Measurement and evaluation of agricultural technological innovation efficiency in the Yellow River Basin of China under water resource constraints

Abstract

Improving the efficiency of agricultural technology innovation is an inevitable requirement for ecological protection and sustainable agricultural development in the Yellow River Basin. Under the background of prominent water resources constraints in the Yellow River Basin, the actual level and regional differences of agricultural technology innovation efficiency in the basin are analyzed, which will provide theoretical basis and data reference for the development plan of agricultural modernization in the Yellow River Basin. The construction of evaluation index system and the choice of method are the main factors that affect the measurement results. Therefore, this paper first selects input indicators such as water-saving technology level and output indicators such as total agricultural output value to construct an innovative evaluation index system of agricultural technology innovation efficiency in the Yellow River Basin under the consideration of water resources constraints. Secondly, the three-stage DEA model was used to eliminate the interference of external environmental variables, and the overall and regional agricultural technology innovation efficiency of the Yellow River Basin during 2011–2020 was measured with the data of prefecture-level cities under the constraint of water resources. Finally, from the perspective of the whole and the region, the spatio-temporal dynamic evolution law is analyzed and evaluated. The results show that: on the whole, the agricultural technology innovation efficiency in the Yellow River Basin is good and rising in a wave trend, the adjusted pure technology efficiency increases, while the scale efficiency decreases. From the regional perspective, although there is regional heterogeneity, the overall development trend is good, and the lower Yellow River has the highest efficiency, followed by the upper reaches and the middle reaches. From the perspective of the change law, the spatio-temporal evolution distribution shows a multi-polarization trend, and the different regions in the upper, middle and lower reaches show great differences. Therefore, promoting the innovation of water-saving technology and the integration of agricultural science and technology, promoting the integration of production, study and research, and strengthening the regional linkage mechanism are helpful to improve the competitiveness of agricultural science and technology and achieve sustainable agricultural development in the Yellow River Basin.

1. Introduction

As the most fundamental and basic sector in the national economic industrial system, the improvement of technological innovation efficiency and sustainable development of agriculture have important strategic significance for the high-quality development of China's economy [1]. At present, China's agricultural development is facing the double challenges of the loss of domestic resources and environment comparative advantage and the intensification of international agricultural technology competition. To realize the diversification and sustainable development of agricultural functions has become the inevitable choice of agricultural modernization. In the context of unprecedented global scientific and technological competition, the state attaches great importance to agricultural technological innovation, and innovation-driven agricultural transformation and upgrading has become an inevitable choice to enhance agricultural competitiveness [2]. In December 2021, China's Ministry of Agriculture and Rural Affairs issued the "14th Five-Year" National Agricultural and Rural Science and Technology Development Plan "clearly pointed out that to achieve a high level of agricultural science and technology self-reliance; In October 2022, the report of the 20th National Congress of the Communist Party of China (the conference to study and decide the most important issues of the Communist Party of China) stressed that it is necessary to strengthen the support of agricultural science and technology and equipment, accelerate the realization of high-level agricultural science and technology self-reliance, the core weapon of agricultural power lies in scientific and technological innovation, and science and technology is the primary driving force for the modernization of agriculture and rural development. It can be seen that agricultural technology innovation is the basis for sustainable agricultural development and social progress, and is the most fundamental and critical means to deal with the dual challenges of resource and environmental constraints and promote the development of modern agriculture.

The adoption of the Yellow River Basin Ecological Protection and High-quality Development Plan in 2021 and the Yellow River Protection Law of the People's Republic of China elevated the sustainable development of the Yellow River Basin to a national strategic level. The rapid development of modern science and technology has accelerated the transformation from traditional agriculture to modern agriculture, and the extensive application of agricultural technological innovation results in agricultural production has improved the quality and efficiency of agriculture. However, as the birthplace of China's agricultural civilization and an important national agricultural production base, the Yellow River Basin is an important area related to the construction of national food security, agricultural product quality and ecological security [3]. However, there are still some problems in agricultural technology innovation in the Yellow River Basin, such as insufficient expenditure scale, unreasonable expenditure structure, and obvious regional differences, so it is urgent to change agricultural technology [4]. The sustainable utilization of water resources has always been the most basic problem for the healthy development of the Yellow River Basin, and also the bottleneck restricting the sustainable development of agriculture in the Yellow River Basin [5]. Therefore, this paper explores the level of agricultural technology innovation efficiency in the Yellow River basin under the constraints of water resources and its spatio-temporal evolution law, and then proposes countermeasures to improve the efficiency of agricultural technology innovation in the Yellow River Basin, in order to solve the problems of water resources and environmental constraints as well as agricultural technology competition and improve the competitiveness of agricultural science and technology in the Yellow River Basin.

In the context of the shortage of natural resources in the Yellow River Basin, especially the prominent constraint of water resources, the analysis of the actual level and regional differences of agricultural technology innovation efficiency in the basin will provide theoretical basis and data reference for the formulation of agricultural modernization development plan in the Yellow River Basin, and at the same time help improve the efficiency of agricultural technology innovation in the Yellow River Basin. It is of great theoretical value and practical significance to promote the high quality development of agriculture and economy in the Yellow River Basin. The main achievement of this paper is to construct a set of evaluation system and investigate the efficiency of agricultural technology innovation in the Yellow River Basin, analyze the spatio-temporal dynamic evolution law of the overall and regional levels of agricultural technology innovation efficiency in the Yellow River Basin, and provide new ideas for improving the efficiency of agricultural technology innovation in the Yellow River basin. It also provides important theoretical support for reducing regional differences in the efficiency of agricultural technology innovation in the Yellow River Basin and exploring the driving factors for improving the efficiency of agricultural technology innovation. This provides decision-making reference for local governments to promote the high-quality development of agriculture from the perspective of improving the efficiency of agricultural technology innovation, and has important practical value.

2. Literature review

The study of water resources in the Yellow River Basin has always been the focus of domestic scholars. On the one hand, the existing literature studies the water resources use efficiency of the Yellow River Basin. For example, Zuo Qiting et al. [6] built an input-output evaluation index system from four dimensions of resources, environment, economy and society, and used the super-efficiency DEA model to study the water resources use efficiency of nine provinces in the Yellow River Basin. The temporal variation and spatial distribution characteristics of water resources utilization were identified on multiple scales, and the underlying reasons for the differences were discussed. On the other hand, the research focuses on water resources allocation [7] and economic development [8] in the Yellow River Basin. All these provide a theoretical basis for this paper to explore the efficiency of agricultural technology innovation in the Yellow River Basin under the constraint of water resources. At the same time, with the deepening of research on technological innovation theory, some scholars began to study the effects of technological innovation in agriculture on economic development, including agricultural growth and development [9], farmers' income [10], environmental protection and green economic development [11], poverty alleviation and spatial spillover effect [12]. Alston et al. [13] pointed out that agricultural basic research is greatly influenced by market and other environmental factors, so production factors and individual income distribution are also affected, resulting in the weak position of agriculture in the industry, and agricultural technological innovation can have a relatively obvious transformative effect on agricultural production, thereby changing this situation. Lei Zhendan et al. [14] analyzed the nonlinear effects of agricultural technological progress and agricultural carbon emission efficiency based on the two thresholds of agricultural economic development level and human capital, and found that when agricultural economic development level increased, its impact presented a "positive U-shape", while when human capital level increased, its impact presented an "inverted U-shape". Li Hongli et al. [15] used a spatial econometric model to analyze how and through what channels agricultural technological innovation affects the quality of agricultural development, and found that agricultural technological innovation has a spatial spillover effect on the quality of agricultural development. Agricultural technological innovation in both the province and neighboring provinces can promote the improvement of agricultural development quality, and rural human capital is an important channel for its influence.

Most of the domestic studies on the evaluation of agricultural technology innovation efficiency use the input-output analysis method, and the construction and selection of the index system are not the same. Based on the innovation value chain theory, Huo Ming et al. [16] used the DEA-BCC model to estimate the innovation research and development efficiency and innovation transformation efficiency of 158 national agricultural science and technology parks, and explored the evolution of their spatial pattern by using spatial difference and correlation analysis. Yu Yue [17] selected the funds for agricultural science and technology activities, the total power of agricultural machinery, and agricultural science and technology personnel as input indicators, and selected the number of published scientific and technological papers, the amount of technical contract transactions and the total value of agricultural production as output indicators to construct an evaluation index system for the efficiency of agricultural technology innovation in Henan Province. At the same time, DEA-TOBIT model was used to analyze the influencing factors of agricultural technology innovation efficiency. Based on the relevant data of Guangxi from 2010 to 2016, Du Wenzhong et al. [18] established the agricultural innovation driving process model, screened the indicator system by grey correlation method, and finally used the entropy weight TOPSIS fuzzy matter-element comprehensive evaluation model to measure the efficiency of agricultural technology innovation. Xu Yasong et al. [19] calculated the agricultural technology innovation efficiency of 16 cities in Anhui Province in 2018 based on the DEA model, and further decomposed it into comprehensive technical efficiency, pure technical efficiency and scale efficiency, and used projection analysis to conduct in-depth research on the agricultural technology innovation efficiency and influencing factors of Anhui Province.

Based on the existing researches, the selection of agricultural technology innovation efficiency index is prone to subjectivity and arbitrariness due to scholars' different understanding of agricultural technology innovation efficiency, and the difference of measurement methods also leads to the score difference of results. Taking the selection of input index as an example, most studies take human capital as the input index of agricultural technological innovation, but different research methods have different effects on human capital input. The Yellow River Basin is an important economic belt in China's ecological civilization construction. Agriculture, as a traditional and basic industry, needs scientific and technological innovation to transform new driving forces and improve efficiency to achieve sustainable development of agriculture. According to the existing empirical studies, the innovation elements of the units with lower efficiency will actively transfer to the units with higher efficiency. Then how does the trend of agricultural technology innovation efficiency in the Yellow River Basin change? Although some studies have compared and analyzed the differences in agricultural technological innovation efficiency between different regions, it is not clear whether such differences will persist, and the analysis of the causes of differences and the spatio-temporal dynamic evolution law is also insufficient. Most studies on agriculture in the Yellow River Basin focus on the measurement of agricultural high-quality development and agricultural water use efficiency, while most studies on technological innovation in the Yellow River Basin focus on the correlation effect of technological innovation. In this paper, an index system is established to evaluate the efficiency level of agricultural technological innovation in the Yellow River Basin as a whole and at the regional level (upper, middle and lower reaches). A comprehensive understanding of the changes in agricultural technology innovation efficiency, pure technology efficiency and scale efficiency in the Yellow River Basin is helpful to analyze the restrictive factors of agricultural technology innovation efficiency in the Yellow River Basin from a multi-dimensional perspective, and in-depth analysis of the development status and improvement direction of agricultural technology innovation efficiency.

In addition, the existing literature on the measurement of technological innovation efficiency is mostly confined to the enterprise level or the industrial level, and the relevant research on the systematic analysis of agricultural technological innovation efficiency is relatively scarce, and the analysis of agricultural technological innovation efficiency is mostly carried out from the national level, and few literatures pay attention to the agricultural technological innovation efficiency in the Yellow River Basin. Taking the Yellow River Basin as the research object, this paper measures and evaluates the agricultural technological innovation efficiency of the Yellow River Basin, extends the measurement vision of innovation efficiency from other industrial fields to the agricultural field, and analyzes the Yellow River Basin, which expands the current theoretical research vision to a certain extent and provides a theoretical reference for promoting the high-quality development of agriculture in the Yellow River Basin. In summary, in the context of clarifying the current situation of water resources constraints in the Yellow River Basin, this paper adopted a three-stage DEA model to measure and analyze the overall and regional agricultural technology innovation efficiency level of the Yellow River Basin during 2011–2020 under water resources constraints, and conducted an in-depth exploration of its spatio-temporal evolution law, and then proposed strategies for improving agricultural technology innovation efficiency in the Yellow River Basin. It will provide a useful reference for solving the water resource bottleneck in the Yellow River Basin and improving the competitiveness of agricultural science and technology, and provide decision-making reference for local governments to promote sustainable agricultural development from the perspective of improving the efficiency of agricultural technology innovation.

3. Research design

3.1. Current situation of water resources constraint in the Yellow River Basin

The Yellow River, with a total length of 5464 km, is the second longest river in China. Since ancient times, the Yellow River basin has become the flourishing place of Chinese agricultural civilization due to its unique irrigation function. The water resources of the nine provinces (regions) in the Yellow River basin show obvious differences, as shown in Table 1. In 2020, China's total water resources will be 3.160.53 billion, and the total water resources of the nine provinces (autonomous regions) in the Yellow River Basin will be 649.09 billion, accounting for 20.54 % of the total water resources in the country. However, under the background of rapid industrialization and urbanization, improper human factors and natural factors superimposed on each other, and the impact on the ecological environment of the basin is more obvious. The Loess Plateau is the most serious area of soil and water loss in the Yellow River Basin, with a total land area of 574,600 and soil and water loss area of 213,700, accounting for 37.19 % of the total land area. Among them, the area of hydraulic erosion is 162,900, and the area of wind erosion is 50,800. Serious soil and water loss not only leads to the "water mixing" caused by the extremely high amount of silt in the Yellow River, but also causes the problem of water shortage in the Yellow River Basin. In addition, the extensive use of water resources in the Yellow River basin and the low efficiency of agricultural water use will face severe challenges to the sustainable development of agriculture in the future.

Table 1.

Water resources in the provinces (autonomous regions) of the Yellow River basin.

District	Water condition			Water quality condition
	Water resources quantity（${10}^8{m}^3$）	Proportion of water resources in the basin（%）	It accounts for the proportion of national water resources（%）	Mild（${10}^4{km}^2$）	Moderate（${10}^4{km}^2$）	Severe and above（${10}^4{km}^2$）	Sum （${10}^4{km}^2$）
qinghai	1011.9	15.59	3.20	111453	21259	28353	161065
sichuan	3237.3	49.87	10.24	77759	15027	15325	108111
gansu	408	6.29	1.29	96427	23263	63382	183072
ningxia	11.1	0.17	0.04	10380	3431	1724	15535
neimenggu	503.9	7.76	1.59	378951	65477	133206	577634
shaanxi	419.6	6.46	1.33	38827	14554	1042	54423
shanxi	115.2	1.77	0.36	39391	12110	6490	57991
henan	408.6	6.29	1.29	17806	2123	751	20680
shandong	375.3	5.78	1.19	21852	1044	346	23242
Yellow River basin	6490.9	100.00	20.54	792846	158288	250619	1201753

In October 2021, the Outline of the Plan for Ecological Protection and High-quality Development in the Yellow River Basin was officially released, and the document pointed out that it is necessary to strengthen the economical and intensive use of water resources in the whole basin, increase agricultural water-saving efforts, and build a strong "Chinese water tower". The per capita utilization of water resources restricting the development of agricultural production in the Yellow River Basin is only 27 % of the national average, while the efficiency of water resources development is more than 80 %, far higher than the ecological warning line of 40 %, and 82.6 % of prefecture-level administrative districts are overloaded with water resources. Water is the fundamental condition for sustainable agricultural development and an indispensable resource to ensure economic and ecological security. Considering the significant impact of water resources on the efficiency of agricultural technological innovation in the Yellow River Basin, this paper fully considers the constraints of water resources in selecting the input index of agricultural technological innovation efficiency in the Yellow River Basin.

3.2. Research method

3.2.1. Efficiency measurement method

In the current research on efficiency evaluation, scholars most often use frontier analysis method. Frontier analysis can be divided into parametric frontier analysis and non-parametric frontier analysis. Parametric frontier analysis method needs to construct a definite production function to express the relationship between input and output, and use regression and input-output data to clarify the parameters in the expression under constraints. The most commonly used nonparametric frontier analysis method is data envelopment analysis [20](DEA). Affected by management inefficiency, environmental factors and random interference items, it is difficult to effectively solve practical problems by using a single analysis method, especially the complex problems with multiple input-output such as the efficiency of agricultural technology innovation. On the one hand, the three-stage DEA method can further eliminate the influence of environment and random factors on the basis of the traditional DEA model, so as to distinguish the real change of efficiency from the change caused by external uncontrollable factors. This is essential to accurately assess the efficiency of agricultural technological innovation. On the other hand, through the three-stage DEA model, the efficiency of decision-making unit can be more truly reflected (in this study, it refers to the agricultural technology innovation efficiency of each prefecture level city). This helps identify which regions are doing well in agricultural technology innovation and which regions have room for improvement. Therefore, this paper combines two analysis methods and uses three-stage DEA model to measure agricultural technology innovation efficiency, which can not only solve the problem of multi-output and multi-input, but also exclude the influence of external environment in the process of measuring agricultural technology innovation efficiency. Finally, the true level of agricultural technology innovation efficiency of prefecture-level cities in the Yellow River Basin under the same environment is obtained, and the accuracy of empirical results is improved. The specific three-stage model is as follows.

• (1)The first stage: calculate DMU efficiency and relaxation variables based on DEA-BBC model

Under the ideal condition of constant scale (CRS), CCR model is a good choice, but in practical applications, the scale of most problems is constantly changing, and BCC model is an improvement model proposed by American scholars W.W.Cooper, R.D. Panker and others. When decision-making units are produced under the scale change, BCC model is a good choice. Increasing or decreasing input will affect output. In the first stage, the input-oriented DEA-BCC model is used to conduct a preliminary evaluation of the agricultural technology innovation efficiency of 112 prefecture-level cities from 2011 to 2020, and the comprehensive efficiency value, pure technical efficiency value and scale efficiency value of each year are obtained. The efficiency measurement results of the first stage are biased due to environmental factors, but the efficiency measurement results of the third stage can be compared and analyzed, and the relaxation variable value of the input variable can be calculated as the explained variable of the second stage.

The input-oriented model is shown in equation (1) (with a given output, minimum input is achieved):

$$\begin{array}{c}\min \left[\theta -\epsilon \left(\sum _{i=1}^m{s}_i^{-}+\sum _{i=1}^m{s}_r^{+}\right)\right]\\ s.t.\{\begin{array}{c}\sum _{j=1}^n{\lambda }_j{p}_{ij}+s_i^{-}=\theta p_{ij0}\\ \sum _{j=1}^n{\lambda }_j{q}_{rj}-s_r^{+}=q_{ij0}\\ \sum _{j=1}^n{\lambda }_j=1\\ s_r^{+}\ge 0,s_i^{-}\ge 0,{\lambda }_j\ge 0,j=1,2,\dots ,n\end{array}\end{array}$$ (1)

In this paper, the two input variable vectors are set as ${p_j\left(p_{1j},p_{2j}\right)}^T>0.j=1,2,\dots ,n$, The four output variable vectors are set to ${q_j\left(q_{1j},q_{2j},q_{3j},q_{4j}\right)}^T>0.j=1,2,\dots ,n$, Where n is 17 (17 cities). $p_{ij}$ represents the input of type i for the j city; $q_{rj}$ represents the output of type r in the j city; $s_i^{-}$ denotes the i - th input relaxation; $s_r^{+}$ denotes relaxation of the RTH output; $\theta$ represents the technical efficiency value, 0< $\theta$ <1.

• (2)Phase 2: Stochastic Frontier Model Analysis (SFA)

SFA regression is used to eliminate the influence of environment variables and random disturbance terms in the first stage measurement results. The constructed SFA regression model is shown in equation (2) as follows:

$$s_{ij}=f\left(Z_j;B_j\right)+v_{ij}+{\mu }_{ij}$$ (2)

S_ij is the relaxation value of the input i of the j DMU; Z_j is an environment variable; B_j is the influence of environment on the input relaxation variable; v_ij+μ_ij is mixed error; μ∼N（0，σ_μ²）is management inefficiency, indicating the influence of management factors on input relaxation variables; $\gamma =\frac{{\sigma }_{\mu i}^2}{{\sigma }_{vi}^2+{\sigma }_{\mu i}^2}$，When γ approaches to 1 infinitely, it means that management inefficiency is the main influencing factor; when γ approaches to 0 infinitely, it means that random disturbance term is the main influencing factor. The estimation of management inefficiency is shown in equation (3):

$$E\left({\mu }_i|{\epsilon }_i\right)=\frac{\lambda \sigma }{1+{\lambda }^2}\left[\frac{\phi \left({\epsilon }_i\lambda /\sigma \right)}{\Phi \left({\epsilon }_i\lambda /\sigma \right)}+\frac{{\epsilon }_i\lambda }{\sigma }\right]$$ (3)

Random error condition estimation is further obtained, as shown in equation (4):

$$E\left(v_i|{\epsilon }_i\right)=s_{ij}-f\left(Z_j；B_j\right)-E\left({\mu }_i|{\epsilon }_i\right)$$ (4)

Based on DEA effective prefecture-level cities, the input variables of each prefecture-level city in each year are adjusted, and equation (5) is as follows:

$$x_{\text{ij}}^{*}=x_{ij}+\left[\mathit{max}\left\{f\left(Z_j;B_j\right)\right\}-f\left(Z_j;B_j\right)\right]+\left[\mathit{max}\left\{v_{\text{ij}}\right\}-v_{ij}\right]$$ (5)

$x_{ij}^{*}$ is the adjusted input， $\left[\mathit{max}\left\{\int Z_j；B_j\right\}-\int \left(Z_j；B_j\right)\right]$ is to adjust the external environment， $\left[\mathit{max}\left\{v_{ij}\right\}-v_{ij}\right]$ is to place all DMU at the same level.

• (3)The third stage: the adjusted DEA-BCC model

The DEA-BCC model is used to measure the adjusted input and output data of agricultural technology innovation efficiency, and the value of agricultural technology innovation efficiency that can objectively reflect each prefecture level city at the same level is obtained, and the comparability among prefecture level cities is strengthened.

3.2.2. Spatiotemporal dynamic evolution analysis method

• (1)Bayesian space-time hierarchical nonlinear model

Combining the hierarchical model and the spatio-temporal interaction model, the Bayesian spatio-temporal hierarchical nonlinear model can optimize the small samples and autocorrelation problems existing in the spatio-temporal data to some extent, and estimate the posterior distribution result of the spatio-temporal parameters under the premise of making full use of the population, samples and prior information [21]. The efficiency of agricultural technological innovation in the Yellow River Basin is characterized by continuity and can be regarded as a continuous variable. In other words, the likelihood function of agricultural technological innovation efficiency in the Yellow River Basin at each time node is estimated using a multidimensional normal distribution. As shown in equation (6), equation (7) and equation (8):

$$Y_{it}\sim MVN\left({\mu }_{it},{\sigma }_Y\right)$$ (6)

$${\mu }_{it}\sim MVN\left({\phi }_{it},{\sigma }_{\mu }\right)$$ (7)

$$\ln {\phi }_{it}=\alpha +S_i+\left(b_{0}t+v_t\right)+b_{1i}t+0.5b_2{t}^2+{\epsilon }_{it}$$ (8)

Where, i and t represent prefecture-level cities and years respectively; $Y_{it}$ represents the efficiency level of agricultural technology innovation in the Yellow River Basin; ${\mu }_{it}$ is the variance of innovation efficiency of each prefecture-level city; ${\sigma }_Y$ represents the expected value of innovation efficiency; ${\phi }_{it}$、 ${\sigma }_{\mu }$ represents the expectation and variance of innovation efficiency expected value, respectively; α representative constant; ${\epsilon }_{it}$ represents random interference terms;S_i represents the overall spatial pattern of agricultural technology innovation efficiency in the Yellow River Basin; $b_{0}t+v_t$ represents the overall sequential evolution situation， $b_{0}t$ represents the linear evolution trend， $v_t$ express random effect; $b_{1i}t$ represents the local evolution rate of agricultural technology innovation efficiency， $b_{0}t+v_t$ represents the local first linear evolution rate. In addition, in order to quantitatively evaluate the interpretation of the stable component of the Bayesian spatio-temporal decomposition to the entire spatio-temporal change process, this paper calculated the variance component coefficient, as shown in equation (9). The larger the variance component coefficient VPC, the higher the interpretation of the spatio-temporal component decomposition to the spatio-temporal change process, and vice versa.

$$VPC=\frac{VAR\left(\stackrel{i}{s}+\stackrel{0}{b}\underset{*}{t}+\stackrel{t}{v}\right)}{VAR\left(\stackrel{i}{s}+\stackrel{0}{b}\underset{*}{t}+\stackrel{t}{v}\right)+VAR\left(\stackrel{0}{b}\underset{*}{t}+\stackrel{it}{\epsilon }\right)}$$ (9)

• (2)Kernel density estimation

Kernel density estimation is to describe the deviation degree and distribution state of agricultural technological innovation efficiency in the Yellow River Basin through continuous density curve. With Kernel density estimation, we can distinguish the location, shape, extensibility and spatio-temporal evolution of the bias distribution of agricultural technological innovation efficiency in the Yellow River Basin. The height of the kernel density curve represents the concentration degree of agricultural technological innovation efficiency in the Yellow River Basin. Width represents the characteristics of efficiency differentiation. The number of wave crest indicates the degree of dispersion between regions; The ductility of the curve represents the regional efficiency gap, and the longer the tail, the greater the difference. The relevant calculation equation (10) and equation (11) are as follows:

$$\mathrm{Y}=\frac{1}{Nh}\sum _{i=1}^{N}K\left(\frac{X_i-x_0}{h}\right)$$ (10)

$$\mathrm{Z}=\frac{1}{\sqrt{2\pi }}\exp \left(-\frac{x^2}{2}\right)$$ (11)

Where, Y is the Kernel density function corresponding to random variable x.N represents the number of sample areas,，X_i and x₀ represents the value of study object i and the mean of x, respectively，h as bandwidth，h = 0.9SN^-08，Z is a Gaussian kernel function.

3.3. Index selection and data source

In the selection of agricultural technology innovation efficiency input index, scholars generally believe that factor input is mainly composed of material capital and human capital. In terms of physical capital, the increasingly prominent constraints on water resources restrict the agricultural production in the Yellow River Basin, which is not conducive to the sustainable utilization of water resources and cannot support the high-quality development of agriculture in the Yellow River Basin. Therefore, this paper takes agricultural irrigation water consumption as the first input index [22], which represents the status and conditions of water resources required by agricultural production activities in the Yellow River Basin. The use of water-saving equipment also means that the input of water resources is reduced, thus improving the efficiency of agricultural technology innovation. Therefore, the number of water-saving irrigation equipment is selected in this paper to measure the level of water-saving technology [23]. At the same time, referring to the research of Zhao Lijuan et al. [24], agricultural science and technology activity funds, soil nutrient technology level, and agricultural mechanization level were selected as input indicators. Among them, the funds for agricultural science and technology activities are a strong guarantee for carrying out agricultural technology innovation activities, cultivating innovative talents and technology research and development, which reflects the importance of local governments to scientific and technological innovation. The scientific and technological level of soil nutrient was measured by the conversion amount of agricultural fertilizer, which reflected the scientific and technological input of soil nutrient transformation in a region. The level of agricultural mechanization is measured by the total mechanical power in the process of agricultural production, including irrigation, harvesting, transportation, etc., which reflects the level of technical input in agricultural production to a certain extent. In terms of human capital, referring to the existing studies [25], the degree of scientific and technological literacy is selected as the input variable. The higher the degree of scientific and technological literacy, the richer the human resources of agricultural research that universities can invest and the stronger the scientific research strength. See Table 2 for specific indicators.

Table 2.

Index system of agricultural technology innovation efficiency in Yellow River Basin.

Index attribute	index	Measurement method
Input index	Technical level of water saving	Water-saving irrigation machinery (set)
	Water consumption for agricultural irrigation	Agricultural irrigation water consumption (billion/m3)
	Agricultural science and technology activities	R&D expenditure × (Total output value of agriculture, forestry, animal husbandry and fishery/Gross product) (ten thousand yuan)
	Scientific and technological level of soil nutrients	Conversion amount of agricultural fertilizer application (tons)
	Degree of scientific and technological literacy	Number of students in regular institutions of higher learning (10,000)
	Level of agricultural mechanization	Total power of agricultural machinery (10,000 kW)
Output indicator	Gross agricultural output value	Total agricultural output value (ten thousand yuan)
	Grain production capacity	Grain yield per unit area (kg/ha)
	Rural-urban income ratio	Rural disposable income/urban disposable income
	The pulling effect of the primary industry on the total output value	Output value of primary industry/Total output value
	Urbanization process	Urban population/total population
Environmental index	Level of regional economic development	GDP per capita (Yuan)
	The level of rural economic development	Per capita disposable income of rural residents (Yuan)

In terms of the selection of output indicators, this paper refers to the ideas of Wang Hao et al. [26] and selects five indicators: total agricultural output value, grain production capacity, urban-rural income ratio, pulling effect of primary industry on total output value, and urbanization process. Among them, the total output value of agriculture can directly reflect the efficiency and development level of agricultural technology innovation. Grain production capacity can directly reflect the improvement of agricultural technology innovation efficiency. Both the rural-urban income ratio and the urbanization process can reflect the living standard of rural residents and the convenience and universality brought by agricultural technology. The driving effect of the primary industry on the total output value is measured by the proportion of the output value of the primary industry in the total output value. The greater the proportion of the primary industry, the higher the regional emphasis on agriculture, and the more willing to increase the investment in agriculture, so the more conducive to the improvement of scientific research output efficiency and agricultural innovation efficiency. See Table 2 for specific indicators.

In the selection of external environment variables, the external factors affecting the evaluation decision-making unit are mainly considered. Considering the characteristics of agricultural technology innovation and development in the Yellow River Basin, although all the nine provinces in the Yellow River Basin belong to the northern regions, there are great differences in natural conditions, customs, nationalities and personality characteristics. The external environment variables selected should not only satisfy the significant impact on the measurement of agricultural technology innovation efficiency, but also ensure that the variables cannot be subjectively controlled. Therefore, this paper uses the existing practice [27,28] to select environmental variables from two aspects of regional economic development level and rural economic development level, and measures regional economic development level with per capita GDP. The level of rural economic development is measured by the income level of rural residents. See Table 2 for specific indicators.

Due to the complexity of the study, which involves a large amount of data collection, collation and analysis, and the lag of release and update of some data, we cannot obtain the latest data. In addition, considering the consistency and comparability of the studies, we need to maintain the consistency of the study period, so we did not use only partially updated data. In summary, based on the availability and consistency of data, we pay more attention to the accuracy and reliability of the research, and finally select the data of 112 prefecture-level cities in the Yellow River Basin from 2011 to 2020 to analyze the measurement results of agricultural technology innovation efficiency in the Yellow River Basin from the overall and regional levels. According to the Yellow River Protection Law of the People's Republic of China, the Yellow River basin refers to the relevant administrative areas involved in the water collection area of the main stream, tributaries and lakes of the Yellow River. Among them, the upstream region includes Qinghai, Gansu, Ningxia and Sichuan, the middle region includes Shaanxi, Shanxi and Inner Mongolia, and the downstream region includes Henan and Shandong. The original data comes from China Statistical Yearbook, China Rural Statistical Yearbook and the statistical yearbook of each province.

4. Empirical results and analysis

4.1. The first stage DEA analysis

4.1.1. Analysis of the overall measurement results of the Yellow River Basin

The overall measurement results of agricultural technology innovation efficiency in the Yellow River Basin are shown in Table 3 and Fig. 1. It can be found that the efficiency value shows a slow rise in the past 10 years, and the overall efficiency value is relatively high, which is 0.803 in 2011 and 0.822 in 2020, with an increase of 2.37 %. Among them, it was relatively stable from 2011 to 2017, reached the lowest value in 2018, and then maintained a rising trend, which indicates that the change trend of agricultural technology innovation efficiency in the Yellow River Basin is unstable, and there is a large space for development. In addition, the agricultural technological innovation efficiency in the Yellow River Basin was decomposed into pure technical efficiency and scale efficiency. As can be seen from Table 3 and Fig. 1, the value of pure technical efficiency showed an overall fluctuating trend from 2011 to 2020. The initial value in 2011 was 0.941, followed by a short but stable decline, and began to decline after reaching the highest value in 2015. The pure technical efficiency value remained at a low level by 2018, and rebounded to 0.88 in 2020. From 2011 to 2020, the average scale efficiency of agricultural technology innovation in the Yellow River Basin was about 0.878, and the scale efficiency value was good. Except for a short decline in 2014–2016, the scale efficiency value did not fluctuate greatly and showed an overall upward trend. By observing the evolution trend of the two curves, it can be found that the main factors affecting innovation efficiency gradually change from pure technical efficiency to scale efficiency during the study period.

Table 3.

Analysis of agricultural technology innovation efficiency in Yellow River Basin.

Year	Overall efficiency	Pure technical efficiency	Scale efficiency
2011	0.803	0.941	0.853
2012	0.779	0.900	0.862
2013	0.788	0.903	0.868
2014	0.839	0.907	0.92
2015	0.859	0.939	0.91
2016	0.751	0.863	0.864
2017	0.762	0.842	0.905
2018	0.618	0.743	0.832
2019	0.667	0.795	0.836
2020	0.822	0.880	0.934

Fig. 1.

The first stage analysis of agricultural technological innovation efficiency in the Yellow River Basin.

4.1.2. Analysis of regional measurement results in the Yellow River Basin

Only measuring and analyzing the overall situation of the Yellow River Basin to study the agricultural technology innovation efficiency is not enough to reveal the change trend. Therefore, this paper analyzes the agricultural technology innovation efficiency of the upper, middle and lower reaches of the Yellow River Basin. It can be found from Table 4 and Fig. 2 that the overall level of agricultural technology innovation efficiency of the upper, middle and lower reaches of the Yellow River Basin is higher than 0.750. But there are still big differences between regions. The efficiency of agricultural technology innovation in the upper reaches of the Yellow River Basin showed a relatively flat trend, and there was no significant fluctuation during the study period. The lower level of economic development and the poor strength of agricultural scientific research in the upper reaches of the Yellow River Basin resulted in the inability to greatly improve the efficiency of agricultural technology innovation. The efficiency of agricultural technology innovation in the middle reaches of the Yellow River Basin fluctuated greatly during the study period, but the overall efficiency level showed an increasing trend. The middle reaches have agricultural colleges with strong scientific research strength, which can improve the efficiency of agricultural technology innovation to a certain extent. However, the economic development level in the middle reaches also has the problem of unbalanced development, which may also lead to obvious fluctuations in the efficiency of agricultural technology innovation. The efficiency of agricultural technology innovation in the lower reaches of the Yellow River Basin fluctuated during the study period, but remained at a high level. Henan Province and Shandong Province in the downstream area are both big agricultural provinces, among which Shandong Province ranks first in the country in terms of total agricultural output value, agricultural added value and other agricultural indicators, and its agricultural technology innovation ability and achievement transformation ability are strong. Henan Province is affected by a variety of factors such as population. Although the agricultural development is strong, there are problems such as lack of technological innovation ability and low quality of agricultural practitioners, which also make the efficiency of agricultural technological innovation fluctuate greatly in the downstream areas.

Table 4.

Agricultural technological innovation efficiency in the upper, middle and lower reaches of the Yellow River Basin.

region	2011	2012	2013	2014	2015
Upper reaches of the Yellow River	0.843	0.866	0.877	0.893	0.860
Middle reaches of the Yellow River	0.823	0.825	0.827	0.946	0.858
Lower Yellow River	0.857	0.905	0.918	0.951	0.881
region	2016	2017	2018	2019	2020
Upper reaches of the Yellow River	0.863	0.889	0.841	0.825	0.829
Middle reaches of the Yellow River	0.847	0.941	0.814	0.841	0.832
Lower Yellow River	0.876	0.896	0.826	0.788	0.869

Fig. 2.

The first stage of agricultural technology innovation efficiency in the upper, middle and lower reaches of the Yellow River basin.

4.2. The second stage SFA returns

In the first stage, this paper selects the original data from 2011 to 2020, uses DEAP2.1 software to calculate the comprehensive technical efficiency, pure technical efficiency, scale efficiency and target input value of agricultural technology innovation efficiency in 112 prefecture-level cities in the Yellow River Basin, and calculates the relaxation variable of agricultural technology innovation input based on the target input value and original input value. Therefore, in the second stage, this paper takes the slack variable of agricultural technology innovation as the explained variable, per capita GDP and rural residents' income as the explanatory variables, establishes the panel data SFA regression equation, and uses Frontier4.1 software to obtain the regression results from 2011 to 2020. Limited by space, the regression results of 2015 are shown in Table 5, and most coefficients are significant at the test level of 10 %.

Table 5.

SFA regression result.

variable	Technical level of water saving		Total power of agricultural machinery		Agricultural science and technology activities
	coefficient	T-value	coefficient	T-value	coefficient	T-value
Constant term	0.152**	1.701	0.052**	1.454	0.033**	1.185
Income level of rural residents（W2）	−0.091**	−1.739	−0.026**	−1.403	−0.037**	−1.577
Average GDP（W2）	0.072**	1.384	0.059**	−1.591	0.015**	1.157
${\sigma }^2$	8176.89**	3.33	2302.33**	7.83	169.34**	7.52
$\gamma$	0.891		0.793		0.852

variable	Scientific and technological level of soil nutrients		Degree of scientific and technological literacy		Water consumption for agricultural irrigation
	coefficient	T-value	coefficient	T-value	coefficient	T-value
Constant term	0.111**	1.631	0.13	1.954	0.076	1.523
Income level of rural residents（W2）	−0.054**	−1.557	−0.192	−1.62	−0.057	−1.674
Average GDP（W2）	0.015**	1.101	0.106	1.588	0.098	1.769
${\sigma }^2$	5000.81**	3.43	568.76**	7.40	3255.55**	1.88
$\gamma$	0.697		0.784		0.1754

As can be seen from Table 5, input index belongs to management inefficiency, input redundancy plays a major role, which is reflected in the relaxation variable γ values of input index are close to 1, and pass the significance test of 1 %. LR unilateral likelihood ratio test passed the significance test of 1 %, and the coefficients of explanatory variables all passed the significance test of 1 %, which also indicated that the six input relaxation variables were all significantly affected by two external environmental factors, and SFA regression in the second stage was reasonable and necessary. The specific analysis is as follows:

Rural disposable income (W1): The regression results of disposable income of rural residents and all input variables are negative, indicating that the disposable income of rural residents and agricultural productivity do not change in the same direction. With the increase of disposable income of rural residents, agricultural production relies on the original technical support and carries out production activities through expansion of scale, resulting in unreasonable allocation of capital structure and resources. The investment of agricultural technology innovation funds has been reduced. At the same time, blindly increase the input of agricultural production activities, the result is not effective integration of input resources, resulting in a great waste, can not effectively improve the efficiency of agricultural production.

Per capita GDP (W2): The regression results of per capita GDP in all input variables are positive, consistent with theoretical expectations. The overall improvement of rural income level has a positive impact on agricultural labor to master advanced production technology and improve agricultural production efficiency. Due to the relatively perfect infrastructure in developed regions, large amount of water resources and sufficient supply of resources, high level of science and technology, and good market atmosphere, they have significantly supported the development of agricultural modernization and improved agricultural production efficiency.

4.3. The third stage adjusted efficiency

4.3.1. Evaluation of the overall efficiency of the Yellow River Basin after adjustment

After removing the interference of environmental factors, the overall measurement results of agricultural technological innovation efficiency in the Yellow River Basin are shown in Table 6 and Fig. 3. The comprehensive efficiency value of most provinces has changed, and the efficiency value has decreased compared with the first stage, which indicates that the efficiency of agricultural technological innovation is overestimated, and the adjusted efficiency value can more truly reflect the efficiency level of agricultural technological innovation. In the past 10 years, the efficiency of agricultural technology innovation in the Yellow River Basin has fluctuated and increased, and the overall efficiency value is relatively high, increasing by 8.90 %, but the change trend is unstable and there is a large room for development. From 2011 to 2015, the efficiency showed a rising trend, and then it declined and reached the lowest value in 2018, and then it rapidly rose to 2020 and showed a good efficiency level. On the one hand, more agricultural science and technology parks have been established in the Yellow River Basin in the past decade, and the efficiency of agricultural technology innovation has been relatively developed, but the uneven distribution of science and technology parks also makes the efficiency of agricultural technology innovation at a low level in some underdeveloped areas. On the other hand, water resources in the Yellow River Basin gradually evolved from the historical contradiction of "more water, less water, dirty water and muddy water" to the main contradiction of "less water" in the new era. The shortage of water resources also made water resources a bottleneck restricting the sustainable development of agriculture in the Yellow River Basin, resulting in the development trend of agricultural technological innovation in the Yellow River Basin.

Table 6.

Analysis of agricultural technology innovation efficiency in Yellow River Basin.

Year	Overall efficiency	Pure technical efficiency	Scale efficiency
2011	0.708	0.824	0.859
2012	0.779	0.900	0.862
2013	0.788	0.903	0.868
2014	0.839	0.907	0.920
2015	0.859	0.939	0.910
2016	0.751	0.863	0.864
2017	0.762	0.842	0.905
2018	0.618	0.743	0.832
2019	0.785	0.940	0.836
2020	0.771	0.949	0.812

Fig. 3.

The third stage analysis of agricultural technological innovation efficiency in the Yellow River Basin.

In addition, after eliminating the interference of environmental factors, the pure technical efficiency value increased compared with the first stage, while the scale efficiency value decreased. This indicates that the pure technical efficiency of the Yellow River Basin in China will be underestimated without considering the external environment and random interference, and the scale efficiency is overestimated. However, the evolution curves of pure technical efficiency value and scale innovation efficiency value of agricultural technology innovation in the Yellow River Basin as a whole are interwoven, and the evolution trend is roughly similar to that of comprehensive innovation efficiency value, indicating that agricultural technology innovation efficiency in the Yellow River Basin is jointly promoted by pure technical efficiency and scale efficiency, which can further expand the physical capital investment in agriculture. Better match the inputs and outputs of agricultural technological innovation. More reasonable factor allocation, higher utilization rate of agricultural technology innovation and actual output gradually approaching the maximum output all bring the level of agricultural technology innovation in the Yellow River Basin to a new level. Therefore, technical efficiency and scale efficiency are equally important, and the application of agricultural technology and innovation resources cannot be achieved without any one person. Only by coordinating the development of both can the efficiency of agricultural technology innovation in the Yellow River basin be effectively improved.

The above analysis reveals the relevant temporal characteristics of agricultural technology innovation efficiency from the perspective of the overall change of the Yellow River basin, and excludes the influence of environmental factors. At the same time, in order to prevent possible extreme values from interfering with the mean data, this paper will further select four time cross sections in 2011, 2014, 2017 and 2020, and analyze the dynamic evolution law of agricultural technology innovation efficiency in the Yellow River Basin by comparing the kernel density curve, so as to conduct supplementary demonstration on the above analysis results. As can be seen from Fig. 4, the nuclear density curves of the four years all have double peaks, indicating that the agricultural technology innovation efficiency of the Yellow River Basin in the third stage has a relatively obvious polarization phenomenon. Compared with 2011, the kernel density curve shifted to the right, indicating that the efficiency of agricultural technology innovation in 2014 showed an upward trend, but the gap between prefecture-level cities was gradually expanding. Compared with 2014, the kernel density curve shifted to the left and the wave crest became thinner, indicating that the efficiency of agricultural technology innovation in 2017 showed a downward trend, while the gap between prefecture-level cities gradually narrowed. In 2020, compared with 2017, the curve shows a leftward trend, and the wave peak is located in the low level area, indicating that the efficiency of agricultural technology innovation in 2020 shows a downward trend, and the gap between prefecture-level cities is gradually narrowing.

Fig. 4.

Kernel density distribution of agricultural technological innovation efficiency in the Yellow River Basin in the third stage.

4.3.2. Regional efficiency assessment of the Yellow river basin after adjustment

After taking into account the influence of environmental variables, the agricultural technology innovation efficiency and its change trend in the three regions of the upper, middle and lower reaches of the Yellow River Basin are shown in Table 7 and in Fig. 5, and the overall efficiency level is higher than 0.700. Similar to the results before the treatment of environmental variables, with 2011 as the base period, the lower reaches of the Yellow River Basin had the highest efficiency of agricultural technology innovation, followed by the upper reaches, and the middle reaches the lowest. There is regional heterogeneity in the efficiency of agricultural technology innovation in the three regions, but the overall development trend is good.

Table 7.

The third stage of agricultural technology innovation efficiency in the upper middle and lower reaches of the Yellow River basin.

region	2011	2012	2013	2014	2015
Upper reaches of the Yellow River	0.593	0.789	0.793	0.730	0.772
Middle reaches of the Yellow River	0.504	0.643	0.644	0.911	0.882
Lower Yellow River	0.541	0.797	0.820	0.886	0.904
region	2017	2018	2019	2020	average
Upper reaches of the Yellow River	0.680	0.692	0.704	0.646	0.714
Middle reaches of the Yellow River	0.741	0.548	0.581	0.655	0.669
Lower Yellow River	0.811	0.600	0.684	0.718	0.752

Fig. 5.

The third stage of agricultural technology innovation efficiency in the upper, middle and lower reaches of the Yellow River basin.

The fluctuation of agricultural technology innovation efficiency curve in the upper reaches of the Yellow River basin is relatively gentle, but the overall trend is downward. This may be because the upstream region is located in the inland, the economy is still underdeveloped, the education level and scientific research ability are also insufficient, coupled with the low education level and older age of most agricultural employees, so there are obstacles to the promotion and application of agricultural technology innovation in the upstream region. At the same time, most areas in the upper reaches of the Yellow River have scarce rainfall, serious water shortage, and most agricultural workers seldom use scientific irrigation methods, resulting in 87.02 % of agricultural water use. The low utilization efficiency of water resources and unreasonable irrigation methods aggravate the waste of agricultural water, which is not conducive to the improvement of the efficiency of agricultural technological innovation.

The efficiency level of agricultural technology innovation in the middle and lower reaches of the Yellow River Basin in 2014–2015 was the highest in 10 years. During this period, the management and development level of the Yellow River Basin was worse than that in the later period. Drought resulted in the reduction of agricultural water consumption, which forced the improvement of agricultural technology innovation efficiency to a certain extent. As for the middle reaches of the Yellow River, its fluctuation trend fluctuates greatly, but the overall efficiency level shows an upward trend. From 2011 to 2014, it showed an upward trend and then a downward trend. During this stage, problems such as water shortage, serious soil erosion, ecological fragility and environmental pollution in the middle reaches of the Yellow River all led to a slowdown in the improvement of agricultural technology innovation efficiency. However, with the implementation of ecological protection policies in the Yellow River Basin in 2018, the efficiency value rebounded.

The cumulative growth rate of agricultural technology innovation efficiency was the highest in the lower reaches of the Yellow River basin. Specifically, the level of agricultural technology innovation in this region showed an upward trend from 2011 to 2015. With the implementation of the new soil and water conservation law, the efficiency of agricultural technology innovation reached the highest point, but later showed a downward trend and reached a small peak in 2017. Later, with the complete completion of the Yellow River water conservancy infrastructure project and the proposal of ecological civilization construction at the 18th National Congress, the agricultural technology innovation efficiency in the lower reaches of the Yellow River Basin once again ushered in a stage of rapid growth, and returned to a higher value in 2020, showing an overall rising trend compared with the initial stage of the study.

4.4. Space-time dynamic evolution law analysis

The estimation of the Bayesian spatio-temporal level nonlinear model requires the use of OpenBUGS3.2.1 software to estimate the agricultural technology innovation efficiency of 112 prefecture-level cities in the Yellow River Basin from 2011 to 2020. As can be seen from the calculated results, the variance component coefficient value is 93.26 %, indicating that this model can well explain the spatio-temporal evolution process of innovation efficiency, and also indicates that the spatio-temporal characteristics of agricultural technology innovation efficiency are in a stable state. The Kernel density evolution of Si posterior probability estimation of spatial pattern item of agricultural technology innovation efficiency in 112 prefecture-level cities in the Yellow River Basin during 2011–2020 was measured by kernel density, and the results are shown in Fig. 6 and (a) represents the kernel density map of agricultural technology innovation efficiency, and Fig. 6 (b) represents the contour map of agricultural technology innovation efficiency.

Fig. 6.

Agricultural technology innovation efficiency density contour.

It can be seen from Fig. 6 that the distribution of agricultural technology innovation efficiency in the Yellow River Basin showed a dynamic trend from left to right during the investigation period, with a tendency to tail to the right and a large difference in ductility. The distribution of agricultural technology innovation efficiency in the Yellow River basin showed a multipolar trend. From the perspective of the contour lines representing the kernel density of different densities, if the change trend of the kernel density is large, the center of the contour map is more dense, the number of circles in the kernel density map increases, and the distribution of agricultural technology innovation efficiency in the Yellow River Basin shows a multi-peak evolution process, especially after 2015, there is a clear multi-peak evolution trend. The main peak is concentrated in the region of 0.6–0.8 median value. In view of the large difference in Kernel density distribution trend, this paper further analyzed the Kernel density distribution trend of Si posterior probability estimate of spatial pattern item of agricultural technology innovation efficiency in upstream, midstream and downstream regions, so as to clarify whether agricultural technology innovation efficiency tends to improve or worsen in the three regions. Whether the innovation development difference between regions tends to shrink or expand, the measurement results are shown in Fig. 7 and (a1) is the kernel density map of agricultural technology innovation efficiency in the upper reaches of the Yellow River Basin, and Fig. 7 (a2) is the contour map of agricultural technology innovation efficiency in the upper reaches of the Yellow River Basin. Fig. 7 (b1) is the kernel density map of agricultural technology innovation efficiency in the middle reaches of the Yellow River basin, and Fig. 7 (b2) is the contour map of agricultural technology innovation efficiency in the middle reaches of the Yellow River Basin. Fig. 7 (c1) is the kernel density map of agricultural technology innovation efficiency in the lower reaches of the Yellow River Basin, and Fig. 7 (c2) is the contour map of agricultural technology innovation efficiency in the lower reaches of the Yellow River Basin.

Fig. 7.

The spatial pattern term Si posteriori probability of agricultural technological innovation efficiency in three regions is used to estimate kernel density evolution.

According to al and a2 in Fig. 7, the spatial distribution of agricultural technology innovation efficiency in the Yellow River Basin from 2011 to 2020 presents a single-peak distribution in the upstream region. Combined with the nuclear density contour, the main peak on the left side of the sample observation period shifts from 0.8 to 0.6, but the number of cycles decreases, the height of the density graph decreases and the slope tends to be gentle, showing a gradient diffusion development effect. In addition, the trend of Kernel density distribution showed a left-side tailing in 2011, indicating that there were cities with low efficiency of agricultural technology innovation in the upstream region. However, with the improvement of the efficiency of agricultural technology innovation in the upstream area, the left tail gradually contracted, indicating that the number of cities with higher development level increased in the upstream area, and the upward trend was obvious.

It can be seen from b1 and b2 in Fig. 7 that the Kernel density distribution trend of Si posterior probability estimate of spatial pattern of agricultural technology innovation efficiency in the middle reaches of the Yellow River Basin during 2011–2020 presents a unimodal distribution phenomenon, and the overall development level is similar among regions, while the internal differentiation phenomenon has not yet emerged, which is accompanied by the development of agricultural technology innovation efficiency in the Yellow River Basin. From the core density contour, the core circle continues to shift from 0.5 to 0.7, and has a tendency of agglomeration development in spatial distribution. The agricultural technology innovation efficiency in the Yellow River Basin showed a slight shift to the right, and the right-side trailing phenomenon gradually shrank. However, different from the evolution of the upstream, the single-peak shift to the right during the observation period did not show the double-peak feature, indicating that the polarization development phenomenon was not prominent in the middle reaches.

According to cl and c2 in Fig. 7, the Kernel density distribution trend of Si posteriori probability estimate of spatial pattern of agricultural technology innovation efficiency in the lower reaches of the Yellow River Basin from 2011 to 2020 presents a right-trailing phenomenon, forming a bimodal distribution from single-peak mode to 2016, and the peak height on the left side is low, due to the internal gradient effect. The downstream leads to the trend of differentiation, and the phenomenon of multi-level differentiation is especially prominent. According to the contour line of nuclear density, the core circle is between 0.2 and 0.8, and the contour density changes from sparse to dense, indicating that the peak slope becomes steeper, the height increases, and the overall development level increases. However, although the downstream region has improved overall, its expansion and evolution trend is not as good as that of the upper and middle reaches.

5. Discussion

In the context of unprecedented global scientific and technological competition, the transformation and upgrading of agriculture driven by innovation has become an inevitable choice to enhance agricultural competitiveness. It is an urgent problem to improve the competitiveness of agricultural science and technology and realize the sustainable development of agriculture to seek improvement strategies from the efficiency of agricultural technology innovation in Yellow River Basin. Based on the data of prefecture-level cities, this paper measures and analyzes the overall and upper, middle and lower reaches of agricultural technological innovation efficiency in the Yellow River Basin, and explores the overall level, regional differences and spatio-temporal dynamic evolution law of agricultural technological innovation efficiency in the Yellow River Basin, with a view to measuring the development trend and driving force of agricultural technological innovation efficiency in the Yellow River Basin as accurately as possible. It points out the strategies for improving the efficiency of agricultural technology innovation in the Yellow River Basin, and provides theoretical support and policy reference for breaking through the imbalance between supply and demand of water resources in the Yellow River Basin, conforming to the requirements of the national high-quality economic development strategy, and promoting the sustainable development of agriculture in the Yellow River Basin. Similar to the existing studies at home and abroad, this paper also adopts DEA method to study the efficiency of agricultural technology innovation, but it rarely focuses on the Yellow River basin, an important agricultural area in China, and considers the water resources constraint. Taking the Yellow River Basin as the research object, this paper measures and evaluates the agricultural technological innovation efficiency of the Yellow River Basin, extends the measurement vision of innovation efficiency from other industrial fields to the agricultural field, and analyzes the Yellow River Basin, which expands the current theoretical research vision to a certain extent and provides a theoretical reference for promoting the high-quality development of agriculture in the Yellow River Basin. The effect of environmental factors was eliminated by three-stage DEA method, and the changes of agricultural technology innovation efficiency, pure technology efficiency and scale efficiency in the Yellow River Basin were comprehensively understood. At the same time, Kernel density estimation was used to show the spatio-temporal dynamic evolution law of agricultural technology innovation efficiency in the Yellow River Basin, which is helpful to analyze the constraints of agricultural technology innovation efficiency in the Yellow River Basin from a multi-dimensional perspective, and deeply analyze the development status and improvement direction of agricultural technology innovation efficiency. In addition, when constructing the evaluation index system of agricultural technology innovation efficiency in the Yellow River Basin, this paper referred to a large number of literatures to ensure the rationality of the input and output indicators selected, so as to measure the true level and status of agricultural technology innovation efficiency in the Yellow River Basin more objectively and accurately.

However, the improvement of agricultural technology innovation efficiency has strong theoretical depth and practical complexity, which is limited by objective data and subjective ability. This paper only made a preliminary exploration of agricultural technology innovation efficiency in the Yellow River Basin, and there are still some shortcomings in the paper. In this paper, the efficiency level of agricultural technology innovation and its spatio-temporal evolution are compared and analyzed from the perspective of three traditional regions: upstream, midstream and downstream. In fact, using this method of regional division, due to the large gap between the economic development level and agricultural technology innovation environment of prefecture-level cities, the analysis results are not deep enough. Therefore, in the follow-up research, multi-level and multi-class classification criteria can be considered for more specific and detailed classification of research objects to enhance the pertinence and practicality of research conclusions. In addition, due to space constraints, this paper proposed the path to improve the efficiency of agricultural technology innovation in the Yellow River Basin from the perspective of existing regional differences and spatial and temporal distribution. In the future, the influencing factors of agricultural technology innovation efficiency and the interaction and spatial effects of non-economic factors can be further discussed from a quantitative perspective.

6. Conclusion and countermeasure

6.1. Research conclusion

Based on the agricultural technological innovation efficiency of the Yellow River Basin under the constraint of water resources, this paper selects relevant input-output indicators and uses three-stage DEA model to measure the overall and upper, middle and lower reaches of the Yellow River Basin during 2011–2020, and analyzes its evolution characteristics from the overall and regional perspectives. In addition, the Bayesian space-time level nonlinear model and Kernel density estimation are used to investigate its space-time dynamic evolution law. Specific research conclusions are as follows.

• (1)After eliminating environmental factors and random interference, the agricultural technology innovation efficiency in the Yellow River Basin is significantly different from that in the first stage, and the three-stage DEA model can better improve the accuracy, scientificity and rationality of measurement results. From the overall level, the adjusted agricultural technological innovation efficiency in the Yellow River Basin increased, the scale efficiency decreased, and the comprehensive efficiency level decreased, and the agricultural technological innovation efficiency in the Yellow River Basin was promoted by the pure technical efficiency and scale efficiency. However, from the perspective of the adjusted temporal and spatial characteristics, the overall efficiency of agricultural technology innovation in the Yellow River Basin is at a good level, showing a rising trend of waves during the measurement period, and the efficiency level is closely related to location factors, and the gap between prefecture-level cities is gradually narrowing.
• (2)From the regional perspective, there is regional heterogeneity in agricultural technology innovation efficiency, but the overall development trend is good. The lower reaches of the Yellow River basin have obvious advantages in agricultural technology innovation efficiency compared with the upper and middle reaches provinces and cities, and the cumulative growth rate is the highest. In the middle reaches of China, the mean efficiency has a large fluctuation trend, but the overall level shows an upward trend. However, the fluctuation of agricultural technology innovation efficiency curve in the upper reaches of the Yellow River Basin is relatively gentle, but the overall development trend is negative.
• (3)The overall spatial and temporal evolution distribution of agricultural technology innovation efficiency in the Yellow River Basin showed a multi-polarization trend, and the upper, middle and lower reaches of different regions showed great differences. The upper reaches of the Yellow River basin showed unimodal distribution and gradient diffusion development effect. In the middle reaches, except for unimodal distribution, the internal differentiation has not yet appeared, and the overall development level of the region is similar and there is a trend of agglomeration development. In the lower reaches of the Yellow River, bimodal distribution is gradually formed from unimodal distribution, and multistage differentiation is particularly prominent.

The above research conclusions will provide theoretical basis and data reference for the formulation of agricultural modernization development planning in the Yellow River Basin, and have important theoretical value for improving the efficiency of agricultural technology innovation in the Yellow River Basin and promoting high-quality agricultural and economic development in the Yellow River Basin. In addition, this paper innovatively constructed a set of evaluation index system to investigate the efficiency of agricultural technology innovation in the Yellow River Basin, and analyzed the spatio-temporal dynamic evolution law of the overall and regional levels of agricultural technology innovation efficiency in the Yellow River Basin, providing new ideas for improving the efficiency of agricultural technology innovation in the Yellow River Basin. It also provides important theoretical support for reducing regional differences in the efficiency of agricultural technology innovation in the Yellow River Basin and exploring the driving factors for improving the efficiency of agricultural technology innovation. This provides decision-making reference for local governments to promote the high-quality development of agriculture from the perspective of improving the efficiency of agricultural technology innovation, and has important practical value.

6.2. Countermeasures and suggestions

6.2.1. Promote water-saving technology innovation and improve resource utilization

The level of water-saving technology and agricultural irrigation water are the key indicators of agricultural technology innovation in the Yellow River Basin under the constraint of water resources. Enhancing the level of water-saving technology and improving the efficiency of agricultural irrigation water can promote the efficiency of agricultural technology innovation in the Yellow River Basin from the perspective of "innovation input". In view of the current agricultural development in the Yellow River Basin, some farmers still have weak awareness of water conservation and low efficiency of water resources utilization. Overall planning and planning should be made according to the distribution of water resources in the Yellow River Basin and different crop planting seasons and laws, the agricultural planting structure should be adjusted, some talents in agricultural water management should be trained, and farmers' awareness and skills in water-saving irrigation should be increased. Furthermore, the efficiency of agricultural technology innovation in the Yellow River Basin is improved under the constraint of water resources. At the same time, continuous improvement and research and development of water-saving irrigation technology, emphasis on water pollution prevention and control, and active innovation of contaminated water treatment technology and equipment, in order to improve the efficiency of agricultural technology innovation in the Yellow River Basin from the aspects of reducing facility costs and improving the efficiency of water resources use.

6.2.2. Promote the integration of agricultural science and technology and enhance regional coordination

From the analysis of agricultural technology innovation efficiency, it can be seen that promoting the integration of agricultural technology is an important way to improve agricultural technology innovation in the Yellow River Basin. For the economically developed lower Yellow River region, it is necessary to rely on innovation to actively promote the development of emerging industries, cultivate new growth points and growth poles of agricultural economy, and actively encourage the original agricultural enterprises to transform into emerging agricultural science and technology industries to achieve higher quality development. For the middle reaches of the Yellow River and the upper reaches of the Yellow River, on the one hand, it is necessary to learn from the lower reaches of the Yellow River and other areas with outstanding agricultural science and technology development on the basis of the principle of sustainability and green, establish perfect agricultural science and technology promotion measures and supporting facilities, and fully activate the resource advantages and agricultural science and technology market. On the other hand, it is necessary to develop agricultural industries with unique advantages according to their own resource endowments, actively promote the upgrading of agricultural industry science and technology, and construct a development strategy that conforms to the coordinated promotion of agricultural science and technology development and economic growth in the middle and upper Yellow River regions. At the same time, we should improve the construction of agricultural technology infrastructure, narrow the gap in agricultural technology, strengthen the construction of agricultural technology infrastructure in the less developed provinces in the upper reaches of the Yellow River, further release the promotion potential of agricultural technology in the middle and lower reaches of the Yellow River, and enhance regional coordination.

6.2.3. Promote the integration of industry, university and research, and improve platform construction

From the perspective of the operation of the innovation system in the Yellow River Basin, the agricultural colleges with strong scientific research strength in the region can improve the efficiency of agricultural technology innovation to a certain extent, so promoting the integration of production, study and research is an important strategy for improving the efficiency of agricultural technology innovation in the Yellow River Basin. First of all, agricultural enterprises can participate in the innovation process by providing funds to scientific research institutions such as universities, launching technical project cooperation, and establishing agricultural technology research and development centers, so as to use the scientific research capabilities of scientific research institutions to help themselves solve technological innovation problems, obtain the priority to use the results, and maximize the operational benefits of agricultural enterprises. Secondly, the government can take the initiative to coordinate the help of developed regions to backward regions, and build a comprehensive industry-university-research mechanism for agricultural technology innovation oriented by market demand in the Yellow River Basin to solve the problem of uneven agricultural technology innovation capacity among prefecture-level cities. Finally, scientific research institutions can establish various forms of joint scientific research mechanisms, through the sharing of resources, joint efforts to tackle agricultural technology innovation problems, to avoid duplication of research caused by redundancy and waste of resources.

6.2.4. Strengthen regional linkage mechanism and narrow regional differences

From the efficiency analysis of agricultural technology innovation, it can be seen that there is a certain heterogeneity of agricultural technology innovation efficiency among prefecture-level cities and the upper, middle and lower reaches of the Yellow River Basin. Therefore, it is necessary to give full play to the unique advantages of each region, coordinate regional linkage, and promote the rational flow and efficient aggregation of scientific and technological innovation input factors in various regions. Provinces should focus on the linkage effect between regions, regions with higher efficiency of agricultural technology innovation will radiate other regions, achieve coordination in the allocation of agricultural science and technology resources between regions, fully release the vitality of innovation factors such as knowledge, technology, talent, capital and information, and achieve complementary advantages and win-win cooperation. At the same time, the formulation of science and technology policies should fully consider the regional differences in agricultural science and technology resources, appropriately increase support for areas with weak agricultural science and technology resources, guide the rational distribution of agricultural science and technology resources, so as to improve the current situation of the imbalance in scientific research expenditure between enterprises and scientific research institutions, between agricultural technology innovation activities and the promotion of achievements, and between less developed regions and developed regions. To realize the effective improvement of agricultural technology innovation efficiency in backward areas and narrow regional differences.

Data availability statement

The datasets used and analyzed during the current study are available from the corre-sponding author on reasonable request.

CRediT authorship contribution statement

Menghe Chen: Writing – review & editing, Software, Project administration, Methodology, Formal analysis, Conceptualization. Jingfeng Zhao: Writing – original draft, Validation, Software, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis. Shajunyi Zhao: Writing – review & editing, Visualization, Resources, Funding acquisition, Formal analysis, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.