3.1.1 Entropy weight method.

The entropy weight method is a universally applied objective weighting method, which utilizes the impact of the numerical changes of each indicator on the whole to calculate the entropy value of the indicator, and then calculate the weights. In this paper, the entropy weight method is used to determine the weight of each indicator in the evaluation index system, which can effectively avoid the bias caused by subjectivity. Before the measurement, it is necessary to eliminate the influence of the index scale to standardize the indicators, and this paper refers to the method of Zhang et al. [34] to non-negativize the indicators, the specific practices are as follows: (1) (2) where x_ij is the value of the j th indicator in the i th province, y_ij is the value of the j th indicator in the i th province after standardization, and max(x_1j,x_2j⋯x_nj) and min(x_1j,x_2j⋯x_nj) denote the maximum and minimum values of each indicator, respectively, i = 1,2,…n; j = 1,2,…,m.

Next, the entropy weight method is utilized to determine the weights of the indica-tors: (3) (4) (5)

where P_ij is the weight of the sample value of the ith evaluation object under the jth indicator, E_j is the information entropy, and w_j is the weight of the jth indicator.

Finally, the composite score S_i of each province’s food security level is calculated: (6)

3.1.2 Coupling coordination degree model.

The coupling coordination degree model describes the interaction relationship between two or more different systems. In this paper, the coupling coordination degree model is applied to measure the coupling coordination relationship between the level of digital village construction and the level of high-quality agricultural development to analyze the interaction and coordination status of the two, and to evaluate the overall degree of development of the two [34]. The calculation formula is as follows: (7) (8) (9)

Firstly, Formula (7) is used to calculate the coupling degree C, which reflects the degree of mutual influence and dependence between subsystems, C∈[0,1], U₁、U₂ respectively represents the level of digital village construction and the level of high-quality agricultural development. And then Formula (8) is used to calculate the coordination index D, who reflects the synergistic development between subsystems. α、β are the pending weight coefficients, this paper believes that the two are equally important, so α = β = 0.5. Finally, Formula (9) is used to calculate the degree of coupling coordination, which measures the overall level of coordination development between systems, D∈[0,1]. Referring to related literature [34], the coupling coordination degree of the two systems is divided into ten types, which is convenient to reflect the degree of coordination between the two systems. Table 1 shows the specific grades.

Download:

• PNG
  larger image
• TIFF
  original image

Table 1. Coupling coordination degree classification.

https://doi.org/10.1371/journal.pone.0319090.t001

3.1.3 Kernel density estimation method.

Kernel density estimation is a method that uses a density function to describe the nature of data distribution. In order to demonstrate more intuitively the evolutionary pattern of the coupling coordination relationship between digital village construction and high-quality agricultural development, this paper applies this method to describe the distribution characteristics of the coupling coordination level of digital village construction and high-quality agricultural development. Then it analyzes the dynamic evolution of the coupling coordination level by comparing the kernel density curves of different years [35]. The formula is as follows: (10) where f(x) represents the kernel density. h is the bandwidth, which determines the image characteristics of the kernel density curve. n denotes the total number of provinces. X_i is the level of coupling and coordination between digital village construction and high-quality agricultural development in each province. is the mean value, and is the kernel function.

3.1.4 Spatial autocorrelation analysis method.

Before applying spatial econometric modeling for analysis, the first task is to determine whether spatial correlation exists among economic units. Spatial autocorrelation mainly reveals the global spatial distribution characteristics of a certain geographical observation, which is usually characterized by the global Moran’s I index [35], whose general expression is denoted by: (11) where I is the global Moran’s I index, n is the total number of provinces, ω_ij is the spatial weight matrix, x_i and x_j denote the degree of coupling coordination in the ith and jth provinces, and denotes the mean value of coupling coordination.

3.1.5 Spatial econometric model.

Considering that there may be some spatial correlation between the factors influencing the coupling coordination degree of digital village construction and high-quality agricultural development in different regions, and ignoring this issue may lead to biased results, this paper constructs a spatial econometric model to examine the main factors affecting the coupling coordination degree of them from a spatial perspective [36]. The general expression of the model is: (12) where Y is the dependent variable, that is, the coupling coordination degree of digital village construction and high-quality agricultural development. X is the explanatory variable, including the level of economic development, the degree of government intervention, technological innovation capacity, the level of human capital, financial expenditure on agriculture and upgrading of industrial structure. W is the spatial weight matrix, and we choose the geographic distance weight matrix, ρ is the spatial autoregressive coefficient, β is the regression coefficient, and ε is the random disturbance term. When θ = 0, the model simplifies to a spatial lag model, and when θ+ρβ = 0, the model simplifies to a spatial error model.

3.2.1 Evaluation indicator system for digital village construction and high-quality agricultural development.

This paper constructs the indicator system of digital village construction and high-quality agricultural development level respectively based on the scientific and systematic principles. Referring to the relevant literature and combining the connotation of digital village construction and high-quality agricultural development [14, 37–39], the indicator system of digital village construction covers digital infrastructure, digital industrial development, agricultural digitization and life digitization, and the specific indicator system is shown in Table 2. At the same time, based on the new development concept, the indicator system of the high-quality agricultural development includes agricultural innovation and development, agricultural coordination development, agricultural green development, agricultural openness development and agricultural shared development. Table 3 shows the detailed indicator system.

Download:

• PNG
  larger image
• TIFF
  original image

Table 2. Evaluation indicator system for digital village construction.

https://doi.org/10.1371/journal.pone.0319090.t002

Download:

• PNG
  larger image
• TIFF
  original image

Table 3. Evaluation indicator system for high-quality agricultural development.

https://doi.org/10.1371/journal.pone.0319090.t003

3.2.2 Factors affecting the degree of coupling and coordination between digital village construction and high-quality agricultural development.

Referring to relevant literature [40–42], the level of coupling and coordination between digital village construction and high-quality agricultural development is selected as the dependent variable. And the level of economic development, the degree of government intervention and so on are the explanatory variables for econometric analysis. Table 4 demonstrates the variable descriptions and descriptive statistics of each factor.

Download:

• PNG
  larger image
• TIFF
  original image

Table 4. Description of variables influencing the degree of coupling coordination.

https://doi.org/10.1371/journal.pone.0319090.t004

4.1.1 Temporal evolution analysis.

According to the indicator system and measurement formula in the previous section, we measure the scores of the level of digital village construction and high-quality agricultural development from 2011 to 2022. In order to facilitate further analysis, the study area is divided into the eastern region, central region and western region according to the standard of China’s economic belt division. Table 5 shows the mean values of the scores.

Download:

• PNG
  larger image
• TIFF
  original image

Table 5. Score on the level of digital rural development and high-quality agricultural development.

https://doi.org/10.1371/journal.pone.0319090.t005

From 2011 to 2022, the level of digital village construction and high-quality agricultural development have both increased. The level of digital village construction grows from 0.2722 to 0.3214, an increase of 18.07%. And the level of high-quality agricultural development grows from 0.4155 to 0.4395, an increase of 5.78%. These results are basically consistent with the research of scholars such as Lu et al. [43] and Xiang et al. [20]. Although the level of digital village construction and high-quality agricultural development are at a low stage, both are in an upward trend. Digital village construction has seen a large increase and rapid development. As one of the important strategic directions for rural revitalization, the digital village construction strategy has been developing in recent years, and with the continuous improvement of digital infrastructure in rural areas, the digital economy and digital governance in rural areas have achieved significant results. At present, China’s agriculture is following the new development concept and gradually transitioning to the stage of high-quality development. At the same time, the digital transformation of agriculture has accelerated, and the industrial structure has been optimized. So the level of high-quality agricultural development has steadily increased.

4.1.2 Spatial distribution patterns.

From a spatial point of view, China’s digital village construction and high-quality agricultural development level show spatial imbalance. The digital village construction and high-quality agricultural development in the eastern region far exceed the national average, while the central and western regions are relatively backward, which shows a decreasing trend from east to west. Mainly due to the high level of economic development in the eastern region. And with the establishment of some digital village pilot areas in the eastern region, the digital infrastructure is gradually improved, which lays a good foundation for the construction of digital villages. Li and Wen’s research also shows that the eastern region has a higher level of digital village construction due to a higher level of information infrastructure development, while the western region has a slower start in digital village construction due to the lack of maturity of the basic conditions [44]. In recent years, thanks to the promotion of strategies such as "East data, West computing", the central and western regions have gradually been introduced into the process of digital development, and a series of policies have been implemented to promote digital transformation and continuously improve the level of digital village construction. In addition, the eastern region has an advantageous geographical location, rich agricultural resources, a high level of agricultural mechanization, and large-scale agricultural development, all of which have contributed to the high-quality agricultural development. The central and western regions are constrained by factors such as the resource environment and economic development, and the high-quality agricultural development is relatively backward. But with the continuous improvement of the level of digital village construction, the agricultural infrastructure is constantly being strengthened, and agricultural production methods are transforming to digitalization, which provides a good environment for the high-quality agricultural development.

4.3.1 Spatial correlation analysis.

Firstly, we use Stata15 software to calculate the global Moran’s I index of the coupling coordination degree of digital village construction and high-quality agricultural development from 2011 to 2022 to test the spatial correlation. Table 7 shows the specific results. As can be seen in Table 7, all the Moran’s I indices of the coupling coordination level have passed the 1% significance level test, which indicates that the coupling coordination degree of China’s digital village construction and high-quality agricultural development presents a significant positive correlation in space, so this paper can be analyzed by using the spatial econometric model.

Download:

• PNG
  larger image
• TIFF
  original image

Table 7. Results of global Moran’s I index.

https://doi.org/10.1371/journal.pone.0319090.t007

4.3.2 Spatial econometric model selection.

In order to select the appropriate spatial econometric model, this study further utilizes various methods such as LM test, Wald test, LR test, etc., and the specific results are shown in Table 8. Analyzing the data in Table 8, it can be seen that except for the LM-Lag failing to pass the test of significance, the others pass the test of significance at the 1% level, and the statistic result of Hausman’s test is -85.42, showing a more complex situation. After simulation and analysis, it is found that this is mainly due to the fact that the basic assumption of the random effects model, i.e., the asymptotic assumption, cannot be satisfied. Referring to the related literature, it can be seen that the fixed effect model should be used in this study [46]. Meanwhile, by comparing individual fixed effects, time fixed effects and two-way fixed effects, it is found that two-way fixed effects have the largest Log-likelihood value and the best effect. Therefore, based on the above test results, this paper finally adopts the two-way fixed Spatial Durbin Model (SDM) to analyze the influencing factors of the coupling and coordination of digital village construction and high-quality agricultural development.

Download:

• PNG
  larger image
• TIFF
  original image

Table 8. Results of the spatial measurement model selection test.

https://doi.org/10.1371/journal.pone.0319090.t008

4.3.3 Analysis of influencing factors.

In order to further assess the robustness of the model, this paper also constructs the Spatial Error Model (SEM), Spatial Lag Model (SLM) and Spatial Durbin Model (SDM) of the influencing factors of the coupling degree of coordination between the two, and the specific results are shown in Table 9. The following conclusions can be drawn: First of all, the SDM model has the best effect in spatial econometric analysis of the coupling degree of coordination between the digital village construction and the high-quality agricultural development. By comparing the test results of different models, it can be found that the SDM model has the largest Log-likelihood value, which indicates that it is reasonable and appropriate to use the SDM model to analyze the influencing factors of the degree of coupling and coordination between the two, and this conclusion is consistent with the previous test results. Secondly, the estimation results of the two-way fixed-effects SDM model show that the coefficient estimates of the spatially lagged terms of the economic development level (W*eco), technological innovation capacity (W*tec) and agricultural financial expenditure (W*agr) pass the significance test. This indicates that the level of economic development, technological innovation capacity and agricultural financial expenditure in neighboring regions have a significant positive spatial effect on the local coupling coordination, while the spatial effect of the level of government intervention, human capital level and industrial structure upgrading in neighboring regions on the local coupling coordination is not significant. Finally, there is a significant spatial spillover effect of the coupling coordination degree of digital village construction and high-quality agricultural development. The spatial autoregressive coefficient in the SDM model is -0.5338 and is significant at the 5% level, indicating that for every 1% increase in the coupling coordination degree of neighboring regions, the coupling coordination degree of the local region will decrease by 53.38%. This is mainly due to the fact that the coupling coordination degree of the two in each province is still at a low stage, and the radiation and demonstration effects of the region with high coupling coordination on the neighboring low-value areas have not yet been fully realized. In a society with limited economic resources, the rapid improvement of the digital village construction and the high-quality agricultural development will be attractive to the human and material resources of neighboring regions, creating a siphon effect and showing a negative spatial spillover effect.

Download:

• PNG
  larger image
• TIFF
  original image

Table 9. Results of the spatial econometrics model of coupling coordination.

https://doi.org/10.1371/journal.pone.0319090.t009

In order to more accurately analyze the influence of each factor on the level of coupling coordination, the spatial effects of each influencing factor are further decomposed with the help of partial differential method, and the specific results are shown in Table 10. In terms of the total effect, the influence of the level of economic development, technological innovation capacity, agricultural financial expenditure and industrial structure upgrading on the coupling coordination level of digital village construction and high-quality agricultural development is significantly positive, while the spatial total effect of the degree of government intervention and the level of human capital on the coupling coordination level is not significant. This indicates that the level of economic development, technological innovation capacity, agricultural financial expenditure and industrial structure upgrading have a significant role in promoting the coupling of digital village construction and high-quality agricultural development.

Download:

• PNG
  larger image
• TIFF
  original image

Table 10. Decomposition of spatial effects of coupling coordination.

https://doi.org/10.1371/journal.pone.0319090.t010

The level of economic development is a key factor to promote the coupling coordination development of digital village construction and high-quality agricultural development, showing a significant facilitating effect and positive spillover effect. In terms of the direct impact of the level of economic development, its effect coefficient on the degree of coupling and coordination of them in local region is 0.1079, and it is established at the 1% significance level. This fully indicates that the increase in the level of economic development has a significant role in promoting the coupling coordination development of digital village construction and high-quality agricultural development in local region. Under the condition of assuming that other variables remain unchanged, every 1% increase in the economic level will directly promote the coupling coordination development of local region by 10.79%. In terms of the indirect effect of the level of economic development, the coefficient of its influence on the degree of coupling and coordination of them in neighboring regions is 0.2309, and it is established at a significant level of 1%. This indicates that the increase in the level of local economic development has a significant driving effect on the increase in the degree of coupling and coordination of them in neighboring regions. Under the premise of keeping other variables constant, for every 1% increase in the economic level, the coupling coordination degree of digital village construction and high-quality agricultural development in neighboring regions increases by 23.09%. On the one hand, the improvement of the economic development level attracts more talents and material resources, which lays a material foundation for the digital village construction. On the other hand, the improvement of the economic development level is accompanied by the continuous improvement of the agricultural infrastructure, and the level of the agricultural mechanization shows a significant increase, which accelerates the digital transformation of agriculture, and promotes the coupling and coordination of the digital village construction and the high-quality agricultural development.

The direct and indirect effects of the degree of government intervention on the coupling and coordination of digital village construction and high-quality agricultural development do not pass the significance test, indicating that government intervention does not have a significant impact on the coupling and coordination of digital village construction and high-quality agricultural development in local region and neighboring regions.

The coefficient of the spatial spillover effect of technological innovation capacity on the coupling coordination level of digital village construction and high-quality agricultural development is 0.0395, which passes the test at the 10% significance level, indicating that the improvement of the local technological innovation capacity positively promotes the improvement of the coupling coordination degree in the neighboring regions. Under the condition of assuming that other variables remain unchanged, every 1% increase in technological innovation capacity will promote 3.95% increase in the coupling and coordination degree in neighboring regions. The direct impact effect of technological innovation capacity does not pass the significance test, indicating that the impact of technological innovation capacity on the coupling coordination development of local digital village construction and high-quality agricultural development is not significant. Theoretically, technological innovation is the core driving force of digital village construction and high-quality agricultural development. However, in practice, technological innovation activities often lead to an imbalance in the allocation of funds due to the high requirements of capital investment, which limits the wide application of technological innovation in digital village construction and high-quality agricultural development. At present, China’s digital village construction is in the exploratory stage, and there is still a vast space for improvement of new generation information technology in promoting the synergistic promotion of digital village construction and high-quality agricultural development.

The direct effect of human capital level on the degree of coupling and coordination of digital village construction and high-quality agricultural development is -0.1682, and it is significant at 1% level, which indicates that human capital level has a significant inhibitory effect on the degree of coupling and coordination of local region. Under the condition of assuming that other variables remain unchanged, for every 1% increase in the level of human capital, the degree of coupling coordination will decrease by 16.82%. It indicates that the increase in the level of human capital is not conducive to the development of coupling and coordination in local region, which may be due to the fact that there are some structural deficiencies in the supply of human resources, and the human capital is not yet fully adapted to the needs of digital village construction and high-quality agricultural development. In addition, the underutilization of highly qualified personnel is also an important reason. The indirect effect of human capital level does not pass the significance test, indicating that the spatial spillover effect of human capital level on the coupling and coordination degree of digital village construction and high-quality agricultural development in neighboring regions is not obvious, probably because the study time interval selected is relatively short, and the level of human capital has not changed too much in this interval, which has a certain lag, and the spillover effect on the coupling and coordination degree of digital village construction and high-quality agricultural development has not been played out.

Agricultural financial expenditure, as one of the key factors, has a significant impact on the coupling coordination relationship between digital village construction and high-quality agricultural development, showing a significant facilitating effect and positive spillover effect. The effect of agricultural financial expenditure on the coupling and coordination degree in local region is 0.2593 and significant at 1% level. And the indirect effect on the coupling and coordination degree in neighboring regions is 0.7084 and significant at 5% level. Under the condition of assuming that other variables remain unchanged, every 1% increase in agricultural financial expenditure will directly promote the coupling and coordination degree of local region by 25.93%, and indirectly promote the coupling and coordination degree in neighboring regions by 70.84%. At present, China is in the transition stage from traditional agriculture to modern agriculture, and increasing financial expenditure on agriculture is conducive to solving the difficulties and challenges encountered in the transition. On the one hand, increasing agricultural financial expenditure is conducive to improving the level of rural economic development, accelerating the process of agricultural digital transformation, and providing stronger support for the construction of digital villages. On the other hand, agricultural financial expenditure is committed to improving the financial support for agricultural infrastructure and skills training of workers, which in turn improves the production conditions of agriculture, improves the efficiency of agricultural production, and promotes the high-quality agricultural development.

The direct effect of industrial structure upgrading on the coupling coordination degree of local digital village construction and high-quality agricultural development is 0.1504, and it passes the significance test at 1% level. This indicates that industrial structure upgrading has a significant promotion effect on the coupling coordination degree of digital village construction and high-quality agricultural development. Under the premise of assuming that other variables remain unchanged, for every 1% increase in industrial structure upgrading, the degree of coupling and coordination will increase by 15.04%. Upgrading of industrial structure means that the development level and efficiency of the tertiary industry have been improved. In recent years, the national policy tends to develop the information technology service industry and other directions, the digital industry has been rapidly cultivated. And the process of digital transformation of agriculture has been accelerated, which has transformed the traditional agricultural production structure, and provided industrial and economic support for the digital village construction and high-quality agricultural development. The spatial spillover effect of industrial structure upgrading is positive, but does not pass the significance test, which indicates that industrial structure upgrading does not have a significant impact on the coupling coordination development of the two in neighboring regions. Wang and Tang’s research indicates that factors such as the level of economic, agricultural financial input, industrial structure, and innovation level play a promotive role in the coupling coordination of digital village and green and high-quality agricultural development in China [45], which is basically consistent with the conclusions of this study. The difference lies in that this study explores the spatial spillover effects of various influencing factors from a spatial perspective, whereas Wang and Tang’s research examines the changes in the influence of factors from a temporal dimension.

4.3.4 Robustness test.

In order to test the robustness of the model results, the geographic distance weight matrix was replaced with the economic distance weight matrix and the results obtained are shown in Table 11. From the results, it can be seen that the direction of the influence of each factor remains constant and the degree of significance does not change much, which proves the robustness of the estimation results.

Download:

• PNG
  larger image
• TIFF
  original image

Table 11. Robustness test results.

https://doi.org/10.1371/journal.pone.0319090.t011