to which aggregate values are to be generalized. Further, to the extent that attitude toward paying
is associated with WTP, censorship may simply bias the sample toward individuals who are more
favorably disposed toward paying for public goods.
2
.
1
. The relationship between price, income, and attitude toward paying
In econometric analyses of CV data, WTP is often regressed on variables such as annual house-
hold income, a vector of prices, and a number of variables intended to reflect individual tastes for
the public good. Attitude toward paying is likely to be negatively associated with price when the
latter is perceived to be beyond respondents’ WTP. Alternatively, price may be unrelated to
attitude when respondents’ perceive that there is not enough information to make a decision about
paying, or that the payment vehicle is inappropri- ate in some way. Here, respondents may be will-
ing to pay if information deficits could be alleviated, or if a different payment vehicle were
instigated.
Price and attitude toward paying may also be unrelated when additional household payments
are perceived to be unfair and objectionable in principle. For example, respondents may believe
that: 1 they are entitled to the public good change without having to pay an additional sum;
andor 2 some other party is responsible for paying for the change. In these instances, there
would seem to be little potential to persuade respondents not to protest the CV survey since
their objection is toward the act by which eco- nomic values are measured.
Income may also have a positive, linear rela- tionship with attitude. Low-income respondents
may consider that it is unfair that they should have to pay given their financial constraints. In
contrast, higher income respondents may also protest the act of paying if they believe that they
are unfairly targeted to bear a greater proportion of the cost of intervention. Further, income might
correlate with attitude as a result of potential common correlates such as demographic variables
and environmental values.
2
.
2
. The relationship between price, income, attitude and WTP
Price may have an effect on WTP that is inde- pendent of its indirect effect via attitude. All
previous applications of the dichotomous form of WTP have sought to measure the direct effect of
price on WTP. This relationship is important to the validity of the responses if they are to be
incorporated into efficiency analyses.
Income may also directly effect WTP. Respon- dents with relatively higher household incomes
may be more willing to pay compared with those from low income households. This relationship is
often sought in applications of CV utilizing the open-ended question format. In the absence of a
vector of prices, the effect of income on WTP has been taken to support the validity of the WTP
responses Cummings et al., 1986. These findings are consistent with interpretations of environmen-
tal quality as a normal good.
Finally, WTP responses may reflect individuals’ attitudes toward paying. Respondents who are
unfavorably disposed toward paying might be less willing to pay for a public good change indepen-
dent of the price offered and their level of income. A large proportion of the variability in WTP may
simply be a function of whether respondents be- lieve that additional household contributions are
an equitable means to achieving environmental improvements. To the extent that some respon-
dents pay despite holding a negative attitude to- ward paying, the linear relationship between
attitude and WTP is diminished. Similarly, re- spondents who have a positive attitude toward
paying may still refuse to pay due to a number of factors e.g. strategic reasons, financial con-
straints, a lack of information, etc..
3. An empirical model of attitude toward paying and WTP
Fig. 1 displays a simple recursive structural equation model of WTP. Structural equation
models allow the specification of relations among unobserved, latent variables or common factors
Bollen, 1989; Byrne, 1989; Hoyle, 1995. Each
latent variable is represented by one or more observed or manifest variables included in the
CV questionnaire. The latent variables in the model i.e. price, income, attitude and WTP are
shown as ellipses in the diagram, and the relation- ships between these variables are designated by
the thicker arrows. There are nine observed vari- ables in the model indicated by rectangles which
are linked to one of the latent variables repre- sented by thinner arrows in the diagram.
Structural equation modeling is a confirmatory process. The researcher specifies the form of the
model to be fitted to a variance – covariance ma- trix of observed variables. An estimation proce-
dure e.g. maximum likelihood is used to derive all of the model’s unknown parameters. When the
model is over-identified i.e. there are more known
parameters compared
with unknown
parameters, a variety of goodness-of-fit statistics can be used to assess the statistical adequacy of
the model Bollen, 1989; Browne and Cudeck, 1993.
The attitude factor in the model is represented by the shared variance of six belief items i.e.
protests 1 – 6, but only four indicators are neces- sary for a latent variable to be over-identified.
When the variability in two or more items of a particular factor is complex measures more than
one latent variable the systematic component of their error variances or uniquenesses may co-
vary. At times it is appropriate to adjust the measurement model by allowing error compo-
nents to covary and, therefore, incorporate the effect of residual factors that would otherwise be
unaccounted. All other latent variables in the model are
under-identified since each has only one indicator. The indicator for price is represented without
measurement error, since the practitioner, as part of the CV design, fixes its values. In this respect,
the latent variable corresponds exactly with its observed indicator as is the case in regression
analysis. The income and WTP observed vari- ables, on the other hand, are assumed to contain
measurement error that can be fixed to values derived from the following formula:
d
i
= f
i
1 − p
i
1 where f
i
is the item variance and r
i
is the item reliability. In standard econometric analyses of
CV data, measurement error is assumed to be absent despite contrary evidence Jorgensen et al.,
1998. One benefit of structural equation models over regression models is their capacity to deal
with measurement error Goldberger, 1972. By fixing the error variances of the single indicators
to more realistic and less arbitrary values than zero, the model can be empirically identified and
subject to a goodness-of-fit test e.g. a
x
2
-test. The overall fit of a model is based on the dis-
crepancy between the observed variance – covari- ance matrix and the variance – covariance matrix
implied by the model.
Finally, in structural equation modeling ordinal measures such as WTP may be used to reflect
continuous latent dependent variables. However, when the dependent variable is conceptually cate-
gorical e.g. when it demarcates individuals who take an action and those who do not, latent class
analysis is more appropriate Marcoulides, 1998. In latent class analysis, both the observed indica-
tor and the underlying latent variable are categor- ical. As others have noted Cameron and James,
1987, WTP is a continuous latent variable that may be measured on an observed scale having
ordered categories. As a behavioral intention, rather than actual behavior, responses to dichoto-
mous choice WTP measures can be conceived as representing points on a latent continuum of
WTP.
Fig. 1. Willingness to pay model.
3
.
1
. Hypotheses The preceding discussion highlighted the impor-
tance of understanding the meaning of protest responses. An empirical model was presented as a
means for testing the following hypotheses: 1 protest beliefs are significantly associated with
attitude toward paying; 2 attitude toward paying is significantly associated with income and price;
and 3 attitude toward paying is significantly associated with WTP. These hypotheses corre-
spond to the following model parameters:
1. l
3,1
l
3,2
…l
3,6
not equal to 0. 2. g
1,3
g
2,3
not equal to 0. 3. b
3,4
not equal to 0. The structural equation model described earlier
can be compared across samples in order to test a fourth hypothesis: Attitude toward paying and its
relationships with other variables in the model are invariant with respect to variability in a range of
methodological factors. These methodological factors might include the type of payment vehicle,
the frequency of payments that households are required to pay, and the type of pollution abate-
ment intervention proposed.
If attitude toward paying is simply a reaction to mutable methodological conditions rather than to
the act of paying, it should vary in the presence of different payment vehicles, payment regimes, in-
terventions, etc. The same attitude toward paying that is expressed in reaction to one type of CV
survey would not manifest in the same form when different methodological characteristics apply. If
attitude toward paying is dependent upon such methodological characteristics then variations in
them should be associated with differences in attitude over samples.
Alternatively, attitude toward paying might manifest in exactly the same form if respondents
in different samples perceive similar issues to be at stake where paying for stormwater pollution
abatement interventions are concerned. In other words, the attitude would not be invariant over
different
methodological conditions
so that
changes in these conditions may not solve the presence of protest beliefs.
The process of invariance testing begins with a test of ‘configural invariance’ Steenkamp and
Baumgartner, 1998. This test concerns the extent to which the model takes the same form in each
group i.e. has the same pattern of zero and non-zero factor loadings. If configural invariance
is established, the model’s ‘metric invariance’ can be ascertained by placing equality constraints on
the factor loadings contained in the
L matrix in each group. This step is determined on the basis
of a x
2
difference test between models with and without the equality constraints. If this test is not
significant then it supports the conclusion that the attitude is comparable in each sample. In other
words, the attitude is represented in each group by an equivalent set of indicators associated with
loadings that are not significantly different in either their magnitudes or their variances. Next,
by placing equality constraints on the relation- ships between the exogenous and endogenous
variables in the model contained in the
G and B matrices, conclusions can be drawn about the
invariance of the structural relationships in the presence of methodological variations.
1
4. Method
