Theoretical basis of the DCEs

The DCEs are founded upon the theories of welfare, of Lancaster’s theory of consumers’ choice and ^{Ben-Akiva’s and Lerman’s probabilistic choice theory (1985)}. It is assumed that the choices of the survey respondents reveal the preferences of the individuals, who maximize their utility by providing a given price and budget level.

According to ^{Hanemann (1984)}, the decision of the consumer can be divided into discrete and continual choices; the former, in relation to the good to be chosen, and the latter, in terms of the quantity in which the good is to be consumed. Tudela-Mamani and Leos-Rodríguez (2017) point out that Lancaster broke up with the traditional theory of the consumer’s behavior when assuming that the consumers demand goods by virtue of their characteristics, which generate a given level of utility; therefore, the random utility theory assumes that a rational individual will chose whatever implies the highest expected utility.

Econometrics for the analysis of the DCEs

The analysis of the choices in the DCEs is based on the random utility approach developed by ^{McFadden (1974)}, which creates a bond between the deterministic model and a statistical model of human behavior (^{Hoyos, 2010}).

The specification of the econometric model requires the determination of two fundamental aspects: the definition of the utility function (the form in which the random term is included in the indirect utility function) and the distribution assumption regarding the error component. The most common definition of the utility function assumes that the error component (Є _ij ) is entered as an additive term:

Where:

U _ij = Utility function

V _ij = Deterministic component of the indirect utility function for each alternative j of the choice set C

Z _ij = Attributes

S _i = Socioeconomic characteristics of the users

M _{i =} Income

The user i prefers the alternative m over any of the options of the choice set C, if and only if the utility of m is superior to that offered by each of the other options, i.e., if U _im > U _ij ∀ m ≠ j, where m and j ∊ C. The probability of choosing alternative m is expressed as follows:

The observable component (indirect utility function, V _ij ) can be expressed as a linear function of the explanatory variables (^{Blamey et al., 1999}):

Where

𝛼_j = Alternative Specific Constant (ASC) for alternative j

𝛽_k = Utility coefficients vector associated with explanatory variables vector Z _k

= Coefficient associated to the individual’s income minus the cost of alternative j, (M _i -Cost _j )

δ _p = Coefficients vector of the socioeconomic variables

The ASC is the parameter for each particular alternative represents the role of the unobserved utility sources. According to ^{Riera and Mogas (2006)}, when this element is omitted from the utility function in the estimation process, significant differences in the obtained welfare measures are produced. Although certain studies have opted for excluding the ASC, today the literature that includes it in the discrete choice analysis is more prevalent (^{Hoyos, 2010}; ^{Johnston et al., 2017}).

On the other hand, the error terms are assumed to be independent and identically distributed, with a Gumbel distribution or a Type I extreme value distribution; therefore, the choice model is estimated by means of a logit multinomial model (LMN) (^{McFadden, 1974}; ^{Louviere et al., 2000}):

The previous expression considers the attributes to be assessed, as well as the socioeconomic characteristics of the individuals; it contains a non-estimable, independent scale parameter of the function (^{Álvarez-Farizo et al., 2005}). The parameters of the indirect utility function in the LMN (α, β and δ) are estimated using the maximum likelihood method (^{Greene, 2003}).

The main limitation of the LMN models is the implicit assumption of Independence of Irrelevant Alternatives (IIA), according to which the disturbances are independent and homoscedastic; i.e. the choice probability quotient of two alternatives is independent of any other real or potential alternative. Breach of this assumption leads to biased results (^{Louviere et al., 2000}). Therefore, the Hausman and McFadden test must be applied (^{Greene, 2003}). However, the IIA hypothesis is not always sustainable, and therefore it eventually incorporates the correlation between alternatives (^{Hoyos, 2010}).

In this regard, ^{Train (2009)} points out that the scope and limitations of the LMN models are: i) they can represent systematic variations related with the observed characteristics of the survey respondents (income level, schooling, family size), known as variations in taste, but they cannot represent random variations (preferences) of the survey respondent, known as taste variations; ii) compliance with the IIA assumption in the LMN models does not always reflect realistic situations; and iii) the LMN models handle situations in which unobserved factors are independent, but not when these generate a correlation through time, for example, between alternatives. This limitation is associated with market or labor studies in which the interviewees often participate in various choices through time, and their current decision may be influenced by that of the previous exercise.

There are other generalized extreme value models that relax the IIA assumption, such as the nested logit model, the cross-nested logit model, the network model, the paired combinatorial logit model, and the generalized nested logit model; however, these may exhibit rigidity in their application, and they may have greater computational requirements.

The mixed logit (LMX) model is more flexible (^{McFadden and Train, 2000}) and overcomes the limitations of the previously cited models; ^{Tudela-Mamani and Leos-Rodríguez (2018)} document that the LMX model “evades the limitations of the LMN model, allowing a random variation of preferences, unrestricted substitution patterns, and correlation between unobserved factors through time”.

The use of an LMX model entails three specification problems (^{Hoyos, 2010}): i) the determination of the parameters that must be modeled as randomly distributed; ii) the choice of the mixture distribution for the random coefficients, and iii) the economic interpretation of the randomly distributed coefficients. According to the empirical evidence that exists in the literature about the DCEs, the most commonly used models correspond to the LMN and LMX models (^{McFadden and Train, 2000}; ^{Hoyos, 2010}; ^{Espinal et al., 2014}, ^{Tudela-Mamani and Leos-Rodríguez, 2018}).

Choice Experiment Design

The DCE procedure involves the following stages: A) the design of the DCE and B) estimation procedure and determination of the MWTP. This section addresses the DCE design phase, which in turn includes: a) definition of attributes and supply levels; b) generation of the experimental design; c) development of the questionnaire; d) administration of the survey, and e) codification of variables. Each of these must be carried out comprehensively and will allow providing sequential feedback to the improvement areas identified in the final design of the DCE. Figure 1 summarizes the design phase of the choice experiment.

Source: Prepared by the authors upon the basis of the DCE procedure

Figure 1 Choice experiment design. 

Definition of attributes and levels

Before developing the experimental design, the good or service to be assessed must be characterized; for this purpose, the issue must be formulated in terms of policies or of a program for improvement that will reflect the change between the current situation and the situation expected to result from the intervention (^{Tudela, 2010}). Therefore, several strategies may be used to obtain the information, including bibliographical review, participative diagnosis, interviews with key actors, forming discussion groups, among others.

Based on the attributes, the current situation (statu quo) of the forest service or good to be assessed is described to the interviewees; the levels represent the degree of intervention in which each of these will modify the current status. The attributes may be quantitative (reforestation percentage, level of water supply, reduction of the erosion, etcetera), qualitative (aspect of the water, type of tourism, resilience of the ecosystem, etcetera), generic (the same levels are used for all the alternatives), or alternative-specific.

The process of identifying attributes and levels requires piloting strategies and discussion among target groups in order to ensure that the choice experiment design will incorporate the most important attributes and, thus, prevent uncertainty as to whether any relevant one was left out.

It must be kept in mind that a larger number of attributes and levels increases the quantity of both the choice sets and the alternatives that constitute them. According to ^{Hoyos (2010)}, this situation may violate the assumption of independence from irrelevant alternatives and may have an impact on the conditions of regularity in the choices of the interviewees, thereby limiting the interval of applicability of discrete choice models. For example, adding an alternative that is similar to another within a set of options may increase the likelihood of choosing a third alternative merely because it is different (^{Hoyos, 2010}).

The allocation of the levels of the attribute within the experimental design has an impact on the statistical power of the experiment in terms of its ability to detect potential statistical relationships between the data (^{Rose and Bliemer, 2014}), which is directly related to the size of the study sample. However, the most common sample sizes in empirical researchers may compromise the ability to recover statistically significant parameter estimations, if a deficient design is selected. According to ^{Breffle (2008)}, “although a large sample may compensate a deficient design, this is not necessarily the best way to approach the issue”; furthermore, this type o samples entail greater costs of the research.

When applying the DCEs empirically, it is possible to put forth more than one design, and there is a risk of not selecting the optimal one; therefore, it is crucial that the researcher determines precisely the functional form of the statistical model or utility function (^{Breffle, 2008}; ^{Johnston et al., 2017}). For this reason, it is important to characterize the issue accurately, depending on the techniques utilized to obtain the information. ^{Alpizar et al. (2001)} mention that it is possible to approximate a utility function ex-ante, based on the results of previous studies on the same topic, on the judgment of experts, and on pilot tests, or else, to develop the sequential design approach proposed by ^{Scarpa et al. (2007)}, in which the parameters are updated as more information is added.

Another important aspect regarding which decisions must be made is whether or not to include the statu quo as an attribute level. From the point of view of the consumer theory, this option needs to be considered (^{Hoyos, 2010}); although it will reduce the efficiency of the design, since both the attributes and the levels will be increased. In this regard, the empirical evidence does not exhibit a consensus; while several authors include it in their studies (^{Espinal et al., 2014}; ^{Rocamora et al., 2014}; ^{Villanueva et al., 2017}; ^{Tudela-Manani and Leos-Rodríguez 2018}), others omit it (^{Álvarez-Faricio, 2006}; ^{Birol et al., 2006}; ^{Turner, 2013}). Therefore, the inclusion or exclusion of the statu quo depends on the purpose of the study and must be assessed by the research team.

Generation of the experimental design

The experimental design is the organization of attributes and levels that constitute the alternatives in the choice sets; their identification and efficiency are the main statistical aspects involved in their construction (^{Hoyos, 2010}). Their identification consists in the effects that can be independently estimated; i.e. the specification of the indirect utility function. Their efficiency is associated to the precision of the estimations of the parameters (^{Turner, 2013}).

At this point, decisions must be made regarding: i) the number of attributes and their levels; ii) the number of alternatives, and iii) the number of choice sets (^{Breffle, 2008}).

Once the attributes and levels have been identified, the factorial design, which can be complete or fractioned, must be defined. The complete factorial design includes all the possible combinations of the attributes and their selected levels and independently estimates the main effects and of the effects of the interaction. If the attributes and levels are numerous, a complete factorial design is impossible to apply, and therefore, fractioned designs are resorted to, which comprise a sample of those attributes and levels and can be orthogonal (therefore minimizing the correlation between these (^{Bennett and Adamowicz, 2001}). Statistical packages including SPSS or R are utilized to obtain them.

Based on the number of choice sets obtained, the tasks or choice sets per interviewee are determined. According to ^{Oehlmann et al. (2017)}, there is a greater probability that the interviewees will choose the statu quo when the number of choice tasks per individuals is increased, when the intervals between levels are broader, and when the alternatives are similar; these situations are associated to a larger number of attributes and levels. In order to reduce the choice tasks per interviewee, different versions of the questionnaire are usually made; therefore, the orthogonal design includes the number of versions (blocks) as an additional attribute.

Development of the survey instrument

One of the most vulnerable aspects in the declared preferences methods is the use of questionnaires to obtain information; for this reason, the design attends to the recommendations included in literature for contingent assessment (CA). For example, the scenario is presented from the start in such a way that will allow the interviewee to understand the effects of the hypothetical program under consideration; furthermore, validation questions are integrated in order to verify that the interviewee has understood and accepted the proposed scenario, among others that are applicable to DCEs.

The questionnaires include at least three sections: i) general information and presentation of the ecosystem good or service to be assessed; the purpose of this is to enable the interviewees to make informed decisions based on a homogeneous understanding of the issue and its terminology (^{Turner, 2013}); ii) assessment scenario or choice question; this must represent an incentive and must motivate the interviewees to provide their true preferences, and iii) socioeconomic information. The choice format must recreate, to the furthest possible extent, the context of a real choice (^{Turner, 2013}); therefore, the selected payment method must be consistent with the context of the good or service to be assessed.

In order to obtain good welfare measures, it is necessary to establish a point of comparison with the scenario of change or improvement in the supply of the assessed good, also known as baseline or statu quo, which represents the option of “taking no action” and must be perfectly well understood by the interviewee if the assessment is to be effective. For this purpose, the use of images illustrating the current situation and recreating the intervention scenarios is recommended, for example, using current tools, such as graphic design.

Although the DCE has some advantages over the CA, such as the reduction of sources of bias ─by making the interviewees compensate between the various characteristics of the good─, the breakdown of the total value into the value of its attributes, the obtainment of more information by the interviewees, and a decreased incidence of ethical protests, among others. Its application involves a larger level of complexity, not only for the researcher, when designing the experiment, but also for the interviewees as they carry out the choice task; this is due to the cognitive load demanded by this method, which renders it the main source of bias (^{Raquetonarivo et al., 2016}; ^{Svenningsen and Jacobsen, 2018}), particularly when the exercise is not sufficiently clear for the interviewee.

Therefore, once the questionnarie has been designed, it is advised to apply it within the target group for validation; subsequently, pilot tests must be carried out until the instrument is as fine-tuned and clear as possible.

These tests must verify several factors understood by the interviewees of the questionnaire (especially in the assessment scenario and the choice task) (^{Meyerhoff and Glenk, 2015}) and of the considered attributes and levels, as well as the duration and the time, among others (^{Hoyos, 2010}). Likewise, ^{Carson et al. (1994)} recommend doing “warm-up” choice exercises together with the interviewee in order to reduce the cognitive load and facilitate the understanding of the task.

Application of the survey

Today it is possible to apply the surveys in various ways: in person, by telephone, self-applied through digital platforms, or in mixed schemes (^{Champ and Welsh, 2007}). ^{Turner (2013)} points out that, while the in-person or telephone surveys are equivalent to those implemented via internet, the latter are much quicker to apply and ensure homogeneity in the formulation of the issue and in the assessment exercise. However, this statement must be taken with reserves, as the cognitive demand of the exercise may result in greater sources of bias. Thus, further research on the reliability and precision of web-based surveys is required.

In general, literature recommends applying the interviews in person, rather than by telephone, while telephone interviews are preferred to email surveys.

In any case, there are three fundamental aspects to be considered in DCE surveys: i) sampling bias and non-response, ii) integrity of the experimental design, and iii) administrative cost. The sampling bias and non-response are characteristic of any survey-based research (^{McFaden, et al., 2005}; ^{Turner, 2013}); therefore, sampling must be as random as possible in order to obtain good estimates of the population parameters. For further readings on the advantages and disadvantages of each form of application of the surveys, it is suggested to make a deeper review of the two authors cited above.

The experimental design is a particular concern in the case of DCE surveys (^{Turner, 2013}), and its efficiency greatly determines the success of a reliable sample. The administrative cost is determined by the sampling strategy and the selected confidence level, as well as by the strategies and incentives implemented by the researcher.

Codification of the variables

Previous to the econometric analysis, the explanatory variables must be codified in order to measure their effects on the model; this can be done by codifying the effects or by using dummy codes. The codification of the effects is more widely used in empirical DCE studies, as it prevents correlation with the codes arranged at the baseline and minimizes colinearity of the estimation matrices used for calculating the interactions (^{Hoyos, 2010}). The most usual way of coding the variables is by following the procedure developed by ^{Holmes and Adamowicz (2003)}, which consists in allocating values of -1, 0, or 1 to the variable, according to the interviewee’s choice.

Table 1 shows the hypothetical codification for an attribute with two intervention levels that differ from the statu quo. In this case, a variable is generated for each level of intervention: A1 and A2.

Econometric analysis of the DCEs

Choosing the right model

The econometric analysis includes more than one model before selecting the right one for the data of interest, for which purpose the following aspects must be considered (^{Tudela, 2010}): i) the coefficients of the independent variables must have the expected signs; ii) the coefficients of the independent variables must be significant at a given confidence level; iii) the (Akaike) information criteria must be low, and iv) the model must have a better goodness of fit in terms of MacFadden’s R².

Welfare measures

The parameters estimated based on a linear model (2) can be interpreted as marginal effects of the attribute of the good to be assessed over the possibilities of choosing one of the plans. Therefore, the marginal willingness to pay (MWTP) by intervention area is the willingness to pay for a unitary change in each, while the rest remains constant. The MWTP in any of the analyzed attributes is estimated based on the quotient that results from dividing the estimated coefficient of each attribute (𝛽) by the rate increase coefficient (γ) (^{Alpizar et al., 2001}):

Reliability and validity of the DCEs

Although DCE is one of the most widely accepted economic assessment methods today, its reliability and validity ―i.e. whether the method provides consistent results with different survey designs that may be used to measure the same values― are constantly questioned. Because the assessment exercise is based on a simulated scenario, a “hypothetical bias” may occur (^{Raquetonarivo et al., 2016}), i.e. the preferences expressed by the survey respondents may differ when facing real economic circumstances (^{Hausman, 2012}).

For this reason, validity and reliability tests of the method are constantly researched (^{Hess and Daily, 2014}; ^{Lancsar and Swait, 2014}; ^{Raquetonarivo et al., 2016}).

The validity may be external (convergent) or internal (theoretical and content-related). The tests for the former entail comparisons using different instruments of a DCE survey, while the internal validity tests focus on the basic assumptions of the method.

Internal validity

The results of the DCEs are theoretically valid when the choices of the survey respondents are aligned with the assumptions of the standard choice theory (on which the method is based) (^{Raquetonarivo et al., 2016}), defined by four axioms of expected utility maximization (^{Mas-Colell et al., 1995}): i) continuity, ii) monotonous preferences, iii) transitivity, and iv) stability.

The empirical evidence of the internal validity of the DCEs is mixed; while ^{Carlsson and Martinson (2001)} register no evidence of violation of the assumptions of transitivity and stability, other authors cite inconsistencies in the choice preferences of the interviewees, i.e. violations of the second axiom (^{Deshazo and Fermo, 2002}; ^{Rocamora et al., 2014}; ^{Raquetonarivo et al., 2016}). On the other hand, ^{Day and Prades (2010)} point out the persistence of certain ranking anomalies in the DCEs that are similar to those cited in the contingent assessment method, which entails violations of the assumption of stability.

The researches that include rationality tests for identifying inconsistent responses have gained importance in the empirical applications of DCEs. However, their elimination in order to render the assessment more reliable may induce bias in the sample size and reduce the strength of the estimated models. In this sense, ^{Rocamora et al. (2014)} propose an iterative process for the detection and correction of inconsistencies in the choices by the interviewees, in order to minimize the loss of observations.

According to ^{Carlsson et al. (2010)} and ^{Weller et al., (2014)}, validity studies focus on the continuity axiom. Likewise, ^{Colombo et al. (2013)} provide evidence of the fact that some survey respondents in DCEs do not take into account all the attributes when they make their choices, or are not willing to compensate between them; this suggests a violation of the axiom and reduces the validity and reliability of the method in terms of producing reliable estimations of the economic value.

Recently, ^{Sandorf et al. (2017)} indicate that the level of knowledge of the survey respondents regarding the environmental good to be assessed influences the degree to which they ignore the attributes; a greater knowledge increases the likelihood of considering the attributes to be assessed; they also reveal a lower likelihood that the “cost” attribute will be considered. Therefore, questions reflecting the degree of knowledge of the good or service to be assessed must be added, and the assessment exercise must be made very clear for the interviewees, in order to avoid the omission of attributes leading to conditional estimations of willingness to pay, particularly to lower ones.

External validity

External validity tests may be criterion-related or convergent. The former compare between the actual and the hypothetical behaviors. In general, the DCEs are less prone to hypothetical bias than the CAs (^{Carson et al., 1994}; Alpízar et al., 2001; ^{Carlsson and Martinsson, 2001}) because the choice scenario is closer to a real situation of the interviewee.

The convergent validity tests deal with the correspondence between the measures obtained with DCEs and those obtained with other methods; the most widely used tests for comparing the DCEs results are (^{Raquetonarivo et al., 2016}): i) revealed preferences (travel costs, hedonic prices or production function); ii) contingent assessment or complete contingent classification techniques (^{Christie and Azevedo, 2009}), or iii) through other assessment methods that may or not be consistent with the random utility theory, like the analysis of multiple criteria or attribute classification exercise (^{Azevedo et al., 2009}).

Other theoretical validity tests refer to the sensitivity to the scope, which assumes that the survey responders would be willing to pay more for an important effect than for a subset of this effect (^{Carson and Czajkowski, 2014}). Although, in general, DCEs exhibit less biases than CAs, the empirical evidence points out that the DCE is more sensitive to the scope (^{Foster and Mourato, 2003}).

The preferences obtained in the DCEs are more susceptible to the anchoring or bias effects of the point of departure and more complex, which leads to a strategic behavior by the interviewees. However, the empirical evidence is still not conclusive. Thus, ^{Bateman et al. (2009)} document proofs of this bias, while ^{Day and Prades (2010)} cite the opposite.