Incorporating Policy Outcome Uncertainty in Choice Experiment Valuation
Studies
Abstract:
In stated preference studies it is often communicated to respondents that a new policy will bring
about an evaluated environmental change with certainty, or an explicit degree of uncertainty. In
either case, respondents may factor in their own a priori assessment of the outcome uncertainty in a
manner not observed by researchers.
We address this issue using data from a CE eliciting respondents’ preferences for policy alternatives
targeting the conservation of several groups of birds, whose geographical distribution may be
affected by climate change. Respondents were told that policy alternatives had varying levels of
outcome uncertainty. We set up hypotheses of how this outcome uncertainty may influence utility.
Furthermore, we test the importance of respondents’ prior belief in the outcome of the suggested
policy, on the sensitivity to the attribute ‘outcome uncertainty’ by the use of an indicator variable
and an integrated choice and latent variable model.
Results show that even if outcome uncertainty is defined for an alternative, people may connect it
to specific attributes. They also suggest that respondents’ prior belief in the policy outcome plays a
significant role. Our results stress the importance of incorporating the degree of policy outcome
uncertainty into the valuation exercise, preferably taking into account people’s prior perception.
Keywords: Environmental valuation, climate change, bird populations and distribution, hybrid
choice model, integrated choice and latent variable model, uncertainty
1. Introduction
In the environmental valuation literature, it is common to describe the potential environmental
change arising from a policy alternative as being certain. It may be more or less implicitly said that
the implementation and pursuit of the policy will also bring about the desired environmental
change. This is not necessarily a true reflection of the reality and this creates two important
problems.
The first problem is, that while respondents may in many cases believe the assumption of certainty
in the policy outcome, they may equally well believe some environmental changes as more likely to
come true than others. Hence, they may factor in their own assessment of policy uncertainty in their
valuation of different levels of environmental change, in a manner which the researcher does not
observe (Powe and Bateman 2004).
The second problem is that even if people accept the condition that the postulated environmental
change is a certain outcome of the policy measures suggested, this may not be the relevant scenario.
It is more likely that the relation between an environmental policy, a management change and the
postulated outcomes can at best be described by a probability distribution or perhaps more likely in
broader terms of uncertainty. This may in particular be true if the environmental changes evaluated
hinges on external factors not in direct control of the policy, e.g. the effects of forthcoming climate
changes. Thus, it seems relevant to evaluate what would happen to peoples’ valuation of policy
alternatives if they were in fact informed that the policy outcome is to some degree uncertain.
Roberts et al (2008) and Glenk and Colombo (2011) have investigated this question, and the present
study expands on their work. Both studies described delivery uncertainty in the form of explicit
probabilities of one or more attributes taking on one of two or more values. In the current study, we
have no empirical basis for assigning specific probabilities for different attributes. Instead we assign
a qualitative measure of outcome uncertainty as an attribute incorporated in each alternative, and
referring to the overall outcome of the policy alternative – across attributes.
We use this to address three research questions: i) Do respondents have negative utility of outcome
uncertainty? ii) Does the perceived importance of outcome uncertainty differ with the scope of
attributes or their levels of environmental change? iii) Will individuals’ prior assessment in policy
outcome matter for the evaluation of the stated certainty measures in choice sets and hence the
elicited willingness to pay (WTP)?
We address these questions using data from a CE, where respondents were asked to state their
preferences for different policy alternatives targeting the conservation of different groups of birds,
whose geographical distribution may be affected by climate change. In addition policies came with
varying levels of outcome uncertainty. Prior to the choice sets, respondents own
perception/assessment of the policy ensuring delivery was elicited. To analyse the influence of
outcome uncertainty, we formalise three hypotheses of how outcome uncertainty enters the utility
function. We test these hypotheses by the use of both linear and multiplicative models as well as by
an integrated choice and latent variable model.
The rest of the paper is organised as follows. In Section 2 we outline the existing literature on
uncertainty related to provision, outcome or delivery and set up our hypotheses. Section 3 describes
the questionnaire used for data collection and the experimental design. The econometric models are
set up in Section 4 and results are presented in Section 5. We conclude and discuss the results in
Section 6.
2. Existing literature and our hypotheses
The first issue we address is whether respondents when valuing an environmental change believe
the often implicit assumption of a certain outcome of the policy alternatives proposed. One such
example related to varying degree of belief in the realism in a large scale change scenario relative to
a smaller change is provided by Powe and Bateman (2004), who showed that taking account of
scale-correlated prior beliefs about the realism in proposed environmental changes improved scope
sensitivity of underlying valuation measures. Furthermore, building on Prospect Theory (Kahneman
and Tversky 1979), several studies have produced evidence that people factor in their own
perceptions of risk when evaluating choices involving specific risks and uncertainty. Examples
include research on consumer choices involving gradients in product safety or anglers’ health risks
of consuming the fish they catch (Viscusi and Evans 1998, Jakus and Shaw 2003).
These confirm the more general results on risk aversion and its sensitivity to the scope of the
outcomes (e.g. Holt and Laury 2002, Andersen et al. 2008), which are also reflected in several
contingent valuation studies of environmental change associated with stated or perceived
uncertainty (Macmillan et al. 1996, Powe and Bateman 2004, Isik 2006). In a choice experiment
(CE) context Wielgus et al (2009) find that explicitly stating a high outcome probability improves
goodness of fit of choice models and conclude that omitting information on scenario risk may
contribute to hypothetical bias.
1
The second issue we address is that the relation between an environmental policy and the postulated
outcomes may in many cases be better described by a probability distribution or perhaps even by
more broad terms of uncertainty. Thus, it seems relevant to evaluate what happens to peoples’
valuation of policy alternatives if they were in fact informed that the policy outcome is to some
degree uncertain. This motivated Roberts et al (2008) to investigate how respondents in a splitdesign CE reacted to stated probabilities of experiencing (un-)pleasant water qualities and -levels at
a recreational lake visit. They document that respondents did not interpret stated probabilities in a
standard linear weighted utility manner, but rather under-weight low probability events as compared
to high probability events. This differs from findings by e.g. Tversky and Fox (1995) and Viscusi
and Evans (1998) who find over-weight of low probability events. Accounting for uncertainty,
Roberts et al. (2008) found little difference in WTP among attributes. Glenk and Colombo (2011)
represents another example. In a CE based valuation exercise of agri-environmental measures to
increase soil carbon sequestration (with two additional co-benefits provided along with it: enhanced
biodiversity and job creation), they evaluated the effect of introducing half way through the choice
sets a new attribute describing the outcome uncertainty – in quantitative likelihood measures – for
the change in one attribute: soil carbon sequestration. They found a negative WTP for increasing
uncertainty of outcome, but otherwise found the WTP for other attributes insignificantly affected,
including the soil carbon sequestration attribute. The conclusion from these studies and the general
literature on uncertainty is that stated outcome probabilities will affect the valuation of the attributes
concerned, though the impact will often not be according to a linear weighted utility, and may be
influenced by peoples’ priors (Viscusi and Evans 1998).
In the present study, we look at the outcome uncertainty caused by climate change affecting future
conservation status of different groups of birds in Denmark. The bird groups (attributes) varied in
whether the birds were native to Denmark or potentially would immigrate to Denmark due to
climate change; in their current and predicted future conservation status in Denmark; and their
current and predicted future conservation status in Europe. Furthermore, we included an attribute
describing the outcome uncertainty for each non-status-quo policy alternative. As the scenario here
looks well into the future (15 years), and thus involves uncertainty about the effect of policy
measures as well as about future climate change effects, it would not be credible to assign simple
probabilities to specific outcomes. Thus, we described outcome uncertainty in qualitative terms.
More specifically, respondents were asked to answer six choice sets involving policy alternatives
with no mentioning of outcome uncertainty – as is standard – and then faced a small set of questions
on their assessment of the environmental policy outcome certainty. Following that, another six
choice sets were presented in which a new attribute had been added, which for each policy
alternative indicated a qualitative expert assessment of the overall degree of outcome uncertainty
for the policy alternative. This outcome uncertainty is thus across attributes. Our analyses and
hypotheses concern the later six choice sets, but also takes into account the prior assessment in
outcome certainty.
Drawing on findings and hypotheses of several of the above mentioned studies (notably Viscusi and
Evans 1998, Powe and Bateman 2004, Roberts et al. 2008, Glenk and Colombo 2011) we formulate
the following general hypotheses:
Hypothesis 1: Respondents experience decreased utility of increased outcome uncertainty.
This is a standard finding we also expect to find here, even though we describe uncertainty in
qualitative terms in order to capture multi-faceted and imprecise interpretation of the uncertainty of
2
climate change. The implication is that any parameters capturing increasing outcome uncertainty of
a policy should be significant and negative.
Hypothesis 2: Respondents process, interpret and weight the stated outcome uncertainty differently
across attributes in a policy alternative, and notably associate larger disutility of uncertainty when
it concerns outcomes of larger scope.
This hypothesis draws on the general literature on risk aversion (Holt and Laury 2002, Andersen et
al. 2008), but also on e.g. Powe and Bateman (2004), who find that the larger the scale of an
environmental change, the less realistic respondents found it. That respondents process any
statement on outcome uncertainty and weigh it subjectively draws on much of the above literature
(e.g. Kahneman and Tversky 1979, Viscusi and Evans 1998 and Powe and Bateman (2004) within
valuation). In our case we focus on two outcomes which the respondents may consider more
sensitive to uncertainty than others. The first is the future population size of a species, where
respondents may find a level of ‘Frequent’ more sensitive to outcome uncertainty than a level of
‘Scarce’ (cf. Powe and Bateman 2004). The second is the difference between a native species and
an immigrant species, where people may perceive a higher outcome uncertainty for immigrant
species than native ones, as the latter is already known to be able to establish viable populations in
the habitat. This study is to our knowledge the first to evaluate if such an effect carries over to the
qualitative statements on outcome uncertainty at policy alternative level.
Hypothesis 3: Respondents hold a set of prior beliefs in outcome uncertainty and this affects their
assessment of the expert stated outcome uncertainty.
This hypothesis is inspired by Viscusi and Evans (1998), who model the individual assessment of
stated quantitative measures of risk in a quasi-Bayesian framework. However, we explicitly elicit
priors from respondents in qualitative terms, and use these to test if such prior beliefs about the
outcome uncertainty related to attributes and the evaluation of the outcome uncertainty levels stated
in the policy alternatives.
These qualitative questions were phrased as: ”It is not obvious how initiatives will affect bird
species’ living conditions. When you chose between alternatives, did you assume the alternatives’
ability to secure Danish species frequent in numbers from extinction was…” where the respondent
could answer on a five-point Likert scale ranging from very sure to very unsure.
We designed various model specifications to test these hypotheses formally and present a selection
of these in Section 4.
3. Data
Data were collected in January 2011 using an internet based questionnaire that was tested
thoroughly by means of individual interviews, focus group meetings and a pilot data collection. A
total of 1,600 individuals were invited from an online panel consisting of more than 25,000
members and the data collection was closed when a representative sample of 880 individuals had
responded. Every respondent had to select a preferred alternative from three different options (No
Policy (current), (New) policy 1, (New) policy 2) in six choice sets without any mentioning of
outcome uncertainty. These were followed by questions about the respondents’ prior assessment of
outcome uncertainty. Hereafter another six choice sets were presented where outcome uncertainty
was included explicitly as an attribute. An example of the last six choice sets is given in Figure 1.
3
Figure 1: Example of choice set with the outcome probability attribute
Following the completed data collection, data were scrutinized for anomalies. We identified a
number of serial non-responses (von Haefen et al. 2005), where respondents chose the status quo
alternative (‘No Policy’ option) with a consequential zero tax payment in all six choice sets and
motivated this response pattern with ‘the initiatives should not be financed through income tax’.
These 35 respondents were excluded from the sample. Likewise 19 respondents never choose the
status quo and reasoned it by ‘I only considered whether the price was reflecting what I would like
to contribute to a good cause’. These respondents were excluded too. The final sample contains
826 respondents with a total of 4,954 choices.
The experimental design was a d-optimal design for a multinomial logit model, and the design used
in this study had a d-error at 0.01767 and consisted of 18 choice situations. These were allocated
into three blocks, implying that each respondent had to complete six choice situations. Furthermore,
the ordering of attributes was changed for half of the respondents in order to avoid order-effects.
The ex post d-error for the final model was 0.000919.
The design included four attributes that related to groups of birds, each with three possible future
population levels. In addition one attribute regarding outcome uncertainty and a cost attribute, see
Table 1. The European population for immigrating birds varied between the two levels ‘scarce’ and
‘frequent’ in every other choiceset.
4
Table 1: Attributes and attribute levels
Attribute
Native birds:
- Frequent in Europe
Level in Denmark
Acronym in results
Extinct in 15 years
Scarce in 15 years
Frequent in 15 years
- omitted level
β n_freqEur_scarDK
β n_freqEur_freqDK
Extinct in 15 years
Scarce in 15 years
Frequent in 15 years
- omitted level
β n_scarEur_scarDK
β n_scarEur_freqDK
- Frequent in Europe
Not immigrated in 15 years
Scarce in 15 years
Frequent in 15 years
- omitted level
β i_freqEur_scarDK
β i_freqEur_freqDK
- Scarce in Europe
Not immigrated in 15 years
Scarce in 15 years
Frequent in 15 years
Very certain
Rather certain
Rather uncertain
0-1,250 DKK
- omitted level
β i_scarEur_freqDK
β i_scarEur_scarDK
- omitted level
- merged with previous
- parameter of outcome.
δ tax
- Scarce in Europe
Immigrating birds:
Outcome uncertainty
Tax payment
4. Econometric models and specification
We adopt the standard assumption that the utility of a good can be described as a function of its
attributes, and that individual choice behaviour depends on these observable attributes (Lancaster
1966), as well as individual specific characteristics and preferences. When observing a choice
between different alternatives that vary in attributes, individuals are assumed choose the alternative
with highest indirect utility. The utility function, which is the sum of a deterministic term and an
unobserved random term, is known as the Random Utility Model (McFadden 1974):
U ni = V (ϕ , xni ) + ε ni
(1)
U represents the utility of an individual n from choosing alternative i. The deterministic term
V(β,xin) is a function V of attributes Xni with a vector φ representing the estimated parameters
related to attributes. The random term εni is assumed to be extreme value (IID) distributed.
In testing our hypotheses we specify the utility function in different ways where the outcome
uncertainty attribute appears and interact with the remaining attributes in either a multiplicative
form or as a linear term, potentially with interaction terms.
Considering first the linear specification, we incorporate the outcome uncertainty attribute as in
Glenk and Colombo (2011); simply as a linear term in itself:
J
U ni = α ( sqi =1 ) + ∑ β j ( poplevij ) + γ (outcomei ) − δ (taxi ) + ε ni
(2a)
j =1
5
where the variable poplevij represents the future population levels of both native and immigrating
birds (cf. Tabel 1) for the i’th alternative and the j’th attribute level and βj is the marginal utility
associated with population levels. Tax is a variable describing the tax increase associated with the
policy alternative and represents the change in an individual’s disposable income and thus δ is the
marginal utility of income. For the outcome uncertainty, outcomei is a variable that takes the value
1 if the outcome of the alternative is ‘rather uncertain’ and 0 otherwise (i.e. we merge the two
certain levels ‘rather certain’ and ‘very certain’). The parameter γ is the level of (dis)utility related
to outcome uncertainty. Finally, α is a fixed level of utility related to the status quo (alternative 1) in
every choice set and the term εni represent the stochastic, unobservable, element of choice.
If the estimate of γ (the level of (dis)utility related to outcome uncertainty) is estimated significant
and negative in a model like (2a), we cannot reject Hypothesis 1. We can, however not evaluate
Hypotheses 2 nor 3 by model (2a).
Consider next the multiplicative specification alternative of the utility model in (2b). In this model,
the interpretation is that outcome uncertainty results in a relative reduction common for all
attributes, instead of a simple fixed linear effect on utility independent of other utility elements:
J
U ni = α ( sqi =1 ) + ∑ β j ( poplevij )(1 + η ⋅ outcomei ) − δ (taxi ) + ε ni
(2b)
j =1
The parameter for outcome uncertainty in this multiplicative model we denote as η. Note that in
(2b) the utility of a species group with a high utility value (either due to its β or due to the attribute
level) will be reduced more in absolute terms than a species of lower utility, whereas in (2a) it is
entirely unaffected.
Respondents may think that the outcome uncertainty relates more to specific attributes or specific
attribute levels. This leads to another hypothesis, namely that respondents evaluate outcome
uncertainty as more important if an alternative’s outcome levels are high compared to other attribute
levels. This outcome level dependent assessment of uncertainty might, in turn, be conditional on
whether the bird species is native or a potential immigrant species. In order to test for such a
pattern, we modify (1a) to:
J
S
j =1
s =1
U ni = α ( sqi =1 ) + ∑ β j ( poplevij ) + γ all (outcomei ) + ∑ γ s (outcomei × subgroupis ) − δ (taxi ) + ε ni (3a)
Compared to (2a), we have included interaction term(s) of the outcome uncertainty multiplied by
one or more continuous variables (subgroupi) from a subset S, where each variable represent the
number of times the specific level is ‘frequent’ in an alternative. For native species the variable can
take a value between 0 and 2 and for immigrating species it can take a value between 0 and 1. The
parameters γsubgroup thus represents the extra (dis)utility related to outcome uncertainty for this
subset of attribute levels. There could be more than one subgroup in the same analysis.
Similarly, for the multiplicative specification, we may modify (2b) to allow for respondents
differentiating between two subgroups of attribute levels, A and B and a group representing the
remaining attribute levels C as in (3a), when evaluating the multiplicative effect of outcome
uncertainty:
6
K
U ni = α ( sqi =1 ) + ∑ β k ( poplevik )(1 + η A ⋅ outcomei ) +
k =1
L
∑ β ( poplev
l =1
l
il
)(1 + η B ⋅ outcomei ) +
(3b)
J −K −L
∑β
j =1
j
( poplevij )(1 + η C ⋅ provi ) − δ (taxi ) + ε ni
The restriction that the multiplicative effect is shared across a subset of parameters allows us to
estimate ηA, ηB and ηC and test if they are significantly different. Again we use future outcome level
for both native and immigrating species as the basis for testing Hypothesis 2. Note, that across
models the parameters β, η, γ, δ may of course be different.
To test Hypothesis 3 we set up a model where we include respondent heterogeneity in the form of
respondents’ prior statements regarding their own assumptions regarding outcome uncertainty. This
may function as a prior and anchor the respondent in their assessment of the attribute specifying
outcome uncertainty. We find that respondents quite clearly separate into three groups. Some that
generally assume outcomes uncertain, some that generally assume outcomes certain and finally a
group that mainly answers ‘Don’t know’ to the questions. We test for an effect of this in a simple
extension of model (2a):
J
U ni = αsqi=1 + ∑ β j ( poplevij ) + π (outcomei × individual group) + γ (outcomei ) − δ (taxi ) + ε ni (4)
j =1
Here all parameters and variables are as in (2a) except from the interaction of outcome uncertainty
multiplied by a dummy variable for the group of respondents stating prior assumptions of high
outcome certainty. Thus π captures how this group’s utility of outcome uncertainty differed from
the population mean effect as such, captured by γ.
Several authors argue, that responses to attitudinal questions cannot be incorporated into the choice
model directly as it may lead to measurement error and potential problems with (omitted variable
caused) endogeneity bias (Ben-Akiva et al. 1999, Ashok et al. 2002, Ben-Akiva et al. 2002, Bolduc
et al. 2005, Hess and Beharry-Borg 2012). The same seems to apply to respondents’ stated
assumptions about outcome certainty of policies as we recognize that the actual level of assumed
certainty is unobserved. Therefore, we follow the approach of Hess and Beharry-Borg (2012) and
define the latent outcome uncertainty assessment ρn for respondent n in a structural model given as:
ρ n = g (λ , z n ) + ω n
(5)
where λ is a vector of estimated parameters related to a vector zn of socio-demographic variables
describing respondent n. The term ωn is a random term, which we assume normal distributed,
N(0,σω), across respondents. Taking an individual specific latent variable, ρn into account we can
rewrite the utility function in Eq (1) as:
U ni = V (ϕ , xni , ρ n , θ ) + ε ni
(6)
7
where θ is a vector of interaction parameters between ρn and selected φ’xni. The measurement model
relates the response I that respondent n has given to the k indicator question, in this case the
respondents’ stated assessment of outcome uncertainty for different attributes:
I nk = τ I k + ζ I k × ρ n + υ nk
(7)
Here τIk is a constant for the specific indicator, ζIk is the estimated effect of the latent variable ρn on
the indicator k and νn is an error term assumed normal distributed, N(0,σIk). In this application we
centred the set of indicators around zero by subtracting the mean, thus eliminating the constant τIk
The k indicators in Eq (7) were responses collected on a five point Likert scale ranging from ‘very
unsure’ (1) to ‘very sure’(5) with ‘don’t know’ being the middle point. The four individual
assessments where all introduced with the same sentence stating ‘When you made your choice
between alternatives, did you assume the alternatives’ ability to secure …‘:
I1: Frequent Danish species to become extinct
I2: New species to immigrate and become frequent
I3: That threatened Danish species would survive
I4: That threatened Danish species would become frequent
Rewriting Eq (4) with respect to an integrated choice and latent variable (ICLV) model we specify
our utility model as:
J
U ni = αsqi=1 + ∑ β j ( poplevij ) + θ (outcomei × ρ n ) + γ (outcomei ) − δ (taxi ) + ε ni
(8)
j =1
The log-likelihood function is composed of two components which include the probability of the
observed choice in the choice task (yn) and the probability of the observed responses to the
assessment questions. The combined log likelihood in our joint model is thus given by:
N
LL(ϕ , θ , ξ I σ I , λ ) = ∑ ln ∫ L( yn ϕ , θ ,ρ n ) × L( I n ζ I , σ I , ρ n ) g (ω )dω
n =1
(9)
ω
Both components are dependent on the specification of the latent variable in Eq (5) and need to be
estimated simultaneously in order to achieve efficiency.
We tested our proposed hypotheses by estimating parameters using a conditional logit model
acknowledging potential problems of e.g. independence of irrelevant alternatives. We account for
heterogeneity by estimating interaction effects and by use of the ICLV model. However, we also
estimated a number of Random Parameter models (see Train 2003) in order to examine
heterogeneity, but found mostly insignificant parameters for the parameter distributions, indicating
little heterogeneity in the population’s preferences. These results are therefore not reported here.
The marginal value in terms of WTP of any attribute is computed as the coefficient on that attribute
divided by the negative of the coefficient on the tax payment variable and standard errors for the
WTP estimates are approximated using the Delta Method (see Greene (2000))
8
5. Results
Hypothesis 1
Table 2 shows the estimated parameters of utility functions corresponding to the linear model (2a)
and the multiplicative (2b), using a dummy variable, outcome, for high outcome uncertainty.
Initially, we included all levels of outcome uncertainty in the model, but the level ‘rather certain’
had no effect relative to ‘very certain’, and therefore we merged these two levels of outcome
certainty to one dummy variable in subsequent models. In both models the parameter for high
outcome uncertainty is significant and negative indicating that respondents experience disutility for
higher levels of uncertainty and thus we cannot reject Hypothesis 1. The WTP estimate of -623
DKK based on the linear model defines the monetary value of the disutility of a change in outcome
certainty from ‘very certain’ to ‘rather uncertain’. Note that by the construction of the linear model,
this is constant across all combinations of attribute levels otherwise in the alternative. In the
multiplicative model the parameter for outcome uncertainty represents a proportional discount of
the WTP for each attribute level of the alternative in question, e.g. if all are at the most valuable
level, the discount would be -0.309×(1,322 + 917 + 694) = - 906 DKK. Thus, by construction this
multiplicative model allows for variation with the attribute levels otherwise in the alternative. Other
attributes show the expected signs and levels, i.e. a preference for native (indicated with prefix n_)
over immigrating species (i_). The European population level is indicated with either scarEur for
scarce or freqEur for frequent population size, cf. Table 1. For native species, respondents prefer
higher future population levels to lower, whereas the opposite is observed for immigrating species.
Note how fairly similar the levels of WTP for all population attribute levels are across the model
specifications.
Table 2. Model with effect of outcome uncertainty estimated according to Eq (2a) and (2b)
Parameter
Parameter
estimate
α sq (ASC)
0.0964
β n_scarEur_scarDK
1.0800
β n_scarEur_freqDK
1.5500
β i_scarEur_scarDK
0.8820
β i_scarEur_freqDK
0.7130
β i_freqEur_scarDK
0.6770
β i_freqEur_freqDk
0.4200
β n_freqEur_scarDK
0.8290
β n_freqEur_freqDK
1.0900
δ tax
-0.0012
γ outcome (linear)
-0.7540
η outcome (multiplicative)
Linear model cf Eq (2a)
Std.
pWTP
error value (DKK)
0.0631
0.13 N/A
893
0.0598
0.00
1281
0.0588
0.00
729
0.0863
0.00
589
0.0975
0.00
560
0.0987
0.00
347
0.0973
0.00
685
0.0653
0.00
901
0.0592
0.00
0.0001
0.00 N/A
-623
0.0611
0.00
WTP
95% CI
N/A
760;1026
1126;1436
587;871
440;738
389;730
186;508
566;804
761;1041
N/A
-741;-505
Multiplicative model cf Eq (2b)
Parameter Std.
pWTP
WTP
estimate
error value (DKK) 95% CI
0.1120 0.0687 0.10 N/A
N/A
1.1100 0.0611 0.00
917 784;1051
1.6000 0.0604 0.00
1322 1166;1479
0.8400 0.0973 0.00
694 540;848
0.6870 0.1080 0.00
568 404;732
0.7160 0.1070 0.00
592 411;772
0.4740 0.1030 0.00
392 222;562
0.8130 0.0675 0.00
672 552;791
1.1100 0.0622 0.00
917 772;1063
-0.0012 0.0001 0.00 N/A
N/A
-0.3090 0.0238
N (obs/resp)
LL-value
Chi-square
Adjusted R-square
4954/826
-3931.648
3021.755
4954/826
-3930.124
3024.802
0.276
0.276
0.00
See
text
Hypothesis 2
Respondents were informed that the outcome uncertainty in each alternative concerned the entire
outcome of the alternative and hence all attributes concerning bird populations in the policy
9
alternative. Nevertheless, respondents may have assigned larger importance of outcome uncertainty
for some attributes or levels, compared to others. We formulated the hypotheses given by Eq. (3a)
and (3b) that respondents may put more weight to outcome uncertainty for high population levels
(‘Frequent’) compared to lower levels.
Table 3 shows estimates from a model where the high future levels of both native and immigrating
birds were in the linear model (3a) interacted with dummies representing high outcome uncertainty.
In the multiplicative case (3b) separate utility parameters for outcome uncertainty relative to
attribute levels of low future population levels were introduced. The linear model shows indeed that
respondents find additional losses when uncertainty is in combination with the high level of future
native population levels. In monetary terms, this can be converted to a negative WTP of 257 DKK
in addition to the ‘general’ WTP of -421 DKK related to high levels of outcome uncertainty. Notice
that the result is a lower overall WTP for a policy with uncertain outcome. For the immigrating
species the pattern is reversed. Although only being significant on a 10% level, the interaction
effect can be interpreted as reducing the negative WTP, i.e. -421+ 189. In the non-linear model the
separate disutility for uncertainty related to native species (ηA) is estimated to 42.4% which is
significantly higher than the disutility for all low attribute levels (ηC) on 27.5%. The parameter for
uncertainty related to high outcome level of immigrating species (ηB) is also in this model positive,
although not significantly different from zero as it has a very large standard error.
10
Table 3. Linear and multiplicative model
Linear model cf Eq (3a)
Parameter
Parameter
estimate
Std.
error
pvalue
α sq (ASC)
0.1850
0.0750
0.01
Multiplicative model cf Eq (3b)
WTP
WTP 95%
(DKK) CI
152
23;281
802
662;941
β n_scarEur_scarDK
0.9780
0.0660
0.00
β n_scarEur_freqDK
1.5300
0.0606
0.00
β i_scarEur_scarDK
0.6380
0.1150
0.00
523
β i_scarEur_freqDK
0.4990
0.1130
0.00
β i_freqEur_scarDK
0.5690
0.1030
β i_freqEur_freqDk
0.3440
β n_freqEur_scarDK
β n_freqEur_freqDK
Parameter
estimate
Std.
error
pvalue
0.1600
0.0798
0.04
WTP
(DKK)
WTP
95% CI
129
-4;262
806
696;917
1.0000
0.0690
0.00
1.5600
0.0628
0.00
342;704
0.6930
0.1230
0.00
559
380;738
409
232;586
0.5320
0.1100
0.00
429
266;592
0.00
466
293;639
0.5930
0.1140
0.00
478
301;655
0.1020
0.00
282
114;450
0.3550
0.1120
0.00
286
110;462
0.7740
0.0681
0.00
634
516;753
0.7780
0.0711
0.00
627
525;730
1.1400
0.0629
0.00
934
786;1083
1.1200
0.0669
0.00
903
δ tax
-0.0012
0.0001
0.00
N/A
N/A
-0.0012
0.0001
0.00
N/A
784;1023
N/A
γALL outcome_general
γsubgroup outcome x
high native (interact.)
γsubgroup outcome x
high immig (interact.)
ηA outcome high level
native (multiplicative)
ηB outcome high level
immigrating
(multiplicative)
ηC outcome reminder
levels (multiplicative)
-0.5140
0.1300
0.00
-421
-629;-214
-0.3130
0.1040
0.00
-257
-428;-86
0.2310
0.1350
0.09
189
-23;402
-0.4240
0.0466
0.00
0.2790
0.2900
0.34
-0.2750
0.0575
0.00
N (obs/resp)
LL-value
Chi-square
Adjusted R-square
4954/826
-3928.155
3028.74
0.276
1254 1096;1413
1258 1168;1348
4954/826
-3928.423
3028.205
0.276
Hypothesis 3
In Table 4 we show the result of including an interaction of the outcome uncertainty attribute and
respondents’ stated prior assessment of outcome uncertainty. The prior assessment of outcome
uncertainty from the Likert scale showed that just over 50% of the sample answered ‘very certain’
or ‘rather certain’ to all four of these questions. This group of respondents was identified with a
dummy variable taking the value 1 if a respondent was certain and 0 otherwise. This variable was
interacted with the dummy variable for outcome uncertainty described above. The results show that
there is a disutility related to outcome uncertainty that can be converted to a demand of 835 DKK.
But respondents who from the outset believe policy outcome to be certain seem to let this initial or
prior apprehension of outcome play a role in the valuation of attribute describing outcome
uncertainty, so that the compensation demand is reduced with 393 DKK in this case.
11
Table 4: Incorporating respondents’ prior assessment of outcome uncertainty
Parameter
α sq (ASC)
β n_scarEur_scarce
β n_scarEur_frequent
β i-scarEur_scarce
β i-scarEur_frequent
β i-freqEur_scarce
β i-freqEur_frequent
β n_freqEur_scarce
β n_freqEur_frequent
δ tax
γ outcome (dummy)
π outcome x group of
respondents with prior
of high outcome
certainty (interaction)
θ (Latent variable)
λ constant latent var.
λ old
λ male
λ young
λ education
ζ I1 (extint)
ζ I2 (immigrate)
ζ I3 (survive)
ζ I4 (become frequent)
σ I1 (extint)
σ I2 (immigrate)
σ I3 (survive)
σ I4 (become frequent)
ω
N (obs/resp)
LL-value
Chi-square
Adjusted R-square
a)
Interaction model cf Eq (4)
Parameter
Std.
pWTP
estimate
error value (DKK)
0.0996 0.0632
0.110
N/A
1.0800 0.0599
0.000
893
1.5500 0.0588
0.000
1281
0.8750 0.0866
0.000
723
0.7080 0.0977
0.000
585
0.6710 0.0988
0.000
555
0.4120 0.0976
0.000
340
0.8350 0.0655
0.000
690
1.1000 0.0594
0.000
909
-0.0012 0.0001
0.000
N/A
-1.0100 0.0818
0.000
-835
0.4750 0.0952
4954/826
-3919.05
3046.95
0.278
0.000
393
WTP
95% CI
N/A
797;989
1201;1361
602;844
449;721
394;715
183;498
595;786
804;1015
N/A
-967;-703
239;546
Integrated choice and latent
variable model cf Eq(8)
pParameter
Std.
a
value
estimate
error
0.0994
0.0619
0.11
1.0800
0.0659
0.00
1.5500
0.0632
0.00
0.8740
0.0862
0.00
0.7060
0.0974
0.00
0.6720
0.0960
0.00
0.4120
0.0927
0.00
0.8320
0.0689
0.00
1.1000
0.0583
0.00
-0.0012
0.0650
0.00
-0.7590
0.0630
0.00
n/a
-0.0370
0.2170
0.4150
-0.2270
-0.2380
0.1360
n/a
0.0133
0.199
0.161
0.127
0.154
-0.15
n/a
0.01
0.28
0.01
0.07
0.12
0.88
-0.1650
-0.0826
-0.1870
-0.2110
0.8150
0.9420
0.6570
0.5330
3.9600
4954/826
-29755.05
23364.37
0.281
0.00284
0.00373
0.00353
0.00497
0.0132
0.00817
0.0144
0.0168
0.0633
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Robust standard errors
In Table 4 the ICLV model is shown in full detail and can be considered in three parts. First, we
start by observing that there are no differences in the estimated parameters that relate to the main
attributes in the choice tasks, that is the first set of variables down to parameter of the outcome
uncertainty attribute. Then follows θ, which is the estimate of the parameter for the latent variable
(ρ) in the utility function interacted with the attribute outcome uncertainty (outcome), This variable
is significant and negative which shows that an increase in the latent variable results in an increased
disutility, of outcome uncertainty (cf. Eq. 6). Next follows the parameters λ of the structural model
(eq. (5)), and here only the variable old (age > 57 years) was significant at the 1% level, although
the parameter for males is significant at the 10% level. The positive estimate for the variable old
12
affects the latent variable positively. Thus older people have a larger ρ and hence a larger disutility
of outcome uncertainty. The estimated parameter for male is negative and thus has the opposite
interpretation: a lower disutility of outcome uncertainty.
Finally follows the parameters of the simultaneously estimated indicator function (Eq. 6) showing
how the latent variable ρ affects the likelihood of stating a prior assessment of high outcome
uncertainty. Thus, the negative ζ parameters indicate that an increase in the latent variable results in
a larger probability of stating a prior assessment of outcome being less certain, (since on the used
Likert scale 1 is very certain and 5 is very certain outcomes, cf. also Eq. 7). We note significant
effects for all four variables of the respondents’ measurement model. Thus, again using the
structural model, we find that older people are more likely to state prior assessments of high
outcome uncertainty, whereas for males this is the opposite
Finally,, we see that ζ, for immigrating species is somewhat lower than the estimates of ζ, for the
other categories. At the same time this category has the lowest average stated prior assessment of
outcome uncertainty across all respondents. Thus, we can conclude that the policy for immigrating
species is the one respondents associate with the highest prior assessment of outcome uncertainty,
but at the same time it is also the one where the latent variable has the lowest impact on this
assessment.
Concluding discussion
In the environmental valuation literature, the potential environmental change in focus is often –
implicitly – assumed or communicated as being a certain outcome of the proposed policy
alternatives. This may be a problem for at least two reasons: i) Respondents may factor in their
own assessment of outcome uncertainty in their valuation of proposed environmental changes, in a
manner which the researcher does not observe (Powe and Bateman 2004), and ii) even if people
accept outcome as certain, the relevant scenarios are in many cases uncertain.
On the basis of these observations, we developed a CE, where respondents were asked to state their
preferences for different policy alternatives targeting the future conservation status of different
groups of birds, whose geographical distribution areas may be affected by climate change. In
addition policies came with varying levels of outcome uncertainty, and due to the complexity of
conservation challenges where most sources of uncertainty are exogenous to the policies in
questions (they depend in climate policies and on unknown dynamics of adaptation to climate
change), the outcome uncertainty was described in qualitative levels only. Finally, prior to the
choice sets analysed, respondents own belief in various aspects of the policy outcome was elicited.
We used this to address three research questions: i) Do respondents have negative utility of outcome
uncertainty? ii) Does the perceived importance of outcome uncertainty differ with the scope of
attributes or their levels of environmental change? iii) Will individual prior assessment of policy
outcome matter for the evaluation of the stated measures in choice sets and hence the elicited WTP?
We formalised hypotheses pertaining to these questions and set up both linear and multiplicative
models allowing us to test these hypotheses. We included the prior assessment in policy outcome
directly as an indicator variable and also in an integrated choice and latent variable model. Our
results clearly show that we cannot reject any of the three hypotheses put forward in this paper.
The first albeit simple hypothesis postulates, that respondents experience a negative utility from
outcome uncertainty. We tested the hypothesis in two models, one where the outcome uncertainty
13
entered linearly and one where it entered multiplicatively as an interaction term with a single utility
weight shared across all attributes. Results shows that we cannot reject the hypothesis, and as can be
seen from Table 2 the utility weight attached to outcome uncertainty is of a considerable size – in
the linear model it has the same size as some of the utility weights related to populations. This result
is as expected and only confirms previous studies (Glenk and Colombo 2011). Thus, our results
show that also a qualitative measure of outcome probability can be explicitly included in choice
experiments and processed by respondents.
By using a qualitative measure of outcome uncertainty it is not obvious whether people factor it in
as a linear effect, i.e. independently from the attribute levels, or as multiplicative, i.e. more
important for the attributes or levels that are valued high than for those that are valued low1. While
we do not test which of these specifications is the better, we use both and get very similar results.
We find that in terms of WTP effects at the policy alternative level, the choice between the two
models does not affect the WTP of remaining parameters. We also find that the WTP effect of
outcome uncertainty on the aggregate value of alternatives is of comparable size across models.
Thus, results are robust across these two specifications - the estimate for the attributes and the level
of reductions in WTP for a policy with a given outcome uncertainty changes little.
The second hypothesis postulates that respondents would assign a different utility weight to
outcome uncertainty for different attributes and attribute levels. In the survey, respondents were
informed that the outcome uncertainty in each alternative concerned the entire outcomes of the
alternative and hence all attributes concerning bird populations in the policy alternative.
Nevertheless, respondents may have assigned larger importance of outcome uncertainty for some
attributes or levels, compared to others. Based on studies like (Powe and Bateman) (2004) who
argues that estimates may be biased if respondents themselves weigh the role of outcome
uncertainty differently across attributes and attribute levels, we hypothesised that perceived
importance of outcome uncertainty may vary systematically across attributes and levels.
More specifically, we tested whether the utility effect of outcome uncertainty were valued
differently for the attribute levels comprising high future populations (for both native and
immigrant species) relative to attributes with low future population levels. Again, we tested this
hypothesis in both a linear and a multiplicative formulation. In both cases, we found a negative and
significant parameter of disutility for uncertainty related to outcome that had a high level of native
birds. Thus, respondents assign greater utility weight to the outcome uncertainty in combination
with policies targeting larger populations of birds, than for more moderate future population levels.
This result could indicate, in line with Powe and Bateman (2004), that respondents find outcome
uncertainty to be probably greater for larger than for lower changes – in spite of them being
informed otherwise. However, even if they assign the same levels of outcome uncertainty, risk
averse individuals would require a larger risk premium (experience a larger expected utility loss)
from introducing uncertainty into a change of larger range than a smaller range. These two effects
cannot be separated in our design. Turning to the immigrating birds, we found a weaker effect (in
one case insignificant, in the other significant at the 10% level). We note that one explanation for
the weaker signal might be the relatively low number of observation on this attribute as every
choiceset only contained one immigrating compared to the native species. While not ignoring the
insignificance, we briefly comment on the sign of these parameters, as they are of the opposite sign:
Respondents do not demand extra compensation from uncertainty when we estimate this in relation
to high future population levels of immigrating birds. At a first glance this may seem to be a
1
Because all attributes (except the price) are dummy coded, the levels do not matter. Had the attributes been
quantitative it would.
14
peculiar result. However, investigating the estimated main effects for population parameters related
to immigrating species, we find a general low WTP for letting immigrating species become frequent
in Denmark – in particular if they also are frequent at the European level. This finding is stable
across all our models in this paper. Thus, the positive sign could reflect that the utility of the larger
change – even under certainty – is assessed as lower than utility of the lower change. This would
imply a lower risk premium for an outcome with a high level than for a lower – causing a positive
parameter here.
The third hypothesis, concerns the finding by e.g. Viscusi and Evans (1998), that people may hold
priors regarding the degree of risks (here belief in policy outcome) related to specific issues, which
affect their assessment of any expert-provided degree of uncertainty about policy outcome. Again
we formalise the hypothesis in the linear as well as the multiplicative model, and we use the data on
respondents’ prior assessment of policy outcome for the type of policies presented. Also here, the
hypothesis cannot be rejected. We find that respondents’ priors vary over respondents and
significantly influence the estimated utility of outcome uncertainty. Respondents, who a priori state
that they believe in the outcome of the policies, seem to weigh this into their preference for outcome
uncertainty and demand a significantly smaller compensation when valuing outcome uncertainty.
This, in turn, means that our estimates of uncertainty to a large extend is driven by those who a
priori find the outcome uncertain. We also estimated the effect of prior belief in policy outcome in
an integrated choice and latent variable framework acknowledging potential problems with
endogeneity. In our case the estimates of the main attributes in the CE remain stable across the two
models. The ICLV model gives valuable insight in patterns underlying concepts of belief in policy
outcome and how it influence WTP of outcome uncertainty. The influence from a priori belief in
outcome therefore suggests that the identification of respondents’ assessment of outcome
uncertainty may be equally important as including outcome uncertainty in the choice set. More
specifically we can include more detailed descriptions of the assessment, in this case by a
measurement model with four indicators. Furthermore, it allows us to look at the sociodemographic
characteristics influencing the assessment of uncertainty and outcome probability. In our case we
find that older respondents tend to have a higher latent variable, which again results in them being
more likely not to believe in that the policy will deliver and also have a larger disutility of outcome
uncertainty.
Wielgus et al. (2009) argues that by stating outcome uncertainty directly we may get rid of the
problem that respondents perceive something different from the researcher. Our results, however,
indicate that if this does not correspond with people’s perception of how the outcome uncertainty
works in relation to utility of different attributes, then it need not capture the effect correctly.
Overall, our results suggest rather that practitioners would do well in i) assessing, when ever
relevant, respondents prior belief in policy outcome, ii) incorporate when possible the degree of
uncertainty into the valuation exercise – even if only in qualitative terms, iii) even if the outcome
uncertainty is defined across or only for specific attributes and levels, people may perceive it
differently, and hence estimation and models should take this into account.
15
References
Andersen S., Harrison G.W., Lau M.I. and Rutstrom E.E., 2008. Eliciting risk and time preferences.
Econometrica, 76:583-618.
Ashok K., Dillon W.R. and Yuan S., 2002. Extending discrete choice models to incorporate
attitudinal and other latent variables. Journal of Marketing Research, 39:31-46.
Ben-Akiva M., Mcfadden D., Train K., Walker J., Bhat C., Bierlaire M., Bolduc D., Boersch-Supan
A., Brownstone D., Bunch D.S., Daly A., De Palma A., Gopinath D., Karlstrom A. and Munizaga
M.A., 2002. Hybrid choice models: Progress and challenges. Marketing Letters, 13:163-175.
Ben-Akiva M., Mcfadden D., Gärling T., Gopinath D., Walker J., Bolduc D., Boersch-Supan A.,
Delquié P., Larichev O. and Morikawa T., 1999. Extended framework for modelling choice
behavior. Marketing Letters, 10:187-203.
Bolduc D., Ben-Akiva M., Walker J. and Michaud A., 2005. Hybrid choice models with logit
kernel:applicability to large scale models. In: M. Lee-Gosselin and S. Doherty (Editors), Integrated
land-use and transportation models: behavioural foundations. Elsevier, Oxford, pp. 275-302.
Glenk K. and Colombo S., 2011. How Sure Can You Be? A Framework for Considering Delivery
Uncertainty in Benefit Assessments Based on Stated Preference Methods. Journal of Agricultural
Economics, 62:25-46.
Greene W.H., 2000. Econometric Analysis. Prentice-Hall, New Jersey, 1075 pp.
Hess S. and Beharry-Borg N., 2012. Accounting for Latent Attitudes in Willingness-to-Pay Studies:
The Case of Coastal Water Quality Improvements in Tobago. Environmental & Resource
Economics, 52:109-131.
Holt C. and Laury S., 2002. Risk aversion and incentive effects. American Economic Review,
92:1644-1655.
Isik M., 2006. An experimental analysis of impacts of uncertainty and irreversibility on willingnessto-pay. Applied Economics Letters, 13:67-72.
Jakus P. and Shaw W., 2003. Perceived hazard and product choice: An application to recreational
site choice. Journal of Risk and Uncertainty, 26:77-92.
Kahneman D. and Tversky A., 1979. Prospect Theory - Analysis of Decision Under Risk.
Econometrica, 47:263-291.
Lancaster K.J., 1966. New Approach to Consumer Theory. Journal of Political Economy, 74:132157.
Macmillan D., Hanley N. and Buckland S., 1996. Contingent valuation study of uncertain
environmental gains RID A-1998-2012. Scottish Journal of Political Economy, 43:519-533.
16
McFadden D., 1974. Conditional logit analysis of qualitative choice behaviour. In: P. Zarembka
(Editor), Frontiers in Econometrics. Academic Press, New York, pp. 105-142.
Powe N. and Bateman I., 2004. Investigating insensitivity to scope: A split-sample test of perceived
scheme realism RID F-8011-2010. Land Economics, 80:258-271.
Roberts D.C., Boyer T.A. and Lusk J.L., 2008. Preferences for environmental quality under
uncertainty. Ecological Economics, 66:584-593.
Train K.E., 2003. Discrete Choice Methods with Simulation. Cambridge University Press,
Cambridge, Cambridge, 334 pp.
TVERSKY A. and FOX C., 1995. Weighing Risk and Uncertainty. Psychological review, 102:269283.
Viscusi W. and Evans W., 1998. Estimation of revealed probabilities and utility functions for
product safety decisions. Review of Economics and Statistics, 80:28-33.
von Haefen R., Massey D. and Adamowicz W., 2005. Serial nonparticipation in repeated discrete
choice models. American Journal of Agricultural Economics, 87:1061-1076.
Wielgus J., Gerber L.R., Sala E. and Bennett J., 2009. Including risk in stated-preference economic
valuations: Experiments on choices for marine recreation. Journal of environmental management,
90:3401-3409.
17