Household water price and income elasticities under increasing-block pricing policy in China: an estimation using nationwide large-scale survey data

Figuring out household water demand response is of importance to sustainable water pricing policy making and optimalization. The paper estimates price and income elasticities of residential water demand in China by using the unique dataset from Chinese Household Water Use Behavior Survey 2019 in 50 cities. Two instrumental variables of marginal water price and average water price are used to address the endogeneity in the context of increasing-block water pricing policy. Results show that price elasticity ranges from −0.170 to −0.543, meaning that the demand for water is inelastic. Income elasticity ranges from 0.062 to 0.133, indicating that water is a necessary commodity. It unveils that water scarcity cities have more sensitive price response. It verifies the effectiveness of the differential increasing-block water pricing schemes tailor-made to local water resources endowments. Besides, it shows that high water-consuming households have more sensitive price response. It suggests that implementing more stringent IBWP scheme for those households constitutes a promising policy improvement option in the future.


Introduction
China has been facing increasingly severe water scarcity and its water resources per capita constitute a quarter of the world average [1][2][3].The domestic sector makes the third largest consumer following agricultural sector and industrial sector [4].Residential water demand is the main reason causing the rapid increase in domestic water consumption [5].As one key tool of water demand-side management (DSM) policies, residential increasingblock water pricing (IBWP) policy has been widely implemented in China.It aims to guide residents to conserve water reasonably.The conservation effect depends on household response to the IBWP policy.The paper estimates price and income elasticities of residential water demand, in order to measure residents' response to water pricing policy and explore promising policy improvement.
Price elasticity of demand refers to the change in consumption of a good in relation to the change in its price, and income elasticity refers to the change in the quantity demanded for a good in relation to the change in income [6].The two pivotal parameters have been investigated extensively over last four decades since they reflect household response to pricing policy [7,8].The estimated short-run price and income elasticities of typical studies in different countries or regions are illustrated in figure 1.The reviewed studies can be found in table S1 in the online Supplementary Information.
Visual inspection of figure 1 unveils two pieces of facts.First, the existing studies are seriously unbalanced geographically.Abundant studies have been conducted in developed countries such as the U.S. and European countries.In China, where the contradiction between supply and demand of water resources is pretty fierce, there is limited relevant research to provide pivotal elasticity parameters for urgent water pricing policy assessment [9].This is probably due to data unavailability at household level.The only study of Sun [10] used annual panel data of 10 cities in Shaanxi Province of China from 1995 to 2004 to estimate residential water consumption function.It suffered two drawbacks.For one thing, it used the aggregate data that may ignore household heterogeneity.For another, there was no IBWP policy in residential sector in the research timespan, while the policy constitutes the core topic of the study.Second, the estimated results of price and income elasticities fail to obtain consistent estimation.Although most estimated price elasticities fall between −1 and 0, meaning the good of water is demand inelastic, some studies obtained estimation greater than 1 in absolute term, suggesting that the good of water is demand elastic.Even in the same region such as Denton, Texas, the estimated price response shows differential pattern: Nieswiadomy and Molina [11] concluded that water demand was price inelastic while Hewitt and Hanemann [12] evidenced that water demand was price elastic.It may hint the importance of how to introduce water price variable since the two studies adopted different strategies in estimating water demand function.As for income elasticity, the disparity is even larger.Although most estimations fall between 0 and 1, suggesting that the good of water is necessities, some studies obtained values greater than 1, hinting water is the luxury good [13].Besides, Martins and Fortunato [14] even got a negative value of −0.0005, meaning that the good of water is the inferior good in Portuguese households.The scattered estimated results suggest that it is not reliable to draw on the values of other countries or regions to serve the practice in China.
Another technical headache when estimating price and income elasticities is the endogenous problem of water price brought about by the IBWP policy.As per the official file Guiding Opinions on Speeding up the Establishment and Improvement of the Increasing-Block Water Pricing Policy for Urban Residents, cities should fully implement the IBWP in residential sector by the end of 2015. Figure 2 illustrates briefly the three-ladder IBWP in China.In the IBWP scheme, the block marginal rate charged to households changes in a step-wise fashion with the quantity demanded.It has the issue of simultaneous determination of marginal price and water consumption.How to include water price variable in demand function affects elasticity estimation reliability [11,12].Furthermore, each city has its specific IBWP scheme according to local water resources endowment and economic development level.Table 1 categories three types of IBWP schemes by metering circle and billing circle in the studied 50 cities of the paper.Detailed IBWP schemes can be found in table S2 in the online Supplementary Information.
The specific water consumption in each block is expressed officially in two metering cycles, namely the monthly standard in Type II and Type III cities while the yearly standard in Type I cities in table 1.Furthermore, two fundamentally different water bill calculation cycles are employed, namely 'Monthly' in 15 cities (Type III cities in table 1) and 'Yearly' in the rest 35 cities (Type I and Type II cities in table 1).For monthly water billing cycle, household water bill for metered monthly water amount is calculated according to the monthly IBWP scheme.However, for yearly water billing cycle, water bill is calculated based on yearly rather than monthly blocks of water consumption, even though water consumption is metered monthly.Figure 3 displays the scattered block setting and block rate design of the IBWP schemes in the 50 cities, which gives more intuitive reflection of significant variations.
Other topics focusing on the IBWP policy include the design of proper block water pricing and its effect on household water consumption.As for the design of the IBWP policy, there are in-depth discussion and comparison between China and India [15][16][17][18].Concerning the conservation effect of the IBWP policy, there are mixed conclusions.Some studies have confirmed the effectiveness of IBWP scheme in reducing household water consumption [19,20].But the opposite conclusions also exist [21][22][23].
The paper aims to address two research questions.The first is to estimate price and income elasticities of residential water demand under the IBWP policy in China.Furthermore, it assesses the existing water pricing policy and provides promising improvement direction based on empirical results.The two questions are answered as follows.First, a total of 6,078 household first-hand survey data solves the problem of data unavailability.It comes from the first round Chinese Household Water Use Behavior Survey in 2019 (CHWUBS  The main results of the paper are as follows.First, price elasticity ranges from −0.170 to −0.543.It means that the demand for water is inelastic.Second, income elasticity ranges from 0.062 to 0.133.It indicates that water is a necessary commodity.Third, household heterogenous responses to water price verify the effectiveness of the differential IBWP schemes.Besides, it provides the promising policy refinement tailor-made to household level of water consumption.
The rest of the paper is organized as follows.Section 2 introduces the method.Section 3 provides the estimated results.Section 4 conducts the discussion.Conclusion is outlined in section 5.

Method
2.1.The data Three datasets are used in the paper, which are summarized in table 2. It includes the detailed IBWP dataset spanning 50 major cities in China, the unique first-hand nationwide large-scale household survey data, and two city-level indicator datasets.

Household survey data
Household survey dataset comes from the first round Chinese Household Water Use Behavior Survey 2019 (CHWUBS 2019), conducted by School of Economics, Hefei University of Technology.The survey spans a total of 50 major cities in China, as summarized in table 1.Only individuals aged above 18 years old and acted as the decision maker in the family were allowed to continue the survey.The consent was gained from the participants for this study.A total of 8 household variables are collected, as summarized in table 2.
The data collection was entrusted to one professional survey company, which conducted the survey during September and October, 2019.The surveyed households were obtained based on stratified, multi-stage and cluster probability proportional sampling technique.In the first stratified stage, a total of 100 administrative districts were randomly selected, with 2 areas in each of 50 cities; second, a total of 478 residential communities in those districts were randomly selected; third, in each residential community, households were randomly visited by investigators.Paper and electronic questionnaires were issued to sampling respondents.A total of 27,000 questionnaires were issued during the survey.In the end, 6,078 questionnaires were collected and the Figure 3. Increasing-block water pricing schemes of 50 cities in China.Notes: For each of the listed 50 cities, the green, blue, and red horizontal lines denote water consumption ranges in Bock-1 ladder, Block-2 ladder, and Block-3 ladder, respectively.The orange and yellow vertical lines indicate the correspondence relationships between Bock-1 and Block-2 ladder, Block-2 and Block-3 ladder, respectively.For Type I cities in table 1, water consumption in each block in yearly standard is divided by 12 to obtain the monthly water consumption in each block for ease of comparison with other cities of Type II and Type III in table 1. response rate was 22.5%.The sample sizes in Type I, Type II and Type III cities in table 1 are 3914, 349, and 1815, respectively.The geographical sample distribution in the studied 50 cities is demonstrated in figure 4.

City-level indicators
It is verified that climatic conditions have significant impacts on household water consumption [25][26][27].Two candidate climatic seasonal variables are rainfall and temperature variables.Different from life habit of residents in developed countries, Chinese residents barely have water demand for outdoor use and nearly all residential water demand occurs indoors [28][29][30][31][32]. Thus, rainfall variable would have negligible effect on residential water demand in China.On the other hand, temperature variable is highly prone to affect residential water use because higher temperature pushes more drinking water demand and higher frequency of showering [33].Thus, temperature variable is included to characterize climatic condition in China.The number of hot days across one year is calculated to represent the temperature variable.It is defined as the count of days that have maximum temperature outnumbering 30 Celsius degrees [34].Furthermore, household water-consuming behavior is very likely to be affected by different water resource endowments [35,36].City-level water supply capacity constitutes one key aspect in determining local IBWP scheme in China.The more abundant the water resources, the stronger the water supply capacity.Correspondingly, it leads to the looser set of the IBWP policy and the less water bill burden undertaken by the residents.Thus, the heterogeneity in local water supply capacity is very likely to cause household differential behavioral response to the IBWP policy [37].Thus, investigating potential household heterogeneous responses is of importance for the improvement of the IBWP policy because different cities have heterogenous endowments of water resources.
Per capita water resources ownership in 2019 is calculated based on China City Statistical Yearbook 2020 [24].It is used to characterize the city-level water supply capacity of the 50 cities.The cities with the top 50% water resources per capita are classified as non-water scarcity cities, while the rest are classified as water scarcity cities.The detailed indictor values and the resulting two classification of cities can be found in figure S1 and table S3 in the online Supplementary Information.

Descriptive statistics
Two city-level variables are compiled to correspond to each sampled household.Descriptive statistics of all involved variables, together with their description and unit or coding means, are presented in table 3.
According to China City Statistical Yearbook 2020 [24], in 2019, the average household water consumption of all the 50 cities amounts at 163.8 m 3 , which is slightly higher than the mean in our sample (148.50 m 3 ).The average family size is 3.06 persons, which is slightly smaller than the sampled family size of 3.60.It indicates that our samples are not representative to some extent, which may be overcome when more precious first-hand household data is available in the future.

Instrumental variables for water price
In the context of non-linear IBWP scheme, choosing marginal price (MP) or average price (AP) in residential water demand remains the ongoing debate [38][39][40][41][42].In this study, both MP and AP instrumental variables are considered in modeling residential water demand, in order to obtain reliable elasticities estimations.The MP is the derived specification of Billings' framework [43].The AP is just the quotient of household total water cost and water consumption.

Marginal water price
In terms of instrumental variable of MP, the Billings' framework creates a set of instrumental variables for each legal rate structure that corresponds to the marginal price and income difference parameters [44][45][46].The general steps to establish instrumental variables are as follows.
First, we obtain the minimum and maximum values of water consumption (in m 3 ) of our sampled households under a certain IBWP scheme in each city.Based on 2 m 3 increment from the minimum value to the maximum value, a series of water consumption samples can be derived as follows.
Second, we calculate the theoretical water bill (TWB) for each of these sampled water consumptions (W ä Ω) obtained in the first step as follows.
where p 1 , p 2 , p 3 are the first water block rate, the second block rate, and the third block rate in the IBWP policy in one specific city, respectively; q 1 and q 2 are the upper limits of the first block and the second block of water consumption.
Third, these TWB values are regressed against their corresponding W values to have the following fitted model by using Ordinary Least Squares method.
Fourth, the estimated slope of b ˆis the instrumental variable for the water MP.The estimated intercept a represents the income difference variable I D and I a TWB bW.D ˆˆ= = -One explanation of the income difference variable is the virtual subsidy to households under the IBWP policy [47,48].It measures the difference between the actual water bill paid and the hypothetical water bill under a linear marginal water price.It stems from the income effect brought about by the change of the consumer budget line.Then, the instrumental variable for household income (I IV ) is obtained by surveyed household annual income (I) minus I D , as follows.
The general four steps described above have slight differences when applying to the 50 cities because of three types of metering circle and billing circle, as summarized in table 1. Table 4 and figure 5 combined list the detailed procedures to establish instrumental variables of MP for three types of cities.
The estimated instrumental variables of water MP and income difference are summarized in table 5. Consistent with table 5, the mean instrumental variable of water MP stands at 5.16 Yuan per m 3 and the mean

Average water price
In terms of another instrumental variable for water AP, the general two steps are as follows.First, we obtain the theoretical water bill (TWB) for each of sampled household water consumptions (W) as per the equation (2).
Second, water AP corresponding to each sampled household is obtained as per the following equation (5).6 and figure 6 combined give the detailed procedures to establish instrumental variable of water AP for three types of cities in table 1.

Econometric model specification
Choosing different functional forms when modeling residential water demand may affect the estimates of price and income elasticities [49,50].Since the log-log form both reflects the concept of water as an essential good and provides relatively reliable estimates of elasticities, the log-log econometric model is chosen by the paper, which is as follows [51].Where W i is the i-th household's annual water consumption in 2019; P IV,i is the instrumental variable for water price faced by household i; I IV,i is the instrumental variable for household annual income.In the context of MP, P IV,i is the marginal water price obtained as per the steps in section 2.2.1.I IV,i is calculated by using surveyed annual income of Table 6.Detailed description of operational steps to obtain AP. (2) Based on the variable of W, perform equations (2) and (5) to obtain the variable of AP for each household, as illustrated in figure 6. III

City type
(1) Using each block's monthly water consumption and the monthly water consumption of each surveyed household, perform equations (2) and (5) to obtain the variable of AP for each household, as illustrated in figure 6. household i minus the yearly difference variable I D in the corresponding city in table 5.In the context of AP, P IV,i is the water average price obtained as per the steps in section 2.2.2.I IV,i is equal to the surveyed annual income of household i.
The variables of household head's characteristics, household characteristics, and city-level characteristics are listed in table 3. ε i is the stochastic disturbance term, and α 0 ,K,α 11 are the parameters to be estimated.Among them, α 1 and α 2 are the short-run price elasticity and income elasticity of residential water demand, respectively.Ordinary Least Squares method is used to fit the model specification.The commonly-used independent variables in estimating household water demand function are summarized in table S4 in the online Supplementary Information.The variables of house characteristics (such as age, type, area, number of bathrooms, property value, etc), environmental concern and water durables are not included in our model, due to survey budget constraint.

Nationwide perspective
The whole samples are used to fit the equation (6).It results in household water demand estimation in terms of nationwide perspective.In each context of choosing MP and AP as instrumental variables of water price, results are summarized in table 7.
Comparison between columns (a) and (b) confirms that the two city-level variables do significantly impact residential water demand, according to the estimated significant coefficients and the increase in the Adjusted R-Squared.More hot days across one year mean higher frequency of showing and drinking, leading to higher residential water demand.Compared with households living in non-water scarcity cities, their counterparts in water scarcity cities do decrease their demand for water and thus impose less pressure on local water supply infrastructure.
Regarding elasticities of residential water demand, short-run price elasticities range from −0.170 under MP specification to −0.543 under AP specification, indicating that one percent increase in water price will lead to less than one percent decrease in water consumption.It means that the demand for water is inelastic.Short-run income elasticities under both MP and AP specifications stand around at 0.100, meaning that one percent increase in household annual income will lead to less than one percent increase in water consumption.It indicates that water is a necessary commodity.
As for the characteristics of household head, females tend to perform more water-saving behavior than male counterparts.The older the individual, the higher the level of household water consumption.In addition, more schooling years would generally push the demand for residential water, probably due to the more attention paid to sanitation purpose.
As with family composition, the larger the family size, the higher the water consumption.Although whether having children has no significant impact, having elderly does significantly decrease household water demand.This is maybe due to the thrifty habits of Chinese elderly [52].Besides, households owning the residence tend to consume higher water consumption, which is probably caused by renters being reluctant to boost the water efficiency of owners' water-consuming devices [53].

City-level water scarcity perspective
The degree of water resources abundancy significantly influences residential water demand as confirmed in table 7. Thus, the whole samples are split based on city-level water scarcity to study potential differences in residential water demand determinants.The results are presented in table 8.
Regarding elasticities of residential water demand, short-run income elasticities stand at around 0.100 that well approximates the estimation for the whole sample.However, compared with counterpart cities, short-run price elasticity decreases a bit under both MP and AP instrumental variables in non-water scarcity cities.It means that residents in water scarcity cities have higher sensitive price response to water demand.Moreover, significant heterogeneity can be found in household head characteristics and family composition between water scarcity and non-water scarcity cities, controlling for all other variables in the regression.Specifically, determinants of gender, education level, and family size only matter in non-water scarcity cities, while households having the elderly decreases water demand only in water scarcity cities.

Household water-saving potential perspective
It is of significance to investigate potential heterogeneous responses to price and income variables among households with different water-saving potential because water conservation constitutes the core target of the IBWP policy.Based on China City Statistical Yearbook 2020 [24], annual mean water consumption per household in each of the 50 cities is calculated.Sampled households that consume water higher than annual mean in that city are classified into high water consumption group and the rest are classified into low water consumption group.Empirical results by using the two subsamples are presented in table 9.
As for elasticities of residential water demand, obvious heterogeneity exists among high and low water consumption households.When facing the same IBWP scheme, households with high water-saving potential tend to have more sensitive price response than those with low water-saving potential.Furthermore, households with low water-saving potential have more sensitive response to the same increase in household income than those with high water-saving potential, controlling for all other variables in the regression.
Regarding other underlying covariates, significant heterogeneity exists between low or high household water consumers.Only in households with high water consumption, females tend to consume less water, more family members push water demand and having children significantly decreases water demand.Only in households with low water consumption, having elderly significantly decreases water demand and house owners have significant higher water consumption than renters.

Robustness check
To conduct robustness check, two strategies are used as follows.For one thing, 5% and 95% quantile samples in terms of household water consumption are excluded, respectively.For another, the 2 m 3 increment from the minimum value to the maximum value of household water consumption in the equation (1) shifts to 1 m 3 and 3 m 3 , respectively.The resulting four specific combinations of the two strategies are used to process the data and fit the equation (6).The estimated results are consistent with results summarized in tables 7-9, confirming the robustness of the estimated results.

The effectiveness of increasing-block pricing policy
The core objective of the IBWP policy is to guild households to conduct water conservation reasonably.The more sensitive response to water prices in water scarcity cities confirms the effectiveness of the differential IBWP policies.It shows that households in water scarcity cities have higher price elasticities in the absolute term (−0.197 versus −0.154, −0.500 versus −0.462 in table 8).It means that one unit increase in water price can lead to more water use reduction in water scarcity cities as compared to non-water scarcity cities.On average, the set of residential IBWP policy tend to be tighter in water scarcity cities as compared to nonwater scarcity cities.This is verified by following two points.First, the mean of the upper limit of the first block of annual water consumption in water scarcity cities stands at around 176 m 3 , accounting for about only 74% of that in non-water scarcity cities; the mean upper limit of the second block in water scarcity cities amounts at 273 m 3 , only accounting for 77% of 354 m 3 in non-water scarcity cities.Second, when it comes at water marginal price, each of three average water block rates in water scarcity cities stands at around 3.796, 5.148, and 8.352 Yuan per m 3 respectively, compared with 2.927, 3.981, and 6.386 Yuan per m 3 in non-water scarcity cities.On average, each of three water marginal prices in water scarcity cities is about 1.3 times of those in non-water scarcity counterparts.More stringent IBWP scheme in water scarcity cities results in household more sensitive price response.It verifies the effectiveness of the differential setting of IBWP policies in areas with different water endowments.

The improvement of increasing-block pricing policy
Household-specific IBWP policy may constitute one promising policy improvement direction.It can encourage the water-saving potential in high water-consuming households.It shows that there are heterogenous price responses between high and low water-consuming households (−0.408 versus −0.361, −0.416 versus −0.352 in table 9).It means that one unit increase in water price can bring about more water reduction for high water consumption households as compared to low water consumption households.High water consumption households tend to have large water-saving potential.They are supposed to make the focus of DSM policies.The city-level or regional one-size-fits-all IBWP policy can be further refined tailor-made to household level of water consumption.The results inform policy makers that implementing more stringent IBWP policy for high waterconsuming households in the same city may be a policy consideration to achieve better water conservation effect in the future.

Conclusion
The paper estimates household response to the IBWP policy in residential water demand in China by using the first-hand dataset from Chinese Household Water Use Behavior Survey 2019 in 50 cities.Two commonly-used instrumental variables of marginal water price and average water price are used to obtain reliable elasticities estimations.Results show that price elasticity ranges from −0.170 to −0.543 and falls between −1 and 0, meaning that the demand for water is inelastic.Income elasticity ranges from 0.062 to 0.133 and falls between 0 and 1, indicating that water is a necessary commodity for households.The estimated results are consistent with most studies in other countries or regions.It confirms the variations in estimated elasticities to varying degree by using the two instrumental variables of water price.
There are two implications for the IBWP policy in terms of water supply and demand.For one thing, households have more sensitive price response in water scarcity cities than those in non-water scarcity cities.It verifies the effectiveness of the differential IBWP schemes tailor-made to local water resources endowments.For another, high water consumption households tend to have large water saving potential.The more sensitive price response of high water-consuming households informs policy makers that the city-level or regional one-sizefits-all IBWP policy can be further refined tailor-made to household level of water consumption.Implementing more stringent IBWP policy for high water-consuming households in the same city is likely to bring about promising water conservation effect.
More valuable research directions can be conducted in the future when more precious first-hand household data is available.For one thing, it is of significance to make clusters on the differences in marginal water prices and to evaluate the reasons for these differences between cities in China.For another, it would result in more compelling price and income elasticities when more representative samples and more rich explanatory variables are collected.

Figure 1 .
Figure 1.Graphical presentation of price and income elasticities.Note: The elasticity values obtained from some studies are in the form of ranges, and the upper and lower limits of these ranges are shown in the figure.

Figure 2 .
Figure 2. Illustration of three-ladder increasing-block water pricing in China.

Table 4 . 1 ) 1 ) 2 ) 1 ) 2 ) 3 )
Detailed description of operational steps to obtain MP.City type Description of operations I (Based on the variable of W, perform equations (1)-(4) to obtain yearly b ˆand yearly I IV for each city.The process has been illustrated from Panel (a) and Panel (b) in figure 5. II (Each block's monthly water consumption in each city multiplies by 12 to obtain each block's yearly water consumption.(Based on the variable of W, perform equations (1)-(4) to obtain yearly b ˆand yearly I IV for each city.III (Perform equations (1)-(3) to establish yearly b ˆand monthly I D .(The monthly I D multiplies by 12 to obtain the yearly I D in each city.(Obtain the yearly I IV according to equation (4) in each city.

Figure 5 .
Figure 5.An example of obtaining marginal price and income difference variables.

Description of operations I ( 1 ) 1 )
Based on the variable of W, perform equations (2) and (5) to obtain the variable of AP for each household.The process has been illustrated from Panel (a) and Panel (b) in figure 6. II (Each block's monthly water consumption in each city multiplies by 12 to obtain yearly water consumption.

Figure 6 .
Figure 6.An example of obtaining water average price.

Table 1 .
Three types of IBWP schemes by metering circle and billing circle.

Table 2 .
Three datasets used in the paper.
Water consumption range in each block; Water rate in each block; Metering cycle of each block; Calculation circle of water bill Government official websites of provinces and cities (See table S2 in the online Supplementary Information) CHWUBS 2019 2019 Household level in 50 cities Household average water consumption per month in 2019; Age, Gender, and Education level of household head; Household income; Having children or not; Having elderly or not; House ownership Questionnaire survey City-level indicators 2019 City-level in 50 cities Daily minimum temperature and maximum temperature of the 50 cities in 2019; Per capita water resources ownership in 2019 WIND database (www.wind.com.cn)China City Statistical Yearbook 2020 [24]

Table 3 .
Descriptive statistics.differencevariable is −206.99Yuan.But there is a substantial disparity in water MP among the 50 cities, consistent with the variations in terms of each block rates in figure3.The instrumental variable of water MP ranges from as low as 2.20 Yuan per m 3 in Ganzhou to as high as 12.30 Yuan per m 3 in Handan.The corresponding lowest and highest values of income difference variable in the two cities stand at −14.47 Yuan and −745.46Yuan, respectively. income

Table 5 .
Instrumental variables for water MP and income differences in 50 cities.

Table 7 .
Estimated results for the whole sample.

Table 8 .
Estimated results for sub-samples in terms of city-level water scarcity.

Table 9 .
Estimated results for subsamples in terms of household water consumption.