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Demand Side Management of Residential Water Usage in Fort Collins, Colorado: An Econometric

Approach

Shu Guan Chuah

Submitted to the Department of Economics

Wichita State University

In partial fulfillment of the requirements for the degree of Master of Arts

Spring 2011


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Abstract

Demand Side Management requires utility managers to influence residential water consumption via

price policies and/or non-price policies. This paper uses regression analysis to study the effect of price

policies on residential water consumption amongst single, duplex, and multi-family households in the

City of Fort Collins, Colorado. The effects of income, rainfall, temperature and non-price policies are

also examined. The results are largely consistent with previous findings; the co-integrating regression

indicates that water is price inelastic.


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Acknowledgements

Much gratitude is offered to Mr. Dennis Bode, Fort Collins Utilities Water Manager for providing

information and data on water usage, rate structures, and conservation programs. Much thanks as well

to Dr. Philip Hersch for his invaluable comments, which have greatly improved the quality of the paper.


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INTRODUCTION

There are two approaches to handling water needs of a city. The first approach calls for

expansion of water supplies by increasing production capacity of currently owned water sources or

acquisition of new water supplies by constructing reservoirs, building water catchment areas, harvesting

water from aquifers, and desalination. These projects usually require large amount of financial

investment due to the scope of the project and potential expenditures resulting from feasibility and

sustainability studies prior to project implementation. As nearby water sources reach exhaustion, and

water is obtained from farther sources, the costs of transporting water increases as well. Even in the

case of aquifers, if these are not properly managed, the costs of pumping water will increase as

underground water levels decrease. Furthermore, the potential for environmental degradation needs to

be taken into account.

The second approach calls for planned and responsible management of water demand,

otherwise known as Demand Side Management. In contrast to the above approach that aims to

increase water supplies, Demand Side Management requires utility managers to engage consumers of

water via price policies and/or non-price policies. Water use is usually divided into three categories:

agricultural, industrial, and residential. We focus on residential water usage. Price policies, as the term

suggests, have to do with the amount charged for per unit consumption of water, and also per account

charges and fixed charges per month; non-price policies, on the other hand, are usually associated with

programs that encourage or mandate water conservation, and includes measures such as education

campaigns, adoption of water efficient technologies, and water use restrictions.

This paper investigates how price policies influence residential water consumption in Fort Collins,

Colorado, thus informing city and utility managers about the effects of an increase in the price of water

or implementation of water conservation programs. This is meant to demonstrate that price policies

(despite their unpopularity) should not be abandoned; neither should they be relied on too heavily, as

water is price inelastic. Relying too much on non-price policies is not a solution either, as there is lack of

empirical evidence for the effect of non-price policies on water consumption. What is called for here is

a balance between price and non-price policies.

We find that water is price inelastic for single, duplex and multi-family households. A 10%

increase in water prices respectively generate 3.85%, 3.44% and 8.74% decrease in water consumption


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for single, duplex and multi-family households. Upon implementation of new price policies in January

2003, water consumption would decrease by an additional 2.56% for single households and 2.66% for

duplex households. We find no such effect for multi-family households.

In the following sections we first provide background information on the City of Fort Collins in

specific regards to its water supply and water demand situation, examining the scope and extent of

water demand management in Fort Collins. We then move to a discussion of various topics that are of

relevance of estimation of water demand, such as price elasticity of water demand, income elasticity of

water demand, and effect of price policies. We then present the data, and provide a description of the

econometric method that will be used to estimate water demand. Results are then presented and

discussed, followed by concluding remarks.

1. BACKGROUND

The City of Fort Collins, Colorado, has a population of 138,736 (US Census), and is located 57

miles north of Denver, Colorado. It is situated east of the Rocky Mountains, on the Northern Front

Range. July is the warmest month, with mean temperatures of 71F, annual average precipitation is 15

inches (The Weather Channel); major natural waterways that run through Fort Collins are the Cache La

Poudre River and Spring Creek.

According to the Fort Collins Utilities website, water in Fort Collins comes from three major

sources: (1) The Colorado-Big Thompson (CBT) project, which includes Horsetooth Reservoir (2) The

Cache La Poudre River Basin and (3) portions of the Michigan river basin that flow to the Poudre River

via the Michigan Ditch and Joe Wright Reservoir system. Each year, the City typically delivers 28,000

acre-feet of treated water to customers. In 2009, 10,300 acre-feet of the above treated water was

delivered to households for residential consumption. The City of Fort Collins also owns water rights that

yield approximately 72,000 acre-feet per year. However, due to system capacity (e.g., Size of water

treatment facilities, infrastructure for transporting treated water) and legal constraints (e.g.,

conservation measures adopted by the City), not all of the 72,000 acre-feet is available to meet treated

water demand. Typically, after taking into account the above constraints, the City is able to meet an

average annual demand of 32,000 acre-feet.


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In accordance to the Fort Collins Water Supply and Demand Management Policy dated

September 13, 2003, it was determined that new storage capacity in the range of 12,500 to 14,000

acre-feet shall be pursued. This has culminated in the purchase of the Halligan Reservoir from the

North Poudre Irrigation Company in 2004 (North Forty News, 2005) and subsequently the authorization

to pursue expansion of the Halligan Reservoir from its current capacity of 6,400 acre-feet to 40,000 acre-

feet (Fort Collins Coloradoan, 2009). However, it is also stated that enlarging Halligan Reservoir is a

costly and complicated process, one of the reasons being working through the NEPA (National

Environmental Policy Act) process to obtain a permit is expected to take 2-3 years and cost about $3.9

million. (www.fcgov.com). Chandler Peter, project manager with the U.S. Army Corps of Engineers,

says that a draft Environmental Impact Statement on the proposal to expand Halligan Reservoir is

expected to be complete by early 2011 (Fort Collins Coloradoan, 2009). In light of the above, the

Halligan reservoir does not yet function as a major source of water for the City of Fort Collins.

Having understood the context of how costly and complicated it is to expand the water supply,

we see why Fort Collins has adopted a two-pronged approach tackling water supply and water

demand. In terms of water demand management, the City has outlined the following: (1) Water use

goals (2) Educational programs (3) Rate structures (4) Incentive programs (5) Regulatory measures and

(6) Operational measures (Fort Collins City Council, 2003). Based on data made available by Fort Collins

Water Utilities, we find that there has been much progress in terms of implementation of water

conservations measures to enhance demand side management (DSM) of water resources in the City of

Fort Collins.1 This is in contrast to the slower progress of water supply management in regards to the

expansion of Halligan Reservoir. The following programs were implemented in 2003: (1) Increasing

block rate structure (for single-family and duplex accounts); (2) Seasonal rate structure (for multi-family

accounts); (3) Residential clothes washer rebates; (4) Backwash recycling at water treatment facility; (5)

Restrictive covenants ordinance; and (6) Soil amendment ordinance. In 2007, the City began

implementing a program for dishwasher rebates.

Residential water consumption in Fort Collins is billed based on type of dwelling unit: single-

family accounts, duplex accounts, and multi-family accounts. Single-family accounts are defined as

residential customers with one dwelling unit, duplex being residential customers with two dwelling units,

and multi-family being residential customers with more than two dwelling units. According to Chapter

1A detailed summary of water conservation programs is provided in Appendix 2.


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26 of the Fort Collins Municipal Code and Charter, dwelling unit is defined as one or more rooms and a

single kitchen designed for or occupied as a unit by one family for living and cooking purposes located in

a single-family or multi-family dwelling. Each account type is billed differently.2

The City of Fort Collins has undergone several changes in terms of how monthly water

consumption is billed. The following is a brief description of how single and duplex accounts have been

billed for monthly water consumption. From January 1990 to December 1999, households were billed a

minimum charge for the first 2,000 gallons consumed, and a uniform rate structure for gallons

consumed beyond 2,000; this is in addition to flat rate charges per account and flat rate charges per 100

square feet. From January 2000 to December 2002, instead of being billed a minimum charge for the

first 2,000 gallons consumed, households were billed a per account charge. The uniform rate

structure therefore applied for all gallons consumed (The flat rate charges per account and flat ratecharges per 100 square feet still remained in force). From January 2003 onwards, Fort Collins

introduced a 5-tier increasing block rate price structure for single and duplex residential accounts, doing

away with the uniform rate structure. From May 2004 onwards, the flat rate charges per account and

flat rate charges per 100 square feet were removed; the increasing block rate price structure was

reduced to a 4- tier system. In May 2006, the increasing block rate price structure was reduced to a 3-

tier system.

The billing structure for multi-family accounts is slightly simpler in comparison to single-family

and duplex accounts. From January 1990 to December 1999, there were no charges for consumption of

the first 2,000 gallons. In other words, there was a free allowance of 2,000 gallons per month per

account. Customers were therefore billed a uniform rate structure for gallons consumed beyond the

minimum 2,000; this is in addition to monthly charges per account and monthly charges per additional

unit which have continued to remain in force (recall that multi-family accounts consist of residential

customers with more than two dwelling units). From January 2000 to December 2002, the free

allowance was removed, resulting in residential customers being charged uniform rates for all gallons

consumed. In January 2003, the seasonal rate structure was implemented for multi-family accounts,

resulting in higher tariffs during the summer, and lower tariffs during the winter. According to Chapter

26 of the Fort Collins Municipal Code and Charter, summer is defined as months from May to October,

2A detailed description of the billing structure is provided in Appendix 1.


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and winter is defined as months from November to April. Spring and fall are not given separate

treatment in terms of billing structure.

2. LITERARURE REVIEW

Worthington and Hoffman (2006) in their state-of-the-art review of residential water modelling,

point out that population growth, coupled with the reduction in freshwater supplies, and the increasing

cost of infrastructure, has prompted suppliers to place renewed emphasis on demand management

through pricing structures and other strategies to control consumption.

Much empirical research on residential water consumption has concluded that water is price

inelastic , carrying values of 0.25 to 0.75 (Worthington and Hoffman 2006) meaning that a 10%increase in the price of water will result in a less than 10% reduction in water consumption. This does

not mean that price policies are ineffective in managing water demand, but it does mean that non-price

policies may be desirable to supplement increases in the price of water. As highlighted by Renwick and

Archibald (1998), economists do generally advocate higher residential water prices as a means of

reducing demand, but there are others who argue that non-price policies, which do not affect the price

of water but place direct controls on water use such as rationing, constitute the only viable means to

reduce residential demand. This conclusion relies, in part, on the low price elasticity findings noted

above.

While it is generally agreed that water is price inelastic, the reasons behind the price elasticity

are varied some bearing valid economic reasoning, and some not. One of the more questionable

reasons is that water is considered a necessity to life, meaning consumers cannot do without it. Berk et

al(1980) states that the use of price as an allocation mechanism is constrained by the fact that water is

generally regarded as a basic necessity, even a right, not an economic good. If this is the case, then no

economic policy can change the weak sensitivity of water consumption to price. It is important to note,

however, with specific regards to residential water consumption, not all of it is out of necessity e.g.

washing the car, watering the plants, outdoor swimming pools, etc. Consumers can do with less

frequent carwashes, or cut down on watering activities by planting less flowers/shrubs. This is in

contrast to the argument and misguided view that water is a necessity. (Baumann and Boland, 1997).

The key is that, although part of water usage is a necessity of life, at the margin it isnt. The main


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reasons demand is still likely to be inelastic, even at the margin, is the lack of good substitutes (i.e.,

there are no alternative liquids for drinking or washing), water bills constituting a small portion of

consumer budgets, and the broad definition of the good (i.e., demand for water is inelastic compared to

demand for bottled spring water).

Thus, when water managers and/or city managers consider price measures to enhance

conservation, they should not be afraid to do so in the misguided assumption that residents right to

necessary water use is being violated. What they should bear in mind is that the increase in water rates

will generate less than proportionate reductions in water usage due to water bills constituting a small

part of consumers budgets, and lack of good substitutes of water. Based on recently calculated data, in

2009, 0.44% of average household income in Fort Collins was spent on water. Contrast this with 1990,

whereby 1.68% of average household income in Fort Collins was spent on water. This is due partly to anoticeable reduction in water billing amount, which in turn is caused by Fort Collins removing the flat

rate charges per account and flat rate charges per 100 square feet for monthly water bills in May 2004.

The absence of price information on water bills has been suggested as an explanation for the

low price elasticity of water. According to the law of demand, people decrease consumption when price

increases, as demonstrated by the negative price elasticities for water. However, the law of demand

also implicitly assumes that consumers know prices an unrealistic assumption in markets with ex post

billing. Gaudin (2006) reasons that when prices are not transparent, elasticity estimates are potentially

lower than their full information potential. He therefore hypothesizes that residents sluggish response

to price is partly due to the absence of price information on water bills. On the basis of a sample bills

collected from 383 utilities across the USA, he finds evidence that when price-related information is

given on the water bill, price elasticity increases by 30% or more.

At large, there is no question about the low price elasticity of water. However, when we come to

the issue of which water pricing structure is the most effective in reducing water consumption, the

conclusions are varied and mixed, i.e. there is no general consensus among economists as to which

pricing structure is more conservation oriented. This is an important issue to highlight as many utility

managers have moved away from a uniform rate structure to an increasing block tariff in the belief that

the latter results in water conservation. In the year 2000, approximately one-third of U.S. urban


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residential water customers faced increasing block tariffs, up from 4% in 1982 (OECD 1999; Raftelis

1999).

Young, Kinsley and Sharpe (1983) have proposed that an increasing rate is more effective in

reducing water consumption than a uniform or a decreasing rate structure. Dandy, Nguyen and Davies

(1997) however offers a counter-argument: Economic efficiency requires that the marginal benefit of

water to consumers be equal to the marginal cost of supplying water. They expect marginal cost to be

about the same for consumers consuming different amounts of water, therefore a uniform rate identical

for all consumers appears to be preferable on the grounds of economic efficiency to either an increasing

or decreasing block rate. However, they do allow an exception for the increasing block rate structure,

explaining that this can be justified on the grounds of system expansion costs, whereby water supply

exhibits increasing Long Run Marginal Costs (LRMC) instead of constant LRMC. Finally, Nauges andThomas (2000) state that the increasing tariff is sometimes advocated in that it better protects water

resources.

Nieswiadomy and Cobb (1993) shed more light on the topic as their research compared the

price elasticities of increasing and decreasing block structures. They also explain that utility managers

commonly adopt increasing block structures in the belief that they are conservation-oriented. This is in

due in part to Wilchelns (1991) non-econometric analysis of marginal pricings impact in irrigated

agriculture, which associates increasing blocks with reduction in water use per acre. The findings of

Nieswiadomy and Cobb find that increasing block structures are apparently conservation-oriented. The

authors warn of a selection bias in this finding whereby in cities where people are more interested in

conservation, utility managers may be more likely to select a rate structure that they believe is

conservation oriented that belief being an increasing block structure.

Olmstead et al(2007) investigate whether price elasticity may depend on price structures. The

sample of households surveyed consisted of either increasing block households or uniform rate

households. While the paper is not explicitly focused on whether increasing block structures are

conservation oriented, the estimated price elasticity of respective household types does throw light on

whether residential consumers under increasing block structures are more sensitive to price changes.

The findings of the paper indicate greater price elasticity for increasing block households. However, the

authors also state, ... given our remaining selection concerns, we cannot definitely say IBPs [increasing


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Research concerning estimation of water demand is usually accompanied with information on

income elasticity. The inclusion of income variables in estimation of water demand is motivated by basic

economic theory which suggests that income is a key determinant of demand. Water consumption, as a

normal good, should then be positively related to income. This can be explained by the fact that income

is also positively related to many other water-using goods, such as swimming pools, dishwashing

machines, and gardening activities. Furthermore, higher income levels are also correlated with larger

house size, which increases water consumption as well. This would tie in well with conventional

economic theory which suggests a positive relationship between income and water consumption.

However, it has also been suggested that there may be a negative income effect for water consumption

income through its positive relationship with education may be reflective of water conservation

measures taken by the household through the purchase of water-conserving appliances and planting of

drought-tolerant garden vegetation (Worthington, Hoffman and Higgs 2005). Despite this alternativeexplanation, empirical research has indicated that income elasticity of demand is positive, but inelastic

(Nieswiadomy and Cobb 1993; Dandy, Nguyen and Davis 1997; Renwick and Archibald 1998; Nauges and

Thomas 2003).

In regards to estimation techniques, numerous econometric methods have been employed to

study water demand. For cross-sectional data, techniques employed include ordinary least squares

(OLS), generalized least squares (GLS), two and three-stage least squares (2SLS and 3SLS), logit and

instrumental variables (IV). In terms of time-series data, two common techniques are Vector

Autoregression (VAR) and co-integration methods (Worthington and Hoffmann 2006). However, we are

unaware of any published work that has utilized VAR for estimation of water consumption. This is

because VARs are a-theoretic, its emphasis on forecasting makes it less suited for policy analysis, and

individual coefficients from estimated VAR models are often difficult to interpret (Gujarati 2003). On a

related note, Martinez-Espineira is the only paper to date that has employed co-integration techniques

and Error Corrections Mechanisms (ECMs) to in the estimation of water demand. OLS is a very common

and basic econometric technique used to examine the relationship between dependant and explanatory

variables. However it is important to note that OLS (especially in the case of increasing/decreasing block

rate pricing) may produce biased and inconsistent estimates due to simultaneity issues between water

consumption and price. Researchers have proposed GLS or 2SLS to resolve the problem.


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3. DATA & METHODOLOGY

Data Sources

In this paper, we will use co-integration methods with ECMs to estimate the monthly demand

for water in Fort Collins using a sample of monthly observations for the period January 1990 to

December 2009. The dependent variable is consumption per account measured by thousand gallons

consumed per household account. The explanatory variables are average price, income per capita, total

monthly precipitation, average monthly maximum temperature, and increasing block/seasonal rate

structure. The variables are discussed below. The variables are discussed below.

Consumption per account (Q)

Data on monthly water consumption and number of accounts served by Fort Collins Utilitieswere organized according to account types: single-family, duplex, and multi-family accounts. This was

instrumental in calculating monthly consumption per account for the different types of customer

accounts. Consumption per account was chosen as the dependent variable of choice (instead of

consumption per capita) as we are interested in looking at how the independent variables influence

water consumption at the household level. Furthermore, Fort Collins Water Utilities does not serve the

entire population of Fort Collins, making the number of customers served (i.e. number of accounts) a

more accurate measure of household level behavior. However, it is important to highlight that the

household size for each of these account types will be different as we have pointed out that single-

family, duplex, and multi-family accounts are respectively defined as residential customers with one,

two, or more dwelling units. Thus, estimation procedures will be conducted separately for the different

types of accounts, i.e. monthly consumption per account for single-family accounts will be regressed

against relevant variables discussed below; the same principal applies for duplex and multi-family

accounts. Data for water consumption and number of household accounts were obtained from

Residential accounts and water usage4

Average Price5 (AP)

The choice of average price specification is driven by several factors. Economic theory suggests

that marginal price should be the variable of choice. However, in our previous discussion, several studies

4Data for water consumption and number of household accounts is available upon request

5The background literature in support of average price is drawn largely from Gaudin (2006).


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have shown that consumers tend to respond to average prices of water rather than marginal prices, and

the average price specification is preferred when there are heterogeneous price structures. In the case

of Fort Collins, we have seen how price structures have changed over the examined 20 year period,

resulting in heterogeneous price structures, hence discouraging the use of marginal price. The average

price has been adjusted based on changes in the consumer price index in order to reflect real prices.

Average price is expected to display a negative coefficient. Data for average price were obtained from

Rate History for Residential Accounts6

Increasing Block/Seasonal rate structure (POLICY)

In January 2003, a new price structure was introduced in the City of Fort Collins. Increasing

block rate structures were introduced for single family and duplex residential accounts; seasonal rate

structures were introduced for multi-family residential accounts. In light of this significant policy shift inwater rate structures, we have introduced a policy dummy to measure the effect of the introduction of

this change. Prior to January 2003, when the City of Fort Collins implemented a uniform rate structure,

the policy dummy carries the value 0; from January 2003 onwards, when the policy changes were

introduced, the policy dummy carries the value 1. We will interact this binary variable with AP the

value of AP prior to January 2003 will be 0, the value of AP from January 2003 onwards will carry the

original AP values. This will allow us to examine if policy implementation has an added effect on price

elasticity.

Understandably, interaction of the average price specification with a policy dummy that

introduces marginal price specification raises some questions as to the choice of using AP to measure

how water prices affect the consumption of water. The choice of AP is not meant to convey that MP is

less important. Rather, the choice of AP is driven by several other factors that have been previously

discussed, one of those factors being the fact that Fort Collins faces heterogeneous price structures in

the 20 year period examined. Data for policy implementation of increasing block/seasonal rate

structures were obtained from Conservation Programs Summary.7

Real Income per Capita (INC)

Since we are examining household level water consumption, the corresponding variable of

choice to examine income elasticity of demand would be income per household. However, due to

6See Appendix 1 for rate structures

7See Appendix 2 for implementation of water conservation programs


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limited data availability, we use annual income per capita of Fort Collins-Loveland as a proxy for income

per household. There were no quarterly or monthly income per capita data available at the city, county

or state level. We then deflate Income per Capita with the consumer price index in order to obtain Real

Income per Capita. Real Income per Capita is expected to display a positive coefficient. Data for income

per capita and consumer price index were obtained from Federal Reserve Economic Database (FRED) via

the Federal Reserve Bank of St. Louis online database (Annual data were s used)

Total Monthly Precipitation, Seasonally Adjusted (RAIN)

Monthly precipitation plays an important role in water consumption. This can be attributed to

the fact that outdoor water use is a large subset of total water consumption. Some examples of outdoor

water use are watering activities for the lawn and garden, and carwash activities. The variable is

included here under the assumption that significant amount of rainfall will result in decreased outdoorwater use. Since outdoor water use does not occur much or at all during winter months, we interact

this variable with a non-winter seasonal dummy8; upon interaction, precipitation in the months of

December, January and February carry the value 0, whereas the remainder months retain their

respective precipitation values. Total Monthly Precipitation is expected to display a negative coefficient.

Data for total monthly precipitation were obtained from the Colorado Climate Center;

Average Monthly Maximum Temperature (TEMP)

Previous studies have shown temperature to influence water consumption, with higher

consumption resulting from higher temperatures. The average monthly maximum temperature was

preferred as we can reasonably assume water usage to be influenced by maximum temperatures which

occur during the day, instead of average monthly temperatures which factor in cooler temperatures at

night. Average monthly maximum temperature is expected to display a positive coefficient. Data for

average monthly maximum temperature were obtained from the Colorado Climate Center;

Methodology9

8Non-winter months are defined as months from March to November; the seasonal dummy will carry the value 1

for these months.9

The methodology here is largely drawn from Martinez-Espineira (2005), the only published work known to utilize

co-integration and ECM for time-series analysis of water consumption. Please refer to the above for more detailed

explanations of the different tests and econometric methods.


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Co-integration techniques and error correction mechanism (ECM)10 are used to investigate the

effects of the above explanatory variables on household water consumption. These will also allow us to

measure the short run and long run price elasticity of water. However, before we can conduct a co-

integrating regression, we first need to test for the order of integration of the different time-series data,

i.e. we must find out if they share the same unit root. To do this, we will conduct a series of unit root

tests to investigate order of integration of the time-series data. The following will be used to test for

unit roots: Augmented Dickey Fuller (ADF) test (Dickey and Fuller 1981), Dickey-Fuller Generalized Least

Squares (DFGLS) approach (Elliot et al 1996), and KPSS test (Kwiatskowski et all 1992).

Developed back in 1981, the ADF test is one of the earliestst and traditional tests for non-

stationarity. Maddala and Kim have advocated that the traditional ADF tests should be discarded

(Gujarati 2003). This is due to limitations of the ADF test and modifications done to the ADF test byPerron and Ng, Elliot, Rotheberg and Stock, Fuller, and Leybourne (Maddala and Kim 1998).

Nevertheless the ADF test will still be used here as a starting point for testing unit roots. In testing for

unit roots using ADF, if the null of non-stationarity cannot be rejected, a second test is conducted to

check whether the integration order of the series. In the second test, the series is differenced once. If

the null is rejected during the second test, we say that the series is integrated of order one.

However, it is noted that in small samples, an ADF test can suffer from a lack of power to reject

the null hypothesis of non-stationarity (Eguia and Echevarria 2004). We therefore employ the DFGLS

test which is likely to be more robust than the ADF test (Baum 2001). The KPSS test is applied for two

reasons: It tests for a null hypothesis of stationarity, and in applying this with the ADF and DFGLS tests,

we can examine the consistency of the test results.

Once the time series are determined to be stationary at the same order of integration, a co-

integration regression analysis is conducted. The log-linear specification allows us to directly obtain

elasticity estimates. The co-integrating regression will carry the following expression:

logQt = 0 + 1logAPt + 2 logAP*POLICYt + 3logRAINt + 4logTEMPt + 5logINCt + ut (1)

10Introductory explanations for these can be found in Gujarati, Chap.21 (2003).


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To test for stationarity of residuals (ut) of the co-integrating regression, the Augmented Engle-

Granger (AEG) test is conducted. This test is almost identical to the ADF test except that critical values

have been calculated by Engle and Granger (1987) as the critical significance values from the ADF test

are not quite appropriate.

We also subject the variables to the Levin, Lin & Chu Test, and the Breitung test, to test for unit

roots; these tests assume that the variables share a common unit root process. The temperature

variable employed in Martinez-Espineira (2005) was found to be possibly non-stationary, therefore

coefficients for the climate variables should be treated with caution; we expect temperature variable in

our unit root tests to display non-stationarity. The presence of non-stationary series (or stationary of

different order) could mean that there exists more than one cointegrating relationship in the above

regression, which will influence the stationarity of residuals.

Once the series of variables have been determined to be cointegrated (residuals demonstrated

to be stationary), we would introduce these residuals as an error correction term in the ECM, which

carries the following expression:

logQt = 0 + 1logAPt + 2logAP*POLICYt + 3RAINt + 4TEMPt + 5logINCt + 6ut-1 + t (2)

1 to 5 from equation (1) represent the effect of the various explanatory variables on logQ;

1 ,2 and 5 respectively represent the price elasticity, income elasticity for water, and the effect of price

policy on price elasticity.

4. ESTIMATION AND RESULTS

Unit Root Tests

The results of the ADF test (Appendix 3, Table 4) indicate that logQ, logAP and logAP*POLICY are

integrated of order one for single, duplex and multi-family accounts. The test statistics for logINC

indicate an order of integration higher than one, since the series is not stationary upon 1st

differentiation. The climate variables (logRAIN and logTEMP) are stationary at levels, indicating the

presence of an I(0) series.


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The results of the DFGLS test (Appendix 3, Table 5) present a slightly different picture with

regards to the stationarity of logQ, logAP and logAP*POLICY. In the case of single-family households,

logQ, logAP and logAP*POLICY are all I(1) series. In the case of duplex households, only logAP*POLICY is

an I(1) series. In the case of multi-family accounts, logAP and logAP*POLICY are I(1) series. The test

statistics for logINC are mostly consistent with the results from the ADF test, indicating that logINC has

an order of integration higher than one. The test statistics for logRAIN differ greatly from the ADF test,

indicating that logRAIN might have an order of integration higher than one. The test statistics for

logTEMP are different from the previous ADF test, indicating that the series has an order of integration

higher than one.

We conclude unit root testing with results from the KPSS test (Appendix 3, Table 6). It is

important to note that the null hypothesis for the KPSS test is stationarity of the series being examined.We find that logQ, logAP and logAP*POLICY are not stationary at levels. Upon first differencing, they are

stationary of order one for all single, duplex and multi-family accounts. According to the KPSS test then,

these variables have an I(1) process. Looking at the results for logINC, we find that the series is not

stationary at levels, and still remains non-stationary upon conducting a first difference. According to the

KPSS test, logINC is an I(2) series. Turning our attention to the climate variables, we find that RAIN and

TEMP are stationary at levels.

One of the requirements for conducting a co-integrating regression is that the variables are

integrated of the same order. In our case, we would have liked to see all the variables demonstrate an

I(1) process. For the most part, logQ, logAP and logAP*POLICY from single, duplex and multi-family

accounts demonstrate an I(1) process. logINC is found to be an I(2) process based on the results of the

ADF, DFGLS, and KPSS tests. However, the same cannot be said of the climate variables. logRAIN is

found to have an I(0) process. The unit root process of logTEMP is hard to determine the ADF and

KPSS tests indicate the presence of an I(0) process; the DFGLS test indicate perhaps an I(2) process.

Since we cannot make a definite claim about the degree of integration of the climate variables, the

coefficients generated for logTEMP and logRAIN should be interpreted with caution.

Having shown that the series used in the demand model is non-stationary, except for the

climate variables and INC, we present the results of the co-integrating regression.


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Co-integrating Regression

Table 1: Results of Co-integrating Regression

Single Duplex Multi+

Variables Coefficient Coefficient Coefficient

logAP -0.129

(0.080)

-0.078

(0.076)

-1.135***

(0.165)logAP*policy -0.256***

(0.060)

-0.266***

(0.056)

0.261

(0.163)

logINC -0.731***

(0.266)

-0.838**

(0.264)

N/A

logRAIN -0.071***

(0.024)

-0.064***

(0.024)

-0.020**

(0.009)

logTEMP 2.053***

(0.176)

1.453***

(0.150)

0.895***

(0.052)

Intercept 1.455

(2.676)

5.134*

(2.726)

0.355*

(0.210)

Adjusted R2

0.7984 0.6725 0.7992DW statistic 1.4779 1.2847 1.1735

Number of observations = 238

*** denotes 1% significance level; ** 5%; *10%. Standard errors are in parentheses.+ logINC was removed from the co-integrating regression for multi-family accounts as the inclusion of

the variable resulted in failure to reject the AEG test; coefficient diagnostics revealed that logINC had a

VIF of 22346.23

The results indicate that water is price inelastic for all single, duplex and multi-family households,

with values ranging between -0.344 to -0.874. This means that given a 10% increase in the price of water,

consumption per account will decrease by 3.44% to 8.74%. It is important to note that the coefficients

for logAP for single and duplex households are not statistically significant. However, upon conducting a

general F test, we find that the sum of the coefficients for logAP and logAP*POLICY is different than zero

for single, duplex, and multi-family households.11

Water demand is income inelastic as well, but displays a negative coefficient of -0.731 for

single household accounts and -0.838 for duplex accounts. This means that as per capita income

increases, consumption per account decreases. In other words, there is a negative income effect on the

consumption of water. This is in contrast to most research findings that indicate a positive income

effect for water consumption. 12

11See Appendix 4 for results of General F-test

12It is possible that the co-integrating regression may be misspecified and thus the income elasticity should be

interpreted with caution. More research needs to be conducted to resolve this issue of negative income elasticity.


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20

The interaction of AP with policy implementation produces values of -0.256 for single

households and -0.266 for duplex households. A coefficient of 0.261 was obtained for multi-family

households but this result is statistically insignificant. In regards to single and duplex households, this

implies that during the years of policy implementation (from January 2003 to December 2009), there is

an additional decrease in water consumption per account when the price of water increases. In other

words, implementation of the increasing block tariff has increased the responsiveness of change in

water consumption to change in the price of water. This finding conveys that marginal pricing is

important in promoting water conservation. For single households, there is an additional 2.56%

decrease in water consumption given a 10% increase in the price of water; for duplex households, there

is an additional 2.61% decrease in water consumption given a 10% increase in the price of water.

RAIN displays the expected negative coefficient, and TEMP displays the positive coefficient.RAIN is very inelastic: a 10% rise in rainfall reduces water consumption by 0.71% for single households,

0.64% for duplex households, and 0.2% for multi-family households. In contrast, TEMP is an important

variable, whereby a 10% rise in temperature increases water consumption by 20.53% for single

households, 14.53% for duplex households, and 8.95% for multi-family households. However, as

previously discussed, due to the climate variables being integrated of a different order, the coefficients

should be interpreted with care.

Table 2: Results of Augmented Engle Granger TestH0: Series are not co-integrated

Tau-statistic Prob.

Single -9.124 0.0000

Duplex -8.440 0.0000

Multi -2.677 0.7481

Table 3: Results of Group Unit Root Tests

H0: Unit root (assume common unit root process)

Levin, Lin & Chu Test Breitung t-stat test

Statistic Prob. Statistic Prob.Single 10.215 1.0000 0.814 0.7922

Duplex 7.434 1.0000 0.793 0.7861

Multi 15.402 1.0000 -0.881 0.1893


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Based on the results of the AEG test, we reject the null hypothesis of the series not being co-

integrated for single and duplex accounts. In the group unit root tests, consisting of Levin, Lin & Chu

Test, and Breitung t-stat test, we fail to reject the null hypothesis of the presence of unit root (assuming

common unit root process). From these tests, we infer the series for all account types to be co-

integrated of the same order of integration. This also means that the residual term u t is stationary (in

spite of climate and income variables demonstrating a different order of integration). This allows us to

proceed with the ECM.

Error Correction Mechanism

Upon investigation of the error term from the ECM, we find that the error terms are not random

white noise. The results from the Breusch-Godfrey LM Test demonstrate that the error terms are

serially correlated at 2% for single households, 10% for duplex households and 4% multi-familyhouseholds. Our ECM is thus plagued with problems of heteroskedasticity and autocorrelation of error

terms.

Implications for policymaking

We focus our discussion on the co-integrating regression and the relevance of its coefficients to

policymakers. The findings reveal that price of water is statistically insignificant in regards to influencing

the demand for water. In 2003, implementation of the increasing block tariff and seasonal rate

structures (which are both price policies) have brought about decreased water consumption of 2.56%

for single-family accounts and 2.66% for duplex accounts when water prices are increased by 10%. This

means that, given the continued implementation of increasing block tariffs/seasonal rate structures,

utility managers can expect water consumption for single and duplex households to further decrease,

provided there is an increase in water prices. This finding is in support of the view that increasing block

tariffs encourage water conservation, as it has done so in Fort Collins.

In view of how the above results demonstrate that water remain price inelastic despite the

introduction of additional price policies (in the form of increasing block tariffs and seasonal rate

structures), policymakers should not rely merely on price policies alone to reduce water consumption.

This is demonstrated via the implementation of other conservation programs (or non-price policies) in

conjunction with the implementation of increasing block tariffs and seasonal rate structures in January

2003. The other conservation programs launched include: (1) Residential clothes washer rebates; (2)


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22

Backwash recycling at water treatment facility; (3) Restrictive covenants ordinance; and (4) Soil

amendment ordinance. In 2007, Fort Collins also began implementing a program for dishwasher rebates.

It is possible that the above conservation programs had a role to play in encouraging water

conservation. However, we are not able to confirm that from the existing co-integrating regression. We

attempted to model the effect of the non-price policies listed above by introducing another dummy

variable to the existing co-integrating regression, and obtained questionable results.13 Several

explanations for the questionable results are possible. Firstly, the introduction of these non-price

policies coincided with the introduction of the increasing block tariffs and seasonal rate structures; both

were introduced in January 2003. Secondly, some non-price policies will not generate immediate impact

on water consumption, i.e. time is needed for these policies to have had an impact (e.g. washer rebates,

dishwasher rebates). To overcome these issues, monthly frequencies of the different water programswould be required to isolate their individual impacts on reducing water consumption. The frequency of

the different water programs were recorded annually, therefore having the records in a monthly format

would enable quantification of the impact of the different water conservation programs. This would be

a recommended area for further research, pending data availability.

5. CONCLUSION

The paper confirms prior empirical findings regarding the price inelasticity of water. However,

this is not to be interpreted as an abandonment of price policies. What this conveys is that price policies

by themselves carry a small effect in managing water demand, and should be complemented with non-

price policies. We have shown that in terms of price policies, the introduction of increasing block tariffs

for single-family and duplex accounts have resulted in decreased water consumption. However, we also

offer a note of caution as to how non-price policies might have a role to play in the decreased water

consumption. The effect of non-price policies on water consumption in Fort Collins currently remains

ambiguous. Further empirical research will shed light on the effect of non-price policies and is a

recommended area for further research.

13Please see Appendix 5 for results of modified co-integrating regression.


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APPENDIX 3. Estimation results of ADF, DFGLS, and KPSS Unit Root Tests

Table 4: t-stat values from ADF Test (I = Intercept; T&I = Trend & Intercept)

Single Duplex Multi

Variables I T&I I T&I I T&I

logQ -1.558 -3.771** -1.501 -2.813 -0.605 -2.599

logQ -12.821*** -12.795*** -6.639*** -6.621*** -13.186*** -13.164***

logAP -1.238 -1.541 -1.477 -2.412 -1.069 -2.167

logAP -11.861*** -11.848*** -11.137*** -11.135*** -3.816*** -3.809**

logAP*POLICY -2.669* -3.899** -2.027 -2.949 -0.874 -1.780

logAP*POLICY -12.935*** -12.909*** -14.205*** -14.176*** -10.077*** -10.050***

I T&I

logINC -2.076 -0.844

logINC -2.100 -2.720

logRAIN -3.887*** -4.043***

logRAIN -15.235*** -15.203***

logTEMP -4.526*** -5.086***

logTEMP -13.530*** -13.492***

*** denotes 1% significance level; ** 5%; *10%

Table 5: t-stat values from DFGLS Test (I = Intercept; T&I = Trend & Intercept)

Single Duplex Multi


logQ -2.076** -2.163 -1.902* -1.968 -1.293 -1.344

logQ -5.311*** -12.186*** -1.061 -2.284 -1.387 -2.539

logAP -0.067 -1.627 -0.056 -2.584 -0.238 -1.936

logAP -2.830*** -4.186*** -1.159 -2.212 -2.746*** -3.241**

logAP*POLICY -2.226** -3.695*** -1.622* -2.793* -0.344 -1.495

logAP*POLICY -12.951*** -12.935*** -14.223*** -14.215*** -10.032*** -9.960***

I T&I

logINC -0.523 -1.499

logINC -1.994** -2.052

logRAIN -0.519 -1.802

logRAIN -13.466*** -0.532

logTEMP -0.377 -1.363

logTEMP -0.661 -0.335



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APPENDIX 3. Estimation results of ADF, DFGLS, and KPSS Unit Root Tests (contd)

Table 6: t-stat values from KPSS Test (I = Intercept; T&I = Trend & Intercept)

Single Duplex Multi


logQ 0.866*** 0.627*** 1.307*** 0.059 1.857*** 0.041

logQ 0.066 0.021 0.088 0.060 0.053 0.034

logAP 0.639** 0.294*** 1.077*** 0.295*** 1.811*** 0.207**

logAP 0.014 0.014 0.053 0.055 0.031 0.030

logAP*POLICY 1.315*** 0.163** 1.272*** 0.153** 1.532*** 0.259***

logAP*POLICY 0.049 0.042 0.037 0.034 0.048 0.047

I T&I

logINC 1.718*** 0.426***

logINC 0.424* 0.128*

logRAIN 0.127 0.035

logRAIN 0.272 0.137*

logTEMP 0.034 0.010

logTEMP 0.021 0.009



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APPENDIX 4. Estimation results of General F-test

H0: 1 +2 = 0

Test statistic: F = (R2ur R2

r)/m

(1- R2ur)/(n-k)Number of observations (n) = 238

Number of coefficients (k) = 5

Number of regressors omitted from restricted model (m) = 2

Critical Value: F0.01 (2, 236) = 4.696

Single Duplex Multi

Adjusted R2 (unrestricted) 0.7984 0.6725 0.7992

Adjusted R2 (restricted) 0.7297 0.5743 0.4806

F-ratio 39.7001 34.9332 186.4318


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APPENDIX 5. Results of Co-Integrating Regression with added dummy variable

Single Duplex Multi

Variables Coefficient Coefficient Coefficient

logAP -0.754***

(0.063)

-0.949***

(0.053)

-1.230***

(0.151)

logAP*policy+ 0.650***

(0.082)

0.905***

(0.070)

1.365***

(0.269)

policy_nonprice -1.268***

(0.109)

-1.646***

(0.095)

-0.488***

(0.098)

logINC -0.014

(0.182)

-0.357***

(0.136)

N/A

logRAIN -0.056***

(0.015)

-0.042***

(0.012)

-0.026***

(0.008)

logTEMP 1.431***

(0.114)

0.777***

(0.077)

0.829***

(0.048)

Intercept -2.282

(1.754)

4.362***

(1.350)

0.651***

(0.196)

Adjusted R2 0.9047 0.9169 0.8320

DW statistic 1.2651 0.9798 1.2232

Number of observations = 238

*** denotes 1% significance level; ** 5%; *10%. Standard errors are in parentheses.+ This finding implies that the introduction of increasing block tariffs and seasonal rate structures has

increased water consumption, which means a failure to promote water conservation.


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