Does Digital Village Construction Empower the Green Allocation of Agricultural Water Resources?

: The development of digital villages plays a critical role in advancing green agriculture steadily and with high quality. This study measures the efficiency of agricultural water resource allocation using provincial-level rural data from 2011 to 2022 and a super Slacks-Based Measure model accounting for non-desirable outputs. Using the ArcGIS tool, this study illustrates the spatiotemporal patterns and provincial clustering of the green allocation of agricultural water resources. A spatial Durbin model further examines interactions between digital villages and water resource efficiency. Findings indicate the following: (1) The green water resource efficiency in China’s 30 provinces showed a gradual, steady increase, albeit with notable regional differences, particularly a “north-western depression” in spatial distribution. (2) Moran’s I index indicates a strong positive spatial correlation between digital villages and green water resource efficiency, manifested as either “high– high” or “low–low” clustering. (3) The spatial Durbin model results demonstrate that digital villages enhance the green water resource efficiency of neighboring areas, a phenomenon referred to as the “Matthew effect”. (4) Different aspects of digital village construction, operation, and lifestyle positively influence green water resource efficiency, while digital loops have a negative impact. Aligning resource allocation efficiency with the establishment of digital village infrastructure is paramount. This symbiotic relationship bolsters the structural foundation of agricultural production, optimizing resource utilization and fostering technological advancements in rural settings.


Introduction
Post-production reform, agricultural green resource allocation efficiency and industrial clustering conditions have markedly improved, significantly enhancing grain production and agricultural output value.Capacity expansion has highlighted the increasing occurrence of "grey rhino" events, marked by high pollution, consumption, and low efficiency and quality [1].Furthermore, the possibility of black swan events, including the COVID-19 pandemic, cannot be discounted during the pursuit of sustainable agricultural production.Digital villages, defined as rural areas integrating advanced technologies for sustainable development, play a pivotal role in advancing green agricultural development.Rooted in green and ecological economics, this entails a comprehensive transition towards environmentally friendly practices and the conservation of agricultural resources.Ecological water resource protection is essential for ecosystem balance and ecological services.Recently, a serious spatiotemporal imbalance has emerged, with the Huaihe River Basin and the northern region possessing 62% of the country's farmland and only 20% of its water resources.In addition, the significant heterogeneity of weather conditions between regions also profoundly shapes the spatial and temporal differences in the efficiency of green allocation of agricultural water resources.Under drought conditions, water resources are extremely scarce, which seriously restricts the stability and sustainability of agricultural production, while floods cause damage to farmland and crop damage, posing a direct challenge to agricultural production.China's shift from traditional to modern agriculture continues, but reliance on pollutants like fertilizers and pesticides causes widespread "surface pollution", exacerbating water resource security, scarcity, and quality issues.In response, the central government issued the "National Water Conservation Action Plan" on 15 April 2019.
The progress in internet big data and artificial intelligence has significantly enhanced digital production, improving resource coordination, advocating water-saving irrigation, and rectifying distortions in production factors.In line with present demands, there is a drive to capitalize on the potential and innovation of digital technologies, utilizing the green attributes of the digital economy to revolutionize and amplify the efficiency of green water resource allocation in rural agriculture.The 2018 No. 1 central document emphasized accelerating digital technology integration in rural agriculture, lifestyle, and construction sectors.It emphasized that resource allocation efficiency and digital infrastructure should be closely aligned to empower the structural engine of agricultural production, thereby enhancing the utilization rate of water resources in agriculture.As an industrial reform "accelerator", new technology merges its large-scale benefits with green, low-carbon development, solidifying multi-perspective resource configuration in rural areas.A delayed start in digital development has led to a "snake-like" rapid spread of digitalization from east to west, worsening the "digital rural divide" [2] from north to south.The emerging construction of digital villages poses a question: Can it enhance agricultural green water resource allocation efficiency, and if so, how?This warrants further investigation.
While existing research has examined digital villages and agricultural water resources, opportunities exist to refine research methods, indicators, and frameworks.Scholars primarily discuss the theoretical impact of digital villages on green economic efficiency and total factor productivity, yet few empirical tests examine the theoretical logic and internal mechanisms connecting digital village construction with the efficiency of agricultural water resource allocation.Secondly, evaluation indicators for digital villages are still under exploration without consensus, often neglecting critical indicators' impact.Thirdly, while most studies utilize panel-based models for theoretical analysis and empirical exploration of the green effects and penetration mechanisms of digital villages, they often overlook the spatial spillover effects of digital village construction on the efficiency of agricultural water resource allocation.To bridge these gaps, this study suggests (1) developing an indicator system encompassing "digital infrastructure, management, circulation, and life" to scientifically assess rural digitalization's comprehensive development, and (2) broadening the study scope to include the spatial correlation and spillover effects between digital villages and water resource allocation efficiency, aiming to analyze and test their interaction mechanisms for insights into sustainable green agricultural water resource growth.

Literature Review
In the context of rapid urbanization and industrialization, China faces increasing scarcity of strategic water resources, crucial for food security and ecosystem support [3].Guided by sustainable recycling principles, this approach aims to conserve ecological resources and optimize the utilization, enhancement, and safeguarding of water resources within a circular economy paradigm, thereby maximizing agricultural efficiency and water conservation potential.The circular economy approach to water resource management emphasizes the closure of resource loops, waste prevention, and the restoration of natural systems to sustainably support agricultural production.The majority of studies concentrate on water rights to trading [4], pricing, and irrigation facilities, with others exploring the economic and environmental efficiencies of agricultural water use towards harmonizing social, natural, and ecological benefits [5].Adhering to a people-oriented green development concept [6], Sun et al. [7] use the Geographically Weighted Regression (GWR) model to uncover the drivers of water resource efficiency, enhancing our understanding of green water efficiency in spatial contexts.Global green water efficiency measurement methods are divided into single-factor and comprehensive evaluations.The former assesses resource allocation efficiency in a specific field with one indicator, subject to limitations of subjectivity.Initially, comprehensive evaluations employed Stochastic Frontier Analysis (SFA) [8] and Data Envelopment Analysis (DEA) [9].The SFA model struggled with multiple outputs, and DEA disregarded slack variable impacts.Later, scholars improved the DEA model; Tone [10] added slack variables to inputs and outputs, forming the SBM-DEA model.Lins [11] applied zero-sum game theory for global optimization, creating the ZSG-DEA model and providing fresh insights into water efficiency analysis.He et al. [12] applied the SRM-DEA model to examine the Huai River basin's green efficiency spatial-temporal patterns and mechanisms.Zhang et al. [13] merged the three-stage model with the SDM for sustainable energy efficiency management in the RCEP free trade area, conducting empirical tests.Existing research employs the logarithmic mean Divisia index, panel regression, and spatial econometrics to investigate how technology, structure, and economic factors affect agricultural growth and water scarcity, showing that innovation drives economic growth and mitigates water scarcity [14,15].Synergy between water resource concentration and innovative water-saving technologies mutually enhances benefits [16].Intentional resource integration across regions advances water-saving technology modernization [17], significantly boosting water use efficiency.Additionally, extensive research has been carried out on regional differences and spatial correlations in agricultural water use efficiency [18,19].Li et al. [20] investigated the link between China's water use efficiency, economic status, and spatial distribution, advocating for customized spatial pattern optimization.Yang et al. [21] utilized impulse response functions to study the spatially synergistic effects on water use efficiency.From dynamic and static perspectives, Wang et al. [22] observed that agricultural water use efficiency does not reduce inter-provincial differences over time, but rather achieves a dynamic convergence balance among regions.
In the context of "mass innovation and public entrepreneurship", farmers, being the most demanding and vocal social group, play a crucial role.Incorporating technological innovation into farmers' production practices holds significant transformative and scholarly value.Rural areas are significant in the global network of society, offering unique online resources [23].The ongoing enhancement of digital village infrastructure, including data centers, 5G base stations, and internet access, has merged the digital economy with traditional agricultural sectors [24].This integration has spurred new business models, such as e-commerce and live streaming sales, significantly boosting rural economic growth.Jansson [25] observes that social media often has more symbolic importance for small communities than for large urban areas.Academic research mainly examines the impact of digital villages on urban-rural economic integration, highlighting regional differences and variability, with the east showing greater integration than the west [26].Certain studies investigate the correlation between the digital economy and green development [27], employing indicators of industrial structure adjustment to evaluate spatial correlations and delve into action mechanisms within a unified framework.The utilization of nonlinear and threshold models unveils a digital divide in the advancement of the digital economy, contributing to a "U"-shaped disparity in urban-rural income [28].

Relationship between Digital Villages and the Efficiency of Green Allocation of Agricultural Water Resources
Digital village construction promotes rural industrial structure informatization, new "technology + agriculture" models, and rural digital information services through indirect methods, driving a revolution in rural production information technology comprehensively.Digital villages emphasize technological rationality, aiding precise agricultural planting and production management via information platforms.In addition to improving industrial efficiency, smart agriculture, powered by big data, offers farmers more accessible and inclusive information channels.It establishes a standard system of an optimized internet-based rural information service network, advancing towards the deep integration of the industrial chain within specific geographic areas, thereby fostering green resource allocation efficiency.Existing research explores how the digital economy cultivates a new production economy with a distinctive "green" attribute [29], analyzing and confirming that the digital construction process incurs low marginal costs, thereby maximizing benefits.Environmental impact studies of e-commerce implementation indicate that ecological benefits result in reduced environmental pollution levels [30].The comprehensive management of the digital economy, facilitated by platform services for innovative empowerment of traditional industries [31], improves resource utilization efficiency, effectively realizing green, low-carbon, high-quality planning objectives [32].The development of the digital economy unveils inherent advantages such as green sharing, technological innovation, and low transaction costs, promoting high-quality development of the agricultural green economy and accelerating the efficiency of green water resource allocation.Based on this, the following hypothesis is proposed: Hypothesis 1: The construction of digital villages will synergistically promote the upgrade of the green allocation efficiency of agricultural water resources.

Spatial Spillover Effects of Digital Villages on the Efficiency of Green Allocation of Agricultural Water Resources
Anselin [33] notes that nearly all spatial data demonstrate spatial correlation and interdependence.According to the theory of new economic geography, transaction, factor, and network information technology spillovers will reduce spatial-temporal distances in traditional rural contexts, enhancing horizontal and vertical economic activity connections between provinces, fostering an open environment for cooperation and communication.Technology penetration is viewed as an internal driver for enhancing agricultural total factor productivity (TFP) [34].With the rapid development of transportation and information infrastructure, the flow of agricultural production factors has surpassed geographical constraints, leading to a cross-regional "clearly tiered" spatial spillover effect on agricultural green TFP.The spillover characteristic suggests that the construction of digital villages is likely to influence the mechanism of agricultural resource factors through cross-regional network systems, closely connecting rural agricultural talent, technology, economy, and resources.However, as current digital village infrastructure construction is still in the early stages of exploration, it is common to observe the spatial backflow effect outweighing the diffusion effect.This results in provinces with low digital progress acting as sources of factor outflow, thereby somewhat hindering the enhancement of agricultural green resource allocation efficiency.Based on this, the following hypotheses are proposed: Hypothesis 2a: The construction of digital villages has spatial correlation, having a positive network spillover effect on the green allocation efficiency of agricultural water resources.

Hypothesis 2b:
The construction of digital villages has spatial correlation, having a negative network siphon effect on the green allocation efficiency of agricultural water resources.

Model Setup and Indicator Selection 4.1. Model Setting 4.1.1. SE-SBM Model for Non-Consensual Outputs
Because the traditional DEA model overlooks input-output slackness and does not measure undesirable outputs, leading to overestimated efficiency values, Tone [10] introduced the SBM-Undesirable model to rectify these inaccuracies.As efficiency research progresses, scholars have introduced the SE-SBM model, which integrates non-desirable outputs to enable precise comparisons among decision-making units (DMUs).This approach ensures that efficiency values of 1 accurately reflect the relative magnitudes of efficiency values, enhancing the model's accuracy.A numerical matrix is defined, with each province treated as a separate DMU, employing n DMUs to measure the green allocation efficiency of agricultural water resources.This matrix incorporates t types of input factors, c1 types of desirable outputs, and c2 types of undesirable outputs, as described in Formula (1).In the formula, X t , Y r , and Y c represent matrices consisting of the i-th input, the r-th desirable output, and the c-th undesirable output, respectively, and represent the matrices composed of t inputs, c1 desirable outputs, and c2 undesirable outputs variables for n DMUs.
The final model, represented as Formula (2), involves n decision units, with n = 30 in this study, denoted as DMUj (j = 1, 2, . .., n).Each decision unit comprises i input vectors, r desirable output vectors, and c undesirable output vectors.The described formula represents the SE-SBM model for non-consensual output of the k-th decision unit, indicating the green allocation efficiency value of agricultural water resources, ranging from 0 to 2. Here, t, c1, and c2 denote the input variables, desirable output variables, and undesirable output variables, respectively.minπ =

.2. Spatial Autocorrelation Analysis
Conducting a spatial autocorrelation test is essential to determine the presence and type of spatial dependency between two variables in adjacent areas.Three commonly used methods for testing spatial correlation are Moran's I, Geary's C, and Getis-Ord G (hot spot analysis).Geary's C, akin to Moran's I, compares the cross-multiplication of sample value deviations from the mean in adjacent areas, whereas Moran's I assesses the difference in sample values.Moran's I is commonly favored for correlation testing over Geary's C because Geary's C is highly sensitive to both the type of spatial weight matrix and the sample size, leading to potential biases.Hot spot analysis diverges in its calculation principle from the first two methods by employing the product of sample values in adjacent areas, which is constrained by the spatial matrix.It can only conduct spatial correlation analysis using a spatial distance weight matrix [

Spatial Econometric Model
As the "usage intensity" of the internet deepens and the spatial network system between urban and rural areas becomes more refined, regions will no longer be able to exist independently, and there will be intricate connections between economies.To tackle the challenge of spatial heterogeneity in digital village construction affecting the transmission of green allocation efficiency in provincial water resources, this paper investigates the mechanism behind fluctuations in water resource allocation efficiency values.Drawing on the research of Li et al. [36], this paper selects spatial econometric models to test the mechanism of spatial spillover effects between related variables.Spatial econometric models include the Spatial Lag Model (SLM), Spatial Error Model (SEM), and spatial Durbin model (SDM).The SLM considers the diffusion phenomenon of the dependent variable; the SEM measures the impact of variable errors in neighboring areas on the local area; the SDM considers the spatial spillover effects of both dependent and independent variables [37].Existing studies have shown that the spatial Durbin model is more capable of mitigating the endogeneity problem between variables compared to other spatial econometric models, hence the preference for using the SDM as the empirical analysis foundation in this paper.

Spatial Econometric Model
Wang et al. [38] believe that considering the combined effects of regional economy and distance can more accurately reflect the spatial adjacency between regions [39].Given China's vast agricultural areas and significant regional differences, it is important to consider both geographical and non-geographical proximity relationships to pursue objective reality.The Moran index spatial autocorrelation test utilizes the standardized spatial economic distance weight matrix, denoted as W*, for the analysis.Following the approach of Zeng et al. [40], the geographical spatial adjacency situation is first examined through latitude and longitude to construct the adjacent relationship weight matrix, Wij, followed by calculating the average per capita GDP between provinces from 2011 to 2022, and finally multiplying the two to obtain the economic distance weight matrix.
1, area i and area j are adjacent to each other.0, area i and area j are not adjacent to each other.

Dependent Variables
The efficiency index for allocating green agricultural water resources (Efficiency) was adopted based on Cui et al.'s [41] study.It takes into account modern agricultural contexts and employs scientific variables for precise measurement.The index integrates the "energyecology-economy" concept, aligning with the five-element theory [42] in agriculture and identifying water, land, energy, machinery, and labor as essential inputs.Output variables split into desirable (total agricultural output value) and undesirable (agricultural grey water footprint) metrics for a clearer distinction.The grey water footprint (WFagr-grey) calculation, as per Formula (9), involves the pollutant emission (L), maximum pollutant concentration (Cmax), initial water nitrogen concentration (Cnat), nitrogen fertilizer leaching rate (a), and total nitrogen fertilizer used (Appl) (Table 1).

Explanatory Variables
The digital village construction index (Digital) encompasses digital infrastructure, rural governance, and the digitalization of rural life aspects.This study, concentrating on green water use efficiency, adapts the Peking University Digital Inclusive Finance Index to include digital foundation, operational, circulation, and living digitalization, reflecting the agriculture, rural area, and farmer development concept.Following established frameworks (Table 2), this study adds relevant indicators to ensure comprehensiveness, constructing a robust digital village construction evaluation index.

Control Variables
Considering uncontrollable factors, this study selected control variables such as fiscal expenditure output (Finance), mechanization level (ML), openness (OP), and innovation activity evaluation (Creative) based on prior research [43][44][45].Measurement standards are as follows: (1) Unit fiscal expenditure output = total agricultural output value/expenditure on agriculture, forestry, and water affairs; (2) mechanization level = total mechanical power/total sown area of agriculture; (3) degree of openness = foreign investment amount/total production value; (4) evaluation of technological innovation activities = R&D expenditure/value added of the tertiary industry.

Data Sources and Descriptive Statistics
This study uses balanced panel data from 2011 to 2022.Considering that some provinces have too many missing data, 30 provinces other than Tibet and other provinces are selected as data samples.Regions with severe data shortages are excluded from the analysis.The aim is to investigate the impact of digital village construction on green water resource allocation efficiency.Data for variables were sourced from the "China Statistical Yearbook", "China Rural Statistical Yearbook", "China Environmental Statistics Yearbook", the Peking University Digital Inclusive Finance Index, and Ali Research Institute reports.Descriptive analysis shows Efficiency ranges from 0.486 to 1.311, and Digital from 0.224 to 0.600.Correlation coefficients range from −0.222 to 0.484, and VIF values under 10 suggest no multicollinearity among variables (Table 3).Note: Since vif is used to indicate the degree of collinearity between explanatory variables, the values of the explained variables are represented by "---".

Measurement of Agricultural Green Water Use Efficiency
To identify regional differences in agricultural resources' green allocation efficiency, we divide 30 provinces into four regions according to the National Bureau of Statistics: east (10 provinces including Beijing), central (6 provinces including Shanxi), west (11 provinces including Inner Mongolia), and northeast (Liaoning, Jilin, Heilongjiang).The table below presents the average green allocation efficiency of agricultural water resources across these four regions from 2011 to 2022.The national average fluctuated slightly between 2014 and 2015, remaining around 0.75-0.80.This shift suggests that national policies and green, low-carbon advocacy have transitioned water resource management from extensive discharge to intensive use, yielding positive outcomes.Regionally, the east's average water use efficiency surpasses the west's by 1.23 times.The east consistently outperforms the national average, uniquely achieving an efficiency value above 1.0 in 2022 over the 11-year period.The green allocation efficiency shows a stepwise decrease from east to northeast.The west and northeast exhibit a less optimistic growth trend, indicating a "collapse in the northwest".This phenomenon primarily occurs because technology and data-intensive industries, which are concentrated in the eastern coastal areas, indirectly enhance the local green allocation efficiency of agricultural water resources.Time series analysis reveals that from 2011 to 2013, China's industrial transfer and the development of processing trade drove rapid industrial growth and led to significant improvements in agricultural economics.However, this period saw minor fluctuations and increases in green resource allocation efficiency, indicating that rapid agricultural economic growth compromised agricultural ecological resource efficiency.After the "Opinions on Fully Implementing the River Chief System" were issued in late 2016, regions concentrated on reasonably controlling agricultural water resources.From 2017 to 2022, the central and western regions' green allocation efficiency annually increased and began to stabilize (Table 4).In order to further analyze the spatial evolution of regional differences, provinces were selected as spatial units, and we used ArcGIS tools to draw the spatiotemporal distribution map of agricultural water resources green allocation efficiency in 2011, 2015, 2017, and 2022, as shown in Figure 1.Since the overall value is in the range of 0-1.1, the equal division method is used; we classified agricultural water resource green allocation efficiency into four levels: excellent (0.826-1.1), good (0.56-0.825), medium (0.276-0.55), and poor (0-0.275).A clear stepwise decrease in efficiency is observed from eastern coastal to western inland provinces.Beijing, Tianjin, Heilongjiang, and Shandong consistently achieve excellent levels, benefitting from green technology and provincial development [42], resulting in strong alignment between agricultural development and environmental sustainability.Yunnan and Anhui face significant resource and environmental constraints, hindering their ability to enhance green allocation of agricultural water resources.Spatial spillover effects are evident, where provinces with higher efficiency values boost neighboring regions' efficiency, facilitating regional collaborative growth.The figure reveals that regions adjacent to high-efficiency provinces enhance cooperation via the spatial network, optimizing water resource use from technical, economic, and ecological perspectives.However, they resist transfers to low-efficiency provinces, illustrating a mix of cooperation and exploitation that hinders cross-regional growth.sustainability.Yunnan and Anhui face significant resource and environmental constraints, hindering their ability to enhance green allocation of agricultural water resources.Spatial spillover effects are evident, where provinces with higher efficiency values boost neighboring regions' efficiency, facilitating regional collaborative growth.The figure reveals that regions adjacent to high-efficiency provinces enhance cooperation via the spatial network, optimizing water resource use from technical, economic, and ecological perspectives.However, they resist transfers to low-efficiency provinces, illustrating a mix of cooperation and exploitation that hinders cross-regional growth.

Baseline Regression Analysis of Digital Villages and the Efficiency of Green Allocation of Agricultural Water Resources
The Hausman test suggests a preference for the fixed-effect model over the randomeffect model.The Table 5 below displays regression results for the fixed-effect baseline

Baseline Regression Analysis of Digital Villages and the Efficiency of Green Allocation of Agricultural Water Resources
The Hausman test suggests a preference for the fixed-effect model over the randomeffect model.The Table 5 below displays regression results for the fixed-effect baseline model, with control variables added sequentially across columns (1) to (5).In column (1), without control variables, the impact of the digital village index on agricultural water resource allocation is significant at the 10% level, confirming that digital villages enhance green allocation efficiency.Digital villages optimize and integrate green agricultural resources, facilitating scalable production management and enhancing allocation efficiency [46].The results in columns (2) to ( 5), incorporating control variables, consistently show significance.A comparison of columns ( 1) and ( 5) reveals higher coefficients and significance levels for digital villages in column (5), suggesting that the exclusion of control variables underestimates their green impact.

Spatial Autocorrelation Test
The current academic consensus is that implementing modern information technology in rural areas can drive digital development, stimulate growth, and create significant benefits for agricultural resources, industrial structures, and the labor force.[47].Consequently, digital villages interact with and influence the efficiency of agricultural green water resource allocation.To evaluate their spatial correlation, we utilized the Moran index for analysis.Wang et al. [38] recognize the spatial correlation of provincial economies, refine the traditional σ-convergence method, and highlight the directional relationship between economic disparities and spatial correlation.Consequently, this study applies a standardized spatial economic distance weight matrix considering economic and geographic factors for spatial correlation analysis, calculating global Moran indices for digital villages and agricultural water resource allocation efficiency from 2011 to 2022 (Table 6).Moran's I indices are mostly positive and significant at the 1% level, indicating a strong spatial dependence between digital villages and agricultural water resource allocation efficiency across provinces.Furthermore, the comprehensive Moran I indices for digital villages exhibit a stable trend, indicating consistent spatial dependence.This stability makes them suitable for analyzing their impact on agricultural green development through spatial econometric regression.In summary, apart from 2017, 2018, 2020, and 2022, which lacked significance, the global Moran indices were significantly positive.Given that the global Moran I index measures inter-provincial data, we tested local Moran indices for years with nonsignificant results to better capture within-province spatial correlations (see Figure 2).This study uses local LISA maps instead of traditional scatter plots to visually depict within-province clustering: H-H (high-efficiency provinces surrounded by similar provinces), L-H (lowefficiency provinces near high-efficiency ones), L-L (low-efficiency areas together), and H-L (high-efficiency provinces near low-efficiency ones).LISA maps indicate that, during 2017-2018, five provinces, including Beijing, Tianjin, Shanghai, Jiangsu, and Henan, demonstrated significant local spatial positive correlation.From 2017 to 2018 and 2020 to 2022, the strength of spatial connections and the number of provinces with local positive correlation markedly increased.In 2020, ten provinces showed H-H clustering, demonstrating a positive spatial clustering effect; in 2022, seven provinces exhibited this pattern.These findings suggest that national policies and theoretical practices have contributed to a consistent rise in the local spatial correlation of China's agricultural water resource allocation efficiency.Additionally, they highlight disparities in spatial clustering within provinces, with many provinces exhibiting H-L clustering surrounding H-H clusters.This arises as core cities, seeking enhanced economic production efficiency, often relax environmental regulations, leading to an "east high, west low" pattern in agricultural water resource allocation efficiency.

Analysis of Empirical Results of Spatial Effects
This study conducts LM tests to assess the spatial effects of digital village construction on agricultural water resources' green allocation efficiency across provinces, using

Decomposition of Spatial Effects
Effect decomposition analysis (Table 9), employing robust standard errors to mitigate serial correlation and heteroscedasticity, reveals that the comprehensive digital village level's direct impact on agricultural water resource allocation efficiency is significantly positive, enhancing efficiency by 0.589% per 1% digitalization increase.The indirect spillover coefficient is significantly negative at the 1% level, possibly indicating a Matthew effect, where digitalization disparities cause concentration of talent, resources, and technology in higher-level provinces, worsening inefficiencies in neighboring lower-level areas.The most prominent effect observed among control variables is the technological innovation level.The total effect suggests that for every 1% increase in innovation level, there is a non-significant positive increase of 1.42% in green allocation efficiency.However, it is noteworthy that the indirect spillover contributes positively while the direct impact is negative, underscoring the complexity of innovation's role in resource efficiency.Due to the spatial economic distance weight matrix's sensitivity to economic and geographical differences between provinces, this study excludes the four municipalities in the spatial panel regression to assess the model's robustness (Table 10).Column (1) shows the regression results after excluding the municipalities, revealing no significant change in the coefficients and significance levels of explanatory and control variables before and after exclusion, passing the robustness test.Column (2) shows regression results after changing the explained variable, substituting the original output-oriented agricultural water resource green allocation efficiency with an input-oriented measure.There was no significant change before and after the alteration, further validating the model's robustness.

Changing Spatial Weight Matrices
Acknowledging the spatial weight matrix setting's impact on results (Table 11), this study incorporates distance and adjacency matrices alongside the standardized economic geographical weight matrix.Columns (1) to (3) represent the regression results for distance, adjacency, and economic distance weight matrices, respectively.After changing matrices, variable coefficients and significance levels vary within acceptable ranges, passing the robustness test.

Conclusions, Limitations, and Recommendations
The advancement of digital village infrastructure aligns with the concept of sustainable development, increasingly showcasing "datafication, intelligence, and visualization" in rural development.Spatial regional interactions during this process show that digitalization in villages can promote or inhibit the green allocation efficiency of agricultural water resources in surrounding provinces through spatial clustering or siphoning effects.This study develops an input-output indicator system that integrates ecological, economic, and natural aspects to measure agricultural water resource allocation efficiency.This study uses 2011 provincial data to empirically investigate how digital village construction impacts the green allocation efficiency of agricultural water resources using a time-fixed effects spatial Durbin model.Conclusions include the following: (1) Rural digital economy planning significantly enhances a province's green allocation efficiency of agricultural water resources but may inhibit improvements in neighboring provinces.Varying thresholds of digital development enhancement across provinces suggest that exceeding an optimal level may impede efficiency improvements, underscoring the need to tailor informatization reforms to the realities of rural development.(2) The global Moran index indicates that provincial digital villages create effective spatial spillover effects through a collaborative input-output system, enhancing the green allocation efficiency of agricultural water resources.The local Moran index uncovers "siphon effects" within provinces, with high-high clustering amidst high-low clustering, suggesting that "exploitative neighbor" dynamics outweigh "good neighborliness", impeding cross-provincial advancement.(3) Spatially, advancements in agricultural informatization direct production factor flows within provinces, speeding up the adoption of green technologies in agricultural water resource management and enhancing allocation efficiency.Direct spillover effects of the comprehensive digital village index outweigh indirect effects, suggesting that rural informatization leads to increased green quality development and faster regional water resource allocation efficiency.
In the dataset of agricultural water resource green allocation efficiency, potential biases or limitations of the SE-SBM measurement model exist.These assumptions encompass inadequate control over all variables influencing agricultural water resource green allocation and incomplete capture of potential nonlinear relationships within the model.Moreover, it is imperative to acknowledge the possibility of unobserved variables affecting the relationship between digital village construction and agricultural water resource efficiency.Future research endeavors could address these issues by employing more comprehensive datasets, introducing new control variables, or utilizing more complex models.Additionally, recommendations for future studies include employing a combination of quantitative and qualitative methods and conducting field investigations and experimental research to gain deeper insights into the mechanisms through which digital village construction influences agricultural water resource efficiency.
Recommendations on agricultural water resource management with a focus on circular economy and sustainability include the following: (1) Persisting with a green development strategy centered on digital empowerment and structural upgrading, we must recognize the regional disparities in how digital villages enhance the utilization of green water resources.Localized and dynamic digital village reforms should be adopted to foster collaborative innovation and improve green allocation efficiency.This approach will ensure that water resources are utilized in a sustainable and circular manner, minimizing waste and maximizing efficiency.(2) Accelerating the integration of innovative technologies with traditional agricultural sectors is crucial to achieving in-depth reforms in agricultural water resource allocation.By analyzing spatial-temporal trends in digital village innovation, we can optimize allocation patterns to maximize agricultural green efficiency.Spatial networks can be leveraged to amplify both direct and indirect impacts, promoting a circular economy in water resource management.(3) By deepening the integrated management of regional water resources and building a cross-regional agricultural water use coordination mechanism, we can achieve the optimal allocation and efficient use of water resources.For arid areas, we should increase the research and 35].Moran's I is predominantly selected for spatial autocorrelation testing in most studies.It is categorized into global Moran's I and local Moran's I, represented by Formulas (3) and (4), respectively.Moran's I index ranges from −1 to 1, where positive, zero, and negative values represent spatial positive correlation, no spatial correlation, and spatial negative correlation, respectively.Positive values denote either high-high or lowlow aggregation of green allocation efficiency of agricultural water resources in neighboring areas, indicating spatial clustering characteristics.Negative values indicate either high-low or low-high aggregation, suggesting spatial dispersion characteristics.

Figure 1 .
Figure 1.Spatiotemporal distribution map of agricultural green water use efficiency.

Figure 1 .
Figure 1.Spatiotemporal distribution map of agricultural green water use efficiency.

Systems 2024 ,
12, 214 12 of 19clustering: H-H (high-efficiency provinces surrounded by similar provinces), L-H (lowefficiency provinces near high-efficiency ones), L-L (low-efficiency areas together), and H-L (high-efficiency provinces near low-efficiency ones).LISA maps indicate that, during 2017-2018, five provinces, including Beijing, Tianjin, Shanghai, Jiangsu, and Henan, demonstrated significant local spatial positive correlation.From 2017 to 2018 and 2020 to 2022, the strength of spatial connections and the number of provinces with local positive correlation markedly increased.In 2020, ten provinces showed H-H clustering, demonstrating a positive spatial clustering effect; in 2022, seven provinces exhibited this pattern.These findings suggest that national policies and theoretical practices have contributed to a consistent rise in the local spatial correlation of China's agricultural water resource allocation efficiency.Additionally, they highlight disparities in spatial clustering within provinces, with many provinces exhibiting H-L clustering surrounding H-H clusters.This arises as core cities, seeking enhanced economic production efficiency, often relax environmental regulations, leading to an "east high, west low" pattern in agricultural water resource allocation efficiency.

Figure 2 .
Figure 2. Local Moran index LISA map within the province.

Figure 2 .
Figure 2. Local Moran index LISA map within the province.

Table 2 .
Digital village indicator system.

Table 4 .
Regional measurement of agricultural green water use efficiency.

Table 5 .
Results of the baseline regression model.

Table 6 .
Global Moran's I of independent and dependent variables.

Table 8 .
Regression results of the SDM.

Table 9 .
Regression results of direct, indirect, and total effects.

Table 10 .
Robustness test of spatial effects 1.
Note: *** indicate significance at the 1% significance levels, respectively, and the standard errors are in parentheses.

Table 11 .
Robustness test of spatial effects 2.