Evaluation of China’s water-resource utilization efficiency based on a DEA-Tobit two-stage model

In this paper, a Data Envelopment Analysis-Tobit (DEA-Tobit) two-stage model was used to evaluate the efficiency of water-resource utilization, and the regional differences and influencing factors on water-resource utilization were analyzed. The results of the analysis of regional differences show that China’s water-use efficiency is relatively low. Only Beijing, Shanghai, and Fujian have water-use efficiency higher than 0.8, whereas most other provinces and cities have an efficiency of 0.3–0.8. The eastern region demonstrates a higher water-resource utilization efficiency than the central and western regions. The analysis of the influencing factors of regional differences in water-use efficiency found that per capita water resources, per capita domestic water use, and the proportion of primary and secondary industries all have a negative impact on the efficiency of water use, and per capita GDP has a positive impact on the efficiency of water use. Agricultural water consumption, industrial water consumption, domestic water consumption, and total ecological water consumption all have a negative impact on waterresource utilization efficiency, of which domestic water consumption and industrial water consumption have a greater impact. Technological level and water-resource utilization efficiency show a significant positive correlation.


INTRODUCTION
Water resources, in a broad sense, refers to the total amount of water bodies in the hydrosphere, and more commonly refers to water resources that can be directly used by humans. Water resources endowed with economic significance can be regarded as an important guarantee for maintaining the healthy development of the social economy, protecting the environment, and maintaining the ecological balance. Water is an indispensable natural resource for human development and the material basis on which humans and all living things depend. Today, the water crisis caused by lack of water resources and water pollution seriously restricts the healthy development of the world economy. In the 21st century, countries around the world are generally facing severe water shortages. It is expected that by 2025, 3 × 10 9 (3 billion) people in the world will face water shortages, and 40 countries and regions will be seriously deficient in fresh water. With the development of social economy, population urbanization, and industrialization, water resources are no longer inexhaustible, but have become strategic economic resources and the main factors affecting the ecological environment. The current serious waste of water resources and unreasonable wateruse make the problem of water shortage in China more serious. The issue of supply and demand due to inefficient use of water resources is also very prominent. The shortage of water resources and the contradiction between the supply and demand of water resources have had a large negative impact on China's economic growth, although rapid economic development will also increase pressure on water resources. People pay increasing attention to whether the current water resources can: support the food supply of China's huge population; solve the problems of water shortage, water resource pollution, and ecological degradation; properly deal with the impact of climate change; or support the steady and rapid development of the social economy. Therefore, the rational use of water resources in China is an important issue that needs to be resolved in China at this stage.
Since the beginning of the 21st century, the total amount of water consumption in China has increased.
The proportions of industrial water, agricultural water, and domestic water have changed. In addition to the significant reduction in agricultural water, industrial water and domestic water have increased year by year. China has severe drought. The total freshwater resources are 280 billion m 3 , accounting for 6% of the global total water resources, ranking fourth in the world, but only 2,200 m 3 per capita. In addition, the regional distribution of water resources in China is very uneven. The Yangtze River basin and its southern region have a land area which is 36.5% of the country and with 81% of the country's water resources. The region north of the Yangtze River basin has a land area of 63.5% of the country.
Resources account for only 19% of the country. At the end of the 20th century, more than 400 cities out of more than 600 in China had insufficient water supply.
Among them, there were 110 cities with serious water shortages, and the total amount of water shortages in the country was 6 billion m 3 . Water resources are an important support and guarantee for national economic and social development. With the increasingly obvious impact of global climate change and the acceleration of China's industrialization and urbanization process, the contradiction between socio-economic development and the insufficient capacity of water resources and the water environment will become more prominent. There are many ways to solve the problem of water resources and most experts and scholars agree that an efficient and vital way of doing so is improving the efficiency of water-resource utilization. This could also include promoting the implementation and realization of work to build a water-saving society, implementing a scientific development approach, and coordinating regional development while maintaining the long-term and stable development of society. Increased use of water resources can not only maintain social and economic growth but also protect residents' daily water usage, while achieving cleaner production, protecting the environment, promoting the development of a water-saving society, and achieving sustainable socio-economic and ecological development. Thus, scientifically and objectively evaluating current water-resource utilization efficiency and its regional differences in China, and discussing the factors that affect water-resource utilization efficiency have become an urgent problem to be studied. This paper tries to answer the above questions to provide a solid reference for the formulation of China's policies on water resources.

LITERATURE REVIEW
Connotation and measurement of water-resource utilization efficiency Since the 20th century, the rapid development of industry and agriculture and the rapid increase in population have exacerbated the imbalance between water supply and demand. Many international scholars predict that the world will face serious water problems in the 21st century.
Maintaining the sustainable and effective use of water resources requires a reasonable evaluation of water-resource utilization efficiency which is defined as the ratio of waterresource input to output. Therefore, many countries have Existing research provides a good reference for us to understand the problem of water-resource utilization efficiency in China, and also provides an initial perspective for us to further explore regional differences. The current research deficiencies mainly manifest in the following: first, most scholars equate the amount of water resources input with the amount of resource consumption, excluding the consumption of other resources, so as to conduct an isolated study of water-resource utilization efficiency. Water is a natural resource; its input does not directly bring economic benefits and product output, and must be combined with other production factors to bring real economic output. Therefore, it is too simplistic to directly link water resources input with economic output. Second, domestic and foreign scholars rarely consider environmental factors such as pollution in the evaluation of water-resource utilization efficiency, which cannot reflect the true level of water-resource utilization efficiency, and may even mislead the government when making policy decisions, resulting in sustainable water resources development being negatively affected. Based on the above understanding, this paper evaluates the efficiency of regional water-resource utilization in China from the perspective of total factor productivity, and on this basis characterizes the regional differences in water-resource utilization efficiency, and further explores the possible causes of the existing differences with the help of quantitative-analysis methods.

DEA method
Data envelopment analysis (DEA) was created and devel- Suppose there is one production unit in the water resource production system, each unit has the same input and output indicators, including m input indicators and n output indicators, and the output indicators include n 1 expected output indicators and n 2 types of unexpected output indicator. Then, for the i-th decision unit T i , and where R represents the expected output set, the input index value x i , expected output index value y i , and undesired output index value zi are, respectively: (1) Since the constructed SBM model contains undesired output, the sample unit set T, referring to a collection of all technically feasible input and output models, can be determined as: Combined with the research of the data-envelopment analysis literature, the traditional DEA model measures the difference in the efficiency value of the invalid unit (ρ < 1) under the condition of variable scale returns P n k¼1 The degree is magnified, which is not conducive to the decomposition of scale efficiency. Therefore, the SBM model including undesired output is constructed as follows: s:t: In Equation (3), the objective function ρ 0 is the production unit efficiency value; x k is the input indicator, y k is the expected output indicator, and z k is the undesired output indicator; s À is the input indicator relaxation variable, and s þ is the expected output relaxation variable, s zÀ is the undesired output relaxation amount; λ is the weight of input factors. The model incorporates slack variables into the objective function, taking into account the impact of negative external efficiency factors, optimizes the slack problem of input and output factors, and solves the problem of efficiency measurement when there is undesired output. However, when ρ 0 < 1, the model uses the furthest point on the envelope surface of the production unit as the standard, which results in a small efficiency measurement result. Therefore, it is necessary to further improve the model and adjust the vertex of the production frontier from the farthest distance to the most effective distance: s:t: The improved undesired SBM model can optimize the objective function, which is more in line with the actual situation of social production activities, and the envelope of the effective production unit is still the same as the original model. Therefore: The In the formulas, y i is the dependent variable. When the dependent variable is greater than 0, the value is y*. When the dependent variable is less than or equal to 0, it is truncated at 0; x i is the independent variable and obeys the normal distribution. When y i ¼ 0, its probability distribution function is: where Φ À βX i σ is a standard normal distribution function.
If y i ¼ y Ã i , the probability distribution of y i is equal to the probability distribution of y i * ; thus, the likelihood function class is expressed as: This paper uses the maximum likelihood method to estimate the Tobit model.

RESULTS AND DISCUSSION
Calculation results of water-resource utilization efficiency in China

Variable selection
In the economic model for water-resource use efficiency, the input variables are labour force, fixed asset investment and total water resources, the expected output variable is the regional GDP, and the undesired output variable is the sewage discharge. The selection and calculation methods of these variables are as follows: (1) Labour force (S). China has not yet conducted systematic statistics on labour time, the most direct indicator of labour force. This paper selected the total population of provinces and cities to represent labour input factors.
(2) Capital stock (K). This paper selects fixed capital investment to represent capital stock. The indicator data needed to be deflated, and the base period was set to 2008.
(3) The amount of water resources (E). In this paper, the total water supply of each province and city was selected to represent its water resources, which mainly included surface water (local surface water and cross-basin water transfer), groundwater, reclaimed water reuse, and seawater desalination. The data for this indicator could be obtained directly from the water resources bulletin.
(4) Expected output (Y). Selecting the total production value (GDP) of each province and city to represent the expected output, the indicator data also needed to be deflated. The base period was 2008.   By analyzing the change trend of each region, it can be seen that the difference in regional water-resources usage efficiency was also substantially the same as the difference in the economic development level of each region. The water resource utilization efficiency in the eastern region was relatively high, which corresponds to its high level of development. The market mechanism in the eastern region was relatively complete, and its economy was relatively developed. However, the economic development level in the western region was relatively low, and there was no perfect market management and operation mechanism, which leads to a large amount of redundant input and waste in the production process, which leads to inefficient use of water resources. By comprehensively ranking the waterresource utilization efficiency of various provinces, it can be found that the water-resource utilization efficiency of each province in the eastern region was generally higher, followed by the central region and the western region, which was lowest. There was a general decline in water-resource utilization efficiency from the eastern coastal region to the inland areas.
Tobit regression results of influencing factors of wateruse efficiency

Variable selection
(1) Data source For water-resource utilization efficiency, the data come from the calculation results in this paper.
(2) Explanation of variables Economic development level (ED). The indicators used to measure the ED of various provinces were regional GDP and regional GDP per capita. However, considering the objectivity and rationality of the selection of indicators, regional GDP per capita could measure living standards of people in the region more truly than regional GDP. Therefore, in this regression analysis, the per capita GDP was used as a variable to measure the economic development level of each region.
Regional water-resource richness (WE). Existing research suggests that in regions with abundant water resources, because water resources are relatively easy to obtain, people's awareness of saving water is relatively poor, and there is more waste in the use of water resources, which makes the water-resource utilization efficiency of the region comparably low. By contrast, in areas where water resources are scarce, due to that scarcity, people will consciously reduce the waste of water resources, thereby making water-resource usage relatively efficient. Therefore, differences in regional water resources and natural conditions will affect the efficiency of water-resource usage.
This paper uses per capita water resources as an indicator to measure water resources in different regions.
Industrial structure (IS). The formation of a water resource consumption structure is largely affected by IS, and the rational adjustment of the proportion of each industry has a great impact on the improvement of water-resource utilization efficiency. The indicators used in this paper to study the impact of IS are the proportion of primary industry (ISF) and the proportion of secondary industry (ISS).

Industrial water structure (IW). The Environmental
Kuznets Curve (EKC) shows that environmental quality is also related to industrial structure, and Chinese researchers have also analyzed the relationship between industrial water use structure and water-resource use efficiency. ln WRE ¼ α þ β 1 ln ED i þ β 2 ln WE i þ β 3 ln ISF i þ β 4 ln ISS i þ β 5 ln IWA i þ β 6 ln IWI i þ β 7 ln IWL i þ β 8 ln IWE i þ β 9 ln TECH i þ μ

Regression results
The estimation results of the Tobit model estimation method in this paper are shown in Table 2.
(1) There was a positive correlation between the level of economic development and the efficiency of waterresource utilization. The coefficient of influence of GDP per capita on the efficiency of water-resource utilization was 0.00024, that is, for every 1 percentage point increase in GDP per capita, the efficiency of waterresource utilization increased by 0.00024%, which means that the efficiency of water-resource utilization improved. With the continuous development of the social economy, social production is accelerating, and the demand for water resources will also increase day by day. However, in the case of limited total water resources, people need to find ways to efficiently recycle water resources to meet the needs of social production.
In this case, people will reduce the consumption of water resources through technological innovation, elimination of more expensive equipment, and use of watersaving equipment, which will increase the utilization rate of water resources somewhat. Therefore, the impact of the regional economic development level on the efficiency of water-resource utilization cannot be ignored.
(2) The abundance of regional water resources had a significant negative impact on the utilization efficiency of water resources. Through regression, the coefficient of water resources per capita was negative, which indicates that the water-resource utilization efficiency per capita in a region is diametrically opposed to the trend of water-resource utilization efficiency in that region.
When people are not plagued by a shortage of water resources, they often fail to realize the importance of water conservation, which leads to many problems such as serious waste and inefficient use of water resources. This requires the relevant departments to promote water saving and the recycling of water resources, so that everyone has a sense of water saving and recognizes the seriousness of the water-resources problem.  and it also causes a lot of waste, making for a sub-optimal utilization rate. It can be seen that scientific and reasonable adjustment of the industrial structure can not only improve the efficiency of water-resource utilization but also is highly significant for the construction of a water-saving society.
(4) There is a negative correlation between industrial water use structure and water-resource use efficiency, of which domestic water use and industrial water use have a relatively large degree of influence. That is, whether it is agricultural, industrial, ecological, or everyday water use, it has a negative impact on the environment. The impact of ecological water use is relatively low, which is consistent with the purpose of improving water-use efficiency and improving water-use structure. It may be considered necessary to further analyze the influencing factors of regional differences in water-resource utilization efficiency based on the industrial-water consumption structure and the water consumption of specific industries.

Recommendations
The government should increase its support for improving the efficiency of water-resource utilization The government does a good job of supporting and guiding, increasing investment in science and technology, cultivating technical talent, improving the level of science and technology, and providing technical support for water-resource utilization efficiency, with a view to building the most stringent water resources management system, controlling and using water resources as early as possible, and collecting fees at an appropriate time. External environmental taxes reduce water-resource pollution, and gradually establish and improve water-resource property rights and use a control system. For the eastern zone, the government taps the watersaving potential, improves sewage-treatment capacity and reuses water capacity as much as possible, increases environmental protection publicity, and promotes the construction of a water-saving society. Based on improving the level of science and technology, the central and western regions have strengthened environmental monitoring and government supervision, and established an evaluation system and enforcement mechanism for water-resource utilization efficiency to better promote it.
Formulate reasonable water resource utilization efficiency targets based on regional realities The improvement of water-resource utilization efficiency is based on economic development and requires investment.
The purpose of improving water-resource utilization efficiency is to make socio-economic development better and faster. Then, when formulating the speed and range of regional water-resource utilization efficiency improvement, it must take the economic level of the region into consideration, and it is impossible to blindly formulate development goals for water-resource utilization efficiency without departing from the economic development stage.
If the target value is too high, the investment will be greatly increased, which will inevitably slow down and hinder economic development. If the target value is too low, it cannot effectively limit the increase in water consumption and sewage discharge, and it cannot be reduced. A lot of pressure is put on the ecosystem by a low water supply and inadequate sewage purification, and modest or overambitious goals cannot achieve the ultimate aim of improving the efficiency of water-resource utilization, so it is particularly important to formulate reasonable water-resource utilization efficiency targets.
Vigorously raise awareness of water saving for everyone

Cross-regional cooperation and exchange
With the development of regional economies, the establishment of regional innovation systems at various levels has produced a spillover effect of water-resource utilization efficiency. The key to this spillover effect is whether regions with lower water-use efficiency will absorb water-use technologies and management systems from regions with higher water-use efficiency. Therefore, cross-regional cooperation and exchanges need to gradually change the efficiency of water-resource utilization in the regions from low to high according to their own capabilities. Through convergence analysis of water-resource utilization efficiency of various provinces and cities in China, it was found that there is significant absolute convergence of water-resource utilization efficiency in China, but the convergence is slow, and the gap of water-resource utilization efficiency among provinces and cities still persists. At the same time, the empirical research in this paper also shows that geographical factors have a significant positive effect on China's water-resource utilization efficiency. The level of water-resource utilization efficiency of a region depends to a certain extent on the level of water-resource utilization efficiency of neighbouring regions with similar spatial characteristics. Therefore, for the long-term development of water-resource utilization efficiency in various provinces and cities, it is necessary to further strengthen measures to promote cross-regional economic and technological exchanges, accelerate the process of technology diffusion from advanced regions to developing regions, and improve the level of water-resource utilization efficiency in the latter.

DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.