Temporal and Spatial Analysis: The Impact of Virtual Water Flows on Agricultural Production Efficiency in China

Abstract

Panel data from 30 provinces in China spanning the years from 2007 to 2022 were selected. Regional virtual water flows were calculated based on the principle of social equity, and agricultural production efficiency was measured using the Super-SBM model, which overcomes the issue of being unable to measure efficiency values when they exceed 1 for decision-making units. Based on the aforementioned estimation results, methods such as ArcGis and kernel density estimation were employed to illustrate the changing trends of virtual water flows and agricultural production efficiency in key years. Additionally, a fixed-effects model was used to explore the relationship between the two. The following conclusions are drawn: (1) The overall pattern of virtual water trade in grain exhibits a “north-to-south grain transportation” flow, with the volume of transfers increasing annually, which is contrary to the spatial distribution of water resources. Regions with a net outflow of virtual water in grain are mostly concentrated in major grain-producing areas such as the northeast, while provinces with a net inflow are mainly concentrated in economically developed regions such as South China, Southeast China, and the middle and lower reaches of the Yangtze River. (2) The average agricultural production efficiency shows a fluctuating upward trend, with an overall “S”-shaped pattern in a horizontal view, and the overall differences in production efficiency among provinces have widened. (3) Agricultural production efficiency exhibits an inverted “U”-shaped trend with the increase in virtual water flows, a conclusion that remains valid after a series of robustness tests. Therefore, corresponding suggestions are proposed based on the above conclusions, including formulating a scientific virtual water trade strategy and improving agricultural production efficiency.

1. Introduction

Water is a foundational element for sustaining agricultural survival and development, and the effective allocation of water resources is closely linked to issues such as regional food security and agricultural economic growth [1]. According to the “2024 United Nations World Water Development Report,” agricultural water use accounts for 70% of freshwater usage, with irrigation water accounting for the largest share and increasing annually. However, with the overuse of natural resources and massive emissions of greenhouse gases [2,3], extreme weather events such as high temperatures have become frequent worldwide, leading to a growing shortage of freshwater resources that has severely impacted agricultural development [4,5,6]. Meeting agricultural water demand has thus become a prerequisite for sustainable agricultural development [7].

In recent years, under the constraints of geographical limitations and resource imbalances, issues such as water scarcity and imbalance in water distribution have become increasingly prominent in China, further exacerbating the contradiction between agricultural water supply and demand and thereby endangering agricultural production efficiency. Therefore, China needs to move beyond traditional solutions and urgently seek new measures for water resource allocation. The introduction of the virtual water theory breaks away from the traditional approach of addressing water resource allocation centered solely on “water” and begins to explore measures to solve internal regional problems outside the region where the problems arise. By revealing the flow and transformation processes of water resources within agricultural ecosystems, it provides a new approach to alleviating the imbalance in the spatial distribution of water resources and optimizing the mismatch between water and soil resources. Against this backdrop, a series of important questions arise: What are the dynamic effects of virtual water flows? How do they impact agricultural production efficiency? Clarifying these questions holds significant practical importance for promoting agricultural production efficiency and driving the high-quality development of agriculture, rural areas, and farmers. This paper examines agricultural production efficiency from the perspective of virtual water flow. By revealing the patterns of virtual water movement, it provides references for addressing regional water scarcity issues and, to a certain extent, enriches the assessment of factors influencing agricultural production efficiency, offering a theoretical basis for formulating scientific agricultural development strategies tailored to different regional types.

The research structure of the paper is as follows: Section 2 presents a literature review, Section 3 provides a theoretical analysis, Section 4 introduces the models and variables, Section 5 analyzes the empirical results, and Section 6 offers conclusions and recommendations.

2. Literature Review

Most studies on agricultural production efficiency focus on efficiency measurement, influencing factors, and differential evaluation. Firstly, the mainstream methods for measuring agricultural production efficiency include the Stochastic Frontier Analysis (SFA model), Data Envelopment Analysis model (DEA), extended DEA models (such as SBM and EBM models), and the Malmquist index model [8,9,10,11]. Secondly, regarding influencing factors, agricultural production efficiency is primarily affected by agricultural production factors and their allocation methods. Some scholars have found that digital technology can effectively boost agricultural production efficiency, especially on moderately scaled land [12,13]. However, in China, non-scale agricultural operations account for 98%, with small-scale farmers being the main agricultural operators. Due to long-term capital constraints, small-scale farmers are gradually marginalized in accessing technological factors [14], making it difficult for them to produce according to the optimal input ratio of factors, thus keeping production efficiency at a low level. Gai Qing’en et al. [15] state that the equal distribution of land easily leads to resource misallocation, hindering agricultural green production efficiency [3]. Land transfer can facilitate the conversion from low-efficiency farmers to high-efficiency farmers, thereby optimizing the allocation of resources among factors and improving agricultural production efficiency. Markussen [16] and Melesse et al. [17] argue that land tenure confirmation can significantly enhance farmers’ perception of land tenure stability and security, effectively stimulating their production enthusiasm, with this effect being more pronounced in areas with good basic conditions [18]. Meanwhile, Liu et al. [19] suggested that the government can improve agricultural production efficiency by enhancing the agricultural support service system and formulating cooperative development policies. Additionally, other factor inputs such as agricultural machinery equipment, fertilizer, and energy use also have significant impacts on agricultural production efficiency [20,21]. Thirdly, in terms of differential evaluation, China’s agricultural production efficiency shows an overall steady upward trend but regional disparities are widening. Hsu et al. [22] found that China’s agricultural production efficiency decreases from the east to the west and then to the central regions. Liu Yihang [23] discovered that family farms have significantly higher agricultural production efficiency than small-scale farmers, and the production efficiency of family farms exhibits an inverted “U”-shaped relationship with their operating scale.

The term “virtual water” was first proposed by British scholar Allan, referring to the volume of water embodied in products and services [24]. Virtual water trade breaks the traditional “water-centric” approach to addressing water scarcity by integrating the economic and social systems with the water resource system [25]. Analyzing the invisible flow pattern of water resources embedded in grain trade is of great importance for ensuring food security and revealing the deep logical relationship between agricultural economic development and water resource utilization [26]. In recent years, many scholars have begun to conduct extensive research on virtual water flows. In terms of virtual water flow measurement, global-scale virtual water flows are mainly measured through trade data lookup methods [27], which are only applicable to global or regional contexts with complete trade data. The measurement of virtual water flows within a specific country or region mainly employs methods such as the principle of trade equity [28] and input–output models [29,30]. Existing studies indicate that China’s virtual water flows present a pattern from north to south, from inland to coastal areas, and from economically underdeveloped to economically developed regions [31,32], which is opposite to the spatial distribution of water resources. This flow pattern alleviates water resource pressure in grain-importing regions but also exacerbates the imbalance in water resource allocation between the north and south. In terms of the benefit evaluation of virtual water trade, research has primarily focused on its water-saving and economic effects. Luan et al. [33] argue that grain virtual water trade can ensure food security while saving water through trade, especially in water-scarce regions where implementing virtual water transfer policies can alleviate local water resource pressure [34]. Liu et al. [35] believe that implementing virtual water trade strategies within a local scope can effectively exert their water-saving effects and increase water use efficiency. The economic benefits of virtual water trade are also quite significant, mainly achieved by allocating water resources saved through trade to high-yield sectors [36] or importing agricultural products with high virtual water content by leveraging comparative advantages [37], thereby realizing Pareto improvements in output sectors. Additionally, the ecological, resource, and social benefits of virtual water trade are gradually gaining attention.

The existing literature offers a certain reference value for studying the relationship between virtual water flow and agricultural production efficiency, yet the following issues warrant further exploration: First, few scholars have applied virtual water theory to the agricultural sector. Only by clarifying the internal mechanisms linking virtual water flow and agricultural production efficiency can more effective resource allocation be achieved. Second, previous evaluations of virtual water trade have predominantly focused on theoretical aspects, lacking empirical testing, which leaves room for improvement in applying virtual water theory to practical problems. This study utilizes data from 30 Chinese provinces spanning the years from 2007 to 2022: First, it calculates virtual water flow volumes based on the principle of social equity and employs ArcGis to analyze the spatial patterns and evolutionary processes of virtual water flow. Second, it utilizes the Super-SBM model, incorporating land, labor, capital, irrigated area, and technology as input factors, agricultural gross output value as the desired output, and agricultural non-point source pollution and agricultural carbon emissions as undesired outputs, to measure China’s agricultural production efficiency. Third, it demonstrates the impact of virtual water flows on agricultural production efficiency from both theoretical and empirical perspectives while supplementing suggestions on how to improve agricultural production efficiency, providing a reference for scientifically formulating virtual water trade strategies.

3. Theoretical Analysis

The flow of virtual water in grain essentially reflects the cross-regional transfer of grain. Theoretically, the larger the net outflow of virtual water, the stronger the agricultural production capacity of the region, indicating a lower risk of external constraints on food security and is more favorable for ensuring regional food security. However, when the net outflow of virtual water in grain is too high, the water resources and ecological pressure in the region will significantly increase, which is not conducive to improving agricultural development.

From the perspective of resource endowment, regions with higher water resource endowments can optimize the allocation of water resources in agricultural production, reduce dependence on other production factors, improve the output efficiency per unit of water resources, and thus achieve Pareto improvements in the agricultural production sector. When a region lacks water resources, the sustainability of agricultural production cannot be guaranteed, easily forming “growth resistance” in agricultural development. Therefore, when the net outflow of virtual water in grain increases within a certain range, the region can more fully utilize limited water resources, further improve the output efficiency per unit of water resources by optimizing the production structure, and promote the improvement of agricultural production efficiency through the technology diffusion effect brought by trade. However, given that grain is a water-intensive product, the improvement in agricultural production efficiency brought by the outflow of virtual water in grain exhibits diminishing marginal returns. When the net outflow of virtual water in grain exceeds a certain inflection point, it will have an adverse impact on regional agricultural production efficiency. This is because long-term high virtual water outflow leads to excessive water consumption, sharply increasing the ecological pressure index within the region. Moreover, when a region excessively relies on grain exports, it leads to the simplification of its internal production structure and rigid adjustments to the production structure, which is not conducive to improving agricultural production efficiency.

From the perspective of economic technology, agricultural technological progress is a significant means to promote agricultural and rural modernization and a practical force for improving the production efficiency of “China’s granary.” The realization of technological progress is largely influenced by the local economic level. Regions with stronger economic strength often have stronger technological innovation capabilities and are better able to drive agricultural development. It is worth noting that when the net outflow of virtual water in grain in a certain region is at a high level, it indicates that the region attaches great importance to grain production. However, over the years, the per capita income of rural households in major grain-producing areas has been significantly lower than that in major grain-consuming areas, and the absolute income gap has been widening. Low-income levels lead to significant disadvantages for residents in terms of grain production capacity, trading capacity, and acquisition capacity, which will hinder the improvement of agricultural production efficiency in the long run. Additionally, although virtual water trade has formed a water-saving effect at the national scale, it has also constrained the economic and social development of the exporting regions to a certain extent. From the perspective of economic structure optimization, virtual water exporting regions can obtain partial economic benefits through grain trade, but compared with the secondary and tertiary industries, the agricultural industry still has a significant price disadvantage in terms of revenue acquisition. This phenomenon mainly stems from the lower allocation efficiency of production factors in agriculture compared with the secondary and tertiary industries, and under existing conditions, it is difficult for the agricultural sector to significantly improve production efficiency through technological innovation. Assuming that the water use efficiency of various industrial sectors remains unchanged and the law of diminishing returns to scale is not considered, if all virtual water is invested in the secondary and tertiary industries, the marginal returns of the secondary and tertiary industries will be significantly higher than those that can be obtained by the agricultural sector.

In summary, hypothesis H1 is proposed: The relationship between the net outflow of virtual water in grain and agricultural production efficiency exhibits an inverted “U”-shaped relationship. That is, the net outflow of virtual water in grain is positively related to agricultural production efficiency within a certain range, but beyond a certain inflection point, it will have a negative impact on regional agricultural production efficiency.

4. Models and Variables

4.1. Research Methodology

4.1.1. Calculation of Regional Virtual Water Flows

This study is based on the following three assumptions when calculating virtual water flow:

(1)

Principle of non-interference from external factors: Given that China’s grain self-sufficiency rate remains above 95%, so there is no need to consider the impact of import and export trade on regional virtual water flows in grain [38].

(2)

Principle of social equity: Without considering the actual flow direction of agricultural products, we assume that the per capita grain consumption is the same across all provinces, and that the opportunity for grain to be transferred from importing regions to exporting regions is equal.

(3)

Principle of constant grain reserves: We assume that all grain produced in a given year is consumed within that year.

The specific formula for calculating virtual water flows is as follows:

$$V_{wfj}=\left\{\begin{array}{l}\mathsf{\Delta }{A}_j{V}_{wcj}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}(\mathsf{\Delta }{A}_j\le 0)\\ {\displaystyle \sum _{i=1}^n}\mathsf{\Delta }{A}_{ij}{V}_{wci}\hspace{1em}\hspace{1em}\hspace{1em}(\mathsf{\Delta }{A}_j<0)\end{array}\right.$$

(1)

$$\mathsf{\Delta }{A}_j=G_j-P_{j}G/P$$

(2)

In the formula, Vwfj represents the flow of virtual water in the j-th provincial administrative region; ΔAj represents the grain trade volume of the j-th provincial administrative region, where positive values indicate grain-exporting regions and negative values indicate grain-importing regions; Gj represents the grain production of the j-th province; G represents the national grain production; Pj represents the population of the j-th province; P represents the national population; Vwcj represents the per unit grain virtual water content of the j-th provincial administrative region; ΔAij represents the grain quantity transported from the i-th grain-exporting region to the j-th provincial administrative region, where i = 1, 2, 3……n; Vwci represents the per unit grain virtual water content of the i-the grain-exporting region. (The per unit virtual water content of provincial administrative regions draws on the research by Wang et al. [39].)

$$\mathsf{\Delta }{A}_{ij}=\mathsf{\Delta }{A}_i^{out}{\alpha }_{i-j}$$

(3)

Here, ΔAiout represents the grain export volume of the i-th province; αi−j represents the grain transfer coefficient from the i-th province to the j-th province, indicating the possibility of grain trade between the two regions.

$${\alpha }_{i-j}={\displaystyle \frac{k\frac{\mathsf{\Delta }{A}_i^{out}\mathsf{\Delta }{A}_j}{D_{ij}^2}}{{\sum }_{j=1}^{n}k\frac{\mathsf{\Delta }{A}_i^{out}\mathsf{\Delta }{A}_j}{D_{ij}^2}}}$$

(4)

In the formula, k represents the gravitational coefficient; Dij denotes the distance between the capital city of the i-th province and the capital city of the j-th provincial administrative region.

4.1.2. Super-SBM Model

The traditional DEA does not account for the impact of undesirable outputs on the efficiency of decision-making units (DMUs), and it also suffers from biases due to pre-set perspectives and radial measures. In response to these limitations, Tone [40] proposed the Slacks-Based Measure (SBM) model, which avoids the problem of the inability to calculate slack variables in DEA. However, the SBM model has a limitation in that it cannot compare efficient DMUs during efficiency measurement, often leading to multiple DMUs having the same efficiency score. Therefore, Tone combined the super-efficiency model with the SBM model to propose the Super-SBM model. This model addresses the shortcomings of the aforementioned two models by considering slack variables and overcoming the issue of unmeasurable efficiency values when the efficiency score of a DMU is greater than 1, thus better aligning with practical needs. The specific model is as follows:

$$\rho =\mathit{min}{\displaystyle \frac{\frac{1}{m}{\sum }_{i=1}^m\frac{{\overline{x}}_i}{x_{ik}}}{\frac{1}{s_1+s_2}({\sum }_{r=1}^{s_1}\frac{{\overline{y}}_r^g}{y_{rk}^g}+{\sum }_{t=1}^{s_2}\frac{{\overline{y}}_t^b}{y_{tk}^b})}}$$

(5)

$$s.t.\left\{\begin{array}{c}\overline{x}\ge {\displaystyle \sum _{j=1,j\ne k}^n}{x}_j{\lambda }_j\hfill \\ {\overline{y}}^g\le {\displaystyle \sum _{j=1,j\ne k}^n}{y}_j^g{\lambda }_j\hfill \\ {\overline{y}}^b\ge {\displaystyle \sum _{j=1,j\ne k}^n}{y}_j^b{\lambda }_j\hfill \\ \overline{x}\ge x_0,{\overline{y}}^g\le y_0^g,{\overline{y}}^b\ge y_0^b,{\overline{y}}^g\ge 0,\lambda \ge 0\end{array}\right.$$

(6)

Here, ρ is the efficiency value of the DMU. When ρ ≥ 1, it indicates that the DMU is relatively efficient, and the larger the ρ value, the higher the efficiency of the DMU; k represents the k-th decision-making unit; $x_{ik}$, $y_{rk}^g$, $y_{tk}^b$ respectively represent the actual values of the input variable, expected output variable, and unexpected output variable, while ${\overline{x}}_i$, ${\overline{y}}_r^g$, ${\overline{y}}_t^b$ respectively represent the target values of the corresponding input–output variables; m, s1, and s2 respectively represent the number of indicators for the input, expected output, and unexpected output vectors; λ is the weight vector of the DMU.

4.1.3. Kernel Density Estimation

This method is used to visually display the distribution characteristics of the data itself and is currently a representative statistical method for analyzing differences and changes in geographical features [41]. Compared to traditional parametric estimation, this method allows the research subject to escape the influence of unknown parameters. The specific model is as follows:

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

(7)

Here, N is the sample size, h is the bandwidth, K is the kernel function, Xi are independently and identically distributed sample values, and x is the mean. In this paper, X1, X2, …, Xi represent the agricultural production efficiency of various regions, and f(x) is the estimated value. Since kernel density curve is sensitive to the bandwidth h, this paper selects a small bandwidth to improve the estimation accuracy. Meanwhile, this study adopts the commonly used Gaussian kernel function, as shown in the following formula:

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

(8)

4.1.4. Fixed Effects Model

$$AP{E}_{it}={\alpha }_0+{\alpha }_{1}V{W}_{it}+{\alpha }_{2}V{W}_{it}^2+{\alpha }_{3}Control{s}_{it}+{\lambda }_i+{\mu }_t+{\epsilon }_{it}$$

(9)

In Equation (9), APEit represents the agricultural production efficiency of province i in year t; VWit denotes the net outflow of virtual water for grain in province i in year t; Controlsit indicates a series of control variables that may affect agricultural production efficiency; λi represents the individual fixed effect, μt denotes the time fixed effect; and ϵit stands for the random disturbance term.

4.2. Variable Selection

4.2.1. Dependent Variable

Agricultural production efficiency (APE). Efficiency values are calculated according to Equations (5) and (6). The input variables include the following: (1) land (in thousands of hectares), represented by the sown area of crops; (2) labor (in ten thousand people), represented by the number of the primary sector employees; (3) capital (in hundred million yuan), represented by the investment in productive fixed assets of rural households; (4) irrigation (in thousands of hectares), represented by the effectively irrigated area; and (5) technology (in ten thousand kilowatts), represented by the total power of agricultural machinery. The desirable output indicator is total agricultural production value (in hundred million yuan), while the undesirable output indicators are agricultural carbon emissions and agricultural non-point source pollution.

4.2.2. Core Explanatory Variable

Virtual water flows (VW). Following the approach of Tian Guiliang et al. [42], the net transfer volume of virtual water in grain is selected as the core explanatory variable. The data are calculated based on the principle of social equity and have been standardized.

4.2.3. Control Variables

(1) Education level (EDU), represented by the average years of education per rural resident. Higher education levels among farmers enhance their adaptability to market demands and changes, facilitating the adoption of scientific methods and advanced technologies in agricultural production activities. (2) Rural consumption structure transformation (RCS), represented by the Engel’s coefficient of rural households. The Engel’s coefficient, to some extent, reflects the local economic level. A lower Engel’s coefficient is more likely to prompt farmers to reduce their reliance on traditional intensive agriculture and shift towards more efficient and modern agricultural production methods, thereby improving agricultural production efficiency. (3) Urban–rural income gap (IG), represented by the ratio of per capita disposable income between urban and rural residents. (4) Urbanization rate (UR), represented by the ratio of urban population to the resident population in a given region. Advances in production efficiency often coincide with economic growth, and urbanization is a significant engine driving economic growth in China at this stage, with a notable impact on agricultural production efficiency. (5) Financial support for agriculture (AF), represented by the proportion of agricultural fiscal expenditure in total fiscal expenditure. The government can improve agricultural production conditions by providing infrastructure and also support agricultural technology, promoting the modernization of agriculture and rural areas, which is of great significance for enhancing agricultural production efficiency. (6) Agricultural disaster rate (AD). Represented by the ratio of the affected crop area to the sown area, it primarily reflects the impact of uncontrollable climatic factors on agricultural production efficiency.

4.3. Data Sources and Descriptive Statistics

4.3.1. Data Sources

The research period for this paper spans 16 years from 2007 to 2022. The study covers 30 provinces in China, with Tibet, Hong Kong, Macao, and Taiwan excluded due to limitations in data availability. The specific data sources are as follows: (1) Among the evaluation indicators, data on grain output, sown area of crops, productive fixed asset investment of rural households, irrigated area, total power of agricultural machinery, and carbon emissions are sourced from the China Rural Statistical Yearbook, China Environmental Statistical Yearbook, and statistical yearbooks of various regions from 2008 to 2023, while population-related data are obtained from the China Population and Employment Statistics Yearbook from 2008 to 2023. (2) Data for control variables are primarily derived from the China Statistical Yearbook and statistical yearbooks of various regions from 2008 to 2023. (3) The distances between provinces are based on the distances between their provincial capitals, with data obtained by querying AutoNavi Maps. For a small number of missing data points, linear interpolation or queries from local statistical bulletins were used to fill in the gaps.

4.3.2. Descriptive Statistics

Descriptive statistics were generated using the sum command in Stata 18. According to the results shown in

Table 1. Descriptive statistics of variables.

Variable	Sample Size	Mean	Standard Deviation	Minimum Value	Maximum Value
APE	480	1.03	0.081	0.877	1.58
VW	480	−0.06	17.8	−60.5	88
EDU	480	7.74	0.657	5.72	10.1
RCS	480	0.358	0.066	0.238	0.56
IG	480	2.64	0.439	1.83	4.21
UR	480	0.575	0.134	0.282	0.896
AF	480	0.11	0.033	0.0291	0.204
AD	480	0.176	0.143	0	0.696

, the mean value of agricultural production efficiency is 1.03, with a standard deviation, maximum value, and minimum value of 0.081, 1.58, and 0.877, respectively. This indicates significant regional disparities in agricultural production efficiency, meeting the basic requirements for data differentiation in econometric analysis.

5. Empirical Results

5.1. Trends in Virtual Water in Grain and Agricultural Production Efficiency

To better analyze the trends in virtual water flow between regions, this paper divides China’s 30 provinces into northern and southern regions, as well as eight major regions. (In accordance with the practice of the Office of the Soft Science Committee of the Ministry of Agriculture, the 31 provinces are divided into eight major regions: (1) The northeast region includes Heilongjiang, Jilin, Liaoning, and Inner Mongolia; the North China region comprises Beijing, Tianjin, and Shanxi; the Huang-Huai-Hai region covers Hebei, Henan, Shandong, and Anhui; the northwest region consists of Shaanxi, Gansu, Ningxia, Qinghai, and Xinjiang; the southeast region includes Shanghai, Zhejiang, and Fujian; the middle and lower reaches of the Yangtze River region encompasses Jiangsu, Hubei, Hunan, and Jiangxi; the South China region comprises Guangdong, Guangxi, and Hainan; the southwest region includes Chongqing, Sichuan, Guizhou, Yunnan, and Tibet. (2) The northern region consists of the Northeast, North China, Huang-Huai-Hai, and northwest regions, while the southern region includes the southeast and middle and lower reaches of the Yangtze River, South China, and southwest regions.), These regions are based on the classification principles of the Soft Science Committee Office of the Ministry of Agriculture. Based on this classification, and using the principle of social equity and Formulas (1) to (4), inter-provincial virtual water flows from 2007 to 2022 were calculated (

Table 2. Volume of virtual water transfer for grain in each province (Municipality Directly Under the Central Government, Autonomous Region).

Region	Province	Virtual Water Transfer Volume of Grain (in km3)				Region	Province	Virtual Water Transfer Volume of Grain (in km3)
		2007	2012	2017	2022			2007	2012	2017	2022
North China	Beijing	−5.95	−9.36	−11.7	−12	Southeast China	Shanghai	−7.7	−11.1	−12.8	−13.2
	Tianjin	−3.05	−5.21	−5.35	−4.82		Zhejiang	−14.3	−20.6	−27.6	−30.8
	Shanxi	−2.98	−2.95	−3.34	−2.54		Fujian	−8.7	−12.3	−17.7	−17.6
Northeast China	Inner Mongolia	9.46	15.7	22.7	29.5	Middle and Lower Reaches of Yangtze River	Jiangsu	2.21	−1.87	−4.52	−4.54
	Liaoning	2.49	2.32	3.97	6.04		Jiangxi	3.04	1.91	1.18	−0.635
	Jilin	15.4	23.9	32.5	32.3		Hubei	−0.0725	−0.774	0.667	−1.16
	Heilongjiang	27.9	58	81.2	88		Hunan	3.17	1.83	−0.775	−2.33
Huang-Huai-Hai Region	Hebei	1.64	0.876	3.09	2.42	Southwest China	Chongqing	0.0425	−1.9	−4.96	−6.07
	Anhui	7.01	8.85	14.8	14.3		Sichuan	−1.11	−2.46	−5.31	−7.05
	Shandong	4.09	2.2	4.69	4.46		Guizhou	−3.36	−5.98	−6.86	−9.523
	Henan	12.3	11.2	14	14.9		Yunnan	−3.19	−3.36	−4.75	−4.18
Northwest China	Shaanxi	−3.51	−4.4	−7.1	−6.91	South China	Guangdong	−27.7	−40.6	−53.7	−60.5
	Gansu	−1.9	0.0195	−1.1	0.579
	Qinghai	−1.28	−1.96	−2.24	−2.35		Guangxi	−5.02	−6.76	−11.6	−12.5
	Ningxia	1.71	1.71	0.703	0.411
	Xinjiang	1.14	5.5	5.81	10.4		Hainan	−1.71	−2.48	−4.03	−4.48

Note: “−” indicates a net inflow of virtual water in grain.

and Figure 1), leading to the following conclusions:

(1) From an overall flow perspective, grain trade generally exhibits a pattern of “grain flowing from north to south,” with the volume of virtual water in grain flows increasing year by year. As shown in Table 2, in 2007, there were 14 net grain-exporting provinces nationwide, including 10 in the north and 4 in the south, with the volume of virtual water in grain flowing from the north to the south amounting to 64.5 km³. In 2012, there were 13 net grain-exporting provinces, with 11 in the north and 2 in the south, and the net volume of virtual water in grain exported from the north was 106.4 km³. In 2017, there were 12 net grain-exporting provinces, again with 10 in the north and 2 in the south, and the net volume of virtual water in grain exported from the north remained at 152.6 km³. By 2022, the number of net grain-exporting provinces nationwide had decreased to 11, all located in the north, with the volume of virtual water in grain flowing from the north to the south reaching 174.7 km³, an increase of 110.2 km³ compared to 2007. It can be observed that over time, the number of provinces with a net outflow of virtual water in grain in China has decreased year by year, and the pressure of grain production has concentrated in the north. Although this trend has, to some extent, aggregated the resource advantages of the northern region and contributed to achieving Pareto improvements in the agricultural production sector, the excessive concentration of grain production pressure may simultaneously render the northern region more vulnerable to water resource issues. In the long run, this may not be conducive to food security and could affect the overall trend of agricultural production efficiency.

(2) From the overall perspective of grain, the main outflow provinces of virtual water in grain are located in Northeast China and the Huang-Huai-Hai region. In 2022, the combined virtual water outflow from these two regions accounted for 94.67% of the total national outflow. Among them, Northeast China had the largest virtual water outflow, which increased year by year. In 2022, the virtual water outflow in the Northeast region reached 155.8 km³, representing an increase of 182.06% compared to the base year. The virtual water outflow in the Huang-Huai-Hai region in 2022 was 36.1 km³, an increase of 11 km³ compared to 2007, with an average annual increase of 2.94%. The regions with a relatively large inflow of virtual water are South China and Southeast China. In 2022, the combined virtual water inflow from these two regions accounted for 68.45% of the total national inflow. Among them, South China had an inflow of 77.5 km³ billion m³ in 2022, an increase of 43.1 km³ compared to 2007, with an average annual growth rate of 8.35%. Southeast China had an inflow of 61.6 km³ in 2022, an increase of 30.9 km³ compared to 2007, representing a growth rate of 100.65%. Southwest China and North China are also major regions with virtual water inflow. In addition, the middle and lower reaches of the Yangtze River and Northwest China have relatively small volumes of virtual water transfer in grain, basically achieving self-sufficiency in virtual water in grain.

(3) From the provincial perspective, in 2007, the top three provinces in terms of virtual water outflow in grain were Heilongjiang, Jilin, and Henan, with virtual water transfers of 27.9 km³, 15.4 km³, and 12.3 km³, respectively. Correspondingly, the top three provinces in terms of virtual water inflow in grain were Guangdong, Zhejiang, and Fujian, with virtual water transfers of 27.7 km³, 14.3 km³, and 8.7 km³, respectively. In 2022, the top three provinces in terms of outflow were Heilongjiang, Jilin, and Inner Mongolia, all located in the Northeast region. This phenomenon may be attributed to the Northeast region’s special agricultural strategic positioning. As China’s largest grain production base, the Northeast region actively responds to and implements the policy objective of “consolidating the foundation of food security and achieving a balanced domestic grain production–demand relationship,” fully playing its main role in agricultural production and grain supply. Meanwhile, by promoting agricultural modernization and industrial upgrading, it continuously enhances grain production capacity to ensure the stability and security of grain supply. Moreover, the Northeast region boasts significant agricultural resource endowments, including fertile black soil and abundant mineral resources, creating natural advantages for its agricultural production. Correspondingly, the top three provinces in terms of virtual water inflow in grain remain Guangdong, Zhejiang, and Fujian. These provinces, with large populations and rapid economic development, have seen a significant portion of their arable land resources occupied by urban construction, making it impossible to achieve grain self-sufficiency. Therefore, they need to import grain from outside the province.

5.2. Trends in Agricultural Production Efficiency

Based on Equations (5) and (6), we used the Super-SBM model in Dearun v3.2.0.5 software to calculate the agricultural production efficiency values for each province, and the results are shown in

Table 3. Agricultural production efficiency in each province (Municipality Directly Under the Central Government, Autonomous Region).

Province (Municipality, Autonomous Region)	2007	2012	2017	2022	Regional Average
Beijing	1.08	1.11	1.21	1	1.1
Tianjin	1.03	1.02	1.15	1.02	1.06
Hebei	0.833	0.871	0.91	0.894	0.877
Shanxi	0.896	1.02	1.082	0.93	0.982
Inner Mongolia	0.965	0.956	1.01	1.11	1.01
Liaoning	1.02	1.02	0.912	1.05	1
Jilin	1.03	0.992	1.08	1.02	1.03
Heilongjiang	1.13	0.984	1.05	1.03	1.05
Shanghai	1.13	0.859	1.03	1.22	1.06
Jiangsu	1.06	1.05	1.06	1.23	1.1
Zhejiang	1.03	1.01	1.08	1.12	1.06
Anhui	1.02	1.05	1.08	1.04	1.05
Fujian	1.03	1.05	1.08	1.13	1.07
Jiangxi	1.01	1	1.07	1.03	1.03
Shandong	1.21	1.27	1.26	1.25	1.25
Henan	1.12	1.11	1.15	1.14	1.13
Hubei	1.07	1.03	1.07	1.04	1.05
Hunan	1.04	0.893	0.931	1.06	0.981
Guangdong	1.04	1.04	1.06	1.03	1.04
Guangxi	1.03	1.03	1.09	1.06	1.05
Hainan	1.01	1.02	1.08	1.11	1.06
Chongqing	1.1	1.05	1.09	1.11	1.09
Sichuan	1.04	1.04	1.11	1.12	1.08
Guizhou	0.993	1.08	1.15	1.04	1.07
Yunnan	1.03	0.964	1.07	1.11	1.04
Shaanxi	0.999	1.02	1.07	1.1	1.05
Gansu	0.895	1.03	1.17	0.934	1.01
Qinghai	1.13	1.07	1.05	1.02	1.07
Ningxia	0.876	1.02	1.03	1.03	0.989
Xinjiang	1.1	1.05	1.09	1.1	1.09
National average	1.03	1.02	1.08	1.07	1.05

. The average agricultural production efficiency value for China in 2022 was 1.07, with the efficiency values of all provinces except for a few, such as Hebei, Shanxi, and Gansu, exceeding 1. However, there is still significant room for improvement compared to the higher agricultural production efficiencies of some provinces (e.g., Shandong with 1.25). During the sample period, the agricultural production efficiency in China’s major years exhibited a horizontal “S”-shaped trend. The efficiency values of 17 provinces, including Beijing, remained consistently above 1, while the agricultural production efficiency of Hebei Province consistently remained below 1. Compared to 2007, the agricultural production efficiency of six provinces, namely Beijing, Tianjin, Heilongjiang, Hubei, Guangdong, and Qinghai, decreased in 2022, with Qinghai experiencing the largest decline of 9.73%. Ningxia witnessed the largest increase in agricultural production efficiency, growing by 17.58%.

A comparison of China’s virtual water flow and agricultural production efficiency reveals a non-linear relationship between the two. For instance, Heilongjiang, Jilin, and Inner Mongolia—the top three provinces in net virtual water outflow—experienced fluctuating declines in agricultural production efficiency during the study period, despite their high water exports. In contrast, Shandong Province, with a relatively low net virtual water outflow, maintained significantly higher agricultural efficiency.

Figure 2 illustrates the distribution dynamics of agricultural production efficiency in China’s major years during the sample period. Specifically, the center of the kernel density curve generally shifted to the right, and after experiencing fluctuations in peak values, it slightly decreased compared to the base period. This indicates an overall improvement in agricultural production efficiency in China, but with a weakened degree of efficiency concentration and a gradual increase in regional disparities. Additionally, the area on the left side of the kernel density curve gradually decreased, while the area on the right side gradually increased. This suggests that the number of low-efficiency provinces in China has decreased, while the number of high-efficiency provinces has increased. When comparing this with the pattern of virtual water transfer and allocation, it is found that there are both similar and opposite trends in their changes, further indicating a possible non-linear relationship between agricultural water use and agricultural production efficiency.

5.3. Benchmark Regression Results

Using Stata 18, we analyzed the impact of virtual water flow (VW) on agricultural production efficiency.

Table 4. Benchmark regression results.

	(1)	(2)
	APE	APE
VW	0.111 **	0.144 ***
	(−0.172)	(0.088)
VW2	−0.0213 **	−0.0142 **
	(−0.0661)	(−0.0676)
EDU		0.115 *
		(−0.906)
RCS		0.18 **
		(−0.0744)
IG		−0.067 ***
		(−0.016)
UR		−0.081 *
		(−0.062)
AF		0.0735 **
		(−0.031)
AD		0.0811
		(−0.773)
cons	1.77 ***	1.4 **
	(−0.363)	(−0.549)
Individual Effects	Controlled	Controlled
Time Effects	Controlled	Controlled
N	201	201
R2	0.887	0.901

Note: ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. Robust standard errors are presented in parentheses, and the same applies below.

presents the regression results: Column (1) excludes control variables, while Column (2) includes them. Both columns show a significantly positive coefficient for the linear term (VW) and a significantly negative coefficient for the quadratic term (VW²), revealing an inverted U-shaped relationship. The inflection point (5.143) derived from Column (2) suggests that agricultural efficiency initially rises with VW but declines beyond this threshold. Notably, Heilongjiang, Jilin, and Inner Mongolia—provinces with grain-related VW outflows exceeding the inflection point—exhibit reduced efficiency as net outflows grow. Similarly, Henan and Anhui operate near their water endowment limits, while other provinces retain potential to improve efficiency through managed VW transfers. These findings confirm Hypothesis H1, emphasizing the need for regional VW transfer limits to optimize agricultural productivity.

Among the control variables, the education level of rural residents, the Engel’s coefficient of rural households, the urban–rural income gap, the intensity of fiscal support for agriculture, and the urbanization rate all passed the significance test, while the agricultural disaster rate did not. Specifically, the education level of rural residents, the Engel’s coefficient of rural households, and the intensity of fiscal support for agriculture have a significantly positive impact. However, the urban–rural income gap and the urbanization rate have a significantly negative impact. This may be attributed to the following reasons: (1) Regions with a large urban–rural income gap represent internal development imbalances, where labor is more inclined to migrate to urban areas with higher remuneration and better resource endowments. This often leads to a shortage of rural labor, affecting the continuity and efficiency of agricultural production. (2) In the process of promoting urbanization, a significant amount of agricultural production factors are squeezed out, making agriculture potentially more dependent on external resources. This may compromise its autonomy and efficiency, resulting in a decline in agricultural production efficiency.

5.4. Robustness Checks

To mitigate the impact of contingency on the research conclusions, robustness checks were conducted using methods such as replacing the core explanatory variable, controlling for endogeneity, and changing the regression model: (1) Replacing the core explanatory variable: The DEA-Malmquist productivity index method was employed to re-quantify the level of agricultural production efficiency, and regression analysis was performed again. (2) Endogeneity control: Considering the potential bidirectional causality between virtual water flow and agricultural production efficiency, the lagged value of the net virtual water outflow was used as an instrumental variable. The IV-GMM model was then utilized for regression analysis, which also helped to address endogeneity issues arising from time effects. (3) Changing the regression model: Given the possibility of censoring in the measurement of agricultural production efficiency for some samples, consistent estimators might not be obtainable through benchmark regression. Therefore, the panel Tobit model was employed for regression analysis.

Table 5. Robustness tests.

	(1) Replacing Core Explanatory Variable	(2) Endogeneity Control	(3) Changing Regression Model
VW	0.121 **	0.093 **	0.105 ***
	0.053	−0.037	−0.021
VW2	−0.0572 ***	−0.0411 ***	−0.072 ***
	0.006	0.011	0.024
Control Variables	Controlled	Controlled	Controlled
cons	0.231 ***	0.831 ***	0.337 *
	0.0734	0.238	0.187
Individual Effects	Controlled	Controlled	Controlled
Time Effects	Controlled	Controlled	Controlled
N	201	201	201
R2	0.887	0.901

presents the robustness check results. Across all three methods, the linear term coefficients remain significantly positive, while the quadratic term coefficients are significantly negative, aligning with the benchmark regression. This confirms the robustness of the inverted U-shaped relationship between net virtual water outflow and agricultural production efficiency.

6. Conclusions and Policy Implications

6.1. Research Conclusions

Utilizing panel data on virtual water flow and agricultural production efficiency across China’s 30 provinces from 2007 to 2022, this research employed ArcGIS and kernel density estimation techniques to thoroughly analyze the dynamic and static evolution patterns of these two variables. Through a fixed-effects model, the study uncovered several key findings: Firstly, regarding grain virtual water flow, a nationwide “north-to-south” trade pattern emerged, with volumes escalating annually, inversely mirroring the spatial distribution of water resources. Major grain virtual water exporters were predominantly located in northeastern agricultural powerhouses, while importers were clustered in economically advanced southern, southeastern regions, and the middle and lower Yangtze River areas. This flow exacerbated grain production pressures in northern regions, especially the northeast, heightening their susceptibility to water scarcity, potentially jeopardizing long-term food security and influencing overall agricultural production efficiency trends. Secondly, agricultural production efficiency, after undergoing fluctuations, showed a marginal increase compared to the baseline, following a horizontal “S”-shaped trajectory marked by initial decline, subsequent rise, and another decline (with turning points in 2012 and 2017). Inter-provincial disparities in agricultural production efficiency widened, with a decrease in low-efficiency provinces and an increase in high-efficiency ones. Thirdly, an inverted “U”-shaped nexus was identified between net virtual water outflow and agricultural production efficiency, a finding robust against various robustness tests, including variable substitution, endogeneity assessments, and model alterations. This underscores the importance of maintaining regional virtual water transfers within reasonable bounds to optimize water resource utilization. Additionally, rural residents’ education levels, rural Engel’s coefficients, and agricultural fiscal support intensity positively influenced agricultural production efficiency, whereas the urban–rural income gap and urbanization levels exerted negative impacts.

6.2. Discussion

This paper has validated some relevant conclusions and also uncovered some new ones, such as the following: (1) Some studies have indicated that the virtual water flow in China exhibits a zonal pattern of “from north to south” [42], and the water stress index in the north has already reached a high level [43]. This paper similarly finds a comparable trend in virtual water flow, albeit with slight differences at the provincial level. The top three provinces in terms of virtual water outflow are Heilongjiang, Jilin, and Inner Mongolia, with a growing trend of virtual water outflow concentration in the Northeast region. This trend is likely to continue intensifying in the coming period, posing significant risks to China’s food security. (2) When measuring agricultural production efficiency in the past, most scholars only considered agricultural carbon emissions as an undesirable output [44]. However, agricultural non-point source pollution, an important output factor in agricultural production activities, has rarely been taken into account in the literature, leading to potential biases in the measured agricultural production efficiency. By incorporating both carbon emissions and agricultural non-point source pollution into consideration, this paper finds that the overall level of agricultural production efficiency in China has improved, exhibiting a horizontal “S”-shaped trend of “decline-rise-decline again” during the sample period. (3) Current research on the evaluation of virtual water trade primarily focuses on its water-saving effects, economic effects, social effects, and ecological effects. Scholars have found that provinces with stable virtual water exports of grain, such as Heilongjiang, Inner Mongolia, Jilin, and Henan, often exhibit characteristics such as lagging economic development, rigid industrial structures, and unstable ecological benefits, with all indicators lagging behind those of major grain-consuming provinces [45]. Additionally, provinces experiencing a reduction in virtual water outflow during the transition period, such as Jiangsu, Sichuan, and Shandong, have seen a significant increase in economic growth while reducing their reliance on grain trade to sustain local fiscal revenues. This paper also points out in its analysis that the economic benefits derived from grain trade lag behind those of the secondary and tertiary industries. However, grain trade can, to a certain extent, promote the improvement of local agricultural production efficiency, but exceeding a certain limit will inhibit its development.

Therefore, based on the above analysis, the following targeted measures are proposed: (1) In response to the increasingly severe water stress index, lagging economic development, and fragile ecological environment in the northern regions, firstly, a comprehensive virtual water compensation policy should be established. By quantifying the economic and ecological benefits brought by virtual water inflow to regions, subsidies should be levied from areas with high virtual water imports of grain (such as the South China and Southeast regions) and compensated to virtual water export regions, following the principle of “who benefits, who compensates.” Secondly, the water-saving effect of virtual water trade should be fully utilized by moderately increasing imports of high water-consuming crops in international trade, gradually adjusting the regional agricultural product trade structure in the long term, restoring the ecological environment, and promoting balanced economic and social development among provinces. Finally, a new water resource management model that combines physical water and virtual water should be introduced. By fully considering the internal physical water resource endowments of regions, internal and external advantages should be compared, and external advantageous products should be introduced through virtual water strategies to save water resources consumed by the large-scale production of internal disadvantageous products, systematically addressing water scarcity issues. (2) For provinces where the virtual water export of grain exceeds the “U”-shaped inflection point, the outflow of virtual water of grain will reduce their agricultural production efficiency, and the economic benefits derived from grain trade lag behind those of the secondary and tertiary industries, insufficient to alleviate the pressure on the local ecosystem. Therefore, for these regions, firstly, the water-saving potential of crop varieties should be fully exploited by encouraging large-scale production of crops with comparative advantages, such as rice and wheat, while appropriately transferring high water-consuming crops like soybeans to other water-rich regions or regions with lower unit virtual water content for cultivation. Secondly, the improvement of agricultural production efficiency is related to the local economic development level and education level. Therefore, while ensuring national food security, these provinces should actively seek industrial transformation to improve the current slow economic development. In response to the low education level of workers, the state should urgently establish a diversified, full-chain “new farmer” training system to provide targeted skills training for workers at different levels. Additionally, by improving policy support, optimizing the industrial environment, and formulating incentive measures, scientific and technological talents should be attracted to engage in the grain industry, ensuring that talents are “attracted, retained, and utilized effectively,” providing a new engine for improving agricultural production efficiency. (3) To address the increasing regional disparities in agricultural production efficiency, agricultural technology exchange and sharing sessions should be established to promote the sharing and dissemination of agricultural technologies and management experiences from regions with high agricultural production efficiency (such as Shandong and Jiangsu), thereby achieving technological complementarity and coordination within the region and narrowing the gap in agricultural production efficiency among regions.

Limitations of this paper: (1) Relevant data on grain trade across Chinese provinces were not found, so the inter-provincial grain transportation volume was estimated based on the social equity method and the population and geographical distance of each province, which may introduce certain errors compared to the actual virtual water flow of grain. (2) When measuring virtual water, due to the difficulty in obtaining data on the trade flow of economic crop products, only grain crop products were used as the research object. Subsequent research should comprehensively consider the current research status of inter-provincial virtual water flow of agricultural products in China, examine the methods used in various studies, and further accurately calculate inter-provincial grain transportation volumes to better quantify inter-provincial virtual water flow of grain.