Water Conservation and Persuasion in Kelowna: Persistene Pays.
John Janmaat
Department of Eonomis (Unit 8)
I.K. Barber Shool of Arts and Sienes
University of British Columbia
3333 University Way, Kelowna, BC, Canada
john.janmaatub.a
June 30, 2013
Abstrat
Convining residential households to use less water is seen as an important hallenge in Kelowna, a
rapidly growing ity in the semi-arid southern interior of British Columbia. A mixed methods survey
onduted between 2009 and 2010 measured self reported onservation investments and behaviors of 512
Kelowna residents. Partitioning variables and using two stage least squares, in the spirit of the theory of
planned behavior (TPB), nds at best weak support for the TPB. Variables with the strongest preditive
power for engagement with onservation fall outside the sope of the theory. Two of ve Kelowna water
providers harge a volumetri prie; however, paying volumetrially had no signiant impat. Inome
is an important preditor aross a range of model speiations. Beyond inome, onservation message
soures are ommonly important,with soures that have a soial harater standing out for outdoor onservation hoies. The lak of any strong inuene for environmental attitudes, knowledge or eduation
suggests that eduation and moral suasion may have limited suess in enouraging water onservation.
Eorts to inrease outdoor water onservation may be more eetive if they work through soial engagements that demonstrate water onservation and enourage onversations about water onservation..
1 Bakground
The Okanagan valley is, on a per apita basis, one of the most water sare watersheds in Canada [Statistis
Canada, 2003, p8℄.
Kelowna is the largest ity in the Okanagan Valley, with a population of 117,310 in
2012, having grown 9.3% over the preeding ve years [Statistis Canada, 2012℄.
1
Various agenies have
been atively enouraging Okanagan residents to onserve water. Some eorts fous on eduation and moral
suasion, attempting to onvine residents that water is not abundant and that the morally right thing to do
is to onserve. Other eorts are direted at having residents pay a prie that reets the true 'value' of water
in the Okanagan. This researh seeks to shed some light on the relative merits of these dierent approahes
to enouraging water onservation by examining fators that inuene household onservation investments
and behaviors.
The ity of Kelowna lies on the eastern side of the Okanagan Valley, whih lies in the rain shadow
of the Coast and Casade mountains of British Columbia. With average annual preipitation of 340 mm
spread fairly evenly throughout the year, and an average July maximum temperature of
27.6◦ C
[Environ-
ment Canada, 2013℄, Kelowna experienes a signiant moisture deit during muh of the growing season.
Irrigation was a ritial element in developing and sustaining the agriultural eonomy that dominated the
Okanagan well past the middle of the twentieth entury [Wilson, 1989℄. Water is supplied to Kelowna most
residents by ve major water providers, with the residual made up by several small utilities and some individual wells and water drawn from surfae soures [Kelowna Joint Water Committee, 2012℄. The impats of
limate hange together with ontinuing rapid population growth is expeted to lead to urban water demands
exeeding liensed supplies within the foreseeable future [Neale et al., 2007℄. The ve main water providers
(see gure 1) are Blak Mountain Irrigation Distrit (BMID), the ity of Kelowna water utility (CITY),
the Glenmore Ellison Improvement Distrit (GEID), Rutland Water Works (RWW), and the South East
Kelowna Irrigation Distrit (SEKID).
The three irrigation distrits (BMID, GEID and SEKID) draw their water primarily from upland reservoirs, and were designed to deliver this water using gravity to irrigate agriultural parels. They have been
attahing ever more residential onnetions as the ity expands, but at present do not have omplete reords
of residential water onsumption and do not harge residential users by volume.
However, the nature of
their water soures makes them more vulnerable to both quality and quantity issues. The CITY and RWW
utilities developed to supply residential ustomers, with CITY drawing water from Okanagan lake and RWW
relying on groundwater. Both have adopted inreasing blok priing, in an eort to manage demand and in
partiular redue peak summer water use. Figure 2 illustrates the total water monthly water expenditures
in relation to the volume onsumed for the ve main water providers in Kelowna. Estimated base monthly
water demand is about 20.5 ubi meters, with additional monthly demand estimated to peak at 75.9 ubi
meters in July [Kelowna Joint Water Committee, 2012℄. Average water rates range from a low of $294.00 per
year for RWW to $517.00 per year for SEKID [Kelowna Joint Water Committee, 2012℄. Annual household
expenditures are estimated at $73,160 [Central Okanagan Eonomi Development Commission, 2012℄, so
that water aounts for no more than 0.7% of expenditures for the average household.
2
Figure 1: Kelowna Water Providers.
20
40
60
80
BMID
SEKID
GEID
RWW
CITY
0
Monthly Water Bill
100
Kelowna Household Water Expenditure Schedules
0
50
100
150
Monthly Water Use (cubic meters)
Figure 2: Kelowna water expenditure shedules by water provider.
3
The body of researh that examines household water onservation is relatively thin, and emerges from a
variety of disiplines. This likely reets the fat that water might be onsidered a 'omplex' good. At one
level, the onept of water embodies a range of ultural meanings [Strang, 2004, Allon and Sofoulis, 2006℄.
Therefore, the deision about how muh water to use and what to use it for impats on a omplex olletion of
issues for eah individual, with soial inuenes adding to this omplexity. At another level, water delivered
to the home is put to a range of uses.
It is diretly onsumed, used for neessary ativities like bathing
and food preparation, and for luxury ativities like maintaining landsaping and washing vehiles. Further,
so long as water is not ritially sare, it onsumes suh a small share of the household budget that it
attrats little attention. However, when it beomes suiently sare that poliy ation is required, interest
in understanding household water onservation deisions beomes heightened.
At these times, resoures
are made available, and researhers from a range of disiplines have been able to avail themselves of these
resoures.
Studies of water use, as distint from onservation hoies, are more ommon.
Good reviews inlude
Arbués et al. [2003℄ and Worthington and Homan [2008℄. General ndings inlude that the demand for
water is own prie inelasti and that inome elastiity is positive. A ompliating fator in these analysis is the
fat that water is seldom pried at its marginal ost, neessitating more ompliated eonometris [Hewitt and
Hanemann, 1995, Espey et al., 1997, Dalhuisen et al., 2003, Olmstead et al., 2007℄. Critial poliy questions
inlude establishing the water demand eets of dierent approahes to water priing [e.g. Kulshreshtha,
1996℄, and determining the distributional impats of these dierent priing poliies [Whittington, 1992,
Olmstead and Stavins, 2009℄. A textbook level welfare analysis quikly onludes that volumetri priing
is welfare improving, relative to at rate priing independent of volume onsumed.
be more ompliated.
However, things an
Renwik and Arhibald [1998℄ show that quantitative restrition poliies tend to
burden the auent, while prie poliies plae a larger burden on the poor. Inreasing blok priing, long
advoated as a progressive poliy, are also being questioned [Ruijs et al., 2008, Ruijs, 2009, Whittington,
1992, Pashardes and Hajispyrou, 2002℄. Given the ubiquity of non-prie poliies, reent work by Mansura
and Olmstead [2012℄ is partiularly relevant to the present researh.
The authors examine the welfare
impats of non-prie onservation poliies and sarity priing. Household heterogeneity, estimated using
high resolution household water onsumption measurements, drives heterogeneous welfare impats.
The
household observations reveal that most of the observed prie response reets hanges in outdoor water
use.
Their results indiate that outdoor water restritions are onsistent with resident preferenes, but
household heterogeneity means that a sarity prie ould ahieve the same water savings while permitting
more variation in individual household water onsumption and thereby inreasing aggregate welfare.
Water demand studies fous on the water used by households, with the details about how a household
4
responds to a prie hange ignored. However, ommunities put onsiderable eort and resoures into enouraging households to engage in spei water reduing behavior hanges and/or making water onserving
investments. Several authors have attempted to estimate the impats of dierent prie and non-prie onservation programs. Renwik and Arhibald [1998℄ examined water use in two oastal California ommunities
during a drought period. They assumed that water use and investment in water onservation were jointly
determined, and therefore instrumented for onservation investments as part of prediting water use. Poliy
interventions were strongly preditive of water onservation investments, along with inome and water prie.
Renwik and Green [2000℄ use a time series of residential water use for seven California ities to examine
the impat of ve non-prie water onservation programs: information, appliane rebates, free retrot kits,
water rationing and watering restritions. Estimation issues inluded the endogeneity of prie and weather
measures, as both are expeted to inuene water use. Voluntary programs ahieved water redutions omparable to that estimated for a fty perent prie inrease. Mandatory programs generated redutions three
to four times greater yet. Campbell et al. [2004℄ examine household water use for more than 19,000 Phoenix,
Arizona residents over a six year period. A number of onservation programs were tried during the period,
allowing their impat to be assessed.
Demand is own prie inelasti.
Sine a ten perent prie inrease
aounting for less than 0.05% of median household inome, the authors suggest this would be an eetive
onservation tool that would be politially aeptable, seemingly ignoring the experiene of Tuson, Arizona
some years earlier.
Engineering solutions, suh as providing people with free water saving xtures, were
found to be ineetive, induing a rebound eet. Ordinanes requiring water using xtures were eetive.
One shot ommuniation was not eetive, but the results suggest that repeated messages may lead to lower
water use. Ferraro and Prie [2011℄ work with a water utility to experimentally assess the impat of soial
messages. They nd that information alone does not generate muh water savings. Conservation inreases
when the message reets a soial norm, and even more when the onsumer's own water use is ompared
to average use by neighbors. This eet is most pronouned with heavy water users who are less responsive
to prie.
However, the eet also wanes with time, suggesting that suh strategies are best used when a
large, rapid response is required.
Overall, voluntary poliies have mixed eets, with the reent work by
Ferraro and Prie suggesting that the soial ontext plays an important role in determining the onservation
investments and behaviors people hoose.
There are a number of household and respondent harateristis that impat on onservation hoies.
Hamilton [1985℄ ompared self reported estimates of hanges in water use between two years with water meter
reords for Conord, New Hampshire, whih was faing a water shortage in the seond year. Residents are not
very good at estimating their water use. Those who are more ommitted, as evidened by their investment
in water onserving tehnologies and behaviors were more aware of their water use, as were those in a higher
5
soioeonomi lass. Whether a ommitment to onservation leads people to pay more attention to water
use, or whether greater attention to water use leads to more onservation isn't lear. However, Hamilton
suggests that providing residents with more information about their water use, suh as omparisons to past
water use on the utility bill, may play an important role in reduing residential water onsumption. Abrams
et al. [2012℄ segment Sydney households by ownership, house size, and partiipation in retrot programs.
They nd that short and long prie elastiity is overall small, but heterogeneous aross groupings. Owners
and tenants, oupants of single family residenes and those in multiple unit housing, those who partiipate
in retrot programs and those who don't, all respond dierently to prie hanges.
The present work is
most losely related to a reent study by Millok and Nauges [2010℄ that examines four household water
onservation investments by 10,000 residenes aross 10 OECD ountries.
The authors use independent
probit regressions to examine fators inuening the presene of water eient washing mahines, low water
toilets, low ow showers and rain barrels. They nd that a strong preditor of onservation investments is
ommitment to saving water, as measured by behavioral hoies like turning o the shower when soaping
up. Households that are both metered and pay a volumetri water prie are signiantly more likely to have
made the three onservation investments inside the home. The present work onsiders similar onservation
investments for residents of one ity with ve priniple water providers, two of whih meter and harge a
volumetri prie while the remainder harge a at fee.
The soial psyhology literature delves more deeply into the private and soial motivators for behavioral
hoies. The theory of planned behavior was desribed by Ajzen [1991℄, with gure one from Ajzen [1991℄
reprodued as Figure 3 below. If the behavior of interest is water onservation, then onservation ations are
predited by the intention to onserve, potentially modied by the pereived behavioral ontrol. Intentions
themselves are a onsequene of attitudes towards the behavior, subjetive norms, and modied again by
the pereived behavioral ontrol. Finally, attitudes, subjetive norms and pereived behavioral ontrol are
themselves mutually interdependent. The theory of planned behavior and related models are often estimated
using strutural equation modeling [Hoyle, 1995, Kline, 2010℄. The struture suggests that attention should
be paid to the endogeneity of the variables that measure intention.
While the theory of planned behavior is an appealing model, its ability to predit behavior is often
limited.
It is not unommon for researhers to develop ad-ho strutural models in an eort to better
explain behavior.
Cordano et al. [2003℄ explore the eetiveness of the New Eologial Paradigm (NEP,
Dunlap and van Liere, 1978, Dunlap et al., 2000) and a number of other measures as preditors. Sales suh
as the NEP have some preditive power for intention, but rather weak for behavior. Measures related to
other pro environmental behavior, suh as partiipation in ativities of environmental groups, is stronger.
Interestingly, intention to hange own behavior is weaker than intention to support regulations, suggesting
6
Attitude
Toward the
Behavior
Subjective
Norms
Intention
Behavior
Perceived
Behavioral
Control
Figure 3: The Theory of Planned Behavior (Figure 1 in Ajzen [1991℄).
that ativists see the hallenge as hanging aggregate behavior rather than individual behavior. Mobley et al.
[2010℄ examines how experiene with environmental literature inuenes behavior. This experiene predits
behavior better than the NEP and soiodemographi measures, but not as well as environmental onern.
The authors do not onsider the ausality between onsuming environmental literature and environmental
beliefs or onerns.
The theory of planned behavior has been applied to energy and water onservation hoies. Costanzo
et al. [1986℄ suggest that simple rational adopter and simple attitude hange perspetives underlie many
energy onservation eorts, and fail to aount for the full omplexity of human behavior. They argue that
people must rst internalize the message and then be in a position to at on it. Murphy et al. [1991℄ nd that
knowledge, attitudes and intentions are positively related to water onservation behavior, but only weakly for
knowledge. With a repeat survey, Moore et al. [1994℄ nd that media messages, partiularly television, are
reported by partiipants as positively inuening their water onservation attitude. For a sample of government employees in Kaohsiung City, Taiwan, Lam [1999℄ nds that pereived moral obligation and pereption
of a water right provide additional explanatory power to the theory of planned behavior in prediting the
intention to engage in water onservation. Corral-Verdugo et al. [2003℄ looks at how environmental beliefs,
inluding an early version of the NEP, inuene water onservation behavior. General beliefs tend to predit
onservation spei beliefs, but are not that eetive at prediting behavior. Utilitarian beliefs tend to be
more preditive of onservation behavior than eologial beliefs. Corral-Verdugo and Afrias-Arment [2006℄
nd that personal normative beliefs positively inuene water onservation behavior, while a tendeny to
break soial norms - labeled antisoial behavior - undid this relationship. Corral-Verdugo et al. [2006℄ nds
that people with a stronger future orientation in their beliefs tend to engage in more water onservation
behavior, with the opposite for those with a more present/hedonisti outlook. Corral-Verdugo et al. [2008℄
7
argues that the NEP fails to apture an alternate perspetive, that humans are integrated with the natural
environment. They propose an alternative measure, possibly apturing the loally spei attitudes others
nd as more preditive, and nd this new measure to be weakly superior to the NEP. Overall, the theory of
planned behavior provides a framework for exploring how internal attitudes and norms are translated into
behavioral hoies. For our purposes, this framework highlights the need to aount for endogeneity and for
the relationship between dierent observed behaviors.
2 Model
As a system, the theory of planned behavior an be modeled as
where
yiI .
yiI
and
yjB
yiI
=
X A βiA + X N βiN + X C βiC + Z I βiZ + uIi
(1)
yjB
=
Y I γj + X C θj + Z B θjZ + uB
j
(2)
are variables measuring intention and behavior respetively, with
The matries
X A, X N
and
XC
pereived behavioral ontrol, while
ZI
YI
a matrix with olumns
are measures of attitudes towards the behavior, soial norms and
and
ZB
represent variables outside of those aptured by the theory
of planned behavior that may inuene intentions and/or behaviors.
One immediate hallenge is that most of the observable variables representing
are at best proxies for unobservable latent variables.
yI∗ = Y I φI + ǫI ,
by
yl∗ β I
where
with
yI∗ γj
replaing
yl∗ = X l φl + ǫl .
Y I γj
Y I , X A, X N
and
XC
The model an be extended suh that there is a
in the equations for
yjB ,
and eah of the produts
X l βil
replaed
Strutural equation modeling essentially takes this approah.
Another important hallenge for this analysis is that the survey was not informed by the theory of planned
behavior. The observations were not made to be proxies for the underlying latent variables. Any relationship
that exists is therefore a happy oinidene, and the extent to whih the observations made an be used to
eetively estimate a strutural equation model that examines the theory of planned behavior is limited.
One important impliation of the theory of planned behavior is that endogeneity needs to be aounted for,
a fat that will inform the estimation.
An alternative formulation of the onservation hoie would be to assume the existene of a utility funtion
u(x, y, l|z),
where
y
are the agent's water onservation hoies,
is the leisure time enjoyed by the agent, and
z
x
are the other hoies made by the agent,
l
are variables that modify the utility funtion. Following Lam
[1999℄, the onservation hoies an be divided into urtailment and eieny hoies. Curtailment inludes
reduing shower length, not ushing the toilet, et., while eieny hoies inlude installing a dual ush
8
toilet and/or a high eieny laundry mahine. This division highlights the fat that onservation hoies
impat on both the time and the nanial budget.
Dropping the onditioning variables
z to save spae, the agent's optimization problem an be represented
as
u(x, y, l)
max
s.t.
p′ x + c(y) − qs(y) ≤ w[T − t(y) − l]
(3)
y∈Y
x∈X
0≤l≤T
where
T
Y
is the set of feasible water onservation ombinations,
X
is the set of other feasible hoies, and
is the maximum amount of time that the agent ould onsume as leisure. The produt
of purhasing
x, c(y)
is the ost of onservation hoies
y, qs(y)
p′ x
is the ost
is the value of the water savings
t(y)
is the time required to implement onservation hoies
c(y)
inorporates all osts, inluding amortized purhase osts for devies suh as high eieny washing
y,
and
w
s(y),
is the wage rate. It is assumed that
mahines.
Assuming that there are no interations between
good
x
x and y,
that we an represent
x
as a simple omposite
that has unit prie, and that the agent spends the entire budget, the optimization problem an be
rewritten as
max
u {w[T − t(y) − l] + qs(y) − c(y), y, l}
y∈Y
0≤l≤T
The rst order ondition for the leisure hoie is easily derived as
w = ul /ux ,
the agent hooses an amount
of leisure where the marginal rate of substitution between leisure and the onsumption good is equal to the
wage.
The optimization ondition for the onservation hoies is a bit more ompliated. There are two types of
onservation hoies, those that are ontinuous and those that are disrete. Choies that involve urtailment
are likely ontinuous, while eieny hoies often involve a disrete investment in a apital good. For a
ontinuous onservation hoie
yi ,
the rst order ondition for the level of
yi
solves to
cyi + wtyi = qsyi + uyi /ux
where the subsript
yi
ost of an inrease in
the hoie,
wtyi .
yi
indiates a partial derivative with respet to this onservation hoie. The marginal
is the diret inremental ost
cy i
added to the value of the time ost of implementing
For some hoies, suh as waiting till the washing mahine is full before running it, there
9
may be a time saving rather than a time ost. The marginal benet is the sum of the value of the water
savings,
qsyi ,
and the marginal rate of substitution between the onservation hoie and the onsumption
good. For a hoie suh as only washing full loads of laundry, there is disutility from having to wait to wear
a favorite lothing item, reeted in
u yi .
How frequently one waits is the balaning of this ost against the
value of the water savings and the time savings, and a likely near zero inremental monetary ost
there is a time saving, households with higher inome - larger
w
cy i .
Where
- will likely engage in a higher level of the
ativity. All else equal, where the prie of water is higher, a higher savings should result in a higher level of
the onservation ativity.
For disrete onservation hoies, it is optimal to hoose onservation ativity
yj
when








 w[T − t(y∗ ) − l∗ ]


 w[T − t(y0 ) − l0 ]
j
j
∗ ∗
u
,y ,l
, y0j , l0j
≥u




 +qs(y∗ ) − c(y∗ )


 +qs(y0j ) − c(y0j )
where
y∗
is the optimal vetor of onservation hoies for the agent, and
with hoie
j
u(x, l) + v(y),
y0j
(4)
is the optimal vetor, but
set to zero. If we make the additional assumption that the utility funtion an be written as
the hoie ondition an be rewritten as
∗
v(y ) − v(y0j ) ≥
u w[T − t(y0j ) − l0j ] + qs(y0j ) − c(y0j ), l0j
−u {w[T − t(y∗ ) − l∗ ] + qs(y∗ ) − c(y∗ ), l∗ }
This illustrates that whether or not the agent hooses to implement onservation hoie
v(y∗ ) − v(y0j ),
omparison of the utility gained from doing so,
j
depends on a
ompared to the utility lost on leisure and
the onsumption good that results from implementing this hoie.
Some hoies, suh as the purhase of a high eieny laundry mahine, likely have little time impat
one in plae and being used. If we dene
I∗
to be the expenditure on the omposite good at the optimal
solution, then the omparison an be written as
v(y∗ ) − v(y0j ) ≥ u [I ∗ + ∆I, l∗ ] − u [I ∗ , l∗ ]
where
∆I = q[s(y0j ) − s(y∗ )] − [c(y∗ ) − c(y0j )].
onservation hoie, then
∆I
If the value of the water saved exeeds the ost of the
is negative, and it is optimal to make the investment even if there is no diret
utility benet from doing so. However, if the onservation investment does not pay for itself, then the utility
benet from the investment itself must exeed the utility ost of onsuming less of the omposite good. One
immediate result is that if the prie of water,
q,
is higher, then
10
∆I
will be smaller or negative, and it is more
likely that the agent will hoose the investment. If we assume diminishing marginal utility of the omposite
good, then as inome inreases, all else equal, the dierene
u [I ∗ + ∆I, l∗ ] − u [I ∗ , l∗ ]
will deline. It follows
therefore that inreasing inome should also inrease the likelihood that an agent will hoose to make the
onservation investment.
Several hallenges ompliate parameterizing and estimating a model that follows from the deision
problem set out above.
is required.
The large number of options that make up
y
implies that a very large data set
There are also interations between some onservation hoies, as well as some not being
exatly ontinuous or exatly disrete. Turning o the tap while brushing ones teeth is a disrete hoie.
However, how frequently one does this is loser to a ontinuous hoie. Hysteresis eets are also important.
Replaement of an appliane often ours when the existing appliane fails. Consequently, failure to have
a water eient appliane may be only weakly related to a lesser onern for saving water. Some hoies
may also be partially or ompletely mutually exlusive.
For example, replaing a grass lawn with gravel
and adding organi material to enhane the water holding apaity of the soil are mutually exlusive if
one treatment is applied to the whole yard.
However, they may be omplementary, and a substitute for
xerisaping, if part of the yard is onverted to gravel and the remainder is retained as lawn.
An alternative to treating eah onservation hoie as distint is to sum the onservation hoies and
analyze the total. This requires some additional assumptions if we are to draw inferenes from the ount
of these onservation hoies. If the vetor of onservation hoies
y∈B
where
B = {0, 1}n
represents a
olletion of vetors where eah element represents a binary hoie. The ount of hoies is therefore
a typial ount variable, eah element of
y
Z
utility. Sine the elements of
For
would represent an inident of the same hoie, suh as visits to
the dotor, trips on transit, et. It is reasonable to assume that
the onditioning variables
i′ y .
u(y|Z) > u(ỹ|Z)
when
i′ y > i′ ỹ.
onstant, an inrease in the number of inidents represented in
z are idential,
y
Holding
inreases
their ordering doesn't matter. All that is of onern is the sum.
For the onservation hoies studied here, the hoies are not ounts of an inident.
As independent
hoies, if we are to onsider only the total number of onservation hoies made, we need to assume at least
a weak ordering. In partiular, for every
and
i′ y < i′ ỹ.
y ∈ B,
there does not exist a
ỹ ∈ B
suh that
u(y|Z) > u(ỹ|Z)
If we have one for one substitution between onservation tehnologies, suh that the total is
unhanged, but no ases where a preferred tehnology substitutes for more than one lesser tehnologies, then
an inrease in
i′ y
is still onsistent with an inrease in utility. If this assumption is not reasonable, then we
annot make inferenes from the ount of onservation hoies.
Lam's distintion between urtailment and eieny suggests one division. Another division is between
indoor and outdoor water onservation.
This generates four possible measures of behavior.
In all these
ategories, the number of ativities engaged in should be inreasing in inome and in the prie of water.
11
Other variables that impat on the size of the utility dierene
v(y∗ ) − v(y0j )
are also expeted to predit
the number of onservation ativities. Informed by the theory of planned behavior, some of these will at
through other variables, most partiularly intention.
Provided an appropriate proxy for intention an be
found, a test of the theory of planned behavior would be to see if there are variables that diretly aet
the behaviors, rather than ating through intention. However, this does depend on an appropriate proxy
existing in the data set.
3 Data
From the summer of 2009 through to the fall of 2010 a sample of Kelowna residents was invited to partiipate
in a household water use survey. The sample was build from a list of addresses and telephone numbers harvested from the website Canada411
TM (www.anada411.om), keyed on the forward sortation area identiers
in the postal ode for Kelowna addresses (www.anadapost.a). These addresses where then lassied by
water provider using a GIS layer provided by the City of Kelowna, and distane to the nearest water provider
TM . The sample was stratied to ensure representation from residenes lose
boundary alulated in ArGIS
to the boundary between water supplier servie areas.
The survey instrument was designed in onsultation with several loal water use experts for ontent
and tested with a small set of volunteers for omprehension.
The survey itself was built as a web form
that onneted with a dediated database that was designed and implemented by the author. The system
managed the ontat list for the interviewers, to avoid dupliate alls and ensure that the sampling protool
was maintained.
It also permitted the interviewer to take a partiipant's email address and enter it into
the system, whih would send the partiipant up to four email reminders with information to enable the
partiipant to omplete the survey online. Two interviewers made old alls and onduted interviews for
one week, with 26 surveys ompleted, after whih the survey was again reviewed for omprehension and a
few question and wording hanges were made. As most of the survey was unhanged, these 26 responses are
inluded in the sample.
Data olletion by telephone interview took plae during the summer of 2009. The interviewers attempted
to ontat 741 residenes. These ontats lead to 81 ompleted surveys, with 67.9% the result of people who
opted to omplete the internet version. Given the preferene for internet over telephone on the part of these
partiipants, the survey was ontinued as a mail survey with an internet option. In the spring of 2010 the
remaining sample was sent a letter inviting them to partiipate in the survey. This letter served both as
the initial ontat [following
Dillman et al., 2008℄ and ontained details for aessing the survey through
the internet. About three weeks later a paper survey was mailed to all in the sample for whom the original
12
mailing address was valid and who had neither ompleted the survey on-line nor indiated through the
website that they did not want to partiipate. About two months later a reminder letter was sent, whih
again ontained the aess information for the internet version of the survey.
Against the initial sample
of 2273 residential addresses, the response rate is 22.7%. As 56 of the 741 telephone ontats were not in
servie, and a similar share of the mail surveys were either inomplete addresses or people who had moved
(not separately oded in the data), the nal response rate is likely above 25%.
The variables used in the following analysis are summarized in Table 1. The rst four variables are all
averages of a set of Likert questions. The New Eologial Paradigm of Dunlap et al. [2000℄ uses fteen questions to measure adherene along ve diretions that span degrees of anthropoentriism to eoentriism.
While the NEP inorporates ve dimensions, it is frequently used as a single sale, whih is done here. A
onrmatory fator analysis [see Amburgey and Thoman, 2011℄ does not show any signiant gain from
using ve dimensions instead of one. GROW_BAD, ABUNDANCE, OTHERS_CONS and COMPULSION
are onstruted to measure attitudes about water availability and threats spei to the Okanagan.
The next nine variables are all indiators that an be either true (=
1)
or false (=
0).
The rst blok an
be onsidered largely subjetive and/or losely related to attitude. Being able to identify a water onservation
leader may be a positive inuene over one's own onservation hoies, while those who vote onservative
may be less inlined towards environmental onerns. The next three variables are true if the respondent
indiates that aspets of the loal environment, the loal weather, or loal rereational opportunities are
important reasons for oming to or staying in the area.
The four following indiator variables are more
objetive. Gender is sometimes found to be an important preditor of environmental behavior, as well as
whether there are shool aged hildren in the home and/or whether the respondent is retired. For the urrent
analysis, shool age hildren may be important 'messengers' in the quest to hange attitudes and behaviors.
Conventional eonomi theory suggests that if a household pays for its water, it will be more eient in its
use, and our model results suggest that those who pay are more likely to invest in onservation.
The KNOW variable is somewhat unique. It sores the respondent on their knowledge of four Okanagan
water fats: 1) what is the largest water use in the average Okanagan home, 2) how is water divided between
the four main use ategories, 3) how muh inow is there into Okanagan lake eah year, and 4) what is
the average personal daily water use in the Okanagan. The answers to these questions an all be found on
a publily available poster prepared by the Okanagan Basin Water Board and Natural Resoures Canada
[Turner et al., 2006℄. The grade was alulated as the Eulidean distane between the respondents answer
and the true answer, in a four dimensional spae spanned by the range of answers oered. This results in a
number between zero and one for eah respondent, with one orresponding to getting all the answers orret.
The next four variables are responses to questions for whih a range of options were given, to whih the
13
Table 1: Variable Denitions. Note that all Likert sale items have had missing values replaed following
Raaijmakers [1999℄.
Name
Range
a
7
b
7
7
7
7
NEP
1 -
GROW_BAD
0 -
ABUNDANCE
0 -
OTHERS_CONS
0 -
COMPULSION
0 -
LEADER
0, 1
VOTECON
0, 1
HEREENV
0, 1
HEREWEATH
0, 1
HERELEIS
0, 1
MALE
0, 1
PAY_WAT
0, 1
SCHOOL
0, 1
RETIRED
0, 1
KNOW
0 - 1
EDUC
d
Denition (regression saling in parentheses)
New Eologial Paradigm [Dunlap et al., 2000℄ sale.
Inreasing as feel growth threatening water availability.
Inreasing as feel water is abundant in the Okanagan.
Inreasing in pereption of others wasting water.
Inreasing in onvition that water must be onserved.
=1
=1
=1
=1
=1
=1
=1
=1
=1
if respondent an identify a water onservation leader.
if vote for onservative oriented party in reent eletion.
if respondent reports environment as reason for living here.
if respondent reports weather as reason for living here.
if respondent reports leisure as a reason for living here.
if respondent self identies as male.
if water provider harges a volumetri prie.
if shool age hildren in household.
if respondent retired.
Average sore on Okanagan water knowledge questions.
1 - 6
Inreasing in amount of advaned eduation, seleted from list.
0.5 - 75
Years living in Kelowna, one of 32 ranges oered.
INCOME
e
e
10 - 300
Household inome, thousands, ten point sale (1 = $1,000,000).
OCCUPANTS
1 - 7
0 - 7
f
Count of people living in residene.
MSG_PRIV
MSG_SOC
0 - 5
f
YEARS_KEL
Count from oered list of media/information soures that are
primarily privately onsumed.
Count from oered list of media/information soures with a
soial dimension.
0 - 6
Count of indoor water onservation investments.
ON_YARD
f
f
0 - 9
Count of outdoor water onservation investments.
BEHAVE
0 - 7
Count of indoor water onservation behavior hoies
ASSESS
4.6 - 12,450
Assessed value, in thousands (1 = $1,000,000).
BLDSIZE
72.5 - 582.8
Size of building, in square meters (1 = 1 hetare).
BLDAGE
2 - 99
Age of building (1 = 100 years).
BLDAGE2
4 - 9,801
Square of building age.
LOTSIZE
0.032 - 31.08
Size of lot, hetares.
IN_HOUSE
a Average of fteen Likert questions.
b Average of four Likert questions.
Average of three Likert questions.
d Average of four individually sored items.
e Midpoint for ranges oered in sale.
f Range from number of listed options, with
user supplied additions possible.
14
respondent hose one. For EDUC, the answers were ordered from least to most advaned eduation, where
graduate work at university was onsidered the most advaned. Years in Kelowna and inome were hosen
from a list of options, with the midpoint of the range beoming the value used for this variable. To bring the
estimated parameter values into a similar range, INCOME had to be entered in terms of millions of dollars.
The ve variables that follow are all ounts of items that partiipants seleted from a list, with partiipants
having the option to add extra items for all but the water onserving behaviors. The two message variables
are a deomposition of a single list of message soures, where it was an ex-post assignment to the soial
or private ategory. As far as the partiipant was onerned, there was no dierene between the soures.
The three water onservation variables were presented as separate questions. The distintion was between
outdoor and indoor, and then for indoor between water onserving behaviors and investments in apital that
onserves water.
TM , the
The nal set of ve variables ome from assessment authority data, purhased from Landor
marketing arm of the British Columbia Assessment Authority. All of these variables have been saled to
bring the regression parameter estimates into a similar range.
A seletion of data summaries are presented in Table 2. The summaries are presented for the ve main
water providers (see Figure 1), with a ath-all ategory OTHER for those that draw their water from a well
or some other soure that is independent of the main water providers. For the GROW_BAD, ABUNDANCE
and OTHERS_CONS variables, respondents who reeive water from SEKID are providing responses that
are signiantly dierent from one other water provider.
For ABUNDANCE and OTHERS_CONS, the
dierenes are not surprising. SEKID ustomers live in a rural area, and SEKID has the most vulnerable
water supply of the ve major providers. It is therefore not surprising that they are more likely to agree
that water is in limited supply in the Okanagan, and they are also more likely to notie other people that
they see as wasting water. However, one would expet that they would also pereive growth as a threat to
the ontinued availability of water, an expetation that is not satised.
The four variables, RETIRED, EDUC, YEARS_KEL and INCOME, reet the omposition of the
ommunity.
The CITY water utility supplies most of the properties along the lake, exepting those that
have water lienses or other soures whih predate the expansion of the ity servie area. Thus, it is not
surprising that inome for those provided by CITY is higher than that for all the other water providers, and
to the extend that eduation orrelates with inome, that eduation too is higher among CITY ustomers
than it is for all the other water providers. The exeption to the inome story is the OTHER ategory, whih
has by far the highest reported inome, and the seond highest eduation. To the extent that these are older
properties in prime loations, it also follows that they are likely owned by people with higher inomes. At
the other end, the area supplied by RWW used to be a working lass ommunity several kilometers east
15
Table 2:
Data Summaries.
Planned Behavior.
Variables are grouped into ategories loosely onsistent with the Theory of
Results for multiple omparison analyses are labeled with supersripts to indiate
statistially indistinguishable means. Dierenes are tested using an analysis of variane assuming a normal
distribution for variables that are approximately ontinuous (e.g.
Likert sale), an analysis of variane
assuming a Poisson distribution for ount variables, and a ontingeny table analysis for binary variables.
Signiane is based on
Variable
α = 0.05.
Where all means are the same, no supersript is shown.
N
Mean
P
GROW_BAD
516
4.81
0.027
BMID
CITY
GEID
OTHER
RWW
SEKID
4.993
4.790
4.805
5.203
4.745
4.624
ABUNDANCE
516
3.05
0.038
0.008
ab
5.172
a
4.786
ab
5.077
ab
4.551
ab
5.037
OTHERS_CONS
516
4.95
COMPULSION
516
RETIRED
509
5.57
0.785
5.575
5.524
5.646
0.31
0.003
0.188
0.323
0.440
0.188
0.143
EDUC
483
3.683
0.000
a
20.712
a
21.615
b
39.094
ab
26.303
a
19.911
b
ab
ab
3.150
ab
3.082
5.547
b
b
3.172
ab
a
4.036
ab
a
3.310
a
ab
3.507
ab
ab
2.833
ab
ab
4.000
ab
ab
2.878
5.673
b
2.406
a
b
2.713
b
5.203
5.698
ab
0.361
YEARS_KEL
509
22.4
0.000
INCOME
423
82.1
0.000
68.704
89.021
78.095
132.115
51.953
87.016
IN_HOUSE
516
2.55
0.751
2.754
2.624
2.440
2.250
2.429
2.658
ON_YARD
516
2.55
0.893
2.523
2.591
2.507
2.688
2.486
2.795
BEHAVE
516
4.04
0.688
4.292
4.021
4.013
3.875
3.714
4.288
ab
a
ab
b
of the lake. The fat that among respondents RWW ustomers are the least likely to be retired, have the
lowest average eduation and have the lowest average inome is onsistent with this history. Overall, the
dierenes between the water providers on these four variables suggest that the sample is not inonsistent
with the expeted ommunity prole.
The remaining variables, COMPULSION, IN_HOUSE, ON_YARD and BEHAVE are the variables we
are interested in analyzing. For all four, there is no signiant dierene aross the ve water providers.
If the dierenes are ompared based on paying for water by volume, there is also no signiant dierene
among any of these variables. For COMPULSION and BEHAVE, the average level is higher for those who
do not pay, while for the investments inside the home and on the yard, the average ount is slightly higher.
If we examine the numbers, ustomers of SEKID report either the highest or the seond highest level for all
four of these variables, whih is onsistent with SEKID having being most vulnerable to supply interruptions.
However, the dierenes are small and far from statistially signiant. For the analysis that follows, we
expet that reported values for IN_HOUSE, ON_YARD and BEHAVE are more aurate than would be
self reported estimates of the volume of water used in the home [Hamilton, 1985℄.
Table 3 shows the total number of respondents reporting that they undertake eah of the listed onservation investments or ativities. For the IN_HOUSE ategory, the most ommonly reported investment is the
low ow shower head, with a water onserving toilet the next most ommon. Eient laundry mahines are
next, followed by eient dish washers. The shower, toilet and laundry are important water using ativities,
while washing dishes is not [see Gleik et al., 2003, for detail on water saving potentials℄. Tap aerators are
reported by a remarkably low number of people, given that they are a standard part of many fauets that
16
ab
3.743
ab
27.078
a
Table 3: Conservation investments and behavior ounts.
Count
Ation
366
Timed irrigation
356
Low water toilet
294
Water yard less
261
Soil amendments
200
Gravel yard
164
Xerisaping on yard
134
Eient laundry mahine
245
Eient dish washer
212
Tap aerator
196
Indoor greywater system
BEHAVE
Count
Low ow shower
5
ON_YARD
IN_HOUSE
Ation
Drought tolerant grass
69
Rain barrel
61
Laundry full only
455
Dishwasher full only
435
Pool over
58
Tap o when brushing teeth
414
Moisture probe
12
Srape, don't rinse dishes
257
Greywater system
Flush toilet when needed
248
Wash dishes in basin
203
Shower o when soaping
2
74
one an purhase or have installed. Greywater systems, whih are the most expensive and dediated water
saving investment, are not surprisingly the least ommon. The relatively high reported level of eient dish
washers and the low rate of reported tap aerators suggests that some respondents are onfused about these
water saving investments.
The most popular reported water saving investments on the yard is timed irrigation. Ironially, the water
saving eet of timed irrigation isn't ompletely lear, as timer systems are often unrelated to atual water
need. Sprinklers will be run in the rain by a timer! The next most ommon outdoor water onserving ation
is simply watering less. While this is more of a behavior than an investment, it is inluded in the outdoor
ount. The next four investments are somewhat interonneted. If the entire yard is onverted to gravel,
without any plants, then this is mutually exlusive of the other three.
However, ombined with drought
tolerant plants, it ould be onsidered part of xerisaping a yard. If it is applied to only part of the yard,
then the remainder ould be seeded with drought tolerant grass, and have soil amendments used to inrease
water retention for that grass. Therefore, on some yards these measures may be mutually exlusive, while
on others omplementary. The survey provided no method to assess the extent to whih these treatments
are applied. For the remainder, rain barrels tend to be used by people who are quite dediated to water
onservation, and have an appropriate use for the water, suh as a ower bed.
The use of a pool over
requires a pool, explaining partly the lower relative ount. Having a moisture probe onneted to a watering
system shows a high level of knowledge and sophistiation, and greywater systems that provide water for
use on the yard are expensive, dediated investments.
Finally, the two most popular water saving behaviors are using the laundry mahine and the dishwasher
only when they are full. Suh behaviors ertainly save water, but they may also be driven by a desire to
save time and/or to save soap. Given the model developed above, saving time is likely a larger motivator.
17
Attitudes
Table 4: Classiation of variables.
Pereived
and Norms
Control
Intention
Behavior
COMPULSION
IN_HOUSE,
NEP, GROW_BAD,
KNOW, EDUC,
ABUNDANCE, OTHERS_CONS,
MSG_PRIV,
LEADER, VOTECON,
MSG_SOC
HEREENV, HEREWEATHER,
HERELEIS, MALE,
PAY_WAT
INCOME
ON_YARD,
BEHAVE
BEHAVE
Turning the tap o when brushing ones teeth is also a ommon water onserving ativity, and one that is
frequently promoted.
It saves relatively little water, but may be related to raising awareness.
Sraping,
rather than rinsing dishes before loading the dishwasher is somewhat more speialized, and somewhat less
ommon. Flushing the toilet only when needed is fairly ommon, whih is a bit surprising given the general
disgust expressed in response to If it's yellow, let it mellow. If it's brown, ush it down. Using a basin,
rather than a full sink to wash dishes is also fairly ommon. The least ommon water onserving behavior
is turning o the shower when soaping up. While aknowledging a potential rebound eet - shower longer
after turning it bak on - the low uptake of this behavior is onsistent with the utility tradeo desribed in
the model. The utility lost by temporarily going without the warm water and with having to nd that right
temperature when turning it on again is , for many people. not ompensated for by the value of the water
saved, nor the satisfation of ating to save water.
4 Results
There are a number of estimation issues that need to be onsidered. One issue is the potential for orrelation
in the error terms aross the dierent measures of onservation behavior. A seond issue is the potential
endogeneity of some variables. A third issue is identifying whih variables are individually or olletively
measures of the latent variables implied by the theory of planned behavior. A fourth issue is the appropriate
distribution to assume for tting and testing the model. Counts of onservation hoies are learly not draws
from the standard normal distribution. However, they are also not ounts in the onventional sense. In what
follows we fous on the rst two issues, allowing for orrelation between the error terms and exploring the
role of endogeneity. The role of endogeneity is examined through the lens of the theory of planned behavior,
whih is used to roughly lassify the variables.
Given that the data was not olleted to expliitly test
the theory of planned behavior, no distintion is made between attitudes and norms. The lassiation is
presented in Table 4.
The lassiation is based roughly on whether the variables are purely subjetive and where they ould
t in the theory of planned behavior.
Knowledge, eduation, and messages are expeted to enhane the
18
awareness of the respondent to the options they have, and thus t into the pereived behavioral ontrol
ategory. Whether the household pays for water and what their inome level is are put in this ategory, in
the sense that if the household pays for water, then onserving water is a way of ontrolling expenditures,
and higher inome inreases the options that the household an aord.
However, as these variables are
also predited by the utility theoreti model as having diret impat, they will be maintained in the model
throughout. Compulsion is seen as losest to intention. However, it ould also be onsidered an attitude
variable.
Behavior was measured as omparable to the investment ategories, but as other authors have
onsidered behaviors a measure of ommitment to water onservation [e.g.
Millok and Nauges, 2010℄, they
an also be onsidered as a measure of intention.
The dependent variables, IN_HOUSE, ON_YARD and BEHAVE, are ount like. The analysis relies on
the validity of the assumption that the data an be treated as ounts. The appendix proposes an assessment
of the validity of this assumption, nding that the data is weakly ordered.
Weakly ordered means that
the hoies made are not onsistent with a single ordering while also not being onsistent with eah hoie
being an independent random seletion. It is assumed that this weak ordering is suient justiation for
analyzing the data as if it was ount data.
For a Poisson regression, the onditional expetation of the dependent variable is
A nonlinear regression speiation for this system would be
y = exp(Xβ) + u.
E(y|X) = exp(Xβ).
This speiation lends
itself to several estimation proedures, among whih we hoose nonlinear least squares. As the data is not
preisely a ount, it unlear whether inferenes based on a Poisson regression are appropriate. An equation
by equation generalized method of moment was estimated using the Poisson moment onditions, with results
similar to those reported here. Linear regressions of the form
log(y) = Xβ + u
were also estimated, where
the log-linear speiation ensures that all predited values are greater than zero. The parameter estimates
from these linear regressions were used as starting values for the nonlinear regressions.
The regressions represent three observations of onservation hoies for eah respondent. It is oneivable
that the unexplained variation is orrelated aross the equations. To aommodate this, estimation was as
seemingly unrelated regressions (SUR). The rst regressions were estimated with only the dummy variable
indiating whether water was volumetrially pried and the inome ategory (results not shown). For onservation investments (IN_HOUSE and ON_YARD), inome was strongly signiant while prie was far
from signiant. For BEHAVE, neither was signiant. The inome response is generally onsistent with
the proposed utility model, while the lak of a prie eet is either inonsistent with the model or reets
pries that are too low to indue a signiant response. Sine the BEHAVE hoies do not have a monetary
ost, it is not surprising that there is no inome eet, and the lak of a prie eet may again reet a low
water prie.
19
For onsisteny with the theory of planned behavior, instruments were used in plae of COMPULSION
and BEHAVIOR, with three stage least squares (3SLS) regressions aounting for possible ross equation
orrelations. Both the linear and nonlinear 3SLS regressions were implemented as a two stage least squares
to generate the predited values for the endogenous variables, followed by a GMM estimation for the results
of the system as a whole. Equation by equation Sargan tests for the overidentifying restritions were far
from signiant for the nal 3SLS linear regressions, when the pereived behavioral ontrol variables were
inluded in the regressions. When these were not inluded, the Sargan test was signiant. The inuene
of the variables ategorized as falling into the pereived behavioral ontrol were not well represented by
predited values for BEHAVE and COMPULSION, while there is no evidene that the inuene of those
variables ategorized as related to attitudes and/or norms isn't aptured by these predited values. Equation
by equation Hausmann tests for the endogeneity of the instrumented variables were also estimated. For the
nal system, these failed to rejet, suggesting that the variables that were instrumented for may not be
endogenous. If this is the ase, then the OLS and NLS estimators are onsistent and eient.
The Cragg-Donald
gmin
test statisti [Cragg and Donald, 1993℄, whih Stok and Yogo [2005℄ employ
to test for weak instruments, was alulated for the 3SLS linear regressions. These tests indiate that the
instruments are weak.
The t for the rst stage regressions is also not strongly signiant, with an
F
statisti far below 10, leading to a similar onlusion. There are two onsequenes of the weak instruments
that needs to be onsidered as the following results are disussed.
The validity of the Hausman test for
exogeneity requires a set of exogenous instruments. That the instruments are weak means that it may not
be appropriate to onlude that BEHAVE and COMPULSION are in fat exogenous. However, the weak
instruments also magnies the potential ineieny of the instrumental variables approah, whih some
have suggested means that the OLS results are superior to the instrumental variables results [Doko Thatoka
and Dufour, 2011℄. We therefore report the SUR results as well as the 3SLS results. The rst regressions
exlude the endogenous variables. The seond inlude the potentially endogenous regressors but exlude the
pereived behavioral ontrol variables. The nal regressions inlude the potentially endogenous regressors
and the pereived behavioral ontrol variables. The Sargan test of the overidentifying restritions [Sargan,
1958℄ and Hausmann tests for exogeneity tend to report problems for the simpler models, but not for the nal
regression results. All analysis is done in R [R Core Team, 2013℄, with the
systemt
pakage [Henningsen
and Hamann, 2007℄ used for linear and nonlinear three stage least squares and system regressions.
Table 5 reports the regressions for investment style onservation hoies inside the home. There is no
signiant inuene of a volumetri prie in any of the regressions. Inome is at least weakly signiant for all
the regressions, with the size of the estimated inuene inreasing when the potentially endogenous regressors
are instrumented for. Assessed value is weakly signiant in most of the regressions and strongly signiant
20
for the NLS 3SLS regression. The estimate is always negative, and also inreases when moving from the
SUR and NLS regressions to the 3SLS and NLS 3SLS regressions. However, the estimate is onsistently
less than one fth of the value of the inome estimate. The relationship between inome and assessed value
may reet measurement error in the inome variable. The inluded inome variable is the midpoint of the
interval that respondents suggested. If the expeted value of the assessed value is a more aurate measure of
inome, and if the midpoint of inome is too high - likely if the inome distribution is skewed - then assessed
value will have a negative sign. If assessed value is less well orrelated with inome than the midpoint of the
inome ategory, then the inome measure will still have greater preision.
Among the further regressors assumed to be exogenous to the theory of planned behavior, building
age and building age squared, BLDAGE and BLDAGE2 respetively, are at least weakly signiant in all
the regressions.
The signs are onsistent with Mansura and Olmstead [2012℄.
The minimum number of
onservation hoies ours around 35 years. This minimum is about 0.25 below that predited for an age
of zero. The eet is signiant, but learly not very large. Building size and the number of oupants does
not have a signiant impat on the number of indoor onservation investments.
Of the four variables that are grouped with the pereived behavioral ontrol aspet of the theory of
planned behavior, the number of predominantly private message mediums is at least weakly signiant in
three of the four regressions where it is inluded. In ontrast, those message media that are more soial do
not have a signiant eet. Low ow showers, water onserving toilets and high eieny laundry mahines
do not seem to be topis of onversation, even though people do seem to be inuened by the penetration of
the messages. Knowledge about loal water issues and eduation do not have a signiant eet. Eduation
in partiular we expet to be related to an awareness of the options one ould pursue. However, the eet is
pretty lose to zero.
Finally, when the two potentially endogenous regressors are inluded, BEHAVE is strongly signiant
in the regressions without instrumental variables, while COMPULSION is weakly signiant in two of the
three regressions without instrumental variables. For the instrumental variable regressions, COMPULSION
is more strongly signiant, while BEHAVE is less strongly signiant.
The latter eet is driven by a
muh larger inrease in the standard error of the estimator than in the value of the estimate, while for the
former, the estimate inreases more than the standard error. The sign on COMPULSION is inonsistent
with expetations.
However, as BEHAVE and COMPULSION are expeted to be imperfet measures of
the same latent variable, the fat that the impat of BEHAVE strongly dominates that of COMPULSION
- enough to more than oset the dierent ranges for these variables - is supportive of the general thrust of
the theory of planned behavior.
Table 6 reports the results for the outdoor onservation hoie regressions. As for the indoor onservation
21
Table 5: Regression Results, IN_HOUSE. Dependent variable is
log(IN_HOUSE) for all regressions exept NLS SUR and NLS
+ ≤ 0.10, * ≤ 0.05, ** ≤ 0.01 and *** ≤ 0.001.
3SLS. For these last
two regressions, the dependent variable is IN_HOUSE. Signiane levels are
SUR #1
(Interept)
SUR #2
β
se
1.245***
0.123
log(BEHAVE)
22
INCOME
ASSESS
BLDSIZE
BLDAGE
BLDAGE2
OCCUPANTS
0.815***
0.467***
-0.051+
COMPULSION
PAY_WAT
β
-0.013
1.300*
0.051
0.526
-0.164
0.100
1.310
4.241
-0.758*
1.135*
0.017
0.010
1.205+
-0.178+
1.533
0.578
-0.702+
1.029+
0.020
0.001
0.419
MSG_PRIV
SUR #3
3SLS
se
β
se
0.223
0.760***
0.233
0.096
0.436 ***
0.098
β
0.963*
0.667+
0.029
-0.047
0.029
-0.144*
0.050
0.006
0.050
-0.001
0.512
0.099
4.264
0.420
1.280*
-0.180+
1.576
-0.772+
0.576
1.172*
0.021
0.006
0.037*
0.100
1.436*
-0.209+
4.247
1.312
0.520
0.578
-0.787+
1.155+
0.021
-0.004
0.420
0.015
0.033+
NLS SUR
se
0.490
0.398
0.064
0.054
0.565
0.112
4.462
0.434
β
0.653*
0.447***
-0.057+
0.006
1.132*
-0.260+
2.094
-1.112**
0.594
1.426**
0.027
0.020
0.017
0.042*
NLS 3SLS
se
0.262
β
0.470
0.031
0.851+
-0.141*
0.054
-0.010
0.124
0.138
1.432*
-0.281*
4.791
3.000
0.527
se
0.612
0.455
0.063
0.057
0.585
0.141
4.939
0.544
-1.009*
1.399*
0.022
0.004
0.026
0.016
0.030
0.020
0.423
0.445
0.566
MSG_SOC
-0.015
0.026
-0.013
0.030
-0.028
0.027
-0.031
0.032
KNOW
-0.115
0.133
-0.081
0.138
-0.174
0.145
-0.128
0.152
-0.001
0.018
0.002
0.018
-0.001
0.019
-0.001
0.020
EDUC
R2
0.0383
0.1079
0.1288
0.0849
0.1232
0.0755
investments, paying a volume based prie for water does not signiantly impat the number of outdoor
onservation investments.
However, unlike the indoor hoies, inome has a muh weaker eet.
It is
signiant in only two of the regressions, and then only weakly so. Assessed value is also insigniant. The
weakness of inome, and the relatively limited impat of many variables, may reet the less lear ordering
of these investment hoies.
One variable that stands out as signiant is the number of media soures with a soial dimension where
a onservation message has been heard. This is strongly signiant in all the regressions, while the private
messages are not signiant. Interpreted in the ontext of the theory of planned behavior, notiing these
soial messages seems to be important in enabling people to know how to implement onservation options
that they otherwise might not know about.
Given that these are soial, rather than private messages,
suggests that people learn how to implement onservation hoies on their yard more from interating with
other people than they do through researhing the issue themselves.
Among the potentially endogenous variables, BEHAVE is signiant when it is not instrumented for.
However, when instruments are used, the parameter estimate redues in size and the standard error substantially inreases, leading to estimates that are no longer signiant. The diretion of the inuene remains
onsistent with expetations.
The behavior regression results are shown in table 7. These results were generated for the system with
three dependent variables, in ontrast to the ase where
log(BEHAVE)
was inluded as a preditor and the
system was estimated with two equations. For all of these regressions, paying for water by volume and inome
are not signiant preditors. Unlike the indoor and outdoor onservation investments, these behaviors do
not require an investment. They typially do have a time and/or inonveniene ost, whih is set against
any value of water saved. Given the low prie, the value of the water saved is likely not that important.
Thus, behaviors are likely driven by other utility related variables.
Moving to the further exogenous regressors, the number of oupants and the presene of shool age
hildren are signiant - the former strongly so, the later weakly so. The strong inuene of the number
of people in the house likely reets physial onstraints of the water system in the house. In partiular,
ativities that use warm water, suh as running a long shower, may mean less warm water available for
other users. The presene of shool age hildren was expeted to inuene behavior through the messages
hildren bring home from shool. However, if the survey respondent faes suh pressure, it will be reeted
in the MSG_SOC variable. What is left may be a time eet. Households with shool age hildren are busy
households, and therefore may not have the time to engage in as many onservation behaviors as households
without suh hildren.
For this dependent variable, both types of messages are related to a higher number of onservation
23
Table 6: Regression Results, ON_YARD. Dependent variable is
log(ON_YARD) for all regressions exept NLS SUR and NLS
+ ≤ 0.10, * ≤ 0.05, ** ≤ 0.01 and *** ≤ 0.001.
3SLS. For these last
two regressions, the dependent variable is ON_YARD. Signiane levels are
SUR #1
(Interept)
SUR #2
β
se
1.111***
0.068
β
0.199
3SLS
se
β
NLS SUR
se
β
-0.275
NLS 3SLS
se
β
se
24
0.460***
0.388***
0.217
0.396
0.448
0.970
0.097
0.295
0.308
0.534***
0.299
0.097
0.145
0.008
0.390
COMPULSION
0.026
0.030
0.012
0.029
0.001
0.061
0.022
0.036
-0.042
0.077
-0.017
0.066
-0.056
0.211
β
log(BEHAVE)
PAY_WAT
0.227
SUR #3
se
0.577
0.897+
0.053
-0.040
0.052
-0.045
0.051
-0.051
0.053
-0.080
0.519
0.693
0.509
0.693
0.513
0.674
0.526
1.092+
0.061
INCOME
0.558
0.864
0.615
ASSESS
0.109
0.097
0.119
0.098
0.119
0.097
0.132
0.105
0.076
0.091
0.131
0.107
LOTSIZE
0.118
0.133
0.089
0.134
0.061
0.131
0.065
0.133
0.062
0.125
0.077
0.134
0.018
0.016
0.019
0.016
0.007
0.018
0.008
MSG_PRIV
0.020
MSG_SOC
0.079**
0.026
0.085**
0.029
0.092***
0.028
0.124***
0.033
KNOW
0.182
0.133
0.179
0.136
0.094
0.161
0.038
0.175
EDUC
2
0.010
0.018
0.011
0.018
0.002
0.021
0.001
0.023
R
0.0401
0.1192
0.1668
0.1632
0.1547
0.0879
Table 7: Regression Results, BEHAVE. Dependent variable is
log(BEHAVE) for all regressions exept NLS SUR and NLS
+ ≤ 0.10, * ≤ 0.05, ** ≤ 0.01 and *** ≤ 0.001.
3SLS. For these last two
regressions, the dependent variable is BEHAVE. Signiane levels are
SUR #1
(Interept)
SUR #2
β
se
β
se
β
se
β
se
1.511***
0.065
1.159***
0.114
1.091***
0.054**
0.121
0.993***
0.074*
0.191
0.827***
0.132
0.936***
0.205
25
INCOME
-0.020
YEARS_KEL
0.060***
-0.077+
0.063***
0.031
-0.036
0.292
-0.114
0.016
0.041
0.060***
-0.073+
0.031
-0.038
0.284
-0.103
0.016
0.040
0.061***
-0.077+
0.017
0.030
-0.034
0.287
-0.119
0.016
0.040
0.059***
-0.076+
0.033
0.065***
0.031
-0.028
0.289
-0.071
0.016
0.040
0.055***
-0.072+
0.019
0.055
0.036
0.031
-0.040
0.032
0.294
-0.168
0.015
0.041
0.053***
-0.072+
0.299
0.016
0.041
0.037
0.026
0.037
0.033
0.037
0.028
0.038
0.028
0.039
0.018
0.040
-0.057
0.095
-0.035
0.095
-0.013
0.098
-0.011
0.098
0.031
0.103
-0.007
0.104
MSG_SOC
KNOW
R
0.017
0.043
MSG_PRIV
EDUC
2
NLS 3SLS
se
-0.046
RETIRED
NLS SUR
β
PAY_WAT
SCHOOL
3SLS
se
COMPULSION
OCCUPANTS
SUR #3
β
0.0571
0.1052
0.017+
0.040*
0.009
0.016
0.017+
0.037*
0.009
0.016
0.022*
0.038*
0.010
0.016
0.021*
0.042**
0.010
0.016
-0.034
0.080
-0.039
0.081
-0.044
0.084
-0.060
0.085
0.007
0.011
0.006
0.011
0.008
0.011
0.006
0.011
0.1502
0.1465
0.1588
0.1555
Table 8: Regressions on endogenous variables. The log of BEHAVE is used as the dependent variable.
COMPULSION
β
(Interept)
NEP
MSG_PRIV
se
3.1127***
0.2027**
0.6426
0.0701
log(BEHAVE)
β
se
0.9782***
-0.0187
0.0190*
0.0407*
0.2120
0.0231
0.0095
-0.0027
0.0289
MSG_SOC
0.0779
0.0491
KNOW
0.1826
0.2496
LEADER
0.0228
0.0318
0.0187.
0.0105
EDUC
GROW_BAD
ABUNDANCE
VOTECON
OTHERS_CONS
HEREENV
HEREWEATH
HERELEIS
-0.0045
0.2083***
-0.1582***
0.1625.
0.1236**
-0.0288
0.0162
0.0823
0.0340
0.0035
0.0112
0.0611
0.0283
0.0201
0.0448
0.0005
0.0148
0.0945
0.0352
0.0312
0.0444
0.0399**
0.0146
-0.0193
0.1131
-0.0322
0.0373
0.0603
0.1112
-0.0301
0.0367
0.0238
0.0950
0.0027
0.0313
MALE
-0.1017
0.1010
-0.0188
0.0333
PAY_WAT
-0.0841
0.0949
-0.0283
0.0313
0.8398
0.9625
-0.2634
0.3176
INCOME
ASSESS
BLDSIZE
BLDAGE
-0.0962
0.1918
0.0931
0.0633
2.8228
8.2942
2.8631
2.7367
0.4110
0.8329
0.1634
0.2748
-1.1225
1.1235
-0.1818
OCCUPANTS
0.0276
0.0506
0.0620***
0.3707
LOTSIZE
0.2347
0.2548
0.0530
SCHOOL
-0.0302
0.1293
0.1819
-0.4065
BLDAGE2
RETIRED
YEARS_KEL
0.0167
0.0841
-0.0870*
0.0426
0.1215
0.0456
0.0401
0.3424
-0.0781
2
0.1130
R2 = 0.306
F23,276 = 4.826
R = 0.199
F23,276 = 2.723
behaviors. Neither knowledge about Okanagan water issues nor the level of eduation are signiant. Thus
it seams to be not (only) what people know that is a driver for these behaviors, but how they ome to know
it.
The rst stage regressions for the potentially exogenous variables are shown in Table 8. Compulsion is
dominated by three variables, the new eologial paradigm sore, the belief that growth is bad, and the belief
that there is abundant water. A stronger ommitment to the NEP and a stronger belief that growth is bad
for water availability both inrease the ompulsion sore. The more abundant the respondent believes water
is, the lower the sore. The remaining weakly signiant variable is whether the respondent stated that they
voted for a onservative andidate in the last eletion. Given that ompulsion an be thought of as a duty
to follow partiular ations, this relationship is not surprising.
The BEHAVE regression has as its dominant variable the number of oupants in the house.
The
next most signiant variable is the number of soial onservation message soures that the respondent
26
an identify.
Both of these variables have the expeted sign.
Less strongly signiant variables inlude
the number of private onservation message soures identied, whether the respondent ould identify a
onservation leader, agreement that growth has a negative impat on water availability, and the presene of
shool age hildren in the household. All but the last of these have the expeted sign.
Finding that NEP, LEADER, GROW_BAD, ABUNDANCE, VOTECON and OTHERS_CONS are
signiant preditors for the variables being used to instrument for intentions in the TPB is generally onsistent with the theory. That the Sargan test does not rejet the overidentifying restritions lends further
support, as the inuene of these variables is eetively transmitted through the predited values for BEHAVE and COMPULSION. However, the weakness of the instruments also means that the predited values
for BEHAVE and COMPULSION likely only explain part of the variation in these variables that is related
to IN_HOUSE and ON_YARD.
5 Disussion
A sequene of regressions have been run, loosely informed by the theory of planned behavior. The predition
of the utility theoreti model that inome will be preditive of the number of investments that save water
is supported, and the fat that inome is not preditive for behaviors that save water but have little ost is
not that inonsistent with expetations. That inome is preditive is also not inonsistent with the theory
of planned behavior, if one thinks of higher inome as inreasing pereived behavioral ontrol. The negative
inuene of the assessed value of the residene is interesting. However, the eet is muh smaller than the
impat of inome, and the presene of this eet may be related to the way that inome was measured.
The fat that no support was found for a diret linkage between attitude variables, partiularly the NEP,
and behavior is onsistent with previous work. NEP is a strong preditor of the ompulsion to onserve,
whih itself was a fairly onsistent preditor of indoor onservation. The fat that the impat of ompulsion
on indoor onservation was the reverse of expetations is of ourse troubling.
However, this may also
reet an interation with inome, and in partiular the imperfet measurement of inome.
On its own,
indoor onservation investments and ompulsion are positively orrelated. Another possibility is that the
ausality is reversed. Households that have made onsiderable investments in water onservation may feel
less ompulsion to onserve more water. This is ertainly a weakness that requires further exploration.
The lak of a prie eet is the strongest inonsisteny with eonomi theory.
However, this may be
a simple onsequene of the low prie for water in Kelowna. Investing in water onservation tehnologies
has a limited nanial payo, rendering this payo likely at best a seondary onsideration. Conservation
investments will be driven primarily by other fators, fators that might inlude having a pro-environmental
27
attitude, having an anity for new tehnology, feeling soial pressure to onform to a partiular set of
behaviors, a desire to be seen as a water onserver, et.
The hoies analyzed here are not onventional ount data, and are at best weakly ordered. That building
age is ommonly a signiant preditor for indoor onservation investments highlights the important role of
opportunity in onservation investments. The nanial payo is typially not suient to justify replaing a
relatively new appliane or xture, and only in rare ases are preferenes strong enough in these situations
to dominate the nanial aspet. However, when a toilet or laundry mahine needs replaing, or when a
signiant landsaping projet is to be undertaken, then the inremental ost of making the replaement more
water onserving may be small enough for onservation preferenes to overome the questionable nane.
The relative osts and benets of a onservation investment are therefore heavily dependent on the situation
a household is in. This is of ourse responsible for the weak ordering of the data.
Several other variables are interesting. Neither eduation nor knowledge about Okanagan water issues
have a signiant impat on the ompulsion to onserve or on the onservation investments and behaviors.
Considerable eorts are made to inrease the awareness of water sarity in the Okanagan. The fat that
people who are more informed about Okanagan water issues are no more likely to onserve water suggests
that eduation about water sarity has little impat on behavior. This is onsistent with Murphy et al.
[1991℄, who nds that knowledge is a weaker preditor of water onservation than attitudes and beliefs. The
strong impat of soures of onservation messages is striking, but also onsistent with results in Moore et al.
[1994℄. The number of privately onsumed information soures where a onservation message was reeived
was signiant for indoor water onservation, while the number of soial information soures for onservation
messages was strongly signiant for investments in the yard. Other researh by the author nds support for
a neighbor eet with household water onsumption. The urrent results suggest that people are strongly
inuened by messages from friends, neighbors, through ommunity forums, et., when it pertains to their
yard - an important investment that is visible to the neighbors - and to daily behavioral hoies.
Taking together with the absene of a prie eet and the weak or even negative inuene of the ompulsion to onserve on investment inside the home, the strong impat of message soures may indiate that
water onservation is more a habitual behavior than a response to beliefs or attitudes. Over time, people in
the Okanagan may simply habituate to the pratie of water onservation. This is not on aount of their
believing it is the right thing to do or knowing about water sarity in the Okanagan. Rather, they simply
internalize the messages that they are exposed to. The more messages that people are exposed to, the more
rapidly they internalize this habit.
Water suppliers, loal government, provinial and federal agenies, NGOs, and other stakeholders invest
onsiderable resoures in the Okanagan towards enouraging water onservation. Both the City of Kelowna
28
and Rutland Waterworks have adopted inreasing blok priing, onsistent with most eonomists view that
prie an play an important role in enouraging onservation. However, there are no measurable dierenes
in water onservation behavior among the ve dierent Kelowna water providers, three of whom have no
volumetri omponent to their priing. Unfortunately, the three water providers who harge a onnetion fee
do not have household level water use reords that an rmly establish the absene of a prie eet. Assuming
that the observed results are aurate, the volumetri prie harged in part of the ity is at best serving as
a small reward for those who onserve water, but is ineetive as an inentive to enourage additional water
onservation.
Information ampaigns that attempt to hange people's 'environmental ethi' seem to have limited impat.
Respondents who sore higher on the New Eologial Paradigm are more likely to agree with statements
about the importane of water onservation. However, this agreement only seems to translate into behavior
hanges. It does not impat on water onservation investments. Eorts to hange people's environmental
values as a relatively short term solution to water onservation hallenges is therefore unlikely to be eetive.
Similarly, eduating people about Okanagan water issues has no measurable eet. The assessment of loal
knowledge was based loosely on information in suh an eduation program, inluding a fat lled poster and
a teahers guide, jointly sponsored by the Okanagan Basin Water Board, the Geologial Survey of Canada,
and Siene Opportunities for Kids Soiety [Turner et al., 2006, Siene Opportunities for Kids Soiety,
2008℄. Suh ampaigns are ostly, and at least within this dataset, there is no measurable inuene of the
knowledge onveyed having any impat on water onservation deisions.
The strong eet of the number of onservation message soures is striking. The more ommuniation
media where the onservation message is presented, and the more frequently that message is presented, the
more likely people are to enounter it and internalize it. Muh like advertizing, the goal is not to demonstrate
that your produt is learly superior to the ompetition, be that in terms of ethis or performane or prie,
but rather that when a potential ustomer has a need for a servie your produt provides, your produt
is the rst to ome to mind. The results here suggest that enouraging water onservation is a marketing
hallenge more than a onversion or eduation hallenge.
The distintion between private and soial messages, and the importane of the behavior of others in
the ompulsion to onserve regressions, highlights a soial dimension to both intentions and onservation
behaviors.
This is somewhat onsistent with Costanzo et al. [1986℄, who argue that soial diusion is a
partiularly important way to enourage energy onservation.
This onnetion is partiularly strong for
onservation investments in the yard. The yard is an important visual statement about the owners, and as
suh soial pressures an be expeted to play a larger role here than with other onservation behaviors that
are not that visible. Eorts to enourage onservation an exploit this by helping innovators to adopt visually
29
appealing onservation investments in their yard.
Being both notable and appealing is likely to promote
onversations among neighbors, onversations that appear to play an important part in enouraging the
adoption of onservation investments in the yard.
Outdoor water use is the primary target for most water onservation eorts, as it is disretionary, and is
generally responsible for the peak demand. Reduing summer outdoor water use therefore is beneial both
in terms of ensuring that there is water available later in the season, and if the winter is partiularly dry, into
the following year, and in reduing the need to build exess apaity into the delivery system. The results
presented here suggest that soial ommuniation is a partiularly important vehile for enouraging outdoor
water onservation. Conservation eorts should therefore enourage and sustain onversations about water
onservation. Promoting onservation at ommunity events through presentations and other ativities that
engage with people and are likely to engender a soial onnetion with others who are ative water onservers
appears more likely to sueed than simply distributing pamphlets. People need to feel that they are part
of a ommunity eort, through whih they will either feel a positive reinforement for 'doing their part' or
a negative reinforement for 'failing to do their part.' Water pries are on their own too low to enourage
these investments, and at best are a reward for those who hoose for other reasons to onserve. Sine politis
makes substantial hanges in water priing unlikely, onservation eorts will need to build on these other
reasons to ahieve aggregate water savings.
Referenes
Barry Abrams, Santharajah Kumaradevan, Frank Spaninks, and Vasilis Saradis. An eonometri assessment
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A Mathing to Sequenes
The analysis assumes that the onservation hoies households make an be ordered and estimation an
be done as if the hoies were ounts. Eah household will have its own ordering, based on an individual
omparison of benets and osts for the ontext of that household. To treat the onservation hoies like
ounts, the ordering has to be similar enough aross households that the inuene of shifters is similar aross
households. For example, most households that are more onerned about water sarity should engage in
more water onserving ativities than those that are less onerned. In what follows, a searh for evidene
of ordering in the data is presented.
Consider a set of hoies
[y1 , y2 , . . . , yn ]
be a matrix of observations on
qj ∈ {1, 2, . . . , n}
lar hoie
when
y
n,
and
qj 6= qk
for all
then
then
y
yqk = 0.
T
where
q
Notie that if
if for any
y = in
yi ∈ {0, 1}
individuals.
j, k ∈ {1, 2, . . . , n}
is onsistent with a sequene
yqj = 0,
length
y = [y1 , y2 , . . . , yn ]′ ,
or
is a binary hoie, and let
Let the sequene
q = [q1 , q2 , . . . , q]
represent an ordering of the hoies in
qj 6= qk
y = 0n ,
with
j < k,
where
in
when
and
0n
yqk = 1,
y.
then
Y =
where
A partiu-
yqj = 1
and
are unit and zero vetors of
is onsistent with any sequene. We an dene a data set as being perfetly ordered if all
observations are onsistent with one sequene, and and that sequene as the perfetly ordered sequene. We
an further dene a sequene as weakly ordered if the data are more onsistent with a set of sequenes than
would our if the data were generated randomly.
There are at least two possible data generating proesses. One is that all the hoies are random. In this
ase in a repeated draw, the zero and one values an fall in any position in the vetor
total number of ones is the same in the entire data set. In any partiular draw,
y, so long as the expeted
E[yi ] = E[yj ] = i′n Y iT /nT .
In expetation, there is no ordering to observations drawn from this proess. A seond proess retains the
total number of ones in eah olumn of the data - the total number of any partiular hoie. In this ase,
E[yi ] = yi′ iT .
In this latter ase, the ordering of the expeted values
E[yi ]
identies the perfetly ordered
sequene for this data, were the data perfetly ordered.
Two test statistis are proposed to ompare the observations in
the hoies.
Y
to the set of possible orderings for
The rst is to ompare the frequeny distribution aross the set of possible sequenes of
35
the observations - this set ontains n Pn
= n!
sequenes - that are onsistent with eah sequene to that
for the perfetly ordered sequene and that for a bootstrap resampling from the original data.
Pn!
k=1
qk .
c(Y, qk )/nn!, where c(Y, qk ) ounts the number of observations in Y
This is
that are onsistent with sequene
The seond is to ompare the maximum number of onsistent observations to any sequene against the
maximum number of onsistent observations with the perfetly ordered sequene and the maximum number
of onsistent observations from the bootstrap resampling. Note that for data that is perfetly ordered, the
maximum number of onsistent sequenes is
With
nP n = n!
n.
possible sequenes when there are
n
hoies, omparing eah observation against all
possible sequenes beomes pratially intratable as the number of hoies expands. Two alternatives are
onsidered. For one, a random sample of sequenes are seleted and the data mathed to these sequenes.
This is repeated a number of times, so that a distribution is generated for both the empirial statistis and
the bootstrap distributions. This approah will typially not identify the best mathing sequene and the
number of observations that math to this sequene. Another approah is to identify the perfetly mathed
sequene from the data. As noted above, this is the order of the number of times eah hoie is seleted.
A set of sequenes are then generated as all the permutations that hange the perfet sequene in
positions.
2, . . . , m
The sequene that best mathes the data is likely lose to the perfet sequene, making this
approah more likely to identify the best mathing sequene and the number of observations that math it.
However, the frequeny of mathes will be biased upwards.
Figure 4 shows the math ount for all the possible sequenes for the indoor investment hoies. There
are six hoies and 516 observations. With six hoies, there are 720 sequenes in whih the hoies ould be
ordered. If the data are perfetly ordered, then the perfetly ordered sequene mathes all 516 observations.
In this set of observations, there are 366 respondents who reported having a low ow shower head. For the
perfetly ordered data, low ow shower heads starts all observations, leaving no observations where a low
ow shower head is not hosen and something else is. There are therefore
516 − 366 = 150 observations in the
perfetly ordered data where no option has been hosen. Further, there are ve people who report having
a greywater system. In the perfetly ordered data, these ve respondents will also have hosen every other
option. Thus, these ve observations will also math every sequene. As suh, the minimum total number
of mathes for any sequene in the perfetly ordered data is 155.
The gure also shows the math ount for the data sample.
This line is below the perfetly mathed
data, but mostly above the two bootstrap measures. The ount preserving bootstrap has a shape similar
to the sample, and is ompletely below the sample. This ontrasts with the all hoie bootstrap, whih has
a smaller maximum and a muh atter slope.
The all slope bootstrap will generally have an area larger
than the ount preserving bootstrap, but a lower maximum. If the maximum is used as a statisti to assess
36
500
Match to Sequence Counts
300
200
0
100
Match Count
400
Perfect
Sample
Bootstrap Choices
Bootstrap All
0
100
300
500
700
Sequence Permutations (count ordered)
Figure 4: Mathing hoie sets with sequene possibilities for indoor investment hoies. Six options and
516 observations. Bootstrap resampling by olumn.
ordering of the data, then the ount preserving maximum will be a more onservative assessment. However,
if area is used, then the all hoie bootstrap is the more onservative hoie. For this dataset, the sample
math ount urve both has a greater maximum and a greater area than either bootstrap measure, suggesting
that the data is more ordered than an be expeted by hane.
For the three data sets, key desriptors of the bootstrap test statisti and the observed are reported in
Table 9.
Due to omputation time, exhaustive alulations are only onduted for the IN_HOUSE and
BEHAVE observations. For both of these, the maximum ount of mathes to a sequene for the observations
is greater than that resulting from the two bootstrap methods. These maximum values lie far outside the
standard ondene interval for the bootstrap statistis that are onsistent with the null. When the sequenes
are sampled, the mean area is essentially idential for the sampling as for the exhaustive mathing, for
IN_HOUSE and BEHAVE. The area under the perfetly mathed data is far outside the ondene interval
around this sample statisti for all ases, emphasizing that the data is not perfetly ordered. However, it is
also far from the null statistis estimated with both bootstrap methods.
When organized around the perfetly ordered sequene that is onsistent with the individual hoie totals,
for IN_HOUSE and BEHAVE, the sequene that best mathes the observations is the same sequene that
is follows from the individual hoie totals.
This is evidened from the fat that the maximum number
of mathes ours when the only sequene onsidered is the perfetly ordered sequene. For ON_YARD,
this is not the ase. Among the sequenes examined, the best math ours among those sequenes that
dier from the perfetly ordered sequene in four loations. There may be an even better sequene if more
37
Table 9: Bootstrap test statistis for sequene mathing.
Area
Resample:
n
Sample
Perfet
Maximum Count
Column
µ∗
σ∗
All
µ∗
Column
σ∗
Sample
Perfet
µ∗
σ∗
All
µ∗
σ∗
Exhaustive alulation
IN_HOUSE
0.188
0.397
0.101
0.006
0.122
0.008
239
516
160.12
9.99
80.4
5.87
BEHAVE
0.108
0.318
0.053
0.004
0.074
0.006
232
516
166.94
10.08
54.7
4.24
Bootstrap, 200 samples of 500 sequenes, 39 bootstrap samples for eah
IN_HOUSE
ON_YARD
BEHAVE
µ
σ
µ
σ
µ
σ
0.188
0.397
0.101
0.006
0.121
0.008
236.0
508.3
158.8
9.48
79.6
5.13
0.002
0.004
0.002
0.001
0.001
0.001
4.38
12.57
2.47
1.22
0.82
0.60
0.123
0.340
0.058
0.007
0.077
0.008
163.3
361.2
115.0
8.94
51.5
4.59
0.002
0.003
0.002
0.001
0.001
0.001
7.63
33.56
6.65
1.24
0.69
0.53
0.108
0.318
0.053
0.004
0.073
0.006
214.1
480.8
158.3
9.49
52.3
3.95
0.003
0.005
0.002
0.001
0.001
0.001
14.15
25.05
6.49
0.13
0.66
0.47
Neighbourhood of perfet sequene, 199 bootstrap samples
IN_HOUSE
1
0.463
1.000
0.307
0.020
0.122
0.014
239
516
158.3
10.22
62.9
6.97
IN_HOUSE
2
0.341
0.742
0.214
0.011
0.122
0.010
239
516
159.2
9.06
72.1
5.61
IN_HOUSE
3
0.311
0.679
0.193
0.010
0.122
0.009
239
516
159.9
10.01
75.0
5.35
IN_HOUSE
4
0.279
0.608
0.168
0.008
0.122
0.009
239
516
159.7
9.61
78.2
5.07
ON_YARD
1
0.347
1.000
0.247
0.018
0.080
0.011
179
516
127.3
9.27
41.3
5.66
ON_YARD
2
0.275
0.747
0.184
0.014
0.080
0.010
182
516
128.8
9.76
47.9
4.81
ON_YARD
3
0.260
0.693
0.171
0.013
0.080
0.009
182
516
129.1
9.45
49.4
4.76
ON_YARD
4
0.240
0.628
0.153
0.011
0.080
0.009
184
516
129.3
9.62
51.2
4.76
BEHAVE
1
0.450
1.000
0.314
0.022
0.073
0.011
232
516
162.0
11.24
37.6
5.91
BEHAVE
2
0.291
0.688
0.198
0.011
0.073
0.008
232
516
166.6
10.12
45.8
4.31
BEHAVE
3
0.255
0.616
0.170
0.009
0.073
0.008
232
516
165.0
9.36
48.4
4.03
BEHAVE
4
0.216
0.541
0.142
0.007
0.073
0.007
232
516
166.2
9.42
51.3
3.89
38
alternatives are examined. The olumn total preserving bootstrap generates a largely onstant value for the
null maximum, while when all hoie observations are randomized, the total inreases with the number of
sequenes examined.
When mathing ours for deviations from the perfetly ordered sequene, the area statisti dereases
with the number of sequenes inluded in the omparison set, whether onsidering the sample, the perfetly
ordered data, or the hoie totals preserving bootstrap. For the overall bootstrap, the area measure is almost
onstant, but for a greater preision as the number of sequenes inreases. The area statisti alulated for
the sample is always larger than that generated from either of the bootstrap methods.
The results of these analyses show that the observed data annot be assumed to be generated from a
population where people randomly hoose what onservation investments to make, nor from a population
where people in aggregate hoose the same number for eah type of hoie as observed in the data, but
where there is no presumed ordering of those hoies. However, the data learly do not exhibit a onsistent
ordering. As suh, we an desribe the data as being weakly ordered.
39