E533
Fullerton & Cárdenas | http://dx.doi.org/10.5942/jawwa.2016.108.0156
Peer-Reviewed
Forecasting Water Demand in Phoenix, Ariz.
THOMAS M. FULLERTON JR.1 AND JUAN P. CÁRDENAS2
1Department
2United
of Economics & Finance, University of Texas at El Paso
Bank of Paso del Norte, El Paso, Tex.
Short-term water demand forecasts support water utility
planning efforts. This study applies a linear transfer function
(LTF) approach to model and forecast water demand for singlefamily residential, multi-family residential, and nonresidential
customer categories in Phoenix, Ariz. Among other things,
nonresidential water usage is found to be somewhat more priceresponsive than residential usage. Variations in responses to
weather and economic variables are also documented for the
various customer categories. Out-of-sample demand simulations
are generated for periods when actual demand is known.
Descriptive accuracy metrics and two formal tests are used to
analyze the accuracy of LTF projections against two randomwalk benchmarks. The descriptive accuracy results for percustomer water usage forecasts in most cases favor the LTF
model, but the improvements in accuracy with respect to the
benchmarks are statistically insignificant in most cases. Mixed
accuracy results are obtained from an analysis of the LTF
customer base forecasts.
Keywords: customer categories, forecast accuracy, water demand
Water demand forecasts are used for a variety of purposes.
Water sales projections often serve as inputs to revenue forecasting models developed by utility financial planners (Boland et al.
1982). Demand simulations can also facilitate the rate design
process by illustrating the consequences of changing or maintaining the current water prices (Bithas & Stoforos 2006). Estimates
of future water consumption also help regulatory officials decide
when to implement seasonal water usage restrictions (Maidment
et al. 1985). Finally, short-term demand forecasts can inform
efforts to improve the efficiency and cost-effectiveness of water
supply system operations (Jentgen et al. 2007).
Recent trends in North American water demand highlight
the importance of accurate forecasts. New water-conserving
appliances and changing demographics have contributed to
stagnant or declining water sales at utilities across the continent (Rockaway et al. 2011). Demand erosion complicates
utility financial planning processes because the large fixed
costs of infrastructure will have to be recovered from a shrinking base (Sang 1982). Overprediction of water sales can result
in water requirements overestimation and the development of
needlessly expensive projects (DeOreo & Mayer 2012). In
regions where seasonal demands consistently outstrip local
raw water supplies, accurate forecasts of monthly consumption are of added importance (Fullerton & Elías 2004).
The principal objective of this article is to analyze short-term
water demand behavior in Phoenix, Ariz. Located in the Sonoran
Desert, Phoenix typically receives very limited rainfall. From 1981
to 2010, the metropolitan area received an average of approximately 8 in./year of precipitation (NOAA 2014). Because local
JOURNAL AWWA
water supplies are limited, Phoenix and other cities in the region
have developed infrastructure for importing water from other
areas. However, recent decades have witnessed a shift away from
large-scale water projects and toward water reuse and greater
conservation (Kupel 2003). Demand forecasts are crucial to
ensuring an adequate supply of water and planning for conservation efforts in a region like central Arizona where local water
resources are limited.
For this study, monthly data for 2008 to 2014 were used to
model and forecast single-family and multi-family residential, as
well as nonresidential, water demand. The breakdown of total
water usage by customer category, on average over the course of
the sample period, is illustrated in Figure 1. Because most economic research on water demand has been conducted for residential usage, one contribution of this study is examination and
prediction of nonresidential consumption patterns. Previously,
mixed forecast accuracy results have been found across different
municipal customer categories (Fullerton & Molina 2010). In this
effort, various assessments were used to thoroughly evaluate
forecast accuracy across the three customer classes analyzed.
LITERATURE REVIEW
Key determinants of residential water consumption include price,
income, and weather. Much water demand research indicates that
price increases have negative, but inelastic (less-than-proportional)
impacts on quantity consumed. Several factors help explain why
water demand is usually estimated to be price-inelastic. First,
because the water bill typically represents a small proportion of
family income, consumers are not likely to invest a large amount
2016 © American Water Works Association
OCTOBER 2016 | 108:10
E534
Fullerton & Cárdenas | http://dx.doi.org/10.5942/jawwa.2016.108.0156
Peer-Reviewed
of time in understanding water rate structures, which can be quite
complex. Consequently, reactions to changes in the rate structure
may be muted. Second, no substitutes exist for basic uses of water,
such as personal hygiene, cleaning, and food. Because of that,
customers may not drastically adjust consumption in response to
price changes (Worthington & Hoffman 2008).
Another important variable affecting metropolitan water
demand is income. The relationship between income and water
demand tends to be direct and inelastic (Dalhuisen et al. 2003).
The long-run income elasticity may differ from the short-run
elasticity because changes in the stock of water-using durable
equipment (e.g., dishwashers, clothes washers, bathtubs) may be
possible only over the long run (Woo et al. 2012, Nauges &
Thomas 2003). Monthly frequency studies have used employment
and industrial production as proxies for income (Fullerton et al.
2007, Fullerton et al. 2006, Fullerton & Nava 2003). Income
fluctuations also influence demand indirectly by affecting the
price elasticity. Renwick and Archibald (1998) find that lowincome households are more than five times as price responsive
as wealthier utility customers. That suggests that such households
may account for a disproportionately large share of any reduction
in demand induced by higher prices.
Climatic variables, such as temperature and precipitation, also
affect monthly consumption in statistically reliable manners. In
general, forecast accuracy is improved by including information
on weather variables when modeling water usage (Fildes et al.
1997). In a prior study of Phoenix water demand, Guhathakurta
and Gober (2007) report that when daily low temperatures increase
FIGURE 1
Total water usage by customer category in Phoenix,
Ariz. (2008–2014)
Single-family residential
Nonresidential
Multi-family residential
34%
51%
15%
JOURNAL AWWA
by 1°F, single-family water usage increases by 290 gal/month on
average. Several authors suggest that water demand is more
highly correlated with rainfall occurrence than with the amount
of rainfall itself (Martinez-Espiñeira 2002, Jain et al. 2001).
Seasonal variations in weather conditions may also influence
the price responsiveness of water demand. Price elasticity may
be higher during summer months because of increased discretionary usage (Espey et al. 1997).
Water usage patterns also differ across customer categories.
While residential users typically treat water as a direct consumption good, industrial and commercial customers generally use
water as an input to production (Hussain et al. 2002). Several
studies conclude that the price elasticity of water demand is
higher for the industrial sector than for the residential (Arbués et
al. 2010) and commercial sectors (Williams & Suh 1986). One
possible explanation of this regularity is that industrial customers,
unlike residential users, can often respond to significant price
increases by recycling water used in production (Arbués et al.
2010, Renzetti 1988, Williams & Suh 1986). Water recirculation
is a substitute for water intake and water discharge. While recirculation may not be a viable alternative to intake for all industrial
firms, it is much more prevalent in industry than in other sectors
(Dupont & Renzetti 2001). Pricing policies to improve water
management may have greater effects on industrial usage because
of the greater capacity of manufacturers to increase reliance on
recycled water in the face of rate hikes.
Price elasticities also vary across different categories of residential customers. In a study of Brisbane, Australia, Hoffman
et al. (2006) found the price elasticity of demand in owneroccupied households to be greater than in rental-unit households. This is in large part because rental tenants are entitled to
a free allocation of a reasonable amount of water under local
legislation. More generally, many apartment complexes use
common metering, and this does not provide a strong incentive
to renters to change their water usage behavior in response to
price signals (Agthe & Billings 2002). Even if some apartment
residents regard water as a free good as a consequence of common metering, apartment complex owners react significantly to
price increases by investing in water-saving capital such as lowflow shower heads and faucets (Agthe & Billings 1996).
As a consequence of the diversity in water consumption patterns across customer classes, different specifications are often
employed to model demand in the various categories. The number
of active customers (connections) per class has been used as an
explanatory variable to predict aggregate water usage for various
customer categories (Williams & Suh 1986). Determinants of
multi-family residential water demand may include assessed
property value per bedroom, number of bedrooms, vacancy, age
of the complex, presence of indoor water-saving devices (Agthe
& Billings 2002), and the presence of pools, dishwashers, and
washer–dryers (Wentz et al. 2014). Swimming pool areas, in-unit
dishwashers, and in-unit washer–dryers collectively explain nearly
50% of the total variation in water consumption across complexes (Wentz et al. 2014).
Commercial usage and industrial demand have been modeled
as functions of the respective employment figures for each of
2016 © American Water Works Association
OCTOBER 2016 | 108:10
E535
Fullerton & Cárdenas | http://dx.doi.org/10.5942/jawwa.2016.108.0156
Peer-Reviewed
those sectors (Metzner 1989). Value added in manufacturing
and industrial output measures have also been used to predict
industrial water demand (Renzetti 1988, Williams & Suh 1986).
In a model developed for Zaragoza, Spain, Arbués et al. (2010)
modeled service and industrial demand as a function of a constructed proxy for levels of output, firm surface area (proxy for
size), and numbers of workers. Additionally, categories such as
government and school water usage have been analyzed as functions of total employment (Metzner 1989) or resident population per account (Schneider & Whitlatch 1991). Table 1 summarizes explanatory factors identified in the previous literature
on water demand modeling.
The southwest region of the United States has been the
object of extensive analysis regarding water demand. Residential water consumption in Phoenix has been found to be significantly affected by household characteristics, urban design
features, and landscaping practices (Wentz & Gober 2007).
Also, given the high heat absorption of its urban built structures, water demand in this metropolitan area is affected
by the Urban Heat Island effect (Aggarwal et al. 2012,
Guhathakurta & Gober 2007). Balling et al. (2008) report
that greater weather sensitivity occurs in census tracts with
large lots, swimming pools, and wealthier residents. Lee et al.
(2010) use a Bayesian maximum entropy approach to forecast
residential water demand in Phoenix. Results indicate that
water usage peaks between 2012 and 2017 and gradually
decreases afterward. The initial increase in projected water
consumption is a consequence of expected rapid population
growth. The subsequent reduction in total demand occurs
because falling per capita water usage is expected to outweigh
the effect of continuing demographic growth in the latter part
of the forecast period.
This study extends previous research on Phoenix area water
demand by modeling and forecasting consumption for three
broadly defined rate classes: single-family residential, multifamily residential, and nonresidential. As discussed previously,
patterns of water demand often vary across customer categories,
and water demand modeling efforts may benefit from explicitly
accounting for this heterogeneity. A variety of assessment methods
are used to evaluate the accuracy of the forecasts.
TABLE 1
Potential predictors of water demand
Customer Type
Predictors
All
Price of water
Economic and demographic variables
Temperature
Rainfall
Residential
Housing characteristics
Household socioeconomic characteristics
Vacancy rates
Presence of specific fixtures or appliances
Nonresidential
Sector-specific employment or value added
Firm size
Industrial output
JOURNAL AWWA
DATA AND METHODOLOGY
Monthly frequency time-series data from January 2008 to
December 2014 are used for the analysis of short-term water
demand dynamics in Phoenix. The strategy employed to model
water consumption in Phoenix involves decomposing usage by each
of the three customer classes into demand per account and number
of accounts (Fullerton & Schauer 2001). Modeling customer
accounts and consumption per customer separately can potentially
provide utility managers with more refined information on the
various factors that combine to shape the trajectory of aggregate
water consumption. In total, six regression equations are estimated.
Consumption per account is modeled as a function of average price,
weather variables (cooling degree days and the number of days per
month with rainfall), and economic variables (an economic conditions index, the rental vacancy rate, and the unemployment rate).
The number of customer accounts is modeled as a function of
economic variables (Fullerton et al. 2016, 2007, 2006). Specifically,
total employment and multi-family housing starts are the explanatory variables in the customer base equations.
Data on water billed, total water and sewer revenue, and the
number of customer accounts are provided by the City of Phoenix.
Per-customer water usage is obtained by dividing water billed in
each customer category by the number of customers in the corresponding category. Average price is calculated by dividing
monthly total revenues over total water consumption in the city
of Phoenix. Previous research in the context of electricity demand
indicates that, when faced with complex rate schedules, consumers tend to respond to changes in average prices rather than
marginal prices (Ito 2014, Shin 1985). Similar studies suggest that
it is often appropriate to use average price when modeling water
demand (Nieswiadomy 1992, Griffin & Chang 1990). In order
to obtain real values, the average price figures are deflated using
the consumer price index (CPI).
Total cooling degree days and the number of days with rainfall occurrence are retrieved from the National Oceanic and
Atmospheric Administration. Because of data constraints regarding monthly personal income at the regional level, either an economic conditions index, rental vacancy rate, or the unemployment
rate are used as a proxy for economic conditions. The economic
conditions index is available from the Federal Reserve Bank of
St. Louis. The source for data on the rental vacancy rate and multifamily housing starts is the US Census Bureau. The former is available on a quarterly basis. To create a monthly series, a local quadratic interpolation is performed in which the average of the high
frequency matches the low frequency data actually observed. The
unemployment rate and CPI are collected from the Bureau of Labor
Statistics (BLS). Finally, employment data are obtained from the
Office of Employment and Population Statistics at the Arizona
Department of Administration (ADOA-EPS).
Another factor that sometimes influences water consumption
patterns is the presence or absence of conservation policies
(Renwick & Archibald 1998). Formal drought restrictions were
not in effect during the course of the sample period in Phoenix.
However, numerous conservation measures have historically been
implemented in the metropolitan area and have likely contributed
to reductions in water consumption per customer (Campbell et al.
2016 © American Water Works Association
OCTOBER 2016 | 108:10
E536
Fullerton & Cárdenas | http://dx.doi.org/10.5942/jawwa.2016.108.0156
Peer-Reviewed
2004). While it is not feasible to account for such factors in this
analysis, conservation policies may have lasting effects and would
be especially important to consider in future analyses focusing
on long-term forecasting.
The City of Phoenix Water Services Department serves the
entire Phoenix incorporated area (546 mi2) and approximately
1.4 million customers (Aggarwal et al. 2012). For the variables
unemployment rate, total employment, and multi-family housing starts, data for Maricopa County, which includes Phoenix,
are used. Since no county-level data are available regarding the
rental vacancy rate and the economic conditions index, metropolitan statistical area (MSA) level data are used instead. The
Phoenix-Mesa-Scottsdale MSA includes Maricopa and Pinal
counties. Table 2 lists the variables, definitions, units of measure,
and sources.
The variables used exhibit different orders of integration. First
differencing is applied to the customer base, price, and economic
conditions index variables to achieve stationarity. In addition to
first differencing, seasonal differencing is necessary for the consumption, total cooling degree days, unemployment rate, total
employment, and multi-family housing starts variables. Secondorder differencing is applied to the rental vacancy rate variable,
and the variable that accounts for the number of days with
rainfall appears in level form. Table 3 reports summary statistics
for the sample data.
In this study, the linear transfer function (LTF) modeling
approach is used. LTF is an extension of the univariate autoregressive integrated moving average method (Box & Jenkins
1976). Previously, this approach has been successfully used to
analyze and forecast the demand for residential natural gas, electricity, and regional employment (Trívez & Mur 1999, Tserkezos
1992, Liu & Lin 1991). This approach has also been used for
municipal water demand forecasting (Fullerton et al. 2007, 2006).
In order to determine the potential lag structures of the
explanatory variables, the cross-correlation functions between
the stationary components of the dependent and independent
variables are plotted and inspected. Then, autoregressive (AR)
and moving average (MA) terms are added to the multiple input
transfer function to account for any systematic movement in the
dependent variable that remains unexplained (Wei 2006). Potential AR/MA structures are identified by examining residual
autocorrelation coefficients. Donkor et al. (2014) emphasize the
potential value of this type of approach in which demand is
modeled as a function of appropriate lags of explanatory variables, and autocorrelation functions are used to select AR and
MA parameters.
The specifications for each category of water consumption
and customer accounts are shown in Eqs 1 through 6. An
increase in the price of water is predicted to generate a decrease
in the per-customer water demand. A larger number of cooling
degree days, reflective of warmer temperatures, is expected to
increase water consumption. Conversely, an increase in the
number of days with rainfall is expected to have a negative
relationship with water demand because less watering is
required for gardens and other outdoor water uses. An improvement in economic activity is hypothesized to increase water
JOURNAL AWWA
usage. Therefore, the economic conditions index is expected to
be positively correlated with water demand. For similar reasons,
the rental vacancy rate and unemployment rate are expected to
have an inverse relationship with water usage. Finally, total
employment and multi-family housing starts are both expected
to be positively correlated with the customer base.
A

C
SFUSEt  0   aPRICEt–a   bTCDDt–b   cNODRt–c
a1
b1
c1
D
p
q
d1
i1
j=1
(1)
  d ECIt–d   i SFUSEt–i   jut–j  ut
A

C
b1
c1
MFUSEt  0   a PRICEt–a   b TCDDt–b   c RVRt–c
a1
p
q
i1
j=1
(2)
  i MFUSEt–i   jut–j  ut
A
C

NRUSEt  0   a PRICEt–a   b TCDDt–b   cNODRt–c
a1
b1
c1
D
p
q
d1
i1
j=1
A
p
a1
i1
(3)
  d UNEMPt–d   i NRUSEt–i   jut–j  ut
SFCUSTt  0  a TOTEMPt–a   i SFCUSTt–i 
q
 j vt–j  vt (4)
j=1
A
p
q
a1
i1
j=1
A
p
q
a1
i1
j=1
MFCUSTt  0   a MFHSt–a   i MFCUSTt–i   jvt–j  vt (5)
NRCUSTt  0  a TOTEMPt–a   i NRCUSTt–i   j vt–j  vt (6)
Water consumption appears on the left-hand sides of regression
Eqs 1, 2, and 3 and as the denominator in the average price variable on the right-hand sides of those same equations. Consequently, it is important to test for endogeneity. An artificial
regression test is used for this purpose (Davidson & MacKinnon
1989). The instrumental variable used to conduct the test is the
national capital stock deflator for water systems, which is
obtained from the US Bureau of Economic Analysis. The capital
stock deflator is an adequate instrument because national-level
fluctuations in infrastructure costs are likely to be correlated with
local water rates but are not affected by changes in Phoenix area
water consumption.
Because good in-sample statistical traits do not guarantee
out-of-sample simulation accuracy, forecasting performance
is also analyzed (Leamer 1983). Ex-post forecast accuracy is
investigated by comparing the accuracy of the LTF forecasts
with random-walk (RW) benchmark forecasts. For the percustomer water consumption series, which exhibit a high
degree of seasonality, an RW prediction is defined as the
observed value of demand in the same month of the previous
year. The RW forecast for the customer base, which tends to
move in a non-seasonal pattern, is simply the last historical
2016 © American Water Works Association
OCTOBER 2016 | 108:10
E537
Fullerton & Cárdenas | http://dx.doi.org/10.5942/jawwa.2016.108.0156
Peer-Reviewed
TABLE 2Variables
Variable
Definition
Units
Source
SFUSE
Single-family residential per-customer water usage
Hundred cubic feet
COP
MFUSE
Multi-family residential per-customer water usage
Hundred cubic feet
COP
NRUSE
Nonresidential per-customer water usage
Hundred cubic feet
COP
SFCUST
Number of single-family residential customers
Water accounts
COP
MFCUST
Number of multi-family residential customers
Water accounts
COP
NRCUST
Number of nonresidential customers
Water accounts
COP
PRICE
Real average price
Dollars per hundred cubic feet
COP
TCDD
Total cooling degree days
Cooling degree days
NOAA
NODR
Number of days with rainfall
Days
NOAA
ECI
Economic conditions index
Percentage
St. Louis Fed.
RVR
Rental vacancy rate
Percentage
US Census Bureau
UNEMP
Unemployment rate
Percentage
BLS
TOTEMP
Total nonfarm employment
Thousands
ADOA-EPS/BLS
MFHS
Multi-family housing starts
Housing starts
US Census Bureau
ADOA-EPS—Office of Employment and Population Statistics at the Arizona Department of Administration, BLS—Bureau of Labor Statistics, COP—City of Phoenix, NOAA—National Oceanic and
Atmospheric Administration, St. Louis Fed.—Federal Reserve Bank of St. Louis
TABLE 3
Summary statistics
Units
Mean
Standard Deviation
Minimum
Maximum
Number
SFUSE
Variable
Hundred cubic feet
14.465
3.244
9.007
21.036
84
MFUSE
Hundred cubic feet
96.236
11.626
75.411
120.111
84
NRUSE
Hundred cubic feet
100.614
30.776
53.766
157.056
84
SFCUST
Water accounts
353,054
4,489
339,531
361,617
84
MFCUST
Water accounts
15,670
183
15,269
16,216
84
NRCUST
Water accounts
33,875
254
33,087
34,348
84
PRICE
Dollars per hundred cubic feet
1.94
0.14
1.55
2.19
84
TCDD
Cooling degree days
409
367
0
1,039
84
NODR
Days
2
2
0
12
84
ECI
Percentage
0.51
5.27
–12.50
6.45
81
RVR
Percentage
12.9
3.8
7.6
20.1
84
UNEMP
Percentage
7.5
1.6
3.9
10.3
84
TOTEMP
Thousands
1,721.2
70.5
1,597.3
1,858.7
84
MFHS
Housing starts
315
364
0
1,586
84
ECI—economic conditions index, MFCUST—number of multi-family residential customers, MFHS—multi-family housing starts, MFUSE—multi-family residential per-customer water usage,
NODR—number of days with rainfall, NRCUST—number of nonresidential customers, NRUSE—nonresidential per-customer water usage, PRICE—real average price, RVR—rental vacancy rate,
SFCUST—number of single-family residential customers, SFUSE—single-family residential per-customer water usage, TCDD—total cooling degree days, TOTEMP—total nonfarm employment,
UNEMP—unemployment rate.
JOURNAL AWWA
2016 © American Water Works Association
OCTOBER 2016 | 108:10
E538
Fullerton & Cárdenas | http://dx.doi.org/10.5942/jawwa.2016.108.0156
Peer-Reviewed
observation in that series. Furthermore, a random-walk-withdrift (RWD) forecast is calculated by adding the average
change over time to the RW forecasts.
Descriptive accuracy measures are then calculated. These
include root mean square errors (RMSE) and Theil (1961)
inequality U-statistics. The U-statistic, which is based on the
RMSE, can assume values ranging from 0 to 1, where a value of
0 means that a perfect fit is obtained (Pindyck & Rubinfield
1998). In order to extract additional information about forecast
accuracy, the mean squared error (MSE) can be decomposed into
the following three proportions of inequality: bias (UM), variance
(US), and covariance (UC). The bias proportion measures the
systematic divergence between the means of actual and predicted
values. The variance proportion reflects the forecast’s ability to
replicate the degree of variability in the variable of interest. The
covariance proportion represents unsystematic error. The ideal
distribution of the three inequality proportions is UM = US = 0
and UC = 1 (Pindyck & Rubinfield 1998).
Two formal tests of forecasting precision are also employed.
The first is an error differential regression test that determines
whether the difference between the errors from two competing
forecasts is statistically significant. The LTF predictions are first
compared with an RW benchmark and then with an RWD benchmark. By defining the two variables shown below in Eqs 7 and
8, the null hypothesis of the test can be expressed as Eq 9.
Dt  e1t – e2t (7)
∑t  e1t  e2t
(8)
H0: MSE(e1) – MSE(e2) = [µ(e1)2 – µ(e2)2]  cov(D,∑)  0
(9)
The first two equations represent sums and differences of the
forecast errors generated by the two models at each period t,
respectively. In Eq 9, µ denotes the mean and cov denotes the
covariance. Assuming the means of both sets of errors have the
same sign, a test of cov(D,∑) = µ(D) = 0 can be used to evaluate
the null hypothesis as shown in Eq 10:
Dt  1  2[∑t – µ(∑t)]  ut(10)
where u t is a randomly distributed error term and the 
coefficients are regression parameters. Eq 11 is used when the
error means have opposite signs.
whether one model outperforms the competing model by a statistically significant margin.
The second formal statistical test is used to assess whether
forecasts can accurately predict the direction of change
(increase versus decrease) in the series of interest. For this purpose, Henriksson and Merton (1981) propose a test for forecasting ability that involves probabilities from a contingency
table (Table 4).
In Table 4, p1 is computed as the proportion of increases in
the variable of interest that are correctly predicted, and p2 is
the proportion of decreases that are forecasted correctly. The
null hypothesis of the test, which is stated in Eq 12, is that
forecasts of directional change are independent of the directional changes actually observed. In other words, the set of
forecasts provides no useful information for a given variable’s
directional change.
H0: p1  p2  1
For a forecast with a perfect direction of change prediction,
p1 = 1, p2 = 1, and p1 + p2 = 2. On the other hand, if a model
always forecasts incorrectly, p1 + p2 = 0. For a naïve forecast that
always predicts an increase, p1 = 1 and p2 = 0, which gives the
same result as the null hypothesis shown above (Schnader &
Stekler 1990). A one-tailed test of H0: p1 + p2 ≤ 1 against Ha:
p1 + p2 > 1 is recommended because it does not seem highly probable that forecasts would systematically predict the wrong direction of change (H0 represents null hypothesis; Ha represents
alternative hypothesis). A Fisher exact test can be used to evaluate the null hypothesis (Cumby & Modest 1987).
In the following section, empirical results are reported. Forecasts generated using the LTF methodology are then compared
against RW and the RWD benchmark forecasts. In order to
determine whether the LTF model exhibits better out-of-sample
properties than the benchmarks, Theil inequality coefficients, an
error differential regression test, and a nonparametric directional
accuracy test are used.
EMPIRICAL RESULTS
Table 5 summarizes the LTF estimation results for singlefamily residential, multi-family residential, and nonresidential
per-customer water usage equations. The independent variables affect demand with different lags. The estimated coefficients associated with each of the explanatory variables are
TABLE 4
Probability value contingency table
∑t  1  2[Dt – µ(Dt)]  ut(11)
A positive value for 2 indicates that the model associated with
e2t outperforms the model associated with e1t. The interpretation
of 1 depends on the sign of the mean of e1. If 1 has the same
sign as the mean of e1, this indicates that the forecasts that generated e2t outperform the forecasts associated with e1t. Ashley et al.
(1980) provide guidelines for evaluating the t- and F-statistics
associated with the regression equations in order to establish
JOURNAL AWWA
(12)
Forecast
Actual
Increase
Decrease
Total
Increase
p1
1 – p1
1
Decrease
1 – p2
p2
1
The quantities p1 and p2 represent the probabilities of correct directional change prediction
given the actually observed directional changes.
2016 © American Water Works Association
OCTOBER 2016 | 108:10
E539
Fullerton & Cárdenas | http://dx.doi.org/10.5942/jawwa.2016.108.0156
Peer-Reviewed
significant at the 95% confidence level. Also, all of the coefficient signs are as hypothesized. Two AR parameters are
included to correct for serial correlation in the single-family
residential demand equation. For the multi-family residential
and nonresidential demand equations, AR and MA parameters
are included for the same purpose.
Table 5 shows contemporaneous negative relationships between
movements in the real average price and water usage. Previous
research reports evidence that residential (Ruijs et al. 2008), commercial, and industrial (Hussain et al. 2002) consumers respond
TABLE 5
ARIMA LTF per-customer water use
Dependent Variable
(Variable Names From
Table 2)
C
PRICE
TCDD(–1)
NODR
ECI(–11)
Single-Family
Residential Use
(SFUSE)
Multi-family
Residential
Use (MFUSE)
Nonresidential
Use (NRUSE)
0.188023
–0.010475
3.067299
(1.449518)
(–0.333188)
(3.405795)c
–2.699224
–15.29766
–39.14598
(–2.162453)b
(–2.050600)b
(–3.670341)c
0.005285
0.036991
0.062207
(3.363783)c
(3.440086)b
(4.606663)c
–0.099038
–1.562528
(–2.143868)b
(–4.307935)c
0.226773
(2.481890)b
RVR(–11)
–1.509119
(–2.396267)b
UNEMP(–15)
–6.063227
(–2.519519)b
AR(1)
AR(8)
–0.593101
–0.480628
(–5.347089)c
(–3.350221)c
–0.342149
(–3.036723)c
AR(12)
–0.354100
(–2.709945)c
MA(1)
–0.980975
(–34.68014)c
MA(4)
–0.580557
(–5.299988)c
R2
0.595262
Adjusted
R2
0.691417
0.572459
0.551109
0.661745
0.519016
Log likelihood
–87.57604
–172.7461
–187.2728
F-statistic
13.48172c
23.30239c
10.71164c
Durbin-Watson statistic
2.116557
2.163745
1.996908
AR—autoregressive, ARIMA—autoregressive integrated moving average, C—constant,
ECI—economic conditions index, LTF—linear transfer function, MA—moving average,
NODR—number of days rainfall, PRICE—real average price, RVR—rental vacancy rate,
TCDD—total cooling degree days, UNEMP—unemployment rate
aStatistical
bStatistical
cStatistical
significance at the 10% level
significance at the 5% level
significance at the 1% level
The sample period analyzed is January 2008 to December 2014.
Numbers in parentheses represent t-statistics.
JOURNAL AWWA
to contemporaneous values of average prices. The significant
contemporaneous impacts of price changes point to potential
forward-looking expectations behavior by Phoenix water customers (Fullerton et al. 2006, Fullerton & Elias 2004).
The price elasticity for the single-family usage category is –0.36.
It is calculated by multiplying the price coefficient in Table 5 by
the ratio of mean price to mean usage in that category. It is smaller
in magnitude than the average price elasticity estimate reported by
Worthington and Hoffman (2008). The price elasticity for the
multi-family usage category is –0.31 and is calculated analogously.
Again, it is smaller in magnitude than the price elasticity for multifamily water demand estimated by Agthe and Billings (2002) and
the price elasticity for renter-occupied households reported by
Hoffman et al. (2006). The price elasticity for the nonresidential
usage category is –0.75. That is in between the elasticity estimates
reported for the commercial and industrial sectors by Hussain et
al. (2002). In addition, it is in line with a study that concludes that
the price elasticity of water demand is higher for the industrial
sector than for the residential sector (Arbués et al. 2010).
It is important to test the price variable for endogeneity given that
total water consumption is used to calculate average price and it is
also used to compute the dependent variables in Table 5. The results
obtained using an artificial regression test for this purpose indicate
that there is no feedback between water usage and contemporary
values of average price (Davidson & MacKinnon 1989). Some prior
studies also report evidence that average water price variables are
exogenous (Mylopoulos et al. 2004, Nauges & Thomas 2000).
Regardless of the category analyzed, higher temperatures are
associated with higher water usage with a one-month lag. This is
not surprising given that Phoenix water consumption exhibits a
strong seasonal pattern and reaches peak levels during the summer
months. An increase in the number of days in a month with rainfall
negatively impacts water usage in the same month. Several research
articles document that water demand in other regions responds
to weather conditions in ways similar to those described above
(Fullerton et al. 2016, Martinez-Espiñeira 2002, Jain et al. 2001).
It is noteworthy that none of the variables related to rainfall turn
out to be relevant for predicting multi-family residential water
usage. Automatic irrigation systems are often used by multi-family
complexes, which can preclude water savings on rainy days. Also,
outdoor water usage per apartment varies considerably from one
complex to another, with some complexes having little or no vegetation coverage and limited outdoor water usage (Agthe & Billings
2002). For apartment complexes that use water mainly or exclusively indoors, water consumption is not likely to decrease substantially in months that have more rainy days.
The economic conditions index positively affects single-family
residential water usage with a lag of 11 months. For multi-family
consumption, the rental vacancy rate negatively affects water usage,
also with a lag of 11 months. High vacancy rates are likely to exert
pressure on apartment complexes to reduce water usage costs.
Apartment complexes sometimes seek long-term cost savings by
installing low-flow plumbing fixtures and drip irrigation systems
(Agthe & Billings 1996). Implementing those cost-saving measures
can require substantial time, which may help explain why the
impact of a shift in vacancy rates on water usage evolves over the
2016 © American Water Works Association
OCTOBER 2016 | 108:10
E540
Fullerton & Cárdenas | http://dx.doi.org/10.5942/jawwa.2016.108.0156
Peer-Reviewed
span of several months. Finally, the unemployment rate negatively
affects nonresidential water usage with a lag of 15 months. The
size and timing of the economic impacts on water demand documented in Table 5 are congruent with previous studies using similar economic indicators for other regions (Fullerton et al. 2007,
2006). The results are also consistent with other research showing
that the 2007–2009 recession had important ramifications for
water usage patterns (Kiefer et al. 2016).
Table 6 shows LTF estimation results for the single-family residential, multi-family residential, and nonresidential customer base
equations. With the exception of the parameter corresponding to
total employment in the single-family regression, all other estimated
coefficients associated with each of the explanatory variables satisfy the 5% significance criterion. All of the slope coefficients have
the hypothesized arithmetic signs. In order to correct for residual
serial correlation, AR and MA terms are introduced in the singlefamily and multi-family customer equations.
Total nonfarm employment positively impacts the number of
nonresidential and single-family residential customers, with lags of
11 and 14 months, respectively. That suggests that it takes around
a year for changes in employment to affect the customer bases in
those categories. Also, multi-family housing starts positively impact
TABLE 6
ARIMA LTF number of customers
Dependent Variable
C
TOTEMP(–11)
Single-Family
Residential
Accounts
(SFCUST)
Multi-family
Residential
Accounts
(MFCUST)
Nonresidential
Accounts
(NRCUST)
46.19510
12.89101
–20.23715
(0.351808)
(1.146459)
(–0.638534)
38.12193
(1.901633)a
TOTEMP(–14)
7.926378
(2.185103)b
MFHS(–15)
0.064271
(2.898233)c
AR(2)
–0.549329
(–3.992288)c
MA(1)
–0.511923
(–4.613450)c
MA(2)
0.804975
(5.984684)c
R2
0.173375
Adjusted
R2
0.322503
0.079878
0.144370
0.281853
0.063148
Log likelihood
–532.4142
–304.9025
–388.2049
F-statistic
5.977530c
7.933678c
4.774677b
Durbin–Watson statistic
1.876944
2.115532
2.108623
AR—autoregressive, ARIMA—autoregressive integrated moving average, C—constant,
LTF—linear transfer function, MA—moving average, MFHS—multi-family housing starts,
PRICE—real average price, TOTEMP—total nonfarm employment
The sample period analyzed is January 2008 to December 2014.
aStatistical
bStatistical
cStatistical
significance at the 10% level
significance at the 5% level
significance at the 1% level
JOURNAL AWWA
multi-family residential accounts after 15 months. Previous work
documents similar time lags in the response of the customer base
to changes in economic conditions (Fullerton et al. 2007, 2006).
The delayed effects of business cycle movements on both percustomer water usage and the number of customers requires
further comment. In a survey of the literature on water demand
modeling, Worthington and Hoffman (2008) note that, while
most prior research focuses on the short run, many of the impacts
of economic conditions on water demand fully materialize only
in the long run. A business cycle expansion is likely to affect water
usage by stimulating the purchase of new household appliances
and homes with more extensive landscaping. It is also likely to
encourage industrial and commercial firms to expand the stock
of water-using equipment. The purchase of new properties, industrial equipment, and durable consumer goods typically requires
substantial lead time. Furthermore, the purchase of new homes
and office space that normally accompanies improved economic
conditions may have been delayed in Phoenix during the sample
period due to the lingering effects of the local real estate bust.
This may explain why economic variables are found to affect
water usage and account growth after lags of several months.
Multiple sets of ex-post forecasts for each category of
per-customer water usage and the customer base are generated
for the period between January 2012 to December 2014. Initially, a subsample estimation period is defined from January
2008 to December 2011, with the period covered by the forecast running from January 2012 to December 2012. Then, the
estimation period is expanded by one month to January 2012, and
the forecast period is rolled forward by one month to cover the
period from February 2012 through January 2013. This process is
repeated until the subsample estimation period extends through
November 2014. The results are 36 one-month-ahead (one stepahead) forecasts, 35 two-month-ahead forecasts, 34 three-monthahead forecasts, and so on. Forecasts for each step length are
analyzed separately.
First, RMSE, Theil inequality coefficients, and MSE decompositions are calculated for each forecasted variable. The LTF
demand forecasts outperform RW and RWD benchmarks over
the majority of step lengths considered. For the single-family and
multi-family residential water usage categories, the LTF forecasts
have the smallest RMSE for 58% and 92% of forecast periods,
respectively. For the nonresidential water usage category, the LTF
forecasts are superior to the benchmarks across all forecast periods. The MSE decompositions for the LTF forecast errors exhibit
good characteristics. The bias and variance proportions are relatively low for each set of the forecast step lengths. Consequently,
the covariance proportion remains above the 60% mark for all
step lengths considered. The LTF out-of-sample forecasts provide
good approximations of the systematic movements in Phoenix
per-customer water demand.
The RMSE and U-statistic results are more heterogeneous in the
case of the customer base forecasts. For the single-family residential
customer category, the RWD forecasts outperform those of the LTF
and RW models at all step lengths as judged by RMSE. For the
multi-family residential customer base forecasts, by contrast, the
LTF outperforms the benchmarks at all step lengths. In the case of
2016 © American Water Works Association
OCTOBER 2016 | 108:10
E541
Fullerton & Cárdenas | http://dx.doi.org/10.5942/jawwa.2016.108.0156
Peer-Reviewed
the nonresidential customer base, LTF forecasts outperform the
benchmarks for forecast horizons of more than a few months
ahead, but the RW forecasts are superior for relatively short horizons. Overall, the RW and RWD benchmark forecasts are competitive with the LTF customer base forecasts.
Results are also mixed with regard to the composition of
customer base prediction errors. The errors in the LTF forecasts of residential customer accounts are not primarily random in nature. The U-statistic covariance proportions account
for more than half of the prediction errors after four months
in the case of single-family customer forecasts and after eight
months in the case of multi-family forecasts. The existence of
discernible patterns in those forecast error series suggests that
the residential customer base models would benefit from further refinement. In comparison to the findings regarding LTF
forecast error composition for the residential sector, the findings for the nonresidential sector are more favorable. The
TABLE 7
covariance proportions of LTF nonresidential customer base
forecasts remain above the 80% mark for all step lengths.
In order to formally test whether the difference between
forecast errors from two models is statistically significant, an
error differential equation is used (Ashley et al. 1980). This test
can only be used to compare two sets of forecasts at a time.
Therefore, the LTF forecasts are compared sequentially against
RW and RWD benchmarks. The RW-LTF and RWD-LTF results
are presented side-by-side in Table 7 for each of the six equations analyzed. Rejection of the null hypothesis implies that the
LTF model represents a significant improvement over the
benchmark forecast.
In the case of single-family residential, multi-family residential, and nonresidential per-customer water usage, the differences between the LTF and benchmark forecasts are statistically insignificant with one exception. The lone exception is
the one-month-ahead nonresidential LTF forecast, which
Error differential regression test results (LTF versus benchmark forecasts)
Forecasted Variable
Step Length
One month
Two months
Three months
Four months
Five months
Six months
Seven months
Eight months
Nine months
10 months
11 months
12 months
Benchmark
SFUSE
MFUSE
NRUSE
SFCUST
MFCUST
RW
—
—
—
—
Reject
NRCUST
—
RWD
—
—
Reject
—
—
—
RW
—
—
—
—
Reject
—
RWD
—
—
—
—
—
—
RW
—
—
—
—
Reject
—
RWD
—
—
—
—
—
—
RW
—
—
—
—
Reject
—
RWD
—
—
—
—
—
—
RW
—
—
—
—
Reject
Reject
RWD
—
—
—
—
—
Reject
RW
—
—
—
Reject
Reject
Reject
RWD
—
—
—
—
Reject
Reject
RW
—
—
—
Reject
Reject
Reject
RWD
—
—
—
—
Reject
Reject
RW
—
—
—
Reject
Reject
Reject
RWD
—
—
—
Reject
Reject
Reject
RW
—
—
—
Reject
Reject
Reject
RWD
—
—
—
—
Reject
Reject
RW
—
—
—
Reject
Reject
Reject
RWD
—
—
—
—
Reject
Reject
RW
—
—
—
Reject
Reject
Reject
RWD
—
—
—
—
Reject
Reject
RW
—
—
—
Reject
Reject
Reject
RWD
—
—
—
—
Reject
Reject
LTF—linear transfer function, MFCUST—number of multi-family residential customers. MFUSE—multi-family residential per-customer water usage, NRCUST—number of nonresidential customers,
NRUSE—nonresidential per-customer water usage, RW—random walk, RWD—random walk with drift, SFCUST—number of single-family residential customers, SFUSE—single-family residential per
customer water usage
Rejection of the null hypothesis indicates that the LTF forecasts are more accurate than the benchmark alternative forecasts.
Dashes indicate that the null hypothesis fails to be rejected and the forecast error differences are statistically insignificant.
JOURNAL AWWA
2016 © American Water Works Association
OCTOBER 2016 | 108:10
E542
Fullerton & Cárdenas | http://dx.doi.org/10.5942/jawwa.2016.108.0156
Peer-Reviewed
represents a statistically significant improvement over the
corresponding RWD forecast. Failure to reject the null hypothesis of prediction error equality for the large majority of cases
indicates that the increases in accuracy achieved by LTF
demand forecasts, as measured by RMSE, are relatively insignificant. The competitiveness of RW benchmarks implies that
efforts to predict per-customer water usage in Phoenix should
carefully monitor recent historical consumption behavior.
The LTF customer base forecasts, by contrast, demonstrate a
relatively strong track record when compared with the RW benchmarks using the error differential regression test. This is somewhat surprising given the mixed forecast accuracy results obtained
for the customer base using RMSE and U-statistics as the criteria
for judging accuracy. In the case of single-family residential customers, the LTF represents a significant improvement over the
RW for the last seven step lengths and also outperforms the eightmonth-ahead RWD forecast by a statistically significant margin.
With regard to the number of multi-family residential customers,
the LTF represents a significant improvement over the RW across
all step lengths and the margin of improvement over the RWD is
statistically significant for the last seven step lengths. For the
number of nonresidential customers, the null hypothesis is
rejected in the case of both the RW and the RWD forecasts for
the last eight step lengths.
The ability of a model to accurately predict the direction of
change in a variable of interest is determined using directional
forecast evaluations. Table 8 shows the directional accuracy test
for each category of per-customer water usage and customer
accounts. The null hypothesis states that the forecast fails to
predict directional changes in variable of interest (Henriksson &
Merton 1981). Rejection of the null implies that the model successfully predicts the direction of the movements in water usage.
For the three water usage categories the null hypothesis is never
TABLE 8
rejected for more than a third of the step lengths using a 5%
significance level. For the customer base forecasts, it is not possible to reject the null at any step length. This indicates that
anticipating directional changes for Phoenix water usage and
customer bases is very difficult.
The results in Tables 7 and 8 do not provide very much support
in favor of the per-customer water usage and customer account
models developed for Phoenix. This is true for all three customer
categories, but especially for the two residential categories. The
difficulty of predicting Phoenix water demand, especially in the
residential sector, may be partly attributable to the unstable conditions that prevailed in the Phoenix residential real estate market
following the 2007 housing market collapse. Phoenix experienced
exceptionally large housing price declines in the aftermath of the
housing bubble (Carson & Dastrup 2013). The ensuing financial
crisis further disrupted mortgage lending activity and contributed to the difficulty of predicting residential water demand
during this period. All of the customer base series are somewhat
jagged, partially reflecting the turbulence in the local housing
market and the disruptive effects of the financial crisis. Should
adequate data on additional real estate variables become available, such variables might add explanatory power to the models
developed for this study.
From a practical perspective, results in Tables 7 and 8 also
indicate that municipal water forecasts should monitor the most
recent consumption data closely during periods of regional financial stress. Many time series are characterized by a high degree of
continuity or persistence over time, and RWs are often useful for
characterizing such series. While RWs rarely help predict turning
points in economic activity, such as real estate busts, continuity
often reemerges once the correction or structural shift has
occurred (Clements & Hendry 2008). For utilities in metropolitan
areas experiencing very rapid accumulation of housing stock, it
Henriksson–Merton test results for LTF forecasts
Forecasted Variable
Step Length
SFUSE
MFUSE
NRUSE
SFCUST
MFCUST
NRCUST
One month
Reject
Reject
Reject
—
—
—
Two months
—
—
—
—
—
—
Three months
Reject
—
Reject
—
—
—
Four months
—
—
Reject
—
—
—
Five months
—
—
Reject
—
—
—
Six months
—
—
—
—
—
—
Seven months
—
—
—
—
—
—
Eight months
—
—
—
—
—
—
Nine months
Reject
—
—
—
—
—
10 months
—
—
—
—
—
—
11 months
—
—
—
—
—
—
12 months
—
—
—
—
—
—
LTF—linear transfer function, MFCUST—number of multi-family residential customers, MFUSE—multi-family residential per-customer water usage, NRCUST—number of nonresidential customers,
NRUSE—nonresidential per-customer water usage, SFCUST—number of single-family residential customers, SFUSE—single-family residential per customer water usage
Rejection of the null hypothesis implies that the forecasts provides useful information regarding the direction of change.
JOURNAL AWWA
2016 © American Water Works Association
OCTOBER 2016 | 108:10
E543
Fullerton & Cárdenas | http://dx.doi.org/10.5942/jawwa.2016.108.0156
Peer-Reviewed
may also be useful to examine the underlying factors affecting
the customer base, such as net migration, to determine the sustainable level of long-term growth. Housing booms are often
characterized by overbuilding followed by prolonged periods of
slow growth as excess housing stock is gradually absorbed
(McNulty 2009, Smith & Tesarek 1991). In such situations,
ignoring potential cyclical behavior in housing markets may result
in larger forecast errors.
CONCLUSION
In summary, the LTF estimation results indicate that water
usage in Phoenix is affected by variations in prices, economic
conditions, and weather patterns. There are contemporaneous
negative relationships between movements in real average price
and per-customer water usage. Over the course of the sample
period, real average water prices in Phoenix varied from $1.55
to $2.19 per 100 ft3. The price elasticities for the single-family
residential, multi-family residential, and nonresidential usage
categories are –0.36, –0.31, and –0.75, respectively. Those elasticities are in the neighborhood of results reported in prior studies for various regions.
Statistically significant impacts are also found between
weather conditions and water demand. Higher temperatures
are associated with higher water usage, and an increase in the
number of days in a month with rainfall reduces municipal
water usage. In addition, an improvement in economic activity increases water consumption per customer. The customer
base equations confirm that positive relationships exist
between the number of customers and both employment and
multi-family housing starts. It is important to highlight the
role of economic and housing market variables in influencing
Phoenix water demand in the aftermath of the real estate bust
and the 2007–2009 recession. Business cycle downturns are likely
to affect water usage by delaying the purchase of new properties
and water-using durable goods. Utilities that serve communities
facing turbulent economic conditions or cyclical oscillations in
real estate markets are advised to closely monitor recent trends
in both water demand and its underlying determinants.
After the parameters of each equation have been estimated,
ex-post forecasts are conducted over the course of a 36-month
period as an additional model-validation exercise. Results of the
two forecast evaluation tests employed in this analysis illustrate
the importance of analyzing predictive accuracy from multiple
angles. Descriptive accuracy metrics corresponding to per-customer
water usage forecasts in many cases favor the LTF model. However, the improvements in accuracy over the benchmark models
are not statistically significant in most cases as gauged by the
error differential regression test. Conversely, analysis of the LTF
customer base forecasts yields mixed descriptive accuracy results
but, when those forecasts do outperform the benchmarks, they
usually do so by statistically significant margins. Also, notwithstanding its comparative accuracy as gauged by RMSE, the LTF
model is relatively unsuccessful at predicting the direction of
usage movements in most cases. By applying multiple forecast
evaluation methods, a more nuanced understanding of a model’s
track record in out-of-sample prediction is achieved.
JOURNAL AWWA
More research on per capita water demand and customer
base forecasting appears warranted for this metropolitan
economy. Future efforts may attempt to increase forecast
accuracy by constructing a composite forecast using LTF, RW,
and RWD models. Also, if serial correlation issues can be
resolved, employing a seemingly unrelated regression method
may prove helpful. Additional explanatory variables such as
foreclosure rates and categorical housing stock estimates
might help improve out-of-sample simulation results for the
customer base. Another key factor that is likely to affect the
evolution of water demand over time is the increasing adoption of water-saving home appliances and lawn irrigation
systems. Finally, similar efforts conducted for other regional
water utilities would also help determine whether these results
are unique to Phoenix. Ideally, such analyses would examine
water demand dynamics over a longer time span, allowing for
comparison of forecasting performance during different
phases of the business cycle.
ACKNOWLEDGMENT
The Water Research Foundation provided financial, technical,
and administrative support for the research upon which this
article is based. Additional financial support was provided by
El Paso Water Utilities, Hunt Communities, City of El Paso Office
of Management & Budget, and the University of Texas at El Paso.
Extensive comments and suggestions were provided at various
points during the development of this study by Adam Walke, Jack
Kiefer, Chris Meenan, Paul Merchant, Paul Palley, and José
Ablanedo. Econometric research assistance was provided by
Alejandro Ceballos.
ABOUT THE AUTHORS
Thomas M. Fullerton Jr. (to whom
correspondence may be addressed) is a
professor of economics at the University of
Texas at El Paso, where he holds the Chair
for the Study of Trade in the Americas El
Paso. His research has been published in
Water Resources Research, Water Policy,
Journal AWWA, Economics Letters, Southern
Economic Journal, International Journal of Forecasting, Energy
Economics, Journal of Forecasting, Canadian Water Resources
Journal, Regional Science Policy & Practice, Contemporary
Economic Policy, Economic Development Quarterly, and
Empirical Economics. He received his PhD from the University
of Florida, Gainesville; his MA degree from the University of
Pennsylvania, Philadelphia; his MS degree from Iowa State
University at Ames; and his BBA degree from the University of
Texas at El Paso. He may be reached at University of Texas at
El Paso, 500 W. University Ave., El Paso, TX 79968-0543 USA;
[email protected]. Juan P. Cárdenas is a financial analyst at
United Bank of Paso del Norte, El Paso, Tex.
PEER REVIEW
Date of submission: 04/07/2016
Date of acceptance: 06/30/2016
2016 © American Water Works Association
OCTOBER 2016 | 108:10
E544
Fullerton & Cárdenas | http://dx.doi.org/10.5942/jawwa.2016.108.0156
Peer-Reviewed
REFERENCES
Aggarwal, R.M.; Guhathakurta, S.; Grossman-Clarke, S.; & Lathey, V., 2012. How
Do Variations in Urban Heat Islands in Space and Time Influence
Household Water Use? The Case of Phoenix, Arizona. Water
Resources Research, 48:6:W06518.
Agthe, D.E. & Billings, R.B., 1996. Water-Price Effect on Residential and Apartment
Low-Flow Fixtures. Journal of Water Resources Planning and
Management, 122:1:20. http://dx.doi.org/10.1061/(ASCE)07339496(1996)122:1(20).
Agthe, D.E. & Billings, R.B., 2002. Water Price Influence on Apartment Complex
Water Use. Journal of Water Resources Planning and Management,
128:5:366. http://dx.doi.org/10.1061/(ASCE)0733-9496(2002)128:5(366).
Arbués, F.; García-Valiñas, M.A.; & Villanúa, I., 2010. Urban Water Demand for
Service and Industrial Use: The Case of Zaragoza. Water Resources
Management, 24:14:4033. http://dx.doi.org/10.1007/s11269-010-9645-5.
Ashley, R.; Granger, C.W.; & Schmalensee, R., 1980. Advertising and Aggregate
Consumption: An Analysis of Causality. Econometrica, 48:5:1149. http://
dx.doi.org/10.2307/1912176.
Balling, R.C. Jr.; Gober, P.; & Jones, N.S., 2008. Sensitivity of Residential Water
Consumption to Variations in Climate: An Intraurban Analysis of
Phoenix, Arizona. Water Resources Research, 44:10:W10401.
Bithas, K. & Stoforos, C., 2006. Estimating Urban Residential Water Demand
Determinants and Forecasting Water Demand for Athens Metropolitan
Area, 2000–2010. South-Eastern Europe Journal of Economics, 4:1:47.
Boland, J.J.; Wentworth, R.W.; & Steiner, R.C., 1982. Forecasting Short-Term
Revenues for Water and Sewer Utilities. Journal AWWA, 74:9:460.
Box, G.E.P. & Jenkins, G.M., 1976 (Revised ed.). Time Series Analysis: Forecasting
and Control. Holden-Day, San Francisco.
Campbell, H.E.; Johnson, R.M.; & Larson, E.H., 2004. Prices, Devices, People, or
Rules: The Relative Effectiveness of Policy Instruments in Water
Conservation. Review of Policy Research, 21:5:637. http://dx.doi.
org/10.1111/j.1541-1338.2004.00099.x.
Carson, R.T. & Dastrup, S.R., 2013. After the Fall: An Ex Post Characterization of
Housing Price Declines Across Metropolitan Areas. Contemporary
Economic Policy, 31:1:22. http://dx.doi.org/10.1111/
j.1465-7287.2011.00290.x.
Fildes, R.; Randall, A.; & Stubbs, P., 1997. One Day Ahead Demand Forecasting in
the Utility Industries: Two Case Studies. Journal of the Operational
Research Society, 48:1:15. http://dx.doi.org/10.1057/palgrave.
jors.2600320.
Fullerton, T.M. Jr. & Elías, A., 2004. Short-Term Water Consumption Dynamics in El
Paso, Texas. Water Resources Research, 40:8:W08201.
Fullerton, T.M. Jr. & Molina, A.L. Jr., 2010. Municipal Water Consumption Forecast
Accuracy. Water Resources Research, 46:6:W06515.
Fullerton, T.M. Jr. & Nava, A.C., 2003. Short-Term Water Dynamics in Chihuahua
City, Mexico. Water Resources Research, 39:9:WR002056.
Fullerton, T.M. Jr. & Schauer, D.A., 2001. Regional Econometric Assessment of
Aggregate Water Consumption Trends. Australasian Journal of
Regional Studies, 7:2:167.
Fullerton, T.M. Jr.; Ceballos, A.; & Walke, A.G., 2016. Short-Term Forecasting
Analysis for Municipal Water Demand. Journal AWWA, 108:1:E27.
http://dx.doi.org/10.5942/jawwa.2016.108.0003.
Fullerton, T.M. Jr.; Tinajero, R.; & Barraza de Anda, M.P., 2006. Short-Term Water
Consumption Patterns in Ciudad Juárez, México. Atlantic Economic
Journal, 34:4:467. http://dx.doi.org/10.1007/s11293-006-9031-0.
Fullerton, T.M. Jr.; Tinajero, R.; & Mendoza-Cota, J.E., 2007. An Empirical Analysis
of Tijuana Water Consumption. Atlantic Economic Journal, 35:3:357.
http://dx.doi.org/10.1007/s11293-007-9074-x.
Guhathakurta, S. & Gober, P., 2007. The Impact of Phoenix Urban Heat Island on
Residential Water Use. Journal of the American Planning Association,
73:3:317. http://dx.doi.org/10.1080/01944360708977980.
Griffin, R.C. & Chang, C., 1990. Pretest Analyses of Water Demand in Thirty
Communities. Water Resources Research, 26:10:2251. http://dx.doi.
org/10.1029/WR026i010p02251.
Henriksson, R.D. & Merton, R.C., 1981. On Market Timing and Investment
Performance. II. Statistical Procedures for Evaluating Forecasting
Skills. Journal of Business, 54:4:513. http://dx.doi.org/10.1086/296144.
Hoffman, M.; Worthington, A.; & Higgs, H., 2006. Urban Water Demand With Fixed
Volumetric Charging in a Large Municipality: The Case of Brisbane,
Australia. Australian Journal of Agricultural and Resource Economics,
50:3:347. http://dx.doi.org/10.1111/j.1467-8489.2006.00339.x.
Clements, M.P. & Hendry, D.F., 2008. Economic Forecasting in a Changing World.
Capitalism and Society, 3:2:1. http://dx.doi.org/10.2202/1932-0213.1039.
Hussain, I.; Thrikawala, S.; & Barker, R., 2002. Economic Analysis of Residential,
Commercial, and Industrial Uses of Water in Sri Lanka. Water
International, 27:2:183. http://dx.doi.org/10.1080/02508060208686991.
Cumby, R.E. & Modest, D.M., 1987. Testing for Market Timing Ability: A Framework
for Forecast Evaluation. Journal of Financial Economics, 19:1:169.
http://dx.doi.org/10.1016/0304-405X(87)90033-X.
Ito, K., 2014. Do Consumers Respond to Marginal or Average Price? Evidence
From Nonlinear Electricity Pricing. American Economic Review,
104:2:537. http://dx.doi.org/10.1257/aer.104.2.537.
Dalhuisen, J.M.; Florax, R.J.G.M.; de Groot, H.L.F.; & Nijkamp, P., 2003. Price and
Income Elasticities of Residential Water Demand: A Meta-Analysis.
Land Economics, 79:2:292. http://dx.doi.org/10.2307/3146872.
Jain, A.; Varshney, A.K.; & Joshi, U.C., 2001. Short-Term Water Demand Forecast
Modelling at IIT Kanpur Using Artificial Neural Networks. Water
Resources Management, 15:5:299. http://dx.doi.
org/10.1023/A:1014415503476.
Davidson, R. & MacKinnon, J.G., 1989. Testing for Consistency Using Artificial
Regressions. Econometric Theory, 5:3:363. http://dx.doi.org/10.1017/
S0266466600012573.
DeOreo, W.B. & Mayer, P.W., 2012. Insights Into Declining Single-Family
Residential Water Demands. Journal AWWA, 104:6:E383. http://dx.doi.
org/10.5942/jawwa.2012.104.0080.
Donkor, E.A.; Mazzuchi, T.A.; Soyer, R.; & Roberson, J.A., 2014. Urban Water
Demand Forecasting: Review of Methods and Models. Journal of
Water Resources Planning and Management, 140:2:146. http://dx.doi.
org/10.1061/(ASCE)WR.1943-5452.0000314.
Dupont, D.P. & Renzetti, S., 2001. The Role of Water in Manufacturing.
Environmental and Resource Economics, 18:4:411. http://dx.doi.
org/10.1023/A:1011117319932.
Espey, M.; Espey, J.; & Shaw, W.D., 1997. Price Elasticity of Residential Demand
for Water: A Meta-analysis. Water Resources Research, 33:6:1369.
JOURNAL AWWA
Jentgen, L.; Kidder, H.; Hill, R.; & Conrad, S., 2007. Energy Management Strategies
Use Short-Term Water Consumption Forecasting to Minimize Cost of
Pumping Operations. Journal AWWA, 99:6:86-94.
Kiefer, J.C.; Johns, G.M.; Snaith, S.M.; & Dziegielewski, B., 2016. Water Demand
Forecasting in Uncertain Times: Isolating the Effects of the Great
Recession. Water Research Foundation, Denver.
Kupel, D.E., 2003. Fuel for Growth: Water and Arizona’s Urban Environment.
University of Arizona Press, Tucson, Ariz.
Leamer, E.E., 1983. Let’s Take the Con Out of Econometrics. American Economic
Review, 73:1:31.
Lee, S.-J.; Wentz, E.A.; & Gober, P., 2010. Space-Time Forecasting Using Soft
Geostatistics: A Case Study in Forecasting Municipal Water Demand
for Phoenix, Arizona. Stochastic Environmental Research and Risk
Assessment, 24:2:283. http://dx.doi.org/10.1007/s00477-009-0317-z.
2016 © American Water Works Association
OCTOBER 2016 | 108:10
E545
Fullerton & Cárdenas | http://dx.doi.org/10.5942/jawwa.2016.108.0156
Peer-Reviewed
Liu, L.-M. & Lin, M.-W., 1991. Forecasting Residential Consumption of Natural Gas
Using Monthly and Quarterly Times Series. International Journal of
Forecasting, 7:1:3. http://dx.doi.org/10.1016/0169-2070(91)90028-T.
Maidment, D.R.; Miaou, S.P.; & Crawford, M.M., 1985. Transfer Function Models of
Daily Urban Water Use. Water Resources Research, 21:4:425. http://
dx.doi.org/10.1029/WR021i004p00425.
Martínez-Espiñeira, R., 2002. Residential Water Demand in the Northwest of
Spain. Environmental and Resource Economics, 21:2:161. http://dx.doi.
org/10.1023/A:1014547616408.
McNulty, J.E., 2009. The Long-Run Demand for Housing, the Housing Glut, and the
Implications for the Financial Crisis. Business Economics, 44:4:206.
http://dx.doi.org/10.1057/be.2009.27.
Metzner, R.C., 1989. Demand Forecasting: A Model for San Francisco. Journal
AWWA, 81:2:56.
Mylopoulos, Y.A.; Mentes, A.K.; & Theodossiou, I., 2004. Modeling Residential
Water Demand Using Household Data: A Cubic Approach. Water
International, 29:1:105. http://dx.doi.org/10.1080/02508060408691753.
Nauges, C. & Thomas, A., 2000. Privately Operated Water Utilities, Municipal Price
Negotiation, and Estimation of Residential Water Demand: The Case of
France. Land Economics, 76:1:68. http://dx.doi.org/10.2307/3147258.
Nauges, C. & Thomas, A., 2003. Long-Run Study of Residential Water
Consumption. Environmental and Resource Economics, 26:1:25. http://
dx.doi.org/10.1023/A:1025673318692.
Nieswiadomy, M.L., 1992. Estimating Urban Residential Water Demand: Effects of
Price Structure, Conservation, and Education. Water Resources
Research, 28:3:609. http://dx.doi.org/10.1029/91WR02852.
NOAA (National Oceanic and Atmospheric Administration), 2014. NOWData.
www.nws.noaa.gov/climate/ (accessed Oct. 24, 2014).
Sang, W.H., 1982. The Financial Impact of Water Rate Changes. Journal AWWA,
74:9:466.
Schnader, M.H. & Stekler, H.O., 1990. Evaluating Predictions of Change. Journal of
Business, 63:1:99. http://dx.doi.org/10.1086/296486.
Schneider, M.L. & Whitlatch, E.E., 1991. Under-Specific Water Demand
Elasticities. Journal of Water Resources Planning and Management,
117:1:52. http://dx.doi.org/10.1061/(ASCE)0733-9496(1991)117:1(52).
Shin, J.-S., 1985. Perception of Price When Price Information Is Costly: Evidence
From Residential Electricity Demand. Review of Economics and
Statistics, 67:4:591. http://dx.doi.org/10.2307/1924803.
Smith, B.A. & Tesarek, W.P., 1991. House Prices and Regional Real Estate Cycles:
Market Adjustments in Houston. AREUEA Journal, 19:3:396. http://dx.
doi.org/10.1111/1540-6229.00559.
Theil, H., 1961. Economic Forecasts and Policy. North-Holland Publishing Co.,
Amsterdam, Netherlands.
Trívez, F.J. & Mur, J., 1999. A Short-Term Forecasting Model or Sectoral Regional
Employment. The Annals of Regional Science, 33:1:69. http://dx.doi.
org/10.1007/s001680050093.
Tserkezos, E.D., 1992. Forecasting Residential Electricity Consumption in Greece
Using Monthly and Quarterly Data. Energy Economics, 14:3:226.
http://dx.doi.org/10.1016/0140-9883(92)90016-7.
Wei, W.W.S., 2006 (2nd ed.). Time Series Analysis: Univariate and Multivariate
Methods. Pearson Addison Wesley, Boston.
Wentz, E.A. & Gober, P., 2007. Determinants of Small-Area Water Consumption for
the City of Phoenix, Arizona. Water Resources Management,
21:11:1849. http://dx.doi.org/10.1007/s11269-006-9133-0.
Pindyck, R.S. & Rubinfield, D.L., 1998 (4th ed.). Econometric Models and Economic
Forecasts. McGraw-Hill, New York.
Wentz, E.A.; Wills, A.J.; Kim, W.K.; Myint, S.W.; Gober, P.; & Balling, R.C. Jr., 2014.
Factors Influencing Water Consumption in Multifamily Housing in
Tempe, Arizona. Professional Geographer, 66:3:501. http://dx.doi.org/
10.1080/00330124.2013.805627.
Renwick, M.E. & Archibald, S.O., 1998. Demand Side Management Policies for
Residential Water Use: Who Bears the Conservation Burden? Land
Economics, 74:3:343. http://dx.doi.org/10.2307/3147117.
Williams, M. & Suh, B., 1986. The Demand for Urban Water by Customer
Class. Applied Economics, 18:12:1275. http://dx.doi.org/10.1080/
00036848600000003.
Renzetti, S., 1988. An Econometric Study of Industrial Water Demand in British
Columbia, Canada. Water Resources Research, 24:10:1569. http://dx.
doi.org/10.1029/WR024i010p01569.
Woo, C.-K.; Wong, W.-K.; Horowitz, I.; & Chan, H.-L., 2012. Managing a Scarce
Resource in a Growing Asian Economy: Water Use in Hong Kong.
Journal of Asian Economics, 23:4:374. http://dx.doi.org/10.1016/
j.asieco.2012.03.007.
Rockaway, T.D.; Coomes, P.A.; Rivard, J.; & Kornstein, B., 2011. Residential Water
Use Trends in North America. Journal AWWA, 103:2:76.
Ruijs, A.; Zimmermann, A.; & van den Berg, M.M., 2008. Demand and Distributional
Effects of Water Pricing Policies. Ecological Economics, 66:2–3:506.
JOURNAL AWWA
Worthington, A.C. & Hoffman, M., 2008. An Empirical Survey of Residential
Water Demand Modelling. Journal of Economic Surveys, 22:5:842.
http://dx.doi.org/10.1111/j.1467-6419.2008.00551.x.
2016 © American Water Works Association
OCTOBER 2016 | 108:10