Download Valuing wetland attributes: an application of choice experiments

Ecological Economics 47 (2003) 95 – 103
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ANALYSIS
Valuing wetland attributes: an application of choice experiments
Fredrik Carlsson a, Peter Frykblom b,*, Carolina Liljenstolpe c
b
a
Department of Economics, Gothenburg University, Sweden
Department of Economics, Appalachian State University, Boone, NC 28608-2051, USA
c
Department of Economics, Swedish University of Agricultural Economics, Sweden
Received 4 December 2001; received in revised form 18 June 2002; accepted 2 September 2002
Abstract
The interest for wetlands is increasing, not only because of the possibility of a cost-efficient uptake of nutrients, but also
because wetlands can be designed to provide other services. What values that are supplied depend largely on the design. There
are numerous different design options, and different actors may promote different alternatives. Whether we want to design a
wetland for nutrient retention alone, or one that also serves other interests, policy makers need information about the value of
different options. Conducting a choice experiment, we are able to identify attributes that increase and decrease citizens
perceived value of wetlands. Using a random parameter model we find that biodiversity and walking facilities are the two
greatest contributors to welfare, while a fenced waterline and introduction of crayfish decrease welfare.
D 2003 Elsevier B.V. All rights reserved.
Keywords: Wetland; Valuation; Choice experiment; Random parameter model
1. Introduction
There is an increasing interest in restoration and
construction of wetlands, as a means to increase the
retention of nutrients. In southern Sweden, more than
90% of the original wetlands have been eradicated as
cities, roads and agriculture have expanded. Combined with heavy loads of nutrients, the region suffers
from severe eutrophication damages to coastal and
groundwater. Several projects to protect the water are
being carried out, where construction of wetlands is
* Corresponding author. Tel.: +1-828-262-6081; fax: +1-828262-6105.
E-mail address: [email protected] (P. Frykblom).
0921-8009/$ - see front matter D 2003 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolecon.2002.09.003
one measure to reduce the run-off of nutrients. Studies
by Gren (1993) and Byström (1999) show that wetlands can be a cost-efficient means of nitrogen reduction. While the nitrogen reduction is an important
characteristic, wetlands can further contribute to other
goods that are valuable to society, such as biodiversity, recreation, diversity in the landscape, etc. The
cost-efficiency studies by Gren (1993) and Byström
(1999) are enough to answer a question of why
wetlands are important from a social perspective, if
we assume that the sum of the value of other services
from wetlands is at least non-zero or even positive.
Such an assumption has been supported by studies
where the value of wetland services has been discussed, and in some cases also estimated (see Gren,
1995; Stevens et al., 1995; Oglethorp and Miliadou,
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F. Carlsson et al. / Ecological Economics 47 (2003) 95–103
2000). However, this is not to say that the other
characteristics of a wetland should be disregarded
when constructing the areas. In this paper we try to
identify what characteristics of wetlands, besides
retention of nutrients, that individuals think are important. More precisely, we try to estimate individuals’ marginal willingness-to-pay (WTP) for different
attributes of a wetland. This information can thus be
used as input when deciding what type of wetland that
should be constructed, resulting in both increased
social welfare and a wider acceptance of wetlands.
Individuals’ marginal WTP is estimated through a
choice experiment, in which individuals are asked to
choose between different wetland alternatives with
different characteristics. In the choice experiment we
identify several important attributes. Biodiversity and
walking facilities are the highest valued attributes,
while a fenced waterline and introduction of crayfish
are regarded as something negative.
2. Design of wetlands
Apart from being important for retention of
nutrients, a wetland area can be designed to provide
different additional services and values. A wetland
can for example be designed with surrounding walking facilities, tree plantations and certain water depths
to attract birds or fish. There are a number of
different design options, where different actors may
promote different attributes. No matter whether we
want to design a wetland mainly for nutrient retention
or one that also serves other interests, policy makers
need information about the valuation of the different
attributes.
There are a number of valuation studies of wetlands, see Heimlich et al. (1998) for an extensive
overview of valuation studies. This overview includes
a broad variety of valuation techniques, such as the
contingent valuation method, hedonic price, replacement value, damage avoided and production value.
These studies focus on estimating values of different
types of wetlands or single services provided by
wetlands. It may be difficult to estimate the marginal
value of different attributes within a wetland though,
because of lack of variation in the data. A choice
experiment can solve this problem. The basic idea
behind a choice experiment is to create a hypothetical
market situation and elicit individuals’ preferences for
the attributes by asking them to make choices between
certain alternatives. The roots of choice experiments
can be traced back to Lancaster (1966) and the theory
of demand for characteristics, and random utility
theory (Thurstone, 1927; McFadden, 1974). In recent
years there has also been an increased use of choice
experiments in non-market valuation (see e.g. Adamowicz et al., 1994; Layton and Brown, 2000; Alpizar et al., 2001). The method is particularly suitable
for estimating marginal rates of substitution between
different attributes of for example a wetland. Morrison
et al. (1999) is the only study applying a choice
experiment to the valuation of wetlands, as far as
we know. These authors estimate non-use environmental values of a wetland area in Australia. In
particular they investigate the trade-off between nonuse values in job losses and environmental quality.
The objective of these wetland valuation studies in
general has been to estimate the WTP for a wetland
area itself, in particular the use and non-use values of
improved environmental quality. Our objective is
instead to value the different attributes, including
biodiversity, of a wetland.
3. The wetland choice experiment
3.1. The survey
The choice experiment concerns a wetland area in
Staffanstorp, southern Sweden. The municipality of
Staffanstorp plans to develop a wetland in this area,
and therefore it is highly suitable for our choice
experiment. The survey was conducted in collaboration with the municipality of Staffanstorp, where
there has been a public discussion about the location
and design of the wetland. The respondents were the
local population, members of individuals living in
Staffanstorp.
The questionnaire consisted of two parts. The first
part contained the choice experiment and the second
part questions regarding the respondent’s socio-economic status. The questionnaire and the attributes
used in the choice experiment were developed in
cooperation with researchers specialized on wetlands
from Linköping, Lund and Uppsala University. Several focus group discussions and one pilot study were
F. Carlsson et al. / Ecological Economics 47 (2003) 95–103
97
Table 1
Attributes and attribute levels
Attribute
Description
Levels
Total cost
The total cost for the individual
if the alternative was chosen.
Forest or meadow-land.
The design of the wetland area can
promote the plant, animal and insect life
so that the wetland contains different numbers
of both rare and more common species.
The design of the wetland area can improve the
conditions for species such as bass, pike, roach, etc.
It is possible to surround the water with a 1-m fence in
order to prevent drowning accidents.
It is possible to introduce Swedish crayfish and allow fishing.
It is possible to construct the wetland area for outdoor life with
construction of walking tracks and information signs about the
plant and animal life. The tracks are suitable for walking and jogging.
SEK 200, 400, 700, 850
Surrounding vegetation
Biodiversitya
Fish
Fenced waterline
Crayfish
Walking facilities
Forest, Meadow
Low, Medium, High
No, Yes
No, Yes
No, Yes
No, Yes
a
Biodiversity was described as the number of rare species that would be found in the wetland (none, few or many). This choice of
description was driven by a difficulty to explain the complexity in a meaningful and understandable way.
conducted in the process of designing a working mail
questionnaire.1
In the introduction to the choice experiment, the
purpose of construction of wetlands was briefly explained. The respondents were then informed about the
particular wetland area in Staffanstorp that is about to
be developed, and told that we were interested in their
view on the best possible wetland. Next the attributes
used in the choice experiment were explained. The
respondents were provided with a separate fact-sheet
describing the attributes. In the choice experiment,
each respondent answered four choice sets. In each
choice set they were asked to choose between three
alternatives. The first alternative was always the base
alternative, in which there would be no improvements
to the wetland area, at no cost. The two other alternatives implied a number of improvements to the wetland
area. The attributes and the levels of the attributes are
briefly presented in Table 1, and an example of a choice
situation is presented in Appendix A.
1
In the focus groups, the subjects filled out the questionnaire,
and were later asked written questions on their perceptions. This was
followed up by an open group discussion led by a conductor. After
revisions in the questionnaire were made, the procedure was repeated
with new subjects. Having achieved a questionnaire that worked in
our focus groups, a pilot study was undertaken. The questionnaire
was sent out to 130 randomly chosen individuals. Every fifth
respondent and nonrespondent was later telephone interviewed about
the questionnaire.
The choice sets were created using the OPTEX
procedure in SAS, which is a linear D-optimal
design procedure (see Kuhfeld, 2001). The design
is selected from the collective factorial, where collective factorial is an LAC factorial, where C is the
number of alternatives and where each alternative
has A attributes with L levels. Using the OPTEX
procedure we created 60 choice sets, these were then
blocked into 15 versions each containing four choice
sets.
We also test a hypothesis of stable preferences
during the choice experiment by incorporating a
simple test into the design. Since the respondent faces
all choice situations sequentially in the short time
required to perform the survey, the assumption of
stable preferences seems realistic, but nevertheless it
is often mentioned as a potential problem of choice
experiments. Half of the respondents received the
choice sets in the order {1,2,3,4} and half of them
in the order {4,2,3,1}. We can then test for stability by
comparing the estimated preferences for the two
different orders. This can be done in several ways:
using all choice sets, using only the first and last three,
or only the first and last. Based on the conditional
logit model, the hypothesis of stable preferences
cannot be rejected for any of the tests. Both Carlsson
and Martinsson (2001) and Layton and Brown (2000)
perform similar tests and fail to reject the stability
hypothesis.
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F. Carlsson et al. / Ecological Economics 47 (2003) 95–103
3.2. Econometric specification
In the analysis of the responses we apply a general
type of model, a random parameter logit model. In
such a model, taste variation among individuals is
explicitly treated (see e.g. Train, 1998). A random
parameter logit model is a generalization of a standard
multinomial logit. The advantages of a random parameter logit model are that (i) the alternatives are not
independent, i.e. the model does not exhibit the
independence of irrelevant alternatives property and
(ii) there is an explicit account for unobserved heterogeneity. Define a latent utility function of alternative i for individual q, at choice situation t, consisting
of a systematic and a stochastic part,
Uiqt ¼ aiq þ ci sq þ bq xiqt þ eiqt
ð1Þ
where xiq is a vector of attributes and sq is a vector of
socio-economic characteristics. The alternative specific intercept aiq captures an intrinsic preference for the
alternative and cisq captures systematic preference
heterogeneity as a function of individual characteristics. The coefficient vector bq varies among the
population with density f (b|h), where h is a vector
of the true parameters of the taste distribution. If the
e’s are IID type I extreme value we have a random
parameter logit, or a mixed logit, model (Train, 1998).
The conditional probability of alternative i for individual q in choice situation t is then
expðaiq þ ci sq þ bq xiqt Þ
Pq ðit bq Þ ¼ X
;
expðajq þ cj sq þ bq xjqt Þ
ð2Þ
jaAt
where At={A1,. . ., AN} is the choice set. The conditional probability of observing a sequence of choices,
denoted j( q, t), from the choice sets is the product of
the conditional probabilities
Sq ðbq Þ ¼
Y
Pðjðq; tÞtjbq Þ:
ð3Þ
t
In the choice experiment, the sequence of choices
is the number of hypothetical choices each respondent
makes in the survey. The unconditional probability for
a sequence of choices for individual q is then the
integral of the conditional probability in Eq. (3) over
all values of b:
Z
ð4Þ
Pq ðhÞ ¼ Sq ðbÞf ðbjhÞdb:
In this simple form, the utility coefficients vary
among individuals, but are constant among the choice
situations for each individual. This reflects an underlying assumption of stable preference structures for all
individuals (Train, 1999a). In general the integral in
Eq. (4) cannot be evaluated analytically, and we have
to rely on a simulation method for the probabilities.
Here we will use a simulated maximum likelihood
estimator, using Halton draws, to estimate the models
(see Revelt and Train, in preparation; Train, 1999b). It
is also necessary to make an assumption regarding the
distribution of each of the random coefficients. In
principle any distribution could be applied. However,
the choice is often limited by difficulty of model
estimation and availability econometric software.
The two main alternative assumptions are a normal
and a log-normal distribution. Applying a log-normal
distribution means that we restrict all respondents to
have the same sign of each coefficient. In our case this
is not desirable, since we expect different respondents
to have positive and negative preferences for the
different attributes of the wetland area. Therefore we
assume a normal distribution of all the attributes of the
choice experiment. It is also reasonable to expect that
there is a correlation between the randomly distributed
parameters. Therefore we estimate the full preference
variance –covariance matrix. We then have that the
vector of random parameters is normally distributed
with variance –covariance matrix X, i.e. bqfN(b̄, X).
The random part of the coefficient vector can then be
written bq=b̄+Cgq, where gq is a vector of independent
standard normal deviations. We then estimate b̄and C,
where C is the lower triangular Cholesky factor of the
preference variance– covariance matrix X, i.e. X=CC V.
This type of random parameter model is less
restrictive than standard conditional logit models.
However, we believe that researchers should be cautious in applying these less restrictive models. Apart
from being more difficult to estimate, our experience
is that the results can be rather sensitive to the
distributional assumptions and, for example, the number of draws applied in the simulation. Although
specification tests exist (McFadden and Train,
F. Carlsson et al. / Ecological Economics 47 (2003) 95–103
2000), the approach of finding a correct specification
of the random part of the model is tedious. Furthermore, the gain in terms of precision of the estimates of
willingness to pay is unclear. We therefore also report
the estimates of conditional logit model in which all
coefficients are treated as fixed.
4. Results
The population that the sample was chosen from
was defined as those between 18 and 75 years living
in Staffanstorp; in all 13,000 citizens. A random
sample of 1200 individuals was selected from the
Swedish census register. A mail survey was conducted
in May 2001, a reminder was sent out 2 weeks
afterwards to those that still had not replied. In total
580 (48%) individuals returned the questionnaire, of
which 468 were available for analyses due to nonresponses to various items. Not all of these answered
all four choice sets, however we still chose to include
these individuals in our estimations.
In Table 2 below, the descriptive statistics of the
sample used in the estimations are presented.
Any self-administred survey runs the risk of selfselection bias. Undertaking a comparison of average
age and gender, with data from official records on
citizens in Staffanstorp municipality, a null hypothesis
of equality could not be rejected.
Using Limdep 7 we estimate the random parameter
logit models with simulated maximum likelihood
using Halton draws with 250 replications. For comTable 2
Descriptive statistics observations included in final estimations
Variable
Description
Mean
Std.
Min
Max
Age
Male
Respondent age
=1 if respondent
is a male
=1 if household
has children
47.2
0.47
14.4
0.50
15
0
83
1
0.46
0.50
0
1
Kid
Responses
in choice
experiment
Number
Alt 1. No
improvement
Alt 2.
Alt 3.
408
703
606
99
parison we also estimate a standard conditional logit
model. We include one common alternative-specific
intercept for the two alternatives that imply changes in
the design of the wetland area, i.e. the non-base
alternatives, since these were presented in a generic
form. We let the cost variable be fixed, and not
randomly distributed, for two reasons: (i) the distribution of the marginal willingness-to-pay for an
attribute is then simply the distribution of that attribute’s coefficient, and (ii) we wish to restrict the price
variable to be non-positive for all individuals. The
non-price attributes are all randomly distributed with a
normal distribution, with the exception ‘‘Surrounding
vegetation’’. This variable was insignificant in the
conditional logit model, and in the random model
both the mean and standard deviation were insignificant. We, therefore treat the variable ‘‘Surrounding
vegetation’’ as fixed in the random model. In addition,
a number of individual characteristics are included as
fixed coefficients. These characteristics interact with
the alternative-specific intercept. The results of the
estimations for both the conditional and the random
parameter logit model are presented in Table 3.
The significance of the estimated standard deviations is a sign of heterogeneity in preferences among
the respondents. There is also a correlation in the
heterogeneity of preferences between attributes. This
together with the substantial increase in the likelihood
ratio index indicates the advantage of applying the
random parameter model instead of the conditional
logit model. All attributes except for ‘‘Surrounding
vegetation’’ are significant in the conditional logit
model. This attribute is also insignificant in the random
parameter logit model. All other attributes and their
standard deviations are significant in the random parameter model, except for the mean coefficient for
‘‘Crayfish’’. This implies that there is heterogeneity
in preferences for these attributes. Furthermore, the
relative magnitude of the standard deviations implies
that there is a probability that people have the reverse
preference for a particular attribute. This can also be
seen from column (5) in Table 3, which reports the
probability that the coefficient will have the reverse
sign, compared to the mean estimate. The mean coefficient is negative for both ‘‘Fenced waterline’’ and
‘‘Crayfish’’, so it is more likely that the respondents
dislike these attributes. All other attributes are significant and have a positive coefficient estimate. Even so,
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F. Carlsson et al. / Ecological Economics 47 (2003) 95–103
Table 3
Conditional logit and random parameter logit estimations, p-values in parentheses
High Biodiversity, b1
Medium Biodiversity, b2
Fish, b3
Fenced waterline, b4
Crayfish, b5
Walking facilities, b6
Intercept
Surrounding vegetation is meadow land
Cost
Male
Age
Kid
Log-likelihood
Likelihood ratio index
No. of respondents
No. of observations
Logit
Random parameter logit
Coefficient
( p-value)
Coefficient
( p-value)
Coeff std.
( p-value)
Prob.
reversed
sign
0.782 (0.00)
0.586 (0.00)
0.405 (0.00)
0.195 (0.01)
0.132 (0.03)
0.752 (0.00)
1.041 (0.00)
0.051 (0.40)
0.0012 (0.00)
0.272 (0.02)
0.018 (0.00)
0.251 (0.06)
1656
0.12
2.403 (0.00)
1.648 (0.00)
0.976 (0.00)
0.613 (0.01)
0.188 (0.33)
2.008 (0.00)
1.889 (0.01)
0.022 (0.88)
0.0033 (0.00)
0.128 (0.67)
0.022 (0.03)
0.053 (0.87)
1351
0.27
490
1717
2.570
2.869
2.647
2.322
1.991
3.059
0.17
0.28
0.36
0.39
0.46
0.26
b1
b2
b3
b4
b5
b6
1
0.920
0.485
0.345
0.439
0.236
1
0.637
0.453
0.576
0.310
1
0.089
0.460
0.023
1
0.506
0.330
1
0.273
1
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
Correlation matrix for random parameters
b1
b2
b3
b4
b5
b6
the estimated standard deviations are high, and even for
these attributes there is a non-negligible probability that
the respondents dislike the attributes. From the correlation matrix we see that there is a strong positive
correlation between a positive preference for biodiversity and the other attributes, and that there is a positive
correlation between a positive preference for ‘‘Fish’’
and ‘‘Crayfish’’.2 Among the socio-economic characteristics, only ‘‘Age’’ is significant. The negative sign
indicates that elder respondents are less likely to choose
an improved, and more costly wetland.
The interpretation of the coefficient values is not
straightforward, except for the significance and relative size. We therefore calculate the marginal rates of
substitution between the attributes using the coefficient for cost as numeraire. This implies that we can
2
Most of the elements of Cholesky matrix were significant,
indicating a significant correlation between the attributes.
interpret the ratios as average marginal WTP for a
change in each attribute, as argued by Hanemann
(1984). The results presented in Table 4, then provide
relevant input for a policy maker when designing the
wetland area. Since all attributes are normally distributed, and the cost coefficient is fixed, marginal WTP
will also be normally distributed. The distribution of
the marginal willingness to pay is obtained with the
Krinsky-Robb method (Krinsky and Robb, 1986)
using 5000 replications.3
3
Using this method we randomly draw the coefficients a
number of times from the asymptotic normal distribution of the
parameter estimates, and calculate the fare equivalents for each of
these draws. An alternative method would be bootstrapping where
we create a number of new data sets using the estimated residuals,
and re-estimate the function. The Krinsky-Robb method is less
computationally burdensome. Furthermore, Kling (1991) and Chen
and Cosslett (1998) among others find that the two procedures give
quite similar standard deviations.
F. Carlsson et al. / Ecological Economics 47 (2003) 95–103
101
Table 4
Marginal willingness to pay for attributes, 90% confidence interval
Logit
Surrounding vegetation
is meadow land
High biodiversity
Medium biodiversity
Fish
Fenced waterline
Crayfish
Walking facilities
Random parameter logit
44.19 (136.0 – 40.7)
673.22 (522.1 – 880.6)
504.58 (368.5 – 687.5)
348.48 (252.2 – 471.1)
167.53 (267.7 – 76.7)
113.48 (211.9 – 27.1)
648.06 (519.9 – 826.3)
‘‘Surrounding vegetation’’ has an insignificant
WTP in both models, and in addition the WTP
for ‘‘Crayfish’’ is insignificant in the random parameter model. The marginal WTP is negative for
the two attributes ‘‘Fenced waterline’’ and ‘‘Crayfish’’, i.e. the two variables decrease the average
utility derived from a wetland area. The marginal
WTP is highest for ‘‘High biodiversity’’ and
‘‘Walking facilities’’, followed by ‘‘Medium Biodiversity ’’. The other attributes are all of similar
magnitude. There is no general pattern in the
differences in marginal WTP between the random
parameter model and the conditional logit model.
Consequently, we cannot say that one method in
general gives different results compared to the
other. Furthermore, the differences in WTP between
the two models are not very large, perhaps with the
exception of ‘‘Crayfish’’. Consequently, although
the conditional logit model can be rejected in favor
of the random parameter model, there is no clear
pattern in the gain of the WTP estimates. The
important additional information that the random
parameter model gives is perhaps mainly that there
is a strong heterogeneity in the preferences for the
attributes.
5. Conclusions
What are wetlands good for, besides the uptake
of nutrients? By the use of a choice experiment, we
have identified a number of attributes that either
increase or decrease the utility derived from a
wetland area. The results are contextual, i.e. they
are the result of a certain study conducted in a
specific community. The southwest part of Sweden
6.53 (81.5 – 63.9)
719.75
493.76
292.49
183.55
56.30
601.41
(565.2 – 900.0)
(342.9 – 670.3)
(36.4 – 581.8)
(293.9 – 78.6)
(47.3 – 41.7)
(467.9 – 764.7)
is an area relatively densely populated with few
recreation areas. These circumstances probably affect the result, and the appropriateness of a transfer
of the results to other areas. The possibilities of
transfers are finally an empirical question, i.e. it can
be tested by further studies in similar and different
areas. Keeping this in mind, we can still learn
something by analysis of the obtained results. First,
a comparison of the conditional logit specification
with a random parameter model shows that the less
restrictive latter model can provide us with information that cannot be shown by the standard
model. There are heterogeneous preferences for
several of the attributes, as all the coefficients of
the random attributes have significant standard
deviations and a high probability of a reversed
sign. Second, a negative mean WTP was found
for the three attributes ‘‘Meadow land’’, ‘‘Fenced
waterline’’ and ‘‘Crayfish’’. Following, an inclusion
of these attributes will decrease social welfare.
However, the WTP for ‘‘Meadow land’’ was insignificant in both models. Third, ‘‘Biodiversity’’ and
‘‘Walking facilities’’ have the highest marginal
WTP in our study. A natural extension of this
survey is to estimate the marginal cost of providing
the different attributes of a wetland. In that way, the
results can be used for constructing a socially
efficient design of the wetland.
Acknowledgements
We are grateful for help from Rob Hart, Knut Per
Hasund, Lars Leonardson, Elisabeth Lundqvist, Jan
Lundström, Tore Söderqvist, Stefan Weisner and three
anonymous referees. The study was financed by Vastra.
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F. Carlsson et al. / Ecological Economics 47 (2003) 95–103
Appendix A . Choice situations
Before you chose any alternatives, you should now read the fact sheet.
Choice 1
Of the three alternatives below, mark the alternative you prefer.
Your choice (Mark your choice)
Wetland
Attributes:
Alternative 1 Simple ponds
Alternative 2
Alternative 3
Surrounding vegetation
1. Surrounding vegetation
Forest
Forest
Meadow-land
Water issues
2. Fish
3. Cray fish
No actions
No introduction
Good conditions
Introduction
No actions
No introduction
Other attributes
4. Biodiversity
5. Walking facilities
6. Fence
Total cost per citizen
Low
No walking facilities
No
SEK 0
Low
No walking facilities
No
SEK 850
High
Walking facilities
Fence
SEK 400
References
Adamowicz, W., Louviere, J., Williams, M., 1994. Combining revealed and stated preference methods for valuing environmental
amenities. Journal of Environmental Economics and Management 26, 271 – 292.
Alpizar, A., Carlsson, F., Martinsson, P., 2001. Using choice experiments for non-market valuation. Working Paper in Economics
No. 52, Department of Economics, Gothenburg University.
Byström, O., 1999. Wetlands as a nitrogen sink—estimation of
costs in Laholm bay. In: Boman, M., Brännlund, R., Kriström,
B. (Eds.), Topics in Environmental Economics Klüwer Academic Publishers, Dordrecht.
Carlsson, F., Martinsson, P., 2001. Do hypothetical and actual marginal willingness to pay differ in choice experiments? Application
to the valuation of the environment. Journal of Environmental
Economics and Management 41, 179 – 192.
Chen, H., Cosslett, S., 1998. Environmental quality preference and
benefit estimation in multinomial probit models: a simulation
approach. American Journal of Agricultural Economics 80,
512 – 520.
Gren, I-M., 1993. Alternative nitrogen reduction policies in the Mälar
region, Sweden. Ecological Economics 7, 159 – 172.
Gren, I.-M., 1995. The value of investing in wetlands for nitrogen
abatement. European Review of Agricultural Economics 22,
157 – 172.
Hanemann, M., 1984. Welfare evaluations in contingent valuation
experiments with discrete responses. American Journal of Agricultural Economics 66, 332 – 341.
Heimlich, R.E., Weibe, K.D., Claassen, R., Gadsy, D., House,
R.M., 1998. Wetlands and Agriculture: private interests and
public benefits. Resource Economics Division, E.R.S., USDA,
Agricultural Economic Report 765.10.
Kling, C., 1991. Estimating the precision of welfare measures.
Journal of Environmental Economics and Management 21,
244 – 259.
Krinsky, I., Robb, A., 1986. On approximating the statistical properties of elasticities. Review of Economics and Statistics 68,
715 – 719.
Kuhfeld, W., 2001. Multinomial logit, discrete choice modeling. An
introduction to designing choice experiments, and collecting,
processing and analyzing choice data with SAS. SAS Institute
TS-643.
Lancaster, K., 1966. A new approach to consumer theory. Journal
of Political Economics 74, 217 – 231.
Layton, D., Brown, G., 2000. Heterogeneous preferences regarding
global climate change. Review of Economics and Statistics 82,
616 – 624.
McFadden, D., 1974. Conditional logit analysis of qualitative
choice behavior. In: Zarembka, P. (Ed.), Frontiers in Econometrics Academic Press, New York.
McFadden, D., Train, K., 2000. Mixed MNL models for discrete
response. Journal of Applied Econometrics 15, 447 – 470.
Morrison, M., Bennett, J., Blamey, R., 1999. Valuing improved
wetlands quality using choice modeling. Water and Resource
Research 35, 2805 – 2814.
Oglethorp, A.R., Miliadou, A., 2000. Economic valuation of the
non-use attributes of a wetland: a case study for lake Kerkini.
Journal of Environmental Planning and Management 43,
755 – 767.
F. Carlsson et al. / Ecological Economics 47 (2003) 95–103
Revelt, D., Train, K., 1999. Mixed logit with repeated choices:
households’ choices of appliance efficiency level. Review of
Economics and Statistics (in preparation).
Stevens, T.H., Benin, S., Larson, J.S., 1995. Public attitudes and
economic values for wetland preservation in New England. Wetlands 15, 226 – 231.
Thurstone, L., 1927. A law of comparative judgement. Psychological Review 4, 273 – 286.
103
Train, K., 1998. Recreation demand models with taste differences
over people. Land Economics 74, 230 – 239.
Train, K., 1999a. Mixed logit models for recreation demand. In:
Herriges, J., Kling, C. (Eds.), Valuing Recreation and the Environment Edward Elgar, Cheltenham.
Train, K., 1999b. Halton sequences for mixed logit. Working Paper
Department of Economics, University of California, Berkeley.