Abstract
Stated preference studies tell respondents that policies create environmental changes with varying levels of uncertainty. However, respondents may include their own a priori assessments of uncertainty when making choices among policy options. Using a choice experiment eliciting respondents’ preferences for conservation policies under climate change, we find that higher outcome uncertainty reduces utility. When accounting for endogeneity, we find that prior beliefs play a significant role in this cost of uncertainty. Thus, merely stating “objective” levels of outcome uncertainty will not necessarily solve the problem of people valuing something differently from originally intended: respondents’ prior beliefs must be accounted for. (JEL C53, D62)
I. INTRODUCTION
In the environmental valuation literature, it is common to describe the potential environmental outcome arising from a policy alternative as being certain. However, this is not necessarily a true reflection of the reality, and it creates two important problems.
The first 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 policy-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, qualitative terms of uncertainty. This may in particular be true if the environmental outcomes hinge on factors not under the direct control of policy makers, for example, the interaction between policy measures and forth-coming environmental change. 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. This has been explored by Roberts, Boyer, and Lusk (2008) and Glenk and Colombo (2011, 2013) in a choice experiment (CE) setting, building on earlier work in a contingent valuation setting by MacMillan, Hanley, and Buckland (1996).
The second problem is that while respondents may in some cases be told about the degree of uncertainty regarding a policy outcome, they may equally well hold a priori beliefs about what environmental changes are more likely to come true. Hence, they may factor in their own, prior assessment of outcome uncertainty in their valuation of different levels of environmental change in a manner which the researcher does not usually observe (Powe and Bateman 2004). This problem has so far been left largely unexplored in the environmental valuation literature.
The present study expands in two ways on the work by Glenk and Colombo (2011, 2013) and other earlier studies reviewed below. First, while past studies described outcome uncertainty in the form of explicit probabilities of one or more attributes taking on one of two or more values (outcome-related risks: see Glenk and Colombo 2013), we describe outcome uncertainty in more qualitative terms for reasons outlined below. Second, we elicit peoples’ a priori perceptions about outcome uncertainty and investigate if these beliefs change the way in which they evaluate stated uncertainty measures, and what this implies for willingness to pay (WTP) for a policy option. We address three research questions: (1) Do respondents experience a reduction in utility if a policy is associated with stated outcome uncertainty? (2) Does the perceived importance of stated outcome uncertainty differ with the scope of attributes and the level of environmental change? (3) Will individuals’ prior assessments of outcome uncertainty matter for the evaluation of the stated certainty measures in choice sets, and hence, for the elicited WTP?
We address these questions using data from a CE in which respondents were asked to state their preferences for policy alternatives targeting the conservation of different groups of birds in Denmark whose geographical distribution is projected to be affected by climate change, something already observed in many bird species (Willis and Bhagwat 2009; Barbet-Massin et al. 2009; Klausmeyer and Shaw 2009). The future population levels of these birds, however, may depend on policies implemented regarding habitat protection that is targeted to mitigate the effects of climate change on native species, or to support the immigration of new species. Future biodiversity outcomes depend on the success of implementing these policies under new climatic conditions, and there is no empirical basis for assigning specific probabilities for these different outcomes. Furthermore, focus group interviews indicated little credibility of stating explicit probabilities for situations inherently not based in past experience (a problem of overstated precision). Therefore, we used qualitative measures of the overall outcome uncertainty for each policy alternative. Prior to these choice sets, respondents’ own assessment of the outcome uncertainty was elicited for a set of specific policy outcomes on the same qualitative scale. To analyze the influences of outcome uncertainty on choices, we formalized three hypotheses of how outcome uncertainty enters the utility function. We test these hypotheses using both linear and multiplicative expected-utility-related models as well as an integrated choice-and-latent-variable model.
II. EXISTING LITERATURE
This study expands on the previous environmental valuation literature by addressing the issue of how respondents’ values for environmental change depend on the stated certainty or probability of the outcome resulting from the policy alternatives proposed, and on their own perceptions of outcome uncertainty. We develop an instrument to evaluate the possible effect of respondents’ prior beliefs about outcome uncertainty on the weight assigned to measures of uncertainty provided by the researcher. Powe and Bateman (2004) show that taking account of scale-correlated prior beliefs about the realism of proposed environmental changes improved scope sensitivity of underlying valuation measures. Furthermore, building on prospect theory (Kahneman and Tversky 1979), several studies from behavioral economics have produced evidence that people factor in their own perceptions of risk when evaluating choices involving specific risks and perceived uncertainty. Examples include research on consumer choices involving gradients in product safety, or anglers’ assessments of the health risks of consuming the fish they catch (Viscusi and Evans 1998; Jakus and Shaw 2003).
More generally, empirical findings confirm 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 (Powe and Bateman 2004; Macmillan, Hanley, and Buckland 1996; Isik 2006). In a 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.
Another aspect we address is how people value stated uncertainty over environmental outcomes, when these are stated in qualitative terms. Roberts, Boyer, and Lusk (2008) investigate how respondents in a split-design 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 the they underweight low-probability events as compared to high-probability events. Their design did not allow them to investigate if this was related to prior beliefs, and their result differs from findings by, for example, Tversky and Fox (1995) and Viscusi and Evans (1998), who find that people overweight low-probability events. Accounting for uncertainty, Roberts, Boyer, and Lusk (2008) found little difference in WTP among attributes. Glenk and Colombo (2011) provide another example. In a CE-based valuation exercise of agrienvironmental measures to increase soil carbon sequestration (with additional benefits of enhanced biodiversity and job creation), they evaluated the effect of introducing half-way through the choice sets a new attribute describing the outcome uncertainty—stated probabilistically— for the change in soil carbon sequestration. They found a negative WTP for increasing uncertainty of outcomes but otherwise found WTP for other attributes insignificantly affected, including the soil carbon sequestration attribute.
In a follow-up paper, Glenk and Colombo (2013) use the same data set to explore the implications for preference parameters, model fit, and WTP of different approaches to modeling peoples’ attitudes to outcome risks. The forms of utility functions explored were two expected utility models (linear and nonlinear with respect to risk attitudes; see Riddel 2011); two models based on prospect theory, with nonlinear probability weighting (Roberts, Boyer, and Lusk 2008); and three models incorporating a direct, separable disutility from risk itself (i.e., independent of the outcome regarding emission reductions; e.g., Gneezy, List, and Wu 2006, and Rigby, Alcon, and Burton 2010). Results showed that (1) there was evidence that people disliked uncertainty over outcomes independently of their preference for the probability-weighted outcomes; (2) aside from linear utility from emission reduction models, there was little difference in model fit across the range considered, though the model accounting for a direct disutility performed best; and (3) there were few significant differences in WTP across the alternative models for variations in the expected degree of emission reductions. They concluded with a “cautious advocacy” of nonlinear expected utility models for representing choices over outcome uncertainties. In the current study we test different forms of models assuming a direct utility of uncertainty. In Section IV we relate our different models to these three typologies of Glenk and Colombo (2013).
A similar line of research on attitudes toward outcome risk is pursued by Wibbenmeyer et al. (2013), with the difference that they study risk managers rather than consumers or the general public. Their CE used 583 public agency managers concerned with wildfire risks in the United States. In particular, Wibbenmeyer et al. are interested in whether the choices of these managers are consistent with expected utility theory. Reducing wildfire risks is costly and comes at the cost of forgone expenditures on other desirable forest management actions. Managers’ actions over wildfire risks depend partly on their own preferences, but also on regulations and other institutional factors. Moreover, the incentives they face may encourage a focus on minimizing the probability of outbreaks rather than considering also the benefits of wildfires or the costs of outbreaks. To maximize the net (expected) social benefits of wildfire management, managers should be risk neutral and behave in accordance with expected utility theory. However, Wibbenmeyer et al. found that managers had an S-shaped probability weighting function that tended to overweight actions with a high probability of success, in making their choices; and that their response to low levels of risk to homes or watersheds was disproportionately high. They conclude that this supports a rejection of the standard expected utility theory as a way of modeling choices over risks (Shaw and Woodward 2008).
A related literature concerns preference uncertainty, in which researchers use a number of methods to capture the extent to which respondents in stated preference studies are unsure about their preferences or values. This has been a long-standing research focus in contingent valuation. Van Kooten, Krcmar, and Bulte (2001) take a fuzzy number approach to the representation of the level of utility. They argue there is an “underlying vagueness of preferences” that—both theoretically and econometrically—can best be represented using fuzzy set theory, since this allows for uncertainty that cannot be resolved even with full information or experience. Earlier, a related approach of explicitly adding a random variable in the utility function was suggested by Wang (1997) and Hanemann and Kriström (1995). Ready, Navrud, and Dubourg (2001) conditioned responses to both dichotomous choice and payment card designs for contingent valuation, using statements concerning how sure respondents were about whether they would really pay the amount in question. A development of this approach is given by Alberini, Boyle, and Welsh (2003); it builds on the Welsh and Poe (1998) discrete choice approach, with multiple bids that allow respondents to express valuation uncertainty. Finally, a number of papers use a payment ladder in contingent valuation studies to allow respondents to indicate the most they are sure they would pay and the least they would accept in compensation to forgo an increase in a public good. Determinants of the “uncertainty gap” between these two end points can then be modeled (Hanley, Kriström, and Shogren 2009). Investigations of preference uncertainty, utility differences over alternatives, and design have expanded into CEs (Lundhede et al. 2009; Olsen et al. 2011). Uncertainty over preferences for climate change policy has also been modeled, for example, by Akter, Bennett, and Ward (2012). However, we stress that there is a clear contrast between this literature and the focus of the present research. We are not assuming that people are unsure about their preferences. Instead, we allow the potential outcomes over which they have sure preferences to be uncertain; in making choices, people are assumed to combine an ex ante subjective assessment of outcome uncertainty with information on uncertainty provided in the course of the stated preference exercise.
A conclusion from the literature on outcome uncertainty is that stated outcome probabilities can affect the valuation of the attributes concerned. However, the interaction between the level of uncertainty that the researcher specifies in her description of outcomes and the a priori beliefs of respondents about outcome uncertainty has not been investigated in the environmental valuation literature in spite of related findings elsewhere (Viscusi and Evans 1998).
III. THE CASE STUDY AND HYPOTHESES TO BE TESTED
In the present study, we look at the outcome uncertainty caused by climate change as it relates to the future conservation status of different groups of birds in Denmark, and take care to develop a study reflecting relevant ecological changes (Johnston et al. 2012). Climate change is already believed to be the cause of ongoing changes in the spatial distribution of several bird species (Barbet-Massin et al. 2009; Klausmeyer and Shaw 2009; Araujo and Rahbek 2006). Together with biologists at the Center for Macroecology, Evolution, and Climate,1 we selected a set of relevant species predicted to experience range shifts from climate change, and grouped them according to the kind of changes and their current conservation status. The bird groups (attributes) varied in terms of whether birds are native to Denmark or potentially would immigrate to Denmark due to climate change, in terms of their current and predicted future conservation status in Denmark, and in terms of their current and predicted future conservation status elsewhere in Europe. A series of focus group interviews and test trials confirmed that the problem presented was easily understood by laypeople, and further helped improve and shorten the exposition to what was deemed necessary.
Thus, the questionnaire carefully informed respondents about these predicted environmental changes for bird populations prior respondents’ evaluation of the first set of six choice sets, where alternative policies would result in alternative population levels in the future (15 years ahead) for both native and immigrating species. In this first set, no mention of outcome uncertainty was made. Next, respondents were faced with a set of questions on their assessment of the environmental policy outcome (un)certainty. They were asked to rate whether they thought that policies would be able to ensure specific developments on a scale ranging from “very certain” to “rather certain” and “rather uncertain” to “very uncertain.”2 These options represent a cognitively clear ranking in terms of the outcome likelihood. In addition a “don’t know” option was available. These qualitative questions were phrased, “It is not obvious how initiatives will affect bird species’ living conditions. When you made your choices, did you assume the initiatives’ ability to secure Danish species abundant in numbers from extinction was . . .” They were then presented with an additional six choice sets, which now included an attribute describing the outcome uncertainty for each non-status-quo policy alternative on the exact same qualitative scale and wording.3 We note that, as the policy scenario here looks well into the future (15 years) and specifically involves considerable uncertainty about the effect of policy measures under a changing climate, advice from consulted macroecologists and focus group interviews suggested that it would not be credible to assign specific unique probabilities to specific policy outcomes, as no comparable past experiences exist. Against that background, we chose to describe outcome uncertainty in qualitative terms.4
Our main analyses and hypotheses concern these latter six choice sets, taking into account respondents’ prior assessment of outcome uncertainty. Drawing on the findings of several of the above-mentioned studies (notably Viscusi and Evans 1998; Powe and Bateman 2004; Roberts, Boyer, and Lusk 2008; Glenk and Colombo 2011, 2013) we formulate the following hypotheses for testing:
Hypothesis 1: Respondents experience decreased utility when outcome uncertainty increases.
This is a standard finding we also expect to find here, where our contribution mainly lies in uncertainty being described in qualitative terms. The implication is that any parameters within a choice model or indirect utility function capturing increasing outcome uncertainty of a policy should be significant and negative.
Hypothesis 2: Respondents weigh the stated outcome uncertainty differently across attributes and according to the degree of change in such attributes in a policy alternative.
This hypothesis draws on the general literature on risk aversion (Holt and Laury 2002; Andersen et al. 2008), but also on the work of, for example, 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). In our case we focus on two outcomes that 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 “abundant” more sensitive to policy success and hence outcome uncertainty than a level of “scarce” (cf. Powe and Bateman 2004). The second is the potential difference between a native species and an immigrant species, where people may attach a different weight to outcome uncertainty for immigrant species than for native ones, as the latter are already known to be able to establish viable populations in the country. This study is to our knowledge the first to evaluate if such an effect carries over to the qualitative statements on outcome uncertainty at the policy alternative level.
Hypothesis 3: Respondents’ prior beliefs over outcome uncertainty affect their assessment of stated outcome uncertainty. That is, respondents with a higher a priori rating of outcome uncertainty will assign higher weight to stated uncertainty levels.
This hypothesis is the main and major contribution of our study and is inspired by Viscusi and Evans (1998), who model the individual assessment of stated quantitative measures of risk in a quasi-Bayesian framework. We explicitly elicit priors from respondents in qualitative terms and use these to test if and how such prior beliefs about outcome uncertainty impact the assessment of attributes and the outcome uncertainty levels stated in the policy alternatives. An important potential caveat to consider is that the answers to the questions about prior perceptions of uncertainty, and the answers to the choice sets involving the same kind of uncertainty, could be driven by common individual-specific, unobserved variables, creating an endogeneity problem. We address this by introducing an integrated choice and latent variable (ICLV) model.
IV. DATA
Data were collected in January 2011 using an internet-based questionnaire 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 of the Danish general public, and the data collection was closed when a representative sample of 880 individuals had responded. As described above, following warm-up information on the case study, every respondent had to select a preferred alternative from three different options—No Policy (that is, the current situation), (new) Policy 1, and (new) Policy 2—in six choice sets without any mention of outcome uncertainty. These were followed by questions about the respondents’ prior assessment of outcome uncertainty. Thereafter another six choice sets were presented in which outcome uncertainty was included explicitly as an attribute. An example of the last six choice sets is given in Figure 1.
Example of Choice Set with the Outcome Probability Attribute (10 DKK= 1.8 US$ in October 2013)
Following data collection, data were scrutinized for anomalies. We identified a number of serial nonresponses (von Haefen, Massey, and Adamowicz. 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 chose the status quo due to the reason, “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 used for econometric modeling contained 826 respondents with a total of 4,954 choices.
The experimental design for the choice cards was a D-optimized design for a main-effect multinomial logit model,5 and the design used in this study had a D-error of 0.01767 and consisted of 18 choice cards. 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 to avoid ordering effects. The expost D-error for the final model was 0.000919. The design included four attributes that related to the groups of birds, each with three possible future population levels; one attribute regarding outcome uncertainty; and a cost attribute (Table 1). For immigrating birds, the European population varied between the two levels “scarce” and “abundantly occurring” in every other choice set. Each attribute was illustrated by two paintings of bird species (Figure 1), selected to be similar in appearance, and furthermore randomized within each group.
Attributes and Attribute Levels
V. 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 behavior depends partly on these observable attributes (Lancaster 1966), as well as on individual-specific characteristics and preferences. When observing a choice between different alternatives that vary in attributes, individuals are assumed to 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):
[1]
where 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 distributed (independent and identically distributed).
In testing our hypotheses we specify the utility function in different ways where the outcome uncertainty attribute appears and interacts with the remaining attributes in either a multiplicative form or as a linear term, potentially with interaction terms. Considering first the linear specification, one could incorporate the outcome uncertainty attribute as did Glenk and Colombo (2011) simply as an additional linear term:
[2a]
Here, α is a fixed level of utility related to the status quo (Alternative 1) in every choice set, and the term εni represents the stochastic, unobservable element of choice. The variable poplevij represents the future population levels of both native and immigrating birds (cf. Table 1) for the ith alternative and the jth 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 negative of 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 (we merge the two levels “rather certain” and “very certain”). The parameter γ is the level of (dis)utility related to outcome uncertainty. As for Glenk and Colombo (2013), the assumption of a direct utility effect of a decision alternative being associated with uncertainty draws on Gneezy, List, and Wu (2006). This model is thus similar in assumptions and structure to Glenk and Colombo’s direct utility effect model.
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. However, it is not possible to test Hypotheses 2 or 3 using model [2a]. Moreover, it seems more intuitive that uncertainties are incorporated in a multiplicative fashion into the utility function, as predicted by standard expected utility theory (von Neumann and Morgenstern 1944). As investigated by Glenk and Colombo (2013), there are numerous ways to do this, and here we focus on one of the simplest of these, which is the first model suggested by them. Assume that expected outcomes are sufficient to capture the utility effect (i.e., essentially assuming risk neutrality at the margin, as the respondents’ perceived variance of outcomes is ignored here). Consider therefore a 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:
[2b]
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. Bear in mind though, that here the outcome variable does not measure a continuous range from 0 to 1 of probabilities, but represents a difference between the “certain” and the “uncertain” attribute levels.
Respondents may think that the outcome uncertainty of a policy alternative may relate more to some attributes or attribute levels than to others. This leads to Hypothesis 2, 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 [2a] to
[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 represents the number of times the specific level is “abundant” 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 parameter 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. This model represents an extended version of the direct utility effect model of Glenk and Colombo (2013), where the direct utility effect is now assumed to be related to the overall environmental change (Powe and Bateman 2004), yet not fully in an expected utility theory framework.
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:
[3b]
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 α, β, η, γ, and δ may of course be different. Model [3b] is clearly within the expected utility theory framework, but it differs from previous models (cf. Glenk and Colombo 2013) in allowing the respondent population to assign varying weights across different attributes.
Finally, to test our central Hypothesis 3 we first set up a model where we include respondents’ prior statements about their own assumptions regarding outcome uncertainty. We test for an effect of this in a simple extension of the direct utility effect model [2a]:
[4]
Here, all parameters and variables are as in equation [2a] except for the interaction of outcome uncertainty multiplied by a dummy variable for the group of respondents stating prior assumptions of outcome certainty. About half of the sample (48%) answered “very certain” or “rather certain” to three out of four questions on certainty priors (Table 5). A dummy variable taking the value 1 identified this group of “certain” respondents and the value 0 for all other respondents representing the more “uncertain” group. 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, since this may lead to measurement error and potential problems with endogeneity bias due to omitted variables (Ben-Akiva et al. 1999; Ashok, Dillon, and Yuan 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 individuals’ actual rating of outcome uncertainty is an unobserved variable. Furthermore, this unobserved individual variable affecting their statement on assumed outcome certainty may very well also affect their choices across policy alternatives. Thus, a latent unobservable variable may exist, creating endogeneity between the two subsets of data. To accommodate this, we follow the approach of Hess and Beharry-Borg (2012) and set up a structural ICLV model, which accounts for this. First, define the latent variable driving outcome uncertainty assessment as ρn for respondent n in a structural model given as
[5]
where λ is a vector of estimated parameters related to a vector zn of sociodemographic 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 equation [1] as
[6]
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:
[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 normally distributed, N(0,σIk). In this application we centered the set of indicators around zero by subtracting the mean, thus eliminating the constant τIk.
The k indicators in equation [7] are extracted from respondents statements to the four outcome uncertainty questions, ranging from 1 (very uncertain) to 5 (very certain) with “don’t know” being the midpoint. Rewriting equation. [4] with respect to an ICLV model we specify our utility model as
[8]
The joint log-likelihood function is composed of two components that include the probability of the observed choices in the choice task (yn) and the probability of the observed responses to the a priori uncertainty assessment questions. The combined log likelihood is given by
[9]
Both components are dependent on the specification of the latent variable in equation [5] and need to be estimated simultaneously in order to achieve efficiency.6
We tested our proposed hypotheses by estimating parameters using a simple conditional logit model. We account for heterogeneity by estimating interaction effects and by use of the ICLV model. Furthermore, we also estimated a number of random parameter models (see Train 2003), not reported here, in order to examine heterogeneity, but we found mostly insignificant parameters for the parameter distributions, indicating little heterogeneity in the population’s preferences. All estimations were carried out using Biogeme (Bierlaire 2003). Marginal values of any attribute were computed as the coefficient on that attribute divided by the negative of the coefficient on the tax payment variable; standard errors for the WTP estimates were approximated using the delta method (see Greene 2000).
VI. RESULTS
All our hypotheses and results concern the six choice sets involving an uncertainty attribute and the elicited prior beliefs about uncertainty. However, we also analyzed preferences in the first six choice sets (not shown) and found no reason to believe that respondents changed preferences across sets of choice or were otherwise affected by the elicitation of the uncertainty priors. Furthermore, we saw no evidence of difference in scale between the first and the last sets of responses, or between “certain” and “uncertain” respondents in the first six sets.
Hypothesis 1
Table 2 shows the estimated parameters of utility functions corresponding to the direct disutility model [2a] and the expected utility theory–related 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 into one dummy variable in subsequent models. In both models the parameter for high outcome uncertainty is significant and negative, indicating that respondents experienced disutility for higher levels of uncertainty, and thus we cannot reject Hypothesis 1. The WTP estimate of − 623 DKK based on linear direct utility defines the monetary value of the disutility of a change in outcome certainty from the certain category to the 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; for example, if all are at the most valuable level, the discount would be −0.309(1,322+917+694) = −906 DKK. Other attributes show the expected signs and levels, that is, a preference for native (indicated with prefix n_) over immigrating species (i_). The European population level is indicated with either scarEur for scarce or abunEur for abundant population size (cf. Table 1). Similarly, the Danish population levels are indicated as either scarDK or abunDK. For native species, respondents prefer higher future population levels to lower, whereas the opposite is observed for immigrating species, an interesting result in itself.
Model with Effect of Outcome Uncertainty Estimated According to Equations [2a] and [2b]
Hypothesis 2
Respondents were informed that the outcome uncertainty in each alternative concerned all the outcomes of the alternative and, hence all, the attributes concerning bird populations targeted by the policy alternative. Nevertheless, respondents may have assigned a larger importance of outcome uncertainty to some attributes or levels compared to others. We formulated the hypotheses given by equations [3a] and [3b] that respondents may put more weight on outcome uncertainty for higher population levels (Abundant) than for lower levels, undertaking their own expected utility assessment. 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 increases in outcome uncertainty. In the multiplicative case [3b], separate utility parameters for increases in outcome uncertainty relative to attribute levels of low future population levels were introduced. The linear model shows indeed that respondents experience 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 outcomes. For immigrating species the pattern is reversed. Although being significant only on a 10% level, the interaction effect can be interpreted as reducing the negative WTP, that is, −421+189. In the nonlinear model the separate disutility for uncertainty related to native species (ηA) is estimated to be 42.4%, which is significantly higher than the disutility for all low attribute levels (ηC) of 27.5%. The parameter for uncertainty related to a high outcome level of immigrating species (ηg) is also positive in this model, although not significantly different from zero, as it has a very large standard error. Across models [2a–2b] and [3a–3b] we note that the alternative specific constant is positive in all models, but not significantly different from zero in the first set. We also note that the alternative specific constants are not significantly different from each other across the models, suggesting the differences are mainly due to minor variations in the covariance matrix across the different specifications involving slightly different interaction terms.
Linear and Multiplicative Model
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 in the direct utility model from equation [2a]. The aggregated numbers of how people responded to the set of questions eliciting their prior assessments of outcome uncertainty are shown in Table 5. Bear in mind that the dummy representing respondents’ prior assessments of outcome uncertainty represents approximately half of the sample who answered “very certain” or “rather certain” to three out of four questions on certainty priors. We chose this simple definition to avoid exploding the already large dimension of the models.
Incorporating Respondents’ Prior Assessment of Outcome Uncertainty
Distribution in Percentage of Respondents’ Answers to the Question: When You Made Your Choices, Did You Assume the Initiatives’ Ability to Secure . . .
The dummy variable identifying the a priori “certain” respondents was interacted with the dummy variable for increased outcome uncertainty described above. The results show that there is a disutility related to outcome uncertainty that can be converted to a compensation measure of 777 DKK. But respondents who from the outset believe policy outcomes to be quite certain seem to let this initial or prior apprehension of outcome play a role in the valuation of the attribute describing an increase in outcome uncertainty, so that the compensation demand is reduced by 322 DKK in this case. The WTP reductions from increasing uncertainty are fairly much in the same order of magnitude across models of WTP. However, we note that introducing just this one dummy variable for prior beliefs reduces the likelihood function slightly compared to the almost identical levels of models [2a–2b] and [3a–3b]. Thus, this model fits our choice data slightly better.
Table 4 also shows the ICLV model in full detail. This model is nonstandard in the environmental valuation literature, so we carefully lay out the interpretation for the three parts it consists of. First, we start by observing from the first set of variables in the utility function that compared to the model representing equation [4b] there are no differences in the estimated main effect parameters. This suggests that even if the ICLV model works well here, and is theoretically consistent, there was no omitted variable type endogeneity bias in the main effects (apart—importantly— from the uncertainty parameter) from including the priors as a simple interaction. Then follows the central parameter θ, which represents the interaction between the latent variable (ρ) and the outcome uncertainty (outcome) variable in the utility function. This variable is significant and negative, which shows that an increase in the latent variable of one unit results in an increased disutility of outcome uncertainty (cf. equation [6]) in the range of 30 DKK. Next follow the parameters λ of the structural model determining the range of the latent variable (equation [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 affects the latent variable positively. Thus, older people have a larger ρ and, hence, a larger disutility of increasing outcome uncertainty. The estimated parameter for male is negative and thus has the opposite interpretation: a lower disutility of outcome uncertainty. This completes the utility part of the ICLV model.
The lower panel of the ICLV models shows the parameters (ζ and σ) of the simultaneously estimated indicator function (equation [6]), showing how the latent variable ρ affects the likelihood of stating an a priori assessment of high outcome uncertainty. Thus, the negative ζ parameters indicate that an increase in the latent variable results in a smaller probability of stating a prior assessment of outcome being certain, (since the variable ranges from 1 for very uncertain outcomes to 5 for very certain outcomes (cf. also equation [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 it is the opposite. Combining the results from the lower and upper panel of the ICLV thus shows that if your latent variable is large, you are more likely to state a high prior outcome uncertainty and to have a large disutility of outcome uncertainty. A final note concerns the value of ζ for immigrating species, which 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 projected outcomes for immigrating species are those that respondents a priori associate the most with high outcome uncertainty.
VII. 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 (e.g., Hanley et al. 1998), or some explicit probability measures are assigned to the outcome of one or more dimensions (Glenk and Colombo 2013). The former strategy may be a problem even if people accept outcomes as certain when answering questions, since the relevant scenarios are in many cases uncertain, implying that an important aspect of the policy design problem is omitted. Both strategies are complicated by the fact that whether or not the analyst-defined measures of outcome uncertainty are included, respondents may factor in their own assessment of outcome uncertainty in their valuation of proposed environmental changes in a manner that the researcher does not observe. This may bias estimates of uncertainty effects as well as welfare measures in general.
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. These policies came with varying levels of policy outcome uncertainty, which due to the complexity of conservation challenges were described in qualitative levels only. Importantly, prior to analyzing the choice sets, respondents’ own assessments of the policy outcome uncertainty were elicited.
We used this design to address three research questions: (1) Do respondents experience a decrease in utility when the outcome of a policy is uncertain, compared to an otherwise identical policy with a certain outcome? (2) Does the perceived importance of outcome uncertainty differ with the scope of attributes or their levels of environmental change? (3) Will individual prior assessment of outcome uncertainty matter for the evaluation of the stated uncertainty measures in choice sets and, hence, the elicited WTP? We formalized hypotheses pertaining to these questions and set up both linear direct utility effect and expected utility–related multiplicative models, allowing us to test these hypotheses. We included the prior assessment of outcome uncertainty of various attribute aspects directly as an indicator variable, but more importantly we estimated an ICLV model, which allow us to model respondents’ priors simultaneously with their choices, taking into account possible endogeneity due to latent variables. This is the strongest test of our Hypothesis 3. Our results clearly show that we cannot reject any of the three hypotheses put forward.
The first hypothesis postulates that respondents experience a negative utility from outcome uncertainty. We tested the hypothesis in two models, one where the outcome uncertainty entered linearly as a direct disutility and one where it entered multiplicatively as an interaction term with a single utility weight shared across all attributes, reflecting expected utility theory. Results show 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. This result is as expected and only confirms previous studies (Glenk and Colombo 2011, 2013). Thus, our results also show that qualitative measures of outcome probability can be explicitly included in CEs and processed by respondents.
Using a qualitative measure of outcome uncertainty, it is not obvious whether people factor it in as a linear effect, that is, independently from the attribute levels, or as multiplicative, that is, more important for the attributes or levels that are at a “high” level than for those that are at a “low” level.7 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 change little. Of course, it remains a limitation of our study that while use of a qualitative measure of uncertainty was the best decision here, it hinders our use of explicit nonlinear weighting functions similar to those used elsewhere in the literature (Glenk and Colombo 2013). However, we may still capture considerable heterogeneity, as we see next.
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. Nevertheless, respondents may have assigned a larger importance of outcome uncertainty for some attributes or levels, compared to others. Based on studies like that of Powe and Bateman (2004), which argues that estimates may be biased if respondents themselves weigh the role of outcome uncertainty differently across attributes and attribute levels, we hypothesized that perceived importance of outcome uncertainty may vary systematically across attributes and levels. More specifically, we tested whether the utility effect of outcome uncertainty was valued differently for the attribute levels comprising high future population levels (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 outcomes that had a high future level of native birds. We note that this could also reflect risk aversion, something that cannot be separated in our design.
In their study of several possible specifications, Glenk and Colombo (2013) find that a direct utility model (similar to our [2a] and [3a] models) performs better than various linear (similar to our models [2b] and [3b]) or nonlinear expected utility–based models, in terms of log-likelihoods. However, they “cautiously advocate” for the latter type of models. Our results here show no noticeable difference across these model types, but our results in models [3a] and [3b] perhaps suggest what might have been missed in the Glenk and Colombo models. As their stated outcome related risk concerned only one of their attributes, they consider only expected utility variants manipulating this relation. Nevertheless, it seems likely that respondents might have “extrapolated” the stated risks to concern other attributes also. Omitting that possibility from the model design may disadvantage the expected utility models.
A comment is needed on the weaker effect we found for immigrating birds. We note that one explanation for the weaker signal might be the relatively low number of observations on this attribute, as every choice set contained only one immigrating species compared to the native species. While not ignoring the insignificance, we briefly comment on the sign of these parameters, as they are of 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 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 abundant in Denmark, in particular if they also are abundant 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 environmental change—even under certainty—is assessed as lower than utility of the lower environmental change. This would imply a lower risk premium for an outcome with a high level than for a lower level of environmental change, causing a positive parameter here.
We find that respondents who from the outset believe policy outcomes to be quite certain have a lower compensation demand of outcome uncertainty of 322 DKK relative to respondents with priors of higher uncertainty. This may seem to go against the concept of cognitive dissonance (that holding two or more contradictory beliefs induces mental stress and discomfort). We suggest that this result emerges because respondents discount the stated outcome uncertainty with a rate bringing their weight closer to their prior beliefs.
The core novelty of this paper is our third hypothesis, which tests whether the finding by Viscusi and Evans (1998) that people’s priors concerning uncertainty or risks are important carries over to the choice exercises used in environmental valuation. If so, it may affect their assessment of any expert-provided information about the degree of uncertainty of policy outcomes. We formalize the hypothesis in the linear model, and we use the data on respondents’ prior assessment of policy outcome for the type of policies presented. Here also, the hypothesis cannot be rejected. We find that priors vary over respondents and significantly influence the estimated utility of outcome uncertainty. Respondents who a priori state that they believe the outcome of the policies to be very or rather certain seem to weight this in their preference for outcome uncertainty, and demand a significantly smaller compensation when valuing outcome uncertainty. This, in turn, means that our estimates of the costs of uncertainty are to a large extent driven by those who a priori find the outcome uncertain. We also estimated the effect of prior beliefs in policy outcome in an ICLV framework, acknowledging the potential problem with endogeneity. In our case the estimates of the main attributes in the CE remain stable across the two models. The ICLV model, though, gives valuable insight into patterns underlying concepts of belief in policy outcomes and how they influence the WTP of outcome uncertainty. In our case we find that older respondents tend to have a higher latent variable, which again results in their being more likely not to believe that the policy will deliver, and also have a larger disutility of outcome uncertainty.
Our main finding has practical implications for environmental valuation using stated preference methods. Wielgus et al. (2009) argue that by making outcome uncertainty clear we get rid of the problem that respondents perceive something different from the researcher. Our results, however, indicate that if this researcher-provided measure of outcome uncertainty does not correspond with people’s perception of how the outcome uncertainty works in relation to the utility of different attributes, then simply stating the “objective” uncertainty over a policy outcome does not solve the problem. Overall, our results suggest, rather, that practitioners would do well to (1) assess, whenever relevant, respondents’ prior belief in policy outcome uncertainties and (1) incorporate when possible the degree of uncertainty into the valuation exercise, even if only in qualitative terms. Eliciting priors about uncertainty and their impact on obtained WTP measures may also help cost-benefit practitioners in adjusting benefit estimates of policies, if assessments of actual outcome uncertainties are available.
Acknowledgments
The authors acknowledge the Danish Council for Independent Research, Social Science for financial support (grant no. 75-07-0240) and the Danish National Research Foundation for support to the Centre for Macroecology, Evolution, and Climate.We thank Carsten Rahbek (University of Copenhagen) for assistance in creating realistic scenarios and Jon Fjeldså (University of Copenhagen) for making the illustrations of birds. We also thank two referees and Mikolaj Czajkowski (University of Warsaw) for comments on an earlier version of the paper.
Footnotes
The authors are, respectively, associate professor, Department of Food and Resource Economics and Centre for Macroecology, Evolution, and Climate, University of Copenhagen, Frederiksberg, Denmark; professor, Department of Food and Resource Economics and Centre for Macroecology, Evolution, and Climate, University of Copenhagen, Frederiksberg, Denmark; professor, Department of Geography and Sustainable Development, University of St. Andrews, Scotland, United Kingdom; professor, Department of Food and Resource Economics and Centre for Macroecology, Evolution, and Climate, University of Copenhagen, Frederiksberg, Denmark; professor, Department of Food and Resource Economics and Centre for Macroecology, Evolution, and Climate, University of Copenhagen, Frederiksberg, Denmark.
↵1 See http://macroecology.ku.dk.
↵2 The questionnaire was in Danish, and the Danish terms were on the scale “meget sikkert” (very certain) to “meget usikkert” (very uncertain). These terms refer to varying degrees of likelihood, even if the exact probabilities are not known. Thus, they reflect a level of knowledge above the Knightian uncertainty, yet not as high as being able to specify it in quantitative risks and probabilities. Therefore, we assess that “uncertainty” is nevertheless the best translation available.
↵3 The level “very uncertain” was omitted in the experimental design for technical reasons.
↵4 One may wonder if eliciting prior beliefs about outcome uncertainty before this second set of choices would give a priming effect, which we cannot rule out. However, a number of models where choice sets before and after the elicitation of prior beliefs were included in the same model show no evidence of a priming effect. The alternative, asking them after the choice sets, would, however, involve two things: (1) We would not have a good description of the new uncertainty attribute before its introduction, which is not according to guidelines for proper survey design, and (2) this second set of choice sets would then prime the elicitation of the respondents’ thoughts about uncertainty, essentially making those thoughts more posteriors than priors in a Bayesian sense. Thus, we see no viable alternative.
↵5 We used a prior of — 0.003 for price, and zero for any other attribute.
↵6 Please note that the responses to the indicator questions enter into the log-likelihood equation following the number of choice sets although only given once per respondent.
↵7 Because all attributes (except the price) are dummy coded, the levels do not matter. Had the attributes been quantitative, they would.
