Re-Examining Regional Total-Factor Water Efﬁciency and Its Determinants in China: A Parametric Distance Function Approach

: It is accepted that improving water efﬁciency is a key task for China in achieving water sustainability, as the knowledge of water efﬁciency and its determinants can provide critical information for water policy formulation. To this end, this paper presents a parametric frontier approach to analyze water efﬁciency performance and its inﬂuencing factors in one step. The proposed approach ﬁrst introduces the Shephard water distance function to construct total-factor water efﬁciency (TFWE) index and then adopts the stochastic frontier analysis (SFA) technique to compute the index and its determinants. A case study of regions in China from 2000 to 2015 is presented. The main ﬁndings are summarized as follows: (1) Both the overall China and most of the regions still have room for improvement in water efﬁciency. SFA and data envelopment analysis (DEA) might lead to different results in benchmarking water efﬁciency. Moreover, SFA has higher discriminating power than DEA in this regard. (2) There exists signiﬁcant disparity of water efﬁciency among the regions of China, and the difference in TFWE takes on a U-shaped evolution trend, which ﬁrst decreases in a ﬂuctuation way and then increases monotonically. (3) Factors like industrial structure, import and export trade, environmental regulation and urbanization level have a positive impact on water efﬁciency, while resource endowment and economic level exhibit negative and nonlinear effects, respectively. Finally, several policy recommendations are made to improve water efﬁciency levels and promote water sustainability.


Introduction
It is widely accepted that water resources are both irreplaceable natural resources and strategic economic resources. Water problems are especially challenging in China, as it has the largest population, fastest developing economy, scarce water resources, rising water demand and inadequate governance [1]. With the rapid development of China's economy and society, water issues have become the main bottleneck for the sustainable development of the country [2]. In China, water resource shortages and water environment deterioration are the two major problems restricting water sustainability. It was stated that China's per capita water resource was only one-quarter of the world average in 2014 [3]. Furthermore, the limited water resources are in an unbalanced distribution, 81% of which are distributed in the southern area of China [4]. Additionally, China is faced with a series of water environment problems such as groundwater level decline, water quality deterioration, water analysis (SFA) approach based on distance function to study technical efficiency and its influencing factors. This approach can not only include statistical noises in technical efficiency measurement, but also perform a quantitative analysis on the influencing factors of technical efficiency. As such, the proposed approach in this paper can achieve the synchronous realization of measurement and determinant analysis of technical efficiency and is, therefore, described as the one-step method. As a typical parametric frontier, SFA is an approach where all observations are on both sides of the frontier and it is possible to separate between random errors and differences in inefficiency [45]. The SFA approach was developed by Aigner et al. [46] and has been widely used to the fields of energy and environmental efficiency evaluation [47][48][49][50][51][52][53][54]. Especially, Xu and Yang [49] employed the SFA model based on Shephard energy distance function to analyze the TFWE and its influencing factors in China during 2001-2010. Similarly, Xing et al. [54] adopted the SFA model based on Shephard ecological distance function to analyze regional eco-efficiency and its determinants in China during 2007-2015. Nevertheless, to our best knowledge, there are few studies analyzing the TFWE and its determinants based on the parametric distance function approach.
In this context, this paper proposes a parametric frontier approach to analyze the water efficiency performance and its influencing factors in China. The potential contributions we add to the existing literature could be summarized in three aspects. First, this paper introduces the Shephard water distance function considering environmental constraints to construct a water efficiency index. Second, taking into account statistical noises, this paper proposes a parametric distance function approach to compute water efficiency. Third, the proposed approach can implement the measurement and factor analysis of water efficiency synchronously. The rest of the paper is planned as follows. Section 2 introduces methods and materials. The steps for establishing TFWE index and the SFA model for calculating the index and its determinants are presented in this part. Section 3 presents the results and discussion by which we employ the proposed approach to study the TFWE of regions in China from 2000 to 2015. Section 4 draws conclusions and considers policy implications.

Shephard Water Distance Function
Consider a production process by which each DMU (i.e., each province in China) employs capital stock (K), labor force (L) and water resource (W) as inputs to produce GDP (Y) and waste water (B) as the single desirable output and undesirable output, respectively. Conceptually, the production technology can be defined as: In production theory, T is often assumed to satisfy the following properties: (1) Nothing can be produced without inputs; (2) T is finite; (3) T is bounded; (4) T is convex.
Following the spirit of Shephard energy distance function developed by Zhou et al. [44] and Wu et al. [55], we define a Shephard sub-vector input distance function for water use (hereafter referred to as the Shephard water distance function) as: Equation (2) seeks to estimate the maximum potential reduction in W, while holding the input-output combination within the production technology as defined by Equation (1). It measures the degree to which water use can be reduced. As such, W/D w (K, L, W, Y, B) denotes the hypothetical water use. The total-factor water efficiency (TFWE), defined as the ratio of optimal-to-actual water use [25], can be computed with the following formula: TFWE is equal to the reciprocal of the Shephard water distance function. The definition of TFWE implies that it is less than or equal to one and a higher score means a better water efficiency performance.

SFA Estimation Model
In empirical application, the Shephard water distance function can be estimated within a nonparametric or a parametric framework. DEA is a popular nonparametric technique which does not impose any functional form on the frontier, thereby avoiding model misspecification [56]. However, DEA does not take statistical noises into account, which makes the results obtained from DEA very sensitive to data quality. In light of the limitation, parametric frontier estimation with SFA has attracted increasing attention from researchers [47][48][49][50][51][52][53][54]. Here, we follow Du and Lin [53] to adopt the translog function to specify the Shephard water distance function, which can be described as: where ν t i is a random variable accounting for statistical noises and it is assumed to obey the standard normal distribution. Each β is the parameter to be estimated.
According to the property that the Shephard water distance function is linearly homogenous in water input, we have: The proof of Equation (5) is presented as Equation (S1) in the Supplementary Materials. Substituting Equations (5) into (4) and rearranging it, we obtain: After simple transformation, Equation (6) becomes: where i is a non-negative variable accounting for water inefficiency. As a result, we derive an SFA model presented as Equation (7) for computing the Shephard water distance function. In solving, the maximum likelihood technique is adopted to estimate the parameters in Equation (7). After the estimation of Equation (7), the water inefficiency componentû i of region i can be obtained and the corresponding water efficiency can be further calculated with TFWE i = exp(−û i ). Meanwhile, u t i is assumed to follow the distribution of N µ t i , σ 2 u . Thus, the determinants of water efficiency can be analyzed with the following inefficiency equation: where z t ip denotes the influencing factors of water inefficiency and each δ is the parameter to be estimated.
Notably, all the unknown parameters in Equations (7) and (8) can be computed by a one-step estimation. Therefore, it allows the measurement and determinants of water efficiency to be analyzed simultaneously.

Variables Selection
This paper selects five variables as the input-output indicators. Three variables of capital stock (K), labor force (L) and water use (W) serve as inputs, while GDP (Y) and wastewater discharge (B) are taken as the single desirable output and undesirable output, respectively. As there are no official statistics on capital stock in China, the data are estimated by the perpetual inventory method as described by Equation (9): where K it and K it−1 denote the capital stock of region i in year t and t − 1, respectively. I it denotes the investment of region i in year t. δ i denotes the depreciation rate of region i. Additionally, this paper selects six variables as the contributing factors of water efficiency from the aspects of economy, nature, government and society. The specific variables are described as follows:

1.
Economic Level (EL). In the literature, economic development level and water use efficiency were found to show a U-shaped relationship. It implies that water efficiency decreases with the economic growth at the low-level stage of economic development, while the opposite situation will appear when the economy grows to a certain degree. This paper adopts per capita GDP (in 2000 constant price) to measure local economic level. Meanwhile, its quadratic form is also taken as an explanatory variable in the model to investigate its nonlinear impact on water efficiency [41].

2.
Resource Endowment (RE). This paper adopts water resource supply per capital to measure the rich degree of local water resources. Actually, due to the existence of "Resource Curse", many studies revealed that there is a significantly negative relationship between water efficiency and resource endowment [42].

3.
Industrial Structure (IS). Agricultural and industrial sectors are the largest water consumers in China. Thus, industrial transformation and upgrading is significant for improving water use efficiency [57]. This paper takes the proportion of value added of the tertiary industry to the total output as the measurement of local industrial structure. 4. Import and Export Trade (IET). The import and export demand of products with high water consumption and high pollutant emission would have effects of substitution and promotion on China's relevant industries, respectively [37]. As such, it may affect the water efficiency to a certain extent. This paper adopts the ratio of imports to exports as the measurement of import and export trade.

5.
Environmental Regulation (ER). This can help regulate the utilization behavior of water users, restrict the discharge of wastewater and stimulate technological innovation to reduce water use intensity [58]. According to Shen and Liu [59], we use the following indicator to measure local environmental regulation intensity: where IPCI denotes the investment in industrial pollution control and GIP denotes gross industrial product. The advantage of this index is to make use of GIP/GDP to modify the traditional environmental regulation index, and it can avoid the effect of regional industrial structure differences on the measurement of environmental regulation. 6.
Urbanization Level (UL). The city is a symbol of modern civilization. It has better water supply facilities, water reuse technology and sewage treatment system, which can help improve local water use efficiency [60,61]. This paper adopts the share of urban population as the measurement of local urbanization level.
The variables and their units are summarized in Table 1.

Data Sources
The data for the above variables were collected and compiled from China Statistical Yearbook, China Statistical Yearbook on Environment and Statistical Yearbooks of 30 provinces or cities from 2001 to 2016. Tibet, Hong Kong, Macao, and Taiwan were excluded in this paper due to data limitations. The monetary variables such as capital stock, GDP and economic level were deflated into 2000 constant price. Table 2 shows the summary statistics of the data.

TFWE Estimates
We evaluated the TFWE of regions in China during 2000-2015 by solving Equation (7) with Frontier v4.1 (Centre for Efficiency and Productivity Analysis, Armidale, Australia), and the results were summarized in Table 3. It can be observed that Shandong had the highest average TFWE score of 0.933, and the following nine regions including Shanxi (0.907), Shanghai (0.893), Henan (0.885), Beijing (0.884), Chongqing (0.884), Qinghai (0.856), Shaanxi (0.844), Tianjin (0.828) and Guangdong (0.810) were all found with a score higher than 0.800. On the other hand, Xinjiang was found to have the lowest value of 0.074, and the following five regions such as Neimenggu (0.230), Heilongjiang (0.252), Guangxi (0.337), Jiangxi (0.370) and Ningxia (0.382) had a score lower than 0.400. The above findings imply significant differences of TFWE among various regions in China. for improvement. By comparing the TFWE among the three areas, Middle China was found to have a collapse phenomenon in TFWE. In fact, due to the geographical location, the middle provinces are the first choice for undertaking the water-and pollution-intensive industries transferred from the eastern developed regions. Consequently, the trans-regional pollution transfer caused by the industry transfer is a significant reason for the low TFWE in Middle China.
For comparative purposes, we computed the Shephard water distance function in the nonparametric DEA framework, and the solving program is presented as Equation (S2) in the Supplementary Materials. Also, the TFWE results from the DEA model are listed in Table S2 in the Supplementary Materials. By comparison, we can observe that the choice between SFA and DEA would affect not only the TFWE scores but also the ranks. In addition, several regions had TFWE scores of unity when DEA was used, while this did not occur when SFA was used. This implies that SFA often has higher discriminating power than DEA, which might be considered as an advantage of SFA over DEA in benchmarking water efficiency. Additionally, Table 4 shows the Pearson and Spearman correlations of the two sets of TFWE scores obtained from SFA and DEA models. From this table, we can observe that both the Pearson and Spearman correlations between the two sets of TFWE results from SFA and DEA models were not very strong. This implies that SFA and DEA would possibly lead to different results in benchmarking water efficiency, which is consistent with the previous findings of Zhou et al. [44]. Note: ** Correlation is significant at the 0.01 level (2-tailed); the number in parenthesis is the Spearman rank correlation coefficient.  Figure 1. This fully demonstrates that with economic and technological advantages, Eastern China can make use of water resources more effectively and efficiently, and thus closely approaches the production frontier. Figure 2 indicates the spatial distribution of TFWE in China in 2000, 2005, 2010, and 2015. It can be observed that there existed significant differences of TFWE among various regions in China. Developed regions, such as Beijing and Shanghai, were found to have higher TFWE scores. However, there were those like Jiangsu, the efficiency of which was not consistent with its economic development level. Meanwhile, water-scarce regions such as Shanxi, Henan, Shandong and Shaanxi were found with higher efficiency, while the water-rich ones like Hunan and Jiangxi had a lower efficiency. This implies that the regional disparity of TFWE is a common result induced by multi-factors. Water 2018, 10, x FOR PEER REVIEW 9 of 15  In order to investigate the evolution tendency of TFWE disparity in China, Figure 3 provides the changes in Std. dev. and variation coefficient (VC) of TFWE from 2000 to 2015. The two coefficients can measure the absolute and relative regional differences of TFWE, respectively. Their calculation formulas are presented as Equations (S3) and (S4) in the Supplementary Materials. From this figure, we can observe that the Std. dev. of TFWE took on a U-shaped evolution trend, by which it decreased  In order to investigate the evolution tendency of TFWE disparity in China, Figure 3 provides the changes in Std. dev. and variation coefficient (VC) of TFWE from 2000 to 2015. The two coefficients can measure the absolute and relative regional differences of TFWE, respectively. Their calculation formulas are presented as Equations (S3) and (S4) in the Supplementary Materials. From this figure, we can observe that the Std. dev. of TFWE took on a U-shaped evolution trend, by which it decreased In order to investigate the evolution tendency of TFWE disparity in China, Figure 3 provides the changes in Std. dev. and variation coefficient (VC) of TFWE from 2000 to 2015. The two coefficients can measure the absolute and relative regional differences of TFWE, respectively. Their calculation formulas are presented as Equations (S3) and (S4) in the Supplementary Materials. From this figure, we can observe that the Std. dev. of TFWE took on a U-shaped evolution trend, by which it decreased in a fluctuation way from 2000 to 2011 and monotonically increased from 2011 to 2015. This implies that the absolutive disparity of TFWE showed an ascending tendency during 2000-2011, while the situation was opposite for the period of 2011-2015. Additionally, a similar evolution tendency for the VC of TFWE was also observed. That is to say, the relative disparity of TFWE also experienced a process of decreasing at first and then increasing. Taken together, the TFWE in China was apt to more spatial concentration before 2011, while became more regionally uneven after that point. In view of its enlarging trend, the Chinese government should take regional differences of TFWE as a major consideration when formulating water-saving policies. Additionally, a similar evolution tendency for the VC of TFWE was also observed. That is to say, the relative disparity of TFWE also experienced a process of decreasing at first and then increasing. Taken together, the TFWE in China was apt to more spatial concentration before 2011, while became more regionally uneven after that point. In view of its enlarging trend, the Chinese government should take regional differences of TFWE as a major consideration when formulating water-saving policies.

Influencing Factors
Water efficiency analysis aims to not only evaluate the water efficiency of regions but also reveal determinants for regional differences so that policymakers can focus on those factors when formulating policies and measures to improve local water efficiency. In this context, six influencing factors including economic level, resource endowment, industrial structure, import and export trade, environmental regulation and urbanization level were analyzed in this section. After the computation of Equation (7), we obtained the coefficient estimates of variables and the results are listed in Table 5. Note: ***, **, and * denote the 1%, 5% and 10% significance levels, respectively. Due to the limited space, the other coefficient estimates are not listed here but provided in Table S3 in the Supplementary Materials.

Influencing Factors
Water efficiency analysis aims to not only evaluate the water efficiency of regions but also reveal determinants for regional differences so that policymakers can focus on those factors when formulating policies and measures to improve local water efficiency. In this context, six influencing factors including economic level, resource endowment, industrial structure, import and export trade, environmental regulation and urbanization level were analyzed in this section. After the computation of Equation (7), we obtained the coefficient estimates of variables and the results are listed in Table 5. For the primary and quadratic terms of variable ln(EL), we observed the former did not pass the 10% significance test while the latter had a positive impact on TFWE at the 1% significance levels. Thus, there existed a U-shaped relationship between economic level and TFWE, namely, with the growth of economic level, water efficiency first decreases and then increases. This may be attributed to the fact that the improvement of economic level was taken as the main task in the early period of economic development, while resources and environmental conservation were neglected. Consequently, water efficiency showed a downward trend. However, when the economy grows to a certain level, resource and environmental issues will bring obstacles to its further growth. In this case, people would follow resource-saving and environment-friendly modes to develop the economy and thus improve water efficiency.
For variable ln(IET), it was observed that import and export trade had a positive impact on water efficiency at 1% significance levels. As import and export trade is defined by the ratio of imports to exports, water efficiency was correlated positively with imports and negatively with exports. This is mainly because trade in agricultural and industrial goods that consume large quantities of water will result in the spatial transfer of water resources from export dependent regions to import dependent ones. This would increase burdens on the water resources supply of the former and alleviate that of the latter. As a result, imports and exports pose opposite impacts on water efficiency, and the ratio of imports to exports is positive.
From the coefficient of variable ln(ER), we observed that environmental regulation intensity had a positive effect on water efficiency at 1% significance levels. Actually, under the state of being restricted by rigid environmental behavioral rules, enterprises have to perfect their production technologies to save water and reduce pollution. Meanwhile, residents would also practice water recycling and re-use to improve water utilization efficiency.
For variable ln(RE), it was found that water resource endowment posed a negative effect on water efficiency at 5% significance levels. This is attributable to the impact of "Resource Curse" which implies that the more abundant water resources are in a region, the weaker awareness of water conservation local people have, thereby resulting in a lower water efficiency. For variable ln(UL), it was found that urbanization level posed a positive impact on water efficiency at 5% significance levels. In fact, urbanization would make agricultural water rapidly transferred to industrial or civil water-using departments. This means water resources would flow from rural to urban areas in the urbanization process. In addition, due to the fact that city has better water supply facilities, water reuse technologies and a sewage treatment system, the rural-to-urban water flows could help improve local water use efficiency and construct a water-saving industrial structure system. Additionally, urbanization development can create conditions for virtual water trade in international and domestic markets. In this case, water-intensive agricultural and industrial products can be imported from other provinces or countries instead of being self-produced, which may help reduce local water consumption to a certain extent. Taken together, urbanization can restrain the growth of the total amount of social and economic water consumption by promoting the optimal allocation of water resources.
From the coefficient of variable ln(IS), we observed that the industrial structure positively impacted water efficiency at 10% significance levels. Actually, agricultural and industrial sectors in China consume substantial water resources and emit considerable pollution. Moreover, water-saving and environmental protection technologies have not been widely used by agricultural production units and industrial enterprises. For example, in China's agricultural production, flood irrigation is often adopted, while sprinkling irrigation and drip irrigation are seldom used. Consequently, the water efficiency of these industries is at low levels. On the other hand, unlike the primary and secondary industries, tertiary industries consume much lower amounts of water resources and therefore are not highly sensitive to water supply. Thus, the growth of tertiary industries would promote water efficiency improvement. Notably, it is necessary to investigate whether the variable should be included in the model in the context of its marginal significance. To this end, we re-perform the model with the exclusion of the variable. By comparison, we can observe that the inclusion of this variable would indeed result in an improvement in overall model performance. Therefore, variable is worthy of discussion in this model. The regression results are listed in Table S4 in the Supplementary Materials and the detailed discussions are provided there as well.

Conclusions and Policy Implications
In this paper, we propose a parametric distance function approach to estimate the water efficiency performance index and its influencing factors from the production efficiency viewpoint. Empirically, the proposed approach is applied to 30 regions of China from 2000 to 2015. The findings are as follows: Both China overall and most of the regions still have room for improvement in terms of water efficiency. SFA and DEA would possibly lead to different results in benchmarking water efficiency. Moreover, SFA often has a higher discriminating power than DEA. Middle China was found to have a collapse phenomenon in TFWE, which may be attributed to the trans-regional pollution transfer caused by the industry transfer from Eastern China. There existed significant regional disparity in water efficiency of China and the difference was found to take on a U-shaped evolution trend. The regression results indicate that factors like industrial structure, import and export trade, environmental regulation and urbanization level have a positive impact on water efficiency, while resource endowment and economic level exhibit negative and nonlinear effects, respectively.
Based on the above findings, the following policy implications are provided as follows: 1.
Due to the large regional differences in economic development level, water resources endowment, and water efficiency performance, the "one size fits all" solution should be avoided and differentiated regional water-saving strategies should therefore be formulated. For example, in terms of the province-level decomposition of national water-saving targets, an alternative scheme could be designed by assigning higher reducing targets to provinces with lower water efficiency scores, while assigning lower targets to those with higher scores.

2.
In view of the existence of regional differences in location, transport, natural resources and ecological environment conditions, industrial structure exhibiting a positive impact on water efficiency improvement should be adjusted to suit measures to local conditions and give a full play to the superiority. Specifically, Eastern China should further strengthen the growth of the high-tech tertiary industry and orderly guide transfer industry to give a full play of its technology spillover effect. Middle and Central China should vigorously develop ecological agriculture and tourist industry by right of its geographical position and natural resources endowment. Meanwhile, based on resources and environment carrying capacity, local government should actively undertake transferring industries to promote the scientific upgrading of industrial structure.

3.
Environmental regulation should be implemented on the principle of "common but differentiated responsibilities". Eastern China should strengthen environmental technological innovation to develop more efficient water saving and sewage treatment technologies. Besides, the government should formulate quantifiable wastewater reduction targets and further set up penalty mechanism to punish enterprises that are not qualified. Central and Western China should eliminate backward production capacity and encourage local enterprises to introduce advanced wastewater treatment technologies. In this regard, proper subsidies could be granted to enterprises which adopt environmental protection technologies and implement active measures of protection.

4.
As the shortage of water resources per capita is serious, China should reduce the production of water-intensive products and services but turn to international imports from water rich countries, which is a feasible way to alleviate domestic water pressure. In urban water use, urbanization should be continuously accelerated to exert its scale benefit on reducing the cost of public water facilities and popularizing water-saving and pollution-control technologies. Additionally, the government should establish the reasonable water fee system, enhance the water saving propaganda, and promote the application of water saving instruments to regulate household water use behavior.
Nevertheless, this paper inevitably has some limitations. First, our proposed approach aims to measure static water efficiency performance based on cross-sectional data. Further research may be implemented to extend the proposed approach to study dynamic water productivity index based on panel data (refer to Equations (S5)-(S13) in the Supplementary Materials for more details). Also, whether the trans-regional pollution transfer results in the collapse phenomenon of Middle China in TFWE needs to be further investigated. Additionally, technological heterogeneity among various regions is truly a significant issue worthy of consideration and should be included in the model.
Author Contributions: J.Z. designed the research and drafted the manuscript; H.Z. collected the data and conducted the model simulation; Z.X. reviewed, commented on, and revised the manuscript. All authors have read and approved the final manuscript.