As a typical form of public resource, water resource can also run against the market failure such as ‘the tragedy of the Commons’ during allocation. According to the property right theories in the institutional economics, institutions are endogenous variables that determine the efficiency of economic operation. The clear definition of property rights can effectively mitigate the externalities and correct the market failure of public resource allocation, so as to improve social welfare (Coase, 2013). Therefore, It is a prerequisite for water rights transaction to clearly delimit the right to use water resources and conduct standardized confirmation registration. This system strengthens the exclusivity of water resources and highlights their economic value through market mechanism. Once farmers and organizations recognize the importance and value of water resources, it is cogent to advocate for farmers’ or regional pollution prevention. Studies have proved that building a clear and effectively protected property rights system is essential to encourage individuals to engage in productive activities and foster economic growth. There is a significant positive relationship between farmland right confirmation and farmers’ investment in the quality protection of cultivated land and green production (Qian et al., 2021; Zhou et al., 2023). This demonstrates that the effective delimitation and protection of property rights can stimulate the resource protection behaviors.

Even if the property rights are determined, there are various manifestations to express rules of competitive property rights. The price mechanism is one of the efficient ways to compete property rights. According to the theory of transaction cost in the institutional economics, one of the kernel goals of economic activities is to reduce the transaction cost. The direct impact of water rights trading on agricultural water use is reflected in the rising opportunity cost of increasing water use. To make the hidden cost of irrigation water explicit can promote water-saving in grain production. Studies have indicated that the low price of irrigation water is a significant contributor to water waste (Webber et al., 2008). The implementation of the water rights trading system has increased the opportunity cost of irrigation water, which has a similar effect to raising water price. Farmers constrained by costs will choose to improve their management mode of water use for grain production and reduce excessive water use. Conversely, water-saving farmers can increase their income through water rights trading. The continuous inefficient water use equals to the loss of potential income from water rights trading, which also encourages farmers to save water. In addition to changing water use habits and irrigation patterns, water rights trading can improve irrigation water efficiency by encouraging farmers to adopt water-saving technologies. Ma et al. (2022) found that the confirmation of water rights leads to increasing irrigation opportunity cost and guides farmers’ adoption of water-saving technologies, such as sprinkler and drip irrigation, to reduce the unit water consumption rate of grain output. Green agricultural technologies, such as the integration of water and fertilizer, not only help to save water, but also effectively promote the reduction of chemical fertilizers and pesticides use. Thus, water rights trading may improve the green efficiency of water use in grain production by raising irrigation opportunity cost and stimulating farmers’ adoption of green technologies. In this sense, the following hypothesis is put forward.

According to the induced innovation theory, disparities in the relative price of factors lead to the emergence of technological progress in different fields, thus affecting the direction of technological advancement and the path of agricultural development (Ruttan, 1977). As the transaction price reflects economic values of water resources within market mechanism, water rights trading market can shape the direction of technological progress by altering the relative price of water and other input factors. Specifically, water rights trading increases the opportunity cost of irrigation water and changes the relative price of grain production inputs, thus encouraging water-saving technology innovation in agricultural production (Fang and Zhang, 2020). In terms of the facilitating effect of factor flow, the transaction cost can be reduced by clarifying the relevant property rights of water resources. This enables water users with higher marginal benefits to secure their desired amount of water, thereby promoting the rational allocation of water resources (Yang et al., 2024). Consequently, water resources flow from agricultural operators with low marginal utility to those with high, achieving a Pareto improvement through optimized resource allocation.

The three-stage DEA model was selected to measure the GWUE of grain production, while the isomeric pollution load computing method (Chen and Xu, 2023; Ji and Jiang, 2024) was used to measure the unexpected output. The three-stage DEA model, originally proposed by Fried et al. (1999), posits that the efficiency loss is caused by random disturbance items, ineffective management and external factors. When influences of random disturbance and external factors eliminated, the measured management efficiency becomes more accurate.

In the first stage, the efficiency values and the slack values are calculated by using the ultra-efficiency mixed distance function including the unexpected output, see Equation (1).

where F_i denotes the GWUE of grain production of the i^th decision unit; x, y and e represent the input variable, expected output variable and undesired output variable respectively; s⁻, s⁺ and s^e- are the slack values while w⁻, w⁺ and w^e- are the weights of x, y and e, respectively; λ⁻ and λ⁺ show the importance of the non-radial part of the undesired output index; θ and γ represent the input and output radial components.

In the second stage, the SFA method is used to analyze the slack value, and then the influence of external factors and random disturbance on the slack is excluded, so as to calculate the adjusted value of S under the same external condition and random disturbance, see Equation (2).

where S_jit represents the slack value of j^th kind of input of i^th decision-making unit in the investigation period t; Z_it is a set of external variables affecting and β_jt is the under-valuation coefficient of Z_it. Besides, v_jit denotes a random disturbance term and follows a normal distribution, u_jit is a management inefficient term, assumed to obey a semi-normal distribution.

After eliminating influences of external factors and random disturbance terms, all decision units are adjusted to the same external environment, and the adjusted input items become X j i t A , see Equation (3).

where X_jit represents the input data of each decision unit before the adjustment; β ^ j t indicates the amount of input that each decision unit needs to adjust to realize the same external condition; v_ijt denotes the amount of input that each decision unit needs to adjust for the same random disturbance condition. In the third stage, estimating the GWUE again, using the adjusted inputs with the same external conditions and random disturbance as in the second stage.

A PSM-DID model is the combination of propensity score matching and difference-in-difference method, accounting for both the sample selectivity bias and self-selection bias to address endogeneity issues. This model is frequently used for the quantitative evaluation of public policies and project implementation outcomes. Specifically, the water rights trading pilot implemented in 2014 is regarded as a quasi-natural experiment, enabling an effective analysis of net impacts of policy implementation across various provinces. The pilot areas were designated as the experimental group, while other provinces and regions serving as the control group. The construction of the model is presented as follows (Equation 4):

where i denotes the i^th province (city, autonomous region) and t represents the time; eff_it is the GWUE of grain production calculated by DEA method; time_i represents the time dummy variable, where the value is 1 at t = 2014, otherwise the value is 0; treated_i represents the dummy variable of the region, where the value equals 1 if the province is a pilot area of water rights trading; μ_i shows the regional fixed effect; η_t denotes the time-fixed effect; and ε_it is a random error term. α₀, α₁ and α₂ represent a fixed intercept term, the policy effect of water rights trading and the coefficient of the control variable, respectively.

Based on the above theoretical analysis, in order to verify the mediation effect of water rights trading mechanism, the mediating effect model is constructed by stepwise regression method as follows (Equations 5–7):

where M_it represents the intermediary variable, selecting the technical improvement variable and the factor flow variable among industries; α₀, β₀, γ₀ represents the fixed intercept term in each type; α₁ ~ α₂, β₁ ~ β₂, γ₁ ~ γ₃ represent the regression coefficients in each category, respectively.

The input–output indicators of three-stage DEA model to measure the GWUE are displayed in Table 2. The load of chemical fertilizer pollution and solid waste are taken as the undesired output variables in grain production. The GWUE, considering undesired output, is corrected to avoid exaggerating or underestimated the impact of water rights trading on the efficiency of food production.

The core explanatory variable is treated_i*time_i, indicating whether the pilot water rights trading is carried out in the region. The pilot water rights trading is regarded as a quasi-natural experiment, where provinces with national and provincial pilot are regarded as treatment group, and non-pilot provinces belong to the control group. Specifically, seven provinces conducting the national water rights trade are Inner Mongolia, Jiangxi, Henan, Hubei, Guangdong, Gansu and Ningxia; while 10 provinces conducting the provincial water rights trade are Xinjiang, Hebei, Shandong, Shanxi, Zhejiang, Shaanxi, Fujian, Liaoning, Jilin and Hunan.

The descriptive analysis of intermediary and control variables selected is presented in Table 3. Previous studies have demonstrated that agricultural production efficiency is influenced by the level of urbanization development, the regional economic development level and its industrial institutions (Li et al., 2022; Chang et al., 2023). The technical efficiency of grain production is associated with the proportion of regional grain production, the irrigation conditions, mechanization conditions and other factors (Zhang et al., 2021a, 2021b). Technological innovation and factor flow are selected as intermediary variables. Technological innovation is measured by the number of utility model patents. Compared with the total amount of patents granted as referenced in existing literature, the amount of utility model patents more accurately reflects the improvement of actual water use through technological innovation. The proportion of agricultural water consumption within the total water consumption is utilized to measure the inter-industry flow of factors.

The GWUE of grain production before and after 2014 were calculated using MatlabR2022a software. Estimation results of the DEA model at both the first and third stage were demonstrated from a comparative perspective (Table 4). Column (1) and (2) displayed results from the first stage, while column (3) and (4) showed efficiency values from the third stage. Results of the SFA regression in the second stage can be found in the Appendix.

Generally, the mean efficiency value decreases from 0.7 at the third stage to 0.5 at the third stage, which proves the existence of influences posed by external factors and random error on efficiency. A more accurate green water use efficiency is obtained using the three-stage DEA model. For most provinces, the GWUE and ranks at the first stage keep accordance with those at the third stage, verifying the robustness of results. Exceptions are Chongqing and Shanghai, two municipalities under direct controls of central government. Reasons are that external factors in the two municipalities pose strong influences, resulting in the variance of efficiency values at the first and the third stage of DEA model. Cao et al. (2023) have also found that the regional economic development level has a significant impact on the GWUE. Besides, the function of grain production in the four municipalities, Beijing, Shanghai, Tianjin and Chongqing, is far from obtaining the outputs because agriculture is organized in different patterns and modernized agriculture takes a large share. In this light, more attention should be paid to the main grain production area of China, including 13 provinces, Heilongjiang, Henan, Shandong, Sichuan, Jiangsu, Hebei, Jilin, Anhui, Hunan, Hubei, Inner Mongolia, Jiangxi and Liaoning. The GWUE of these 13 provinces rank in the first half of the sampled 30 provinces. Therefore, a heterogeneity analysis is conducted in this study, concentrating on the policy effects of water rights trading in different grain production functional areas.

Besides, the GWUEs of provinces in the northern part of China are averagely ranked higher than those in the southern part, indicating that GWUEs have regional differences. On the premise of considering environmental factors, there are 15 provinces obtaining efficiency values lower than the national average level and with great water saving potential, including Guizhou, Yunnan, Shanxi, Guangxi, Shaanxi, Guangdong, Gansu etc. Most of these provinces are located in the southern part of China with better water endowment. A lack of perceptions of water scarcity, weak management of water resources and less promotion of water-saving measurements may be the reason. There are 8 provinces obtaining a GWUE of grain production greater than 1, including Inner Mongolia, Heilongjiang, Henan, Jilin, Shandong, Jiangsu, Sichuan and Hunan.

Results are further summed up from a comparing perspective of the changing range and ranking of the GWUE before and after water rights trading implementation (Table 5). Generally, water rights trading pilot areas have a better performance in improving the GWUE of grain production, which preliminary confirms the research hypothesis (H₁) of this study. The efficiency values of 13 provinces are significantly improved after the implementation of water rights trading, including 5 national pilot areas, 5 provincial pilot areas and 3 non-pilot areas. Although efficiency values of national and provincial pilot areas decreased, the positive effect of water rights trading on efficiency can still be revealed. There are 3 of the 7 national-level pilot provinces still increase their efficiency after water rights trading market establishment, and 4 of the 10 provincial-level pilot areas likewise.

The Malmquist index model is used to further capture the dynamic changes of GWUEs (Figure 1), decomposed into technical efficiency and technological progress, among which the technical efficiency can be further decomposed into net technical efficiency and scale efficiency. It is found that the GWUE of China’s grain production is on the rise, with an average annual growth rate of 5.02%. Indicators fluctuated greatly before the implementation of water rights trading and became relatively flat after 2014. It is worth noting that the net technical efficiency change index has always been greater than 1 since 2014 and showed an overall upward trend. The change of net technical efficiency is mainly related to the water management level, referring to the implementation of comprehensive agricultural water price reform in China and the orderly establishment of water rights trading mechanism since 2014.

Considering the matching effect, the pair of two-caliper nearest neighbor matching method is selected. A year-by-year matching method was adopted to find a matched control group for the treatment group in each year in 2014–2020. The nuclear density before and after matching is shown in Figure 2. It is easy to conclude that the matching effect is acceptable because the propensity score of both treatment group and control group have improved in the values and distribution after matching. The time trend chart of the treatment group and the control group after matching the propensity score is presented in Figure 3. Basically, the efficiency trend of both treatment group and control group changed before the start of the water rights trading pilot. The policy dynamic effect diagram (Figure 4) passes the parallel trend test. To sum up, the matched data basically meet the parallel trend requirements.

The hypothesis H₁ has been verified that the GWUE of grain production has significantly improved in the pilot provinces of water rights trading (Table 6). Results are still robust after adding control variables and with the simultaneous fixation of time and region. This result is in line with the view of scholars that the implementation of water rights trading mechanism can promote the efficiency of water use and agricultural water resources allocation (Wang et al., 2023; Gao et al., 2024). This reveals that policies of water right registration, water right trading and system construction implemented have significant influences on improving the quality and efficiency of grain production. Reasons may be that it increases the welfare of water rights trading participants through market tools, rationally distribution of scarce water resources, and improvements of water use efficiency (Shi et al., 2022).

The implementation of water rights trading can also help to realize the goal of the ‘dual control’ policy in China, which requires strict control over the total amount and intensity of water use. On one hand, water rights trading system breaks down the total water consumption to regional, industrial and user levels. This lays a foundation for the control of total water consumption. On the other hand, the water use intensity of the northern part in China can be alleviated through the balance of the uneven distribution of water resources among regions. The Chinese government has invested in a ‘South-to-North Water Diversion Project’ to alleviate the water shortage problem in the north through water transfer across river basins. However, the water-receiving areas often prefer local water sources, such as groundwater, due to the high cost of transferring water from outside. Water trading rights system provides a market-based tool to solve the problem, promoting the same quality and price for different water sources. Therefore, the optimal allocation and conservation of water resources are achieved under the joint effects of water use policies in China.

In addition, the GWUE of grain production in model (6) is positively affected by the industrial structure, grain production area proportion and effective irrigation degree. This result is consistent with Pan et al. (2023). Good irrigation conditions in major grain-producing areas, investment in water-saving and conservancy infrastructure are conducive to the improvement of agricultural water use efficiency. The coefficient of urbanization and mechanization degree is significantly and negatively connected with the GWUE of grain production, indicating that there is redundancy in grain irrigation water input. Literature has also found a certain coupling relationship between agricultural modernization and urbanization (Jiang and Yan, 2021). The negative coefficient of mechanization degree may be due to the substitution relationship between agricultural mechanization and water saving irrigation. For example, mechanized operations such as land leveling and deep plough enhance the capacity of soil water storage and water retention, and thus increasing the water demand of soil in the current season.

Results of robustness check are shown in Table 7. In model (1) and (2), results are significant after excluding the provincial water right pilots in the treatment group, indicating that the pilot work of water rights trading policy has significantly improved the GWUE of grain production. Results are still stable in the quasi-natural experiment of national pilots. However, estimates in Model (3) and (4) are not significant with the provincial water rights trading pilots. The reason may be that the policy implementation practices in each pilot province has large disparity. For example, the implementation mode and time-line are not unified. So the effects of the provincial water rights trading are hardly to be captured. Generally, it can be inferred that the effect of national pilots trading on the GWUE is more significant than that of provincial pilots. Some scholars have also reached similar findings that the effect of water rights trading is more obvious in national pilots (Gao et al., 2024). Possible reasona may be that national pilots have received more attention and support in policy implementation, having established guidance and contact relationship with the Ministry of Water Resources. Also, most national pilot projects have initiated water rights trading attempts in the earlier period and have richer experience in this exploration.

A placebo test is used to further test the effect of unobservable features (Figure 5). Randomly generating a list of pilot areas for water rights trading, creating a false estimate β ^ r a n d o m . This process is repeated 500 times to produce 500 false β ^ r a n d o m . The distribution of β ^ r a n d o m is depicted (Figure 5A) and follows a normal distribution with only four sampling coefficients located to the right of the benchmark regression coefficient. The distribution of t-values is depicted in Figure 5B and only six t-values locate to the right of the benchmark regression t-values. In conclusion, the randomly generated false estimates were not significant, passing the placebo test.