Research on the impact of environmental regulation on water resources utilization ef ﬁ ciency in China based on the SYS-GMM model

The paper uses the super-ef ﬁ ciency data envelopment analysis (DEA) model to measure the water resources utilization ef ﬁ ciency of 30 provinces in China, and then uses the system generalized method of moments (GMM) model to analyze the impact of environmental regulations on China ’ s regional water resources utilization ef ﬁ ciency. Conclusions as follows: (1) The overall water utilization ef ﬁ ciency is low, and the regions are very unbalanced. The more ef ﬁ cient areas are concentrated in the east, and the less ef ﬁ cient areas are in the west; (2) There is a ‘ U ’ -shaped relationship between the intensity of environmental regulation and water resource utilization ef ﬁ ciency, that is, weaker environmental regulation intensity is not conducive to the improvement of water resource utilization ef ﬁ ciency, but when the intensity of environmental regulation crosses the ‘ in ﬂ ection point ’ , it can promote the improvement of water resources utilization ef ﬁ ciency; (3) The level of economic development has a very signi ﬁ cant positive effect on water resources utilization ef ﬁ ciency, and the coef ﬁ cient of scienti ﬁ c and technological progress is positive, but the impact of scienti ﬁ c and technological input on water resources utilization ef ﬁ ciency is limited and not signi ﬁ cant; industrial structure and water resource utilization ef ﬁ ciency shows a negative correlation; water use structure and water resources ef ﬁ ciency show a negative correlation.


INTRODUCTION
Water resources are an important element of the natural ecosystem, the foundation of human survival and social production, the country's strategic economic resources, and an important part of the overall national strength (Xiao et al. ; Zhang et al. a, b). The contradiction between the supply and demand of water resources in China has become increasingly severe. Extensive economic growth and water pollution have led to serious shortages in water resources in many regions, and have become a bottleneck restricting the coordination and sustainable development of the economy, society, and the ecological environment.
China must change its water resources utilization model as This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). soon as possible (Pan et al. ; Wang ). System governance models such as 'income and reduce expenditure', 'scientific water saving', and 'effective supply and demand management' should be put on the agenda. Water resource efficiency is the ability to minimize the input of water resources under output while considering the ecological and economic value functions of water resources. Therefore, improving water resources efficiency is a way to alleviate and solve water shortages and promote high-quality economic development (Ding et al. ). Since the reform and opening up, the Chinese industrial economy has secured world-renowned achievements and has become the world's second largest industrial manufacturing country.
However, at the same time, some industries are still stuck in a stage of high pollution, high consumption, and low efficiency, which has resulted in great damage to the Chinese water ecological environment. Since the beginning of the 21st century, China's industrialization and urbanization have gradually accelerated, industry has gradually taken a leading role in Chinese industrial structure, industrial enterprises' demand for water resources has been increasing, and the discharge of various major pollutants in industrial wastewater has been high. The constant situation has led to the continuous deterioration of the water environment (Sun et al. ; Zhu et al. ). This poses a threat to the sustainable use of water resources in China. Therefore, under the concept of environmental regulation, it is necessary to strictly regulate the development and utilization of various water subjects, limit the discharge of polluted water resources and strengthen water environmental protection, and ensure that water resources meet domestic and production water. In relation to the water quantity and water quality requirements of ecological water use, improving water resource utilization efficiency is the fundamental way to achieve the above-mentioned daily standards. The efficiency of water resource utilization under environmental regulations can be used to diagnose the problems in the development and utilization of water resources by characterizing the relationship between water resources input, economic output and pollution emissions, to provide a basis for water resources environmental regulations (Graymore & Wallis ). Therefore, during the '14th Five-Year Plan' period, the rational use of environmental regulatory tools, efforts to resolve the contradiction between economic development and water resources and the improvement of water resources comprehensive utilization efficiency have become important measures to promote green and coordinated industrial development (Xing et al. ; Zhang et al. a, b).
The main innovations and contributions of this paper are: (1) Uses the input-output ratio and efficiency evaluation index system, and considers the data envelopment analysis where inputs include m kinds of inputs, and outputs include k kinds of outputs; supposing these m kinds of inputs and k kinds of outputs. The corresponding weight coefficient choosing an appropriate v r , u s can satisfy h i 1, and the larger the h i means the higher the efficiency, the greater the output can be obtained with less input. Therefore, the efficiency evaluation index of iDMU is: (1) Step 1: Charnes-Cooper transformation on the above formula, and then get the formula (2), as follows: (2) Step 2: According to the linear programming duality theory, by transforming the model, the model can be transformed into the following form: In the above formula, S À and S þ are slack variables, indicating that the input redundancy and output of the DMU is insufficient; λ i represents the effective front surface composed of all the effective points in the model, when the water resource efficiency falls on the effective front surface, which means that the water resource efficiency of the area is effective. Otherwise, falling below the effective front surface means that the water resource efficiency is invalid. θ represents the distance between the DMU and the effective front surface. The result of CCR model calculation is a comprehensive efficiency value, including technical efficiency and scale efficiency. Technical efficiency refers to the best results we can get with the given investment; scale efficiency refers to the current scale.
Step 3: Construct a super-efficiency DEA model.
The results of the above two models will produce a situation where multiple units are located on the effective front surface, that is, when the results are all 1, there is no way to sort them. Therefore, in 1993, Andersen and Petersen proposed a super-efficient DEA model, referred to as the SE-DEA model; this model regards all the units located on the effective front as a new system, re-forms a new effective front, and the effective value of the new effective front remains unchanged, so that it can treat all the order of regions is as follows: minθ: In the results of the super-efficiency DEA measurement, the efficiency value below 1 does not change, and for those with an efficiency of 1, the efficiency value must be removed from the setting of 1, so that the result of the calculation will be greater than 1. You can arrange the results.

System GMM model
This paper adopts the system GMM estimation of dynamic panel data, hoping to get a more robust estimation result, the GMM model estimation method is as follows: Step 1: Assume a linear model: If there are no other constraints, the asymptotically effective estimator of β is the ordinary least squares (OLS) estimate.
Step 2: Now suppose that given a piece of information β 2 ¼ 0, we can write the model as, How to estimate β 1 , one way is OLS estimation. However, this method is not necessarily effective. When there are l constraints in the E(x i ε i ) ¼ 0 equation, but the dimension of β 1 is k < l, this situation is called transition recognition. There are more moment constraints with r ¼ l À k than free parameters. We call r the number of transition constraints identified.
Le g(y, z, x, β) be l × 1 equations, the parameter β is k × 1, and k < l, we have: β 0 is the true value of β. In the above linear model, In econometrics, this type of model is called a moment condition model. In statistics, this is called the estimation equation. In addition, we have a linear moment condition model, The dimensions of z i and x i are both k × 1, and there are is transition recognition. The variable z i is a part of x i or a function of x i . Model (8) can be set as, Step 3: The sample mean of GMM estimation model (10) is: The moment estimator of β is to set g n (β) ¼ 0. For the case where k < l equations are greater than the parameters, the GMM estimation idea is to set g n (β) as close as possible to zero.
For l × l weighting matrix Wn > 0, let This is a non-negative measure of the length of the vector g n (β). For example, if Wn ¼ 1, then Step 4: GMM estimation is to minimize J n (β), that is, Note that if k ¼ l, then g n (β) ¼ 0, GMM estimation is the moment estimation method. The first-order conditions of GMM estimation are: Step 5: The GMM of β is estimated aŝ

Indicator selection and data sources
Considering the completeness and availability of data, this article uses the capital stock, labor force, and water and energy input of 30 provinces, municipalities, and autonomous regions across the country from 2008 to 2019 (due to the lack of data, excluding Tibet) as input indicators, The GDP and industrial waste gas emissions of each province and city are used as output indicators to evaluate the undesired output of each province, city, and autonomous region. The actual GDP of each province and city is regarded as the expected output. The specific index selection is shown in Table 1.   the fixed capital formation of each province are obtained.

Indicator interpretation and data processing
Then the fixed asset investment price index of each year is used to deflate the total fixed capital formation of the corresponding year.
Labor force (L). The number of labor force refers to the  Table 2.
It can be seen from Table 2  to study the influencing factors that affect the efficiency of water use, so as to provide a theoretical reference for the implementation of differentiated policies. The following will use empirical analysis to study the influencing factors.
The impact of environmental regulations on water resources utilization efficiency

Indicator selection and data sources
The explained variable. Water use efficiency, the data come from the calculation results above in this article.
Explaining variables. Environmental regulation (ER). As a public product, water resources have not obtained prices and high-efficiency allocation in the market system, which has led to the abuse of water resources by industrial enterprises, resulting in water waste and pollution. As the main body of macroeconomic regulation and control, the government's policies, behaviors and intervention measures to the main body of market economy will inevitably have an impact on enterprises and society. In recent years, the Chinese government has gradually increased the entry barriers of various industries through the pollution discharge fee system and the pollution discharge trading system, using the force mechanism to optimize the industrial structure, and promote the coordinated development of economic society and environmental protection. This shows that government environmental regulations will also have an impact on industrial water efficiency. This paper uses the ratio of China's regional pollution charges to regional GDP to measure the intensity of local environmental regulations.
The level of economic development (GDP). In 1996,

Panayotou proposed the Environmental Kuznets Curve
(EKC), pointing out that the environmental quality presents a U-shaped curve relationship with economic development  Water structure (QS). Different aspects of society have different demands for water resources and different utilization levels of water resources. Therefore, a reasonable allocation of water resources is of great significance to improving the utilization of water resources. This paper selects agricultural water consumption (AQ), industrial water consumption (IQ), and domestic water consumption (LQ) as indicators of water consumption. Some documents believe that factors such as import and export trade, water prices, and water resources policies will also affect regional water consumption. Resource utilization efficiency has an impact, but due to the unavailability of data and indicators that are difficult to measure, indicators such as water prices, water resources policies, and water conservation awareness will not be considered in the measure-

Measurement results
The estimation results of the model based on the system GMM model estimation method are shown in Table 3.
For the environmental regulation variables that this article focuses on, the model estimation results show that the impact of environmental regulation on China's water resources efficiency conforms to a 'U'-shaped nonlinear relationship, and has passed the 1% significance test. This article believes that there is an obvious dependency between water resource utilization efficiency and environmental  Water consumption structure. There is a negative correlation between water consumption structure and water resource efficiency, among which domestic water and industrial water have a relatively large impact. In other words, whether it is agriculture, industry, life, or ecological water use, it has a certain negative impact on the environment, and 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 is possible to consider the factors affecting regional differences in water resources efficiency from the perspective of the water consumption of specific industries in combination with the industrial water use structure.

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