \sum _{h=1}^{j-1}{G}_{jh}(P_j{S}_h+P_h{S}_j)(1-D_{jh})}}$$

(6)

In this paper, we calculate the Gini coefficient for the spatial distribution of high-quality agricultural development in 30 provinces in China from 2009 to 2019 and perform regional decomposition to research the inter-regional differences in high-quality agricultural development.

4.3.3. Kernel Density Analysis

Kernel density estimation is an important non-parametric estimation method that focuses on the data and researches their distribution characteristics [70]. It has become a mainstream method to research unbalanced distribution. This paper uses this method to describe the overall shape and distribution characteristics of high-quality agricultural development. As this method requires no prior information on models and can describe the distribution shape of variables by estimating the continuous density curve of random variables, kernel density estimation curves at different periods can represent the high-quality development statuses at different periods. Using images, this method directly displays the sizes and the changing processes in the regional differences in high-quality development [71]. Assume the density function for the random variable X is f(x), the probability density of point x can be estimated with Equation (7). In the equation, N is the number of observation values, h is the bandwidth, K(·) is the kernel function, which is a weighting function or a smooth transition function, X_i is the independent and identically distributed observation value, and x is the average value.

$$f(x)=\frac{1}{Nh}{\displaystyle \sum _{i=1}^{N}K}(\frac{X_i-x}{h})$$

(7)

$$K(x)=\frac{1}{\sqrt{2\pi }}\exp (-\frac{x^2}{2})$$

(8)

According to the different expression forms of the kernel density functions, the kernel functions can be divided into Gaussian kernel, Epanechnikov kernel, triangular kernel, quartic kernel, etc. This paper selects the commonly used Gaussian kernel function for estimation. The expression of the Gaussian kernel function is shown in Equation (8): as there is no definite function expression for non-parametric estimations, we need to examine the distribution changes using graphic comparison. We can obtain the position, shape, and extensibility of the variable distribution using the graphs for the kernel density estimation results.

This paper uses kernel density estimation to analyze the dynamic evolution of the high-quality agricultural development distribution in China within the sample investigation period. It not only describes the overall shape of the high-quality agricultural development but also grasps the dynamic characteristics of the distribution of the regional high-quality agricultural development distribution using a comparison among different periods.

4.3.4. QAP Method

When exploring the influencing factors for regional differences, we regard the difference between regions as a relationship. Additionally, using relational data can better explore the interaction between two individuals [72]. The econometric model for the relational data set in this paper is as follows:

$$Y={\beta }_0+{\beta }_{1}X+{\beta }_{2}Z+U$$

(9)

where β₀, β₁, and β₂ are the parameters to be estimated; X and Y are the explanatory and explained variables; Z is the control variable; and U is the residual term. In the relational data model, all variables are square matrices of order n, where the observations y_ij, x_ij, and z_ij in the matrix, respectively, represent the difference between the explained variables, explanatory variables, and control variables in two regions, and their values can be obtained by calculating y_i − y_j, x_i − x_j, and z_i − z_j. Since the observations are the differences in indicators between two regions, the main diagonal elements are all 0 when i = j. For the relational data model, the correlation coefficient between the column and row elements in the residual matrix U is not zero; that is, the column and row elements are not independent but correlated, which leads to an autocorrelation issue in the econometric model [73]. In addition to the autocorrelation problem, there is also serious multicollinearity among variables in the form of relational data. If the traditional statistical test method is used, the variance in and standard deviation of the parameter estimates will increase, and the significance test for the variables will be meaningless [74,75]. In order to solve the problem of autocorrelation and multicollinearity in relational data models, QAP, a non-parametric test method based on random permutation, becomes essential [76]. This method converts the relationship matrix into a long vector, calculates the regression coefficients, and then performs random replacements to judge the significance of the parameter estimates. Its implementation consists of the following two steps. The first step is long vector regression. The variable matrix in Equation (9) is transformed into an n × (n − 1)-dimensional column vector, that is, a long vector, and then OLS estimation is performed on the long vector to obtain the regression coefficient set Γ(Y, XZ) and goodness of fit R². As mentioned above, due to the autocorrelation problem of relational data, the standard error obtained using the OLS estimation method is wrong [77], and the significance of traditional statistical test methods (such as t-test and F-test) will no longer be reliable. The second step is random permutation and a statistical test. A linear relationship between X and Z is assumed in Equation (9), as shown in Equation (10), and E is the classical residual term. If δ ≠ 0, then there is multicollinearity between X and Z, and the estimator can be expressed using Equation (11), where $\widehat{\delta }$ is the OLS estimator from Equation (10).

$$X=\delta Z+E$$

(10)

$${\widehat{\epsilon }}_{XZ}=X-\widehat{\delta }Z$$

(11)

Residual matrix permutation requires random permutation of both a row and a column in ${\widehat{\epsilon }}_{XZ}$ to obtain a new residual matrix $\pi ({\widehat{\epsilon }}_{XZ})$. After several random permutations, Equation (12) can be used to estimate the reference value of the test statistic.

$$Y={\beta }_0+{\beta }_1\pi ({\widehat{\epsilon }}_{XZ})+{\beta }_{2}Z+U$$

(12)

At this point, Equation (12) is identical to Equation (9) under the null hypothesis β₁ = 0. If the estimation error $\widehat{\delta }-\delta$ can be ignored, then the residual matrix after random permutation has the same distribution as E, which means the following:

$$\pi ({\widehat{\epsilon }}_{XZ})=\pi [(\delta -\widehat{\delta })Z+E)]$$

(13)

We can repeat this step many times and save the regression coefficients and goodness of fit R² after each random permutation to obtain the regression coefficient set $\mathsf{\Gamma }(Y,\pi ({\widehat{\epsilon }}_{XZ}))$; then, we can estimate the standard error of the statistic. Assuming that after m_total random permutations, the number of times that the regression coefficient generated with the permutation is greater than or equal to or less than or equal to the long vector regression coefficient in the first step is expressed using m_large and m_small, respectively. Then, we can obtain two proportions: one is the proportion of regression coefficients generated with random permutations that are greater than or equal to the regression coefficients of the long vector in the first step, denoted using p_large, where p_large = m_large/m_total; the other one is the proportion of regression coefficients generated with random permutations that are less than or equal to the regression coefficients of the long vector in the first step, denoted using p_small, where p_small = m_small/m_total. Since the conditions of p_large and p_small overlap, their sum need not equal one. In the statistical test, the above two proportions can be directly regarded as the minimum significance level for rejecting the null hypothesis—that is, the statistical p-value [L]. The two-tailed test is used for the regression coefficient. Therefore, if the regression coefficient is positive, p_large is used as the p-value for the statistical test. Conversely, if the regression coefficient is negative, p_small is used as the p-value for the statistical test. In addition to being able to compute the p-values of the regression coefficients, random permutation can also compute the p-values of R². Unlike the two-tailed test for the regression coefficients, R² uses a one-tailed test, so the p-value of R² is expressed as the ratio of the number of times that random permutation produces R² greater than or equal to the long vector regression R² in the first step to the total number of random permutations.

In this paper, the regional differences in high-quality agricultural development are jointly determined using the marketization level, industrial structural level, labor market characteristics, and other factors. This paper uses the differences in economic indexes, such as the index for high-quality agricultural development and the index for marketization degree, between different regions as the data set, the difference matrices formed with various sub-systems as the explanatory variables, and the difference matrices of the high-quality agricultural development indexes as the explained variables. Considering that QAP does not need to assume independence of explanatory variables, which can effectively avoid multicollinearity, this paper applies the QAP regression method to perform a regression analysis on the influential factors for the regional differences in high-quality agricultural development.

This paper applies the annual data from 30 provinces (excluding Tibet) in China’s mainland in 2009–2019 and uses the differences in the high-quality agricultural development in the provinces as the explained variables, the inter-regional differences in marketization indexes as the explanatory variables, and the differences in the industrial structure, the urbanization rate, the old age dependency ratio, and the geographical distance as the control variables. The explained variables, the explanatory variables, and the control variables are set as follows:

The regional differences in high-quality agricultural development. This paper uses the above-mentioned high-quality agricultural development indexes for the provinces to construct the matrix of the regional differences in high-quality agricultural development.

The regional differences in marketization. Applying the marketization indexes for the provinces as the proxy variables of marketization to construct the matrices of regional differences in marketization, this paper also further investigates the impacts of the five sub-indicators of marketization degree, including the degree of governmental regulation of the economy, the development of the non-state-owned economy, the development of the product market, the development of the factor market, and the level of market order. This helps us to investigate the mechanism by which the marketization degree influences the regional differences in high-quality agricultural development from the micro-perspective.

Regional differences in industrial structure. As the industrial development level in each region differs, the development of the industrial structure in each region is not synchronous. The industrial structural level impacts high-quality development. In order to avoid measurement error in high-quality agricultural development caused by the differences in industrial structure, this paper uses the proportion of the added value from the tertiary industry to the added value from the secondary industry as the proxy variable for the industrial structure to construct the matrix of the regional difference in the industrial structure.

Regional differences in the urbanization rate. The level of urbanization varies from region to region, with different numbers of people engaged in agricultural production and different regions. In order to avoid measurement error in high-quality agricultural development caused by the differences in agricultural scale in the regions, this paper uses the urbanization rate (the proportion of the urban population to the total population) as the proxy variable for urbanization and constructs the matrix of regional difference in urbanization based on the urbanization rate measurement.

Regional differences in the old age dependency ratio. The population’s age level impacts the regional economic vitality and the agricultural labor supply level. In order to avoid measurement error in high-quality agricultural development caused by differences in age, this paper uses the regional differences in the old age dependency ratio as one of the control variables and uses the proportion of the elderly population to the gross population as the proxy variable for the old age dependency ratio, and thus constructs the matrices of regional difference in the old age dependency ratio for the provinces.

Geographical distance. Due to the spillover and spread effects of technology and innovation, the regions geographically close to each other always share similar technology and innovation levels. In order to avoid errors in high-quality measurement in adjacent regions caused by technology spillover, this paper uses geographical distance as one of the control variables. The interprovincial geographical distance is calculated and obtained using ArcGis.