Residential Water Demand Model Economics Essay
Water resource management plays an increasing role in dealing with water scarcity problem of semi-arid urban area of developing countries. For sustainable and adequate water management of the city, it is essential to analyzed the impact of socio-economic and demographic variables on water use. This paper presents an econometric water demand model for forecasting future residential water demand of highly dense area of Jaipur city, India addressing the relationship between residential water use and socio-economic and demographic variables. The study applies an ordinary least squared (OLS) regression model to measures the impact of household income (I), age of respondent (A_R), household size (SIZE), age of home (A_H), wealth (W) , asset score (AS) , dwelling status (DWELL), monthly expenditure on water supply (EXP_WS), number of bathrooms (BATHR) and number of rooms (RMS) on residential water use applying the 2009 survey data of 149 households . Empirical results indicate that residential water demand of the study area is characterized by I, SIZE, EXP_WS, and AS, where SIZE and AS are a major influencing explanatory variables as shown by their value of standardized model coefficients at 95% confidence interval. Standardized model coefficient for SIZE and AS is 0.542 and 0.418 respectively. Percentage difference between observed and predicted value is -3.05% and value of R2 (0.829) implies that estimated equation is considered as an equation of very good fit and also applying to other area having similar socio-economic and demographic variables.
Key words: Econometric water demand model, ordinary least squared (OLS), asset score (AS). Residential water use(RWU), water scarcity, socio-economic and demographic variables
Introduction
Forecasting of residential water demand is a crucial component in the successful operation of water supply system of a city. It is used in short, medium, and long-term horizons for capacity planning, scheduling of maintenance, future financial planning and optimization of the operations of water supply system. In addition, adequately forecasted demand will be a basis for the strategically decision making on future water sources selection, upgrading of the available water sources and designing for the future water demand management options , so that water resources are not exhausted, and competing users have adequate access to those resources (Khatri, K.B. et al 2009).
Most of the previous water demand studies reveals that residential water demand is depends on household size, monthly household income, wealth of household, seasonal variation in temperature and population etc (Reynaud, 2002; Arbues et al, 2003, Nieswiadomy and Molina 1989). Most Water demand studies have also included one or more household variables to capture variation in indoor water use. Nieswiadomy et al (1989) relied on only two household-specific variables, house size and lawn size in residential water demand studies whereas Hewitt and Hanemann (1995) gave more attention on the number of bathrooms. They find that bathrooms variable was significant in comparison to house size variable, suggesting that the number of bathrooms may be a better proxy for household size (and by extension, indoor water consumption). Renwick and Green (2000) used a much more involved process to model the effects of climate and seasonality variable on water use. Climatic variables included maximum daily air temperature and cumulative monthly precipitation, expressed as deviations from 30-year historical means. An adjustment for seasonal effects was made by regressing temperature and rainfall data on harmonic (sine and cosine) terms, so that the climatic variables represented only the effects of deviations of climate from normal patterns. Chang et al (2010) identified that single family residential (SFR) water consumption was mostly explained by key building structural variables, namely building size, building density and building age. Econometric forecasting approach captured all these socio-economic and demographic variables in water demand studies. It is based on statistically estimating historical relationship between different factors (independent variables) and water consumption (the dependent variable) assuming that this relationship will continue into the future (Zhou et al 2000).
Therefore on the lime-light of the above discussion, this paper tries to explore the relationship between residential water demand and household socio-economic and demographic variables using the computing tool (XLSTAT 2010). It also attempts to assess the main governing drivers’ variables (socio-economic and demographic) for the future water demand studies in highly dense area of old Jaipur city.
Case Study: Old Jaipur City
Old walled area of Jaipur city (Figure 1) is located in 26055’ N latitude and 75052’ E longitude in eastern part of Rajasthan, India and a main commercial, industrial and historical tourist centre of the country. It faces the severe water scarcity problems due to inadequate irregular rainfall pattern, prevailing drought condition, absence of perennial water sources, in addition to explosive population growth rate due to high growth of urbanization and industrialization (Rajasthan State Water Supply Department 2000). This situation is aggravated by old and deteriorating water supply assets reporting high leakages and burst (44% of the total water supply). The main source of water is groundwater (97%), which is depleting at an average rate of 2.49 m/year (Central Groundwater Board, 2007). To reduce the dependence on groundwater resources the state water supply department brings water from the distant source on Banas river by Bisalpur Dam. But this is also not a sustainable and viable solution therefore there is a need of residential water management through demand management approach. Residential water demand is characeritized by socio-economic and demographic variables of the respondents. Socio-economic and demographic characteristic of the old walled city reveals that most of the most of the houses are old, and in dilapidated conditions and average age of the houses are more than 100 years. Most of the respondents are from lower and lower middle income group (GOI, 2006).
Figure 1: Study Area
Survey Design and Methodology
To accomplish the specific objectives of the study, we collect primary data of household socio-economic and demographic variables from 149 households through well designed questionnaire using a random sampling method and main preference were given to females because they faces the water fetching and collecting problems more. Questionnaire used for the present study was designed on the basis of previous literature and consultation with the experts from Water Supply Department, academician and local representative people. The designed questionnaire was first pre-tested on a sample group of representatives to minimize the strategic, hypothetical and compliances biases arises during the survey. Problematic and ambiguous questions were rephrased during the pre-testing of questionnaire if the respondents were not responding on that question. Developed questionnaire solicit information on household socio-economic & demographic variables from the study area. The detailed description of the study area and sampling profile is given in Table 1.
TABLE 1: SAMPLING PROFILE OF STUDY AREA
S.No.
Area
Sampling Locations
Sampling ID
Ward No.
No of respondents
1
Pink City(Old Jaipur City)
Purani Basti
1
40
99
Brahmpuri
2
59
50
Methodology
The data obtained from the preliminary household survey was used for data analysis and modeling purpose as shown by the methodological framework given in Figure 2. The sets of independent data used for water demand modeling are socio-economic and demographic variables. These data sets were first checked for normality, linearity and homogeneity and the variables don’t match the following assumptions were excluded. Then among the n sets of independent variables, significant variables were selected on the basis of factor score (eigen value) through Principal Component Analysis(PCA). Then econometric water demand model was developed using the significant independent variables and dependent variable through multivariate regression analysis and validate with an independent data sets. Validate model was used for forecasting the residential water demand by assuming that same statistical relationship will exist between independent and dependent variables.
Analysis Data
Data TestingDATA
Assumption Checking
TESTING
Excluded no
Factor analysis
Factor extraction
Influential Variable Analysis
Factor score
Regression AnalysisFACTOR
ANALYSIS
Model Validation
Regression Model
Forecasting single family residential water demand
Figure 2: Flowchart shows the methodological framework for water demand
Software Used
Software used for the present study is XLSTAT 2010, it is a leading data analysis and statistical software for Micrsoft Excel. The use of Excel as an interface makes XLSTAT a user friendly and highly efficient software package. It relies on Visual Basic Application for the interface and on C++ for the mathematical and statistical computation. It offense a wide variety of functions to enhance the analytical capabilities of Excel, making it the ideal tool for our everyday data analysis and statistical requirements (Addinsoft, 2010).
Analytical Approach
In order to find out the structural relationship between the household water use and socio-economic and demographic variables, multivariate statistical analysis will be used (Goldberg, et al 2003 and Zhang et al 2005), The general model used for the present study are given by equation (1).
Q=f(X1, X2,………Xn)+u…………..(1)
Where, Q is the quantitative household water use , u is the error term and f(.) denotes the function of explanatory independent socio-economic and demographic variables i.e household size, monthly household income, wealth of household, age of home and expenditure on water supply etc.
Residential Water Use
In this study specific household socio-economic and demographic variables were used to assess their influence on residential water use (RWU). The independent variables selected for the present study are household income (I), age of respondent (A_R), household size (SIZE), age of home (A_H) , wealth (W) asset score (AS) , dwelling status (DWELL), monthly expenditure on water supply (EXP_WS), number of bathrooms (BATHR) and number of rooms (RMS) . These variables were used because they were deemed to most likely influence the domestic water demand. Household size (SIZE) variable is intended to examine the impact of family size on the variation of residential water use. Age of respondent (A_R) and age of home (A_H) is defined in terms of years while household Income (I) and expenditure on water supply (EXP_WS) are measured in Indian Ruppess. Asset Score (AS) is a proxy of the living standard of the respondent and calculated by putting the weighted score on household assets, such as washing machine, cooler, two vehicles and four vehicles. The weighted score used for cooler, washing machine, two vehicles and four vehicles are 1, 2, 1.5 and 5 respectively. Wealth (W) is a dummy variable and takes value of 0 if owner otherwise 1. It is a proxy of ownership of the house and wealth. More is wealth of the household, more is the water consumed in leisure and other activities. Dwelling (DWELL) is dummy variable and take value of 0 if single storey building and 1 otherwise. In addition to number of rooms (RMS) and bathrooms (BATHR) were also employed to investigate their impacts on the water use of households. This study used the household level data to investigate the influence of explanatory variables on RWU as mentioned below by equation 2. Where D, I, A_R, SIZE, A_H, W, AS, DWELL, BATHR, RMS, EXP_WS are predicted water demand, average monthly household income, age of respondents, size of household, age of home, wealth of household, dwelling status, number of bathrooms, number of rooms and expenditure on water supply respectively for the representative household.
D=f(I, A_R, SIZE,A_H,W, AS,DWELL, BATHR, RMS, EXP_WS)………….(2)
Results and Discussion
Residential water use of the representative household is mainly determined by income (I), household size (SIZE), expenditure on water supply (EXP_WS) and Asset Score (AS) as shown by equation 3.
The empirical results indicate that residential water demand of a representative household increase with increase in the value of SIZE, AS and I as shown by their positive estimated regression coefficients with respect to water demand as given in Table 2. Estimated regression coefficient with respect to SIZE, AS and I are 82.46, 27.216 and 0.111, this account for the fact that as SIZE increase more is the aggregated water demand for day to day activities. Income is the proxy of affluence, therefore more is the income higher the water consumption in leisure activities. In the similar way, more is the AS, higher the living standard and more water required for water consuming activities. Negative price elasticity (-0.435) observed in this case because most of the people living in this area are from lower and lower middle income group, so they don’t prefer to spend more money on water supply services.
Table 2: Model parameters of Water Demand Model
Estimation Results for
Source
Value
Standard error
t
Pr > |t|
Lower bound (95%)
Upper bound (95%)
Intercept
32.616
41.186
0.792
0.430
-48.786
114.018
I
0.011
0.006
1.821
0.071
-0.001
0.022
SIZE
82.468
6.451
12.784
< 0.0001
69.718
95.218
EXP WS
-0.435
0.260
-1.676
0.096
-0.948
0.078
AS
27.216
6.928
3.928
0.000
13.522
40.909
There is evidence that no relationship between age of respondent (A_R), age of home (A_H), number of rooms (RMS), number of bathrooms (BATHR) and dwelling (DWELL) are observed in this case as shown by Table 2. These imply that these explanatory variables had no impact on residential water use. Effect of RMS ,BATHR and DWELL are not observed on residential water use because this is highly dense and populated area of the city i.e. 58207 persons/square km (GOI 2006) so single house is shared by more than 2-3 families at meager living standard. Most of the families live in one room and share bathrooms and toilet by more than 2-3 families. No effect of A_R is observed because most of the respondents are at younger age, so give the same response on water use. Little or no variation in A_H is observed because most of the houses are old (more than 100 years old) so less equipped with modern bathroom/toilet and sanitary fitting arrangements; therefore lower is the water consumption 125.313lpcd. Value of standardized model coefficients at 95% confidence interval reveals that SIZE (0.542) and AS(0.418) have a major influence on residential water use as shown by the Table 3 and Figure 3. Standardized Model coefficients account for the dependence on different parameter magnitudes by scaling the equation coefficients by their estimated standard deviations.
Table 3: Standardized Model coefficients of different variables
Source
Value
Standard error
t
Pr > |t|
Lower bound (95%)
Upper bound (95%)
I
0.204
0.112
1.821
0.071
-0.017
0.425
SIZE
0.542
0.042
12.784
< 0.0001
0.458
0.625
EXP WS
-0.108
0.064
-1.676
0.096
-0.235
0.019
AS
0.418
0.106
3.928
0.000
0.208
0.629
Value of coefficient of determination (R2) is very good i.e 0.778 as shown by the goodness of fit statistics as given in Table 4, so estimated equation is considered as an equation of very good fit and 77.8 % of the variation in water use is explained by independent variables and remaining 22.2% is unexplained by the model.
Table 4 :Goodness of fit statistics:
Observations
150.000
Sum of weights
150.000
DF
145.000
R²
0.778
Adjusted R²
0.772
MSE
20784.941
RMSE
144.170
MAPE
17.136
DW
1.585
Cp
5.000
AIC
1496.212
SBC
1511.266
PC
0.237
To check the validity of above developed model, we used 50 independent data sets from the study area and compared the observed and predicted water demand by plotting the predicted value in y-axis (abscissa) versus observed value in x-axis (ordinate) as shown in Figure 4. The slope of the equation and R2 value (0.829) is find to be very near to 1 and percentage difference between observed and predicted value is -3.04%. Therefore the above developed model is also use for other area having the same socio-economic and demographic conditions
Conclusion
Residential water demand of the highly dense area of Jaipur city is characterized by income (I), household size (SIZE), expenditure on water supply (EXP_WS), and asset score (AS), where SIZE (0.542) and AS (0.418) are major influencing determining variables as shown by their standardized model coefficients value at 95% confidence interval. Goodness of fit statistics reveals that value of R2 is 0.778 so 77.8% of the variation in water use in explained by independent variables and remaining 22.2% variation is unexplained by the model. Percentage difference between observed and predicted water demand is -3.05% therefore the above developed model is also use for other area having the same socio-economic and demographic conditions
