Modelling price non-attendants as true protesters in Discrete Choice Experiments
Romain Crastesa *
a
AGRI'TERR, ESITPA
3 rue du Tronquet, 76130 Mont Saint Aignan, France
* Corresponding author at : Unité AGRI'TERR, ESITPA, 3 rue du Tronquet, 76130 Mont Saint Aignan,
France. Tel.: +33 6330 47867; fax: +33 2350 52740;
email: rcrastes@gmail.com
1
Modelling price non-attendants as true protesters in Discrete Choice Experiments
Abstract
Non-attendance to the price attribute is a major issue in the Discrete Choice Experiments field.
Indeed, respondents who ignore the price attribute do not make the tradeoffs required for estimating
their marginal willingness-to-pay. Price non-attendance is now widely inferred by the mean of latent
class models. The use of random parameter latent class models has shown to greatly reduce the rates
of non-attendance to the price attribute. Yet, the solutions for treating the remaining price nonattendants are limited and consist either in considering that these respondents have zero willingnessto-pay or that they have the same marginal utility of money as price attendants. In this paper, we
propose to treat price non-attendants as 'true' protesters and delete them from the survey sample.
We use data from a survey on erosive runoff events and estimate a latent class model where
respondents' characteristics are introduce at the class membership level. Posterior class membership
probabilities are then estimated for each respondent of the sample. Respondents who are identified
as price non-attendants are then deleted from the sample. Several deletion thresholds are tested, up
to a maximum which corresponds to the average price non-attendance class membership probability.
Additional models are then estimated in order to test the effect of deleting price non-attendants on
welfare estimates. Results indicate significant improvements in goodness-of-fit. Marginal willingnessto-pay estimates are also found to be greatly reduced. The random parameter logit model with a lognormally distributed price coefficient is found to be a suitable specification when removing price nonattendants.
1. Introduction
Attribute non-attendance (ANA) is a common behavior in Discrete Choice Experiments (DCE) which
refers to the situation where some respondents only consider a varying subset of the attributes
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entering the choice alternatives rather than the whole set. ANA may be accounted for by using a
wide range of approaches. It is nowadays widely inferred by the mean of latent class models. Latent
class modeling allows for different preference structures between respondents. In some classes, one
or several attribute coefficients are set to zero to reflect ANA, while, for each attribute, a single nonzero coefficient is estimated and enters all the classes where it is attended. In such context, class
membership probabilities are interpreted as ANA rates.
In a recent paper, Collins et al. (2013) reviewed the different interpretations of ANA in the literature.
In some contexts, ANA is neither a problem nor a bias, but reflects behaviorally plausible
phenomenon. Indeed, some attributes might just have no value for some respondents. Alemu et al.
(2013) found that respondents declared to ignore attributes not only because they did not care
about them but also because they considered the choice situation unrealistic, wanted to make their
choice situation easier, found it too be too difficult or did not want to trade a given attribute for
some others, which partially matches with the reasons for expressing protest behavior in the
literature (von Haefen et al., 2005; Meyerhoff and Liebe, 2010; Thiene et al., 2012). Price nonattendants may hence be interpreted as a form of protest, as also suggested by Colombo et al. (2013)
and Alemu et al. (2013) who state that there is no a priori reason why protest behavior could not
play a role at the attribute level rather than at the overall survey level.
According to Meyerhoff and Liebe (2010), who conducted a meta-analysis on the determinants of
protest answers in Contingent Valuation (CV) and DCE, protesters are often arbitrarily identified and
deleted from survey databases. Moreover, according to Thiene et al. (2012) on a study on serial
nonparticipants (a category of respondents which are likely to be protesters as well) such
respondents may just have a different preference structure and should be kept in the sample.
However, this may only hold if the respondents are expressing their preferences in terms of WTP,
which is not the case of price non-attendants. Price non-attendants are both common and largely
present among survey samples in the literature (Scarpa et al., 2009). Indeed, these respondents are
3
not necessarily indifferent to the price attribute but estimation results state they have a zero
coefficient because they ignored it, which is in total contradiction with economic theory (Campbell et
al., 2012 ; Alemu et al., 2013). As a result, it is not possible to derive their Willingness-To-Pay (WTP)
for the set of non-monetary attributes considered. In the literature, solutions for treating inferred
price non-attendants consist either in considering that they have the same marginal utility of money
as those who attended the price coefficient (Scarpa et al., 2009) or consider that they have a zero
WTP (Scarpa et al., 2009 ; Carlsson et al., 2010 ; Colombo et al., 2013).
In this paper, we argue that these solutions may be misguided and propose an alternative procedure
where inferred price non-attendants are treated as 'real' protesters and deleted from the sample.
We use data from a DCE on the management of erosive runoff-events in a severely flood prone
watershed of France. We use latent class modeling and estimate posterior probabilities of notattending the price coefficient. This procedure allows identify whether each respondent of the
sample is attending the price coefficient or not. Respondents who are the most likely to be price nonattendants are excluded from the sample. Several deletion thresholds are introduced for testing
sensitivity. New models are then estimated using the 'price non-attendance free' samples. Results
show significant increase in model fit according to AIC/n measures, especially when compared to the
more conservative and still common approach where only 'traditional' protesters are excluded from
the sample. Moreover, results indicate very significant drops in mean WTP estimates, suggesting that
appropriately addressing the issues with price non-attendants may contribute to design more
realistic policies.
The rest of this paper is organized as follows: Section 2 describes the methodology for identifying
price non-attendants using the ANA model. Section 3 describes empirical settings. Results are
presented in Section 4. A discussion and a conclusion are given in Section 5.
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2. Methodology
2.1. Inferring ANA
Inferring ANA by the mean of latent class modelling is now a well known research field, which has
been very active in the past few years (Scarpa et al., 2009 ; Hensher and Greene, 2010 ; Campbell et
al., 2012 ; Collins et al., 2013 ; Hess et al., 2013). Various forms of models exist. These models are
generally referred to as ANA models in the literature (Collins et al., 2013). In its basic form, the ANA
model approach consists in a latent class model where Q classes are defined by the researcher to
account for different combinations of attendance and non-attendance across attributes (Hess et al.,
2013). Only a subset of the attributes entering the DCE may be considered for non-attendance. For
each attribute considered, there exists a single coefficient estimated which enters all the Q classes
where the attribute is attended, while its value is set to zero in all the classes where the coefficient is
non-attended. This model is often referred to as the 2K model. Indeed, if K refers to the number of
attributes entering a given choice experiment, then 2K refers to the maximum combinations of
different attendance and non-attendance classes possible. In practice, researchers only estimate
non-attendance for a subset of attributes or a subset of the 2K combinations of attendance and nonattendance possible because certain attributes may always be attended while some combinations of
attribute attendance and non-attendance may have a zero (or extremely small) class membership
probability. As shown by Greene and Hensher (2002), the central behavioral model is a logit model
for discrete choice among
alternatives. The probability for respondent i to make choice j in choice
situation t depending on its class membership q corresponds in such context to:
(1)
The probability for the specific choice made by an individual is then formulated as such:
(2)
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with
corresponding to the specific choice made. For the given class assignment, the joint
probability of the sequence
] corresponds to:
(3)
The class assignment is unknown by the researcher. Still following Greene and Hensher (2002),
corresponds to the prior probability for attendance class q for individual i. In our case, it takes the
following form:
, q = 1...,Q,
= 0,
(4)
is a set of observable characteristics that influence class membership probabilities and
a set of
parameter estimates. ANA rates may hence be explained by respondents' characteristics and attitude
towards the valued good. As shown by Collins et al., (2013), only few studies have attempted to
estimate the effect of respondents' characteristics and attitudes on ANA rates beyond stated ANA.
Yet, it may be of interest to identify the determinants of inferred ANA, and more especially the
profile of respondents who are the most likely to ignore the price attribute. Price non-attendance is a
major concern in the ANA literature. Important price non-attendance rates have been found in a
number of studies (Collins et al., 2013). Several reasons have been proposed for explaining price nonattendance. Scarpa et al. (2009), for whom the rate of price non-attendance was found to be over
80%, suggest that this might be an outcome of specific decision heuristics worsen by the hypothetical
context where incorrect choices are not penalized. Respondents may have also lacked of familiarity
with trading-off environmental goods against money and as a result were not able to rationalize the
choice task, which matches with the reasons found by Alemu et al., (2013) for ANA, although they did
not attend price non-attendance in their study. Yet, these reasons match with the reasons for
protesting found in the literature as previously stated (von Haefen et al., 2005 ; Meyerhoff and Liebe,
2010; Thiene et al., 2012) and also suggested by Alemu et al., (2013). This does not necessarily
involve that price non-attendants are expressing protest behavior, but that this category of
6
respondents should be treated as protesters. Some solutions proposed in the literature for reducing
ANA rates, and especially price non-attendance, are similar to the now well known solutions for
reducing protests and include proposing more realistic scenarios, attributes and levels. Yet, some
recent approaches have been specifically designed for reducing ANA, and more particularly price
non-attendance.
Hess et al., (2013) proposed to introduce continuously distributed random parameters in the 2 K
model in order to avoid confounding low preferences for a given attribute with zero preferences.
Results showed a significant drop in ANA rates as well as an increase in models fit. Such model has
also been used and extended by Collins et al., (2013) who reported a significant drop in the
probability of price non-attendance. However, the authors expressed some concern when applying
this approach to reduce price non-attendance by choosing a log-normally distributed coefficient as it
is usually done. Indeed, in addition to the usual 'exploding' marginal WTP problem associated with
the use of such distribution (Giergicny et al., 2012), the mass near zero in the continuous distribution
may compete with the ANA mass point. The model may then underreport the price non-attendance
rate. Other distributions such as the truncated triangular distribution may be used to avoid
confounding price non-attendance with low-sensitivity. However, the latent class random parameter
logit model which has to be used for such purpose is very sensitive (Greene and Hensher, 2012).
Collins et al. (2013) provide extensive guidelines to achieve convergence when using such models for
measuring ANA rates. They report numerous issues that may lead to instability and identification
problems. For these reasons, the authors state that inferred ANA rates may be questionable and
argue that completely unentangling low attribute sensitivity and ANA may be impossible.
Distributions should hence be chosen with care when using a random parameter ANA model for
measuring price non-attendance.
In addition, Campbell et al., (2012) introduced Probabilistic Decision Process (PDP) models, which are
a special form of ANA models that allow to model situations where respondents adopt cost
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thresholds and cut-offs when making a choice. Respondents are segmented based on their
sensitivities to cost. More precisely, this category of models account for the possibility that
respondents may have only considered a subset of levels in the cost attribute. Such models are found
to greatly decrease ANA rates in comparison to ANA models. The price non-attendance rate drops
from 70% to around 10% while model fit is greatly increased and MWTP greatly reduced. Accounting
for heterogeneity in price sensitivities reduces extreme and implausible MWTP estimates. However,
the authors state that this approach does not allow to compute MWTP estimates for the subset of
the sample which did not attend the price attribute at all, as it is usually stated in the ANA literature.
The authors also acknowledge the fact that the reasons why respondents did not attend the price
attribute may also be related to the hypothetical nature of the DCE. Finally, Collins et al., (2013) also
highlight that this approach is computationally challenging.
Welfare estimates could be further evaluated if the WTP for environmental improvements could be
computed for all the respondents of the sample. However, in is not the case in practice. Even when
the price non-attendance rate is reduced by the means of the methods previously presented, there is
still a part of the sample that does not enter WTP calculations. Moreover, it may be questionable to
include the respondents who are found to have an extremely low sensitivity for the price attribute in
the WTP calculations. Indeed, these respondents are found to have behaviorally unrealistic WTP
estimates. Of course, there may be a wide range of reasons why respondents do not attend (or just a
tiny bit) the price attribute, as previously stated. These reasons may be linked with the experiment
design or with respondents’ preferences and attitude toward the valuation process, or choice task.
Price non-attendance is very likely to be a DCE artifact (Hess et al., 2013) and researchers should aim
at reducing the rate of non-attendants due to survey design. Yet, the problem associated with the
share of respondents which does not enter MWTP calculations should also be addressed. In this
paper, we specifically focus on the residual price non-attendance rates derived from ANA models. In
accordance with the literature, we argue that respondents who express behaviorally unrealistic
behaviors regarding the price attribute should be deleted from the sample either because they
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express unaccountable protest behavior or because the survey experimental design failed to properly
address their preferences.
2.2. Excluding price non-attendants
The method we propose for excluding price non-attendants inferred by the means of ANA models
from the sample is very straightforward. At the survey level, our approach consists in gathering data
on whether the respondent clearly knows about the valued good, whether she/he is in favor of the
program and thinks the program valued will be effective and also whether she/he found the choice
task to be difficult or not. Other information on respondents such as age and gender are collected as
well.
At the estimation level, the first step of the approach we propose consists in selecting the
appropriate number of classes in the ANA model. The first step is necessary in order to achieve
convergence during the second step of the procedure. The objective is to propose a model with as
few latent classes as possible and where the price non-attendance rate is not confounded with other
non-monetary attribute non-attendance rates. In other terms, and despite the ANA model is used
here for the sole purpose of identifying price non-attendance, it may be misguided to estimate a
model with only two latent classes, with one class reflecting full attendance to both non-monetary
and monetary attributes and one class reflecting non-attendance to the monetary attribute only.
Indeed, the second class may capture other non-attendance behaviors. It is recommended at first to
follow the guidelines provided by Scarpa et al., (2009) in their founding paper and estimate a series
of models comprising various combinations of attributes attendance and non-attendance, and check
whether adding latent classes significantly improves fit or not. We call these models the extended
non-attendance models. The price non-attendance rates provided by the extended non-attendance
models should then be compared with the price non-attendance rates provided by restricted nonattendance models, where only a subset of the latent classes entering the extended non-attendance
models are considered. The final model is the model that minimizes the number of latent class while
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providing a stable price non-attendance rate in comparison to the extended non-attendance models.
As an illustration, the final model in the application provided in the remainder of this paper
comprises three classes. The first class is the full attendance class. The second class is the price nonattendance class and the third class is the non-monetary attributes non-attendance class.
The second step consists in introducing the variables related to respondents' characteristics,
attendance and understanding of the principles of the DCE in Equation 4. More precisely, these
variables are introduced in the final model at the latent class membership probability level in order
to define the posterior probability of not-attending the price attribute as a function of attitudes,
behaviors and characteristics which are related to protest and non-attendance. The class probability
model may fail to converge or may not provide significant results if the number of classes entering
the ANA model is too high, which justify the first step of the method we propose. Once the
parameter estimates of
denoted
are known, the prior estimates of the class membership probabilities are
(Greene and Hensher, 2002). For each respondent, the posterior estimates of the class
membership probabilities
can finally be obtained using Bayes theorem using:
(5)
The third step consists in deleting from the database the respondents for whom the posterior
probability of being price non-attendants is the highest. As previously stated, price non-attendants
express an unrealistic behavior which is likely to be caused by the hypothetical nature of the DCE.
Keeping these respondents in the sample may results in WTP estimates that do not correspond to
respondents’ true preferences since it does not allow to derive WTP for the whole sample, thus
leading to biased or incomplete WTP estimates and WTP distributions. Respondents who are the
more likely to be price non-attendants should be excluded. The percentage of respondents deleted
should not be superior to the average class membership probability for the price non-attendance
class. This procedure allows to obtain a 'price non-attendance free' sample. Of course, price non-
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attendance rates have been often found to be quite high in the literature and one may express
concern about deleting such a high share of respondents from the database. However, there may be
no 'legal' reason to keep these respondents in the sample either (Alemu et al., 2013). Moreover, the
introduction of random coefficients (if possible) may greatly decrease price non-attendance rates. It
is worth noting that since there are evidences that the ANA model is likely to confound very low
sensitivity with zero sensitivity even when introducing random coefficients (Collins et al., 2013), this
approach comes with the risk of excluding respondents who were actually attending the price
attribute. However, an extremely low sensitivity for the price attribute is likely to produce
behaviorally implausible WTP estimates. Hence, we argue that this category of respondents is also
expressing 'true' protest in the sense that their WTP is likely to be much higher than their available
income, which is in contradiction with economic theory. In other words, these respondents
correspond to what is generally referred to in econometrics as outliers, which are also commonly
deleted from survey samples.
Finally, the fourth step consists in estimating additional models based on the 'price non-attendance
free' sample. In the next sections, we present our empirical setting and comment the differences in
terms of model results between the complete sample, the 'price non-attendance free' sample and
the 'traditional protesters free' sample.
3. Survey description
The data used in this survey come from a DCE on erosive runoff events mitigation measures,
conducted in fall 2011 in Upper-Normandy, France. More precisely, the survey took place in the
Vallée du Commerce (VdC), a watershed severely exposed to events related to erosive runoff, such as
floods, mudslides and landslides. The DCE survey has been fully described in Crastes et al. (2014).
Three non-monetary attributes enter the DCE survey. Each attribute can take two levels, « yes » or
« no ». The first non-monetary attribute, agriculture, consisted in implementing responsible water
management measures in farming production. The second non-monetary attribute, infrastructure,
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consisted in implementing protective infrastructures, which comprises both hydraulic works
(absorbing parking, permeable roads) and heavy structures (dams and dikes). Finally, the third nonmonetary attribute, communication, corresponded to a set of measures for increasing public
awareness about erosive runoffs and develop a better alert system. In addition to the status quo
level, the cost attribute could take three levels: €12.50, €25 and €37.50. The payment vehicle was set
to be an increase in the annual local tax. The price attribute levels have been decided together with
the district authorities using the results from a pre-test survey.
The experimental design has been built following an orthogonal optimal in the difference factorial
design (Street and Burgess, 2007). In addition to the status quo, each choice set comprised two
alternatives, with the second alternative specifically chosen to be the opposite of the first one (the
cost level was also set to be different). 24 choice sets were generated. These choice sets were
divided in 4 blocks of 6 choice sets each. These four blocs have been equally distributed within the
surveyed population.
In addition to the usual questions related to sociodemographics, respondents had to state whether
they clearly understood the survey principle and the information provided, their degree of familiarity
with the valued good and their degree of trust in the institution and the effectiveness of programs
that aim at reducing erosive runoffs in general. Finally, the respondents had to state whether they
considered the whole DCE survey to be difficult to answer or not. 619 respondents provided
complete answer. Respondents were chosen following the quotas method in order to ensure that the
survey sample fits with census data. Information on gender, age, income and localization were also
gathered. Respondents who always chose the status quo, or serial non-respondents, as described by
von Haefen et al. (2005), were asked why they always did so for posterior analysis. Descriptive
statistics for the complete sample are provided together with the 'non-attendance free' samples later
in the paper (Table 3) for comparison purposes.
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4. Results
4.1. ANA models
Survey data were tested using both the ANA model and the random parameter ANA model, based on
the latent class random parameter logit (Greene and Hensher, 2013). However, we encountered
several issues with the latest, which is volatile as reported by Greene and Hensher (2013) and Collins
et al., (2013). In a majority of cases, the model did not converge. We followed the detailed guidelines
proposed by Collins et al., (2013) on distributional assumptions and starting values without obtaining
robust results. Literally hundreds of model specifications were tested on several software. In some
cases, models achieved convergence. However, results did not report any significant heterogeneity in
preferences for the price attribute, thus leading us to use the latent class ANA model instead. It is
worth noting that preliminary estimations were carried out with and without introducing covariates
at the class membership level it order to account for the potential effect of these variables on
convergence.
Table 1 provides class structures for the extended non-attendance model and the restricted nonattendance model, as seen in Scarpa et al., (2009) while Table 2 presents model results.
[Table 1 about here]
[Table 2 about here]
Several class combination structures were tested for the extended non-attendance model. The final
extended non-attendance model allow for 9 classes. It is worth noting that additional classes were
introduced but they were not found to be significant. The final restricted non-attendance model
allows for 3 classes. The Akaike Information Criterion (AIC) is slightly lower for the extended nonattendance model because it accounts for more heterogeneity in preference structures in
comparison to the reduced model. The non-attendance rates for the price attribute are found to be
similar for both models. Indeed, the class membership probabilities from the reduced model indicate
13
that about 37.1% of the respondents are price non-attendants (Class3), while it is 35.3% for the
extended model (Class2, Class7, Class8 and Class9). The price non-attendance rate derived from the
extended model is comprised within the 95% confidence interval of the price non-attendance rate
derived from the restricted model.
The base outcome for the class membership probability model is Class1, which is the full attendance
class. This class has been selected as the base outcome in order to obtain information on the
determinants of price non-attendance in comparison of full-attendance. Class2 is the class related to
price-non attendance. Results for Class2 indicate that the variable info_att is found to be significant
at the 5% level. Respondents who stated to search for information on erosive runoff events on their
own rather than waiting for the documents from the watershed district authorities are more likely to
be price non-attendants. In addition, the variables know is found to be significant at the 10% level.
This result indicates that respondents who proved to know what erosive runoff is (11.77% of the
sample) are more likely to be price non-attendants. These results indicate that the more respondents
state to know about the valued good, the less they are likely to attend the price coefficient. An
interpretation of these results may be that respondents who state to know about the valued good
are too confident during the choice process and tend to not process all the information which are
presented to them. Other results indicate that the respondents who stated to have clearly
understood the survey instructions (understanding = 1) are less likely to attend the price-coefficient.
Respondents may pretend to understand the DCE survey procedure despite they do not. As a result,
they may be more likely to ignore the price attribute because they do not follow the survey rules.
Finally, the variables difficult and study_level have not been found to be significant. Results for Class3
are not commented because this class mixes too many different behaviors.
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4.2. 'Price non-attendance free' models
4.2.1. Sample design
As previously introduced, the results from the reduced model are used in order to identify the
respondents who are the more likely to be price non-attendants and delete them from the data
sample. Following Equation (5), posterior class membership probabilities are estimated for each
respondent of the full sample. Four samples are created for sensitivity testing.
1. S1, where 10% of the respondents who are found to have the highest probability of not-attending
the price coefficient are deleted from the complete sample.
2. S2, where 20% of the respondents who are found to have the highest probability of not-attending
the price coefficient are deleted from the complete sample.
3. S3, where 30% of the respondents who are found to have the highest probability of not-attending
the price coefficient are deleted from the complete sample.
4. Smean, where 37.1% of the respondents who are fond to have the highest probability of notattending the price coefficient are deleted from the complete sample, which corresponds to the full
proportion of price non-attendants according to the model results.
In addition, a fifth sample is created, named Sprotest. Sprotest is a 'protest-free' sample in the
traditional sense of the term. It is introduced for comparisons purpose. This sample has been created
by removing 'traditional' protesters from the full sample. As previously stated, the literature is very
scarce on how protesters are identified and removed. In this survey, we used follow-up questions for
identifying the reasons of non-participating. More precisely, the respondents who stated that their
favorite choice was the status-quo were asked to justify why. There were seven possible answers,
and respondents could only choose one: (1): "I am not concerned with erosive runoff events", (2): "It
is not me who has to pay to improve the situation", (3): "I believe that none of the options will
15
change anything", (4): "I agree with improving the situation, but it costs too much", (5): "I think that
the collected money will be used for other purposes", (6): "I did not understand the choice
experiment", (7): "Others". In this study, and in accordance with what has been done in a precedent
study using this dataset, respondents choosing item (2), (5) and (6) were considered as protesters in
the traditional sense of the term (von Haefen et al., 2005; Meyerhoff and Liebe, 2010 ; Crastes et al.,
2014). As a result, 189 respondents were deleted from the full sample (30.53% of the sample). Table
3 presents descriptive statistics for the six samples. Estimation results from the full sample as well as
the five samples newly designed are given in the next section.
[Table 3 about here]
4.2.2. Model results
For each sample created, two models have been estimated. A multinomial logit model (MLM) and a
random parameter (mixed) logit model. The MLM has been chosen because it is a basic model which
is still commonly used as the baseline model in numerous DCE survey. The random parameter logit
(RPL) model has been selected because it is nowadays the most common model for treating DCE data
for policy design. This specification has shown to greatly increase fit due to the fact that in can
account for unobserved continuous preferences in preferences. It is also known for providing
'exploding' WTP estimates, especially when the negative of the cost coefficient is set to be lognormal. Indeed, such specification accounts for extremely low sensibility for the price attribute. As a
result, it is of great interest for our analysis to specify the negative of the price coefficient to be lognormally distributed. Indeed, deleting inferred price non-attendants from the sample, i.e. deleting
respondents with a very low or a non-existing sensitivity to the price attribute may be likely to
reduce the extend at which such model overestimates WTP measures. Since these models are only
provided for illustrating the effects of treating price non-attendants as 'real' protesters, some other
appropriate econometric treatments are not considered in this analysis. More precisely, the rather
high number of protesters in our sample suggests that a latent class logit model or a random
16
parameter latent class logit model would have been more appropriated for policy design, as
suggested by Thiene et al. (2012). However, these models have been shown to be either challenging
to estimate with this dataset as previously mentioned, or not as illustrative for the purpose of our
analysis in comparison to the RPL model.
[Table 4 about here]
[Table 5 about here]
[Table 6 about here]
Table 4 and 5 present model results while Table 6 presents WTP estimates. Results from the MNL
model indicate that deleting the inferred price non-attendants from the sample dramatically
increases model fit according to the AIC/n measure. As an illustration, the AIC/n score for the MNL
model based on the sample S3 (where 30 % of the respondents expressing the highest probability of
not-attending the price attribute are deleted) is equal to 0.857, while it is equal to 1.152 for Sprotest,
where around 30% of the respondents comprised in the full sample are excluded as well. Moreover,
results indicate that excluding the price non-attendants from the sample increases the sensibility to
the price coefficient. Although this result was expected, it indicates that price non-attendants were
properly identified. It is worth noting that this effect is regular from Sfull to Smean. As a result,
MWTP values for each of the three non-monetary attributes considered are found to greatly
decrease when excluding price non-attendants from the sample. The MWTP for agriculture is 29.56 €
for the full sample MNL model, while it is equal to 5.03 € for the Smean MNL model, which
represents a decrease of about 83%. Similar results are found for the other attributes.
The RPL specification increases the differences between the MWTP estimates from the full sample
and the MWTP estimates from the 'price non-attendance free' sample in comparison to the MNL
model. The RPL models are specified as such: agriculture, infrastructure and communication are
specified to be normally distributed, as it is commonly done with non-monetary attributes, while the
17
negative of the price coefficient is set to be log-normally distributed. Each of the coefficients is found
to be significant at the 1% level in most cases, apart from the standard deviation of communication,
which translates homogeneous tastes for this attribute. Again, deleting price non-attendants from
the sample results in better goodness-of-fit while deleting 'traditional' protesters from the full
sample decreases model fit. Comparing MWTP estimates between the full sample and the Smean
sample reveals that the MWTP for agriculture is 99.54 % lower for the 'price non-attendance free'
sample. Of course, the MWTP values provided by the full sample are unrealistic because of the
specification of the price attribute. Yet, removing price non-attendants from the sample results in
realistic MWTP estimates despite the negative of the price coefficient has been set to be lognormally distributed. This is in our opinion an important result, because it shows that it is possible to
model continuous unobserved heterogeneity for the price attribute without causing MWTP to
'explode'. The problems associated with the use of the log-normal distributions may hence be a
consequence of issues encountered at the survey level rather than being intrinsically related to the
distribution itself. MWTP distributions for the full sample and the Sprotest sample picture untenably
heavy tails which are due to the fact that these models must account for zero sensibility for the price
attribute. The distributions obtained from the 'price non-attendance free' samples are much more
realistic despite still being heavy tailed.
Finally, it is worth noting that the MWTP measured derived from the Smean sample do not
necessarily correspond to the 'true' MWTP for reducing erosive runoff events in the VdC district.
Indeed, the price non-attendance rate is likely to have been overestimated because our latent class
model could not distinguish low sensibility for the price attribute from price non-attendance. A
recent study from Crastes et al., (2013) proposed a methodology for assessing the external validity of
WTP estimates using the exact same dataset. They found that the 'true' average WTP for any given
combination of attributes is likely to be located between 18 € and 26 €, which approximately
corresponds to the results obtained from S2. However, the exact price non-attendance rate for this
study remains unknown. Future developments in the econometrics of ANA may allow to distinguish
18
low sensibility for the price attribute to non-attendance in our dataset, which would allow to better
illustrate the methodology we propose in this paper.
5. Discussion and Conclusion
Recent advances in the DCE literature showed that respondents do not consider all the attributes
they are asked to consider when making choices. This behavior is referred to as Attribute nonAttendance. ANA may be caused by a wide range of factors, many of which are also likely to
influence other behaviors such as protest and serial non-participation. While non-attendance to nonmonetary attributes is not an issue, price non-attendance is particularly concerning. Indeed,
respondents who ignore the price attribute do not accomplish the tradeoffs which allow to derive
their WTP. As a result, they have recently been compared to protesters (in the traditional sense of
the term) in the literature. The main contribution of this paper is to propose a method for actually
treating these respondents as protesters and delete them from the survey sample.
The method we propose is based on inferring the price non-attendance rate of the study sample by
the mean of latent class logit models (Scarpa et al., 2009). In addition, we introduce covariates
related to knowledge about the valued good and cognitive abilities in order to identify the
respondents who are the most likely to ignore the price attribute in our sample. Finally, we compute
posterior class membership probability estimates. Respondents who are identified as price nonattendants are then deleted from the sample, as it is usually done with protesters (in the traditional
sense of the term in the stated preferences literature). Several deletion thresholds are tested.
Additional models are then estimated based on the 'price non-attendance free' samples. Results
show a significant increase in model fit according to AIC/n measures, especially when compared to
the usual approach where only 'traditional' respondents are deleted from the sample. Moreover, our
results indicate that deleting price non-attendants from the sample considerably reduces mean
MWTP. One of our main finding is that the use of a RPL model with a log-normally distributed price
coefficient is perfectly suitable for estimating realistic MWTP. Indeed, such specification is usually
19
associated with 'exploding' mean MWTP estimates. However, our results indicate that this problem
may be caused by the presence of price non-attendants in the sample rather than the specification
itself.
Although our results indicate that treating price non-attendants as 'real' protesters may contribute to
better policy design by leading to the estimation of more reasonable MWTP estimates, the present
study is limited by the fact that we have not been able to identify the 'true' price non-attendance
rate in our sample. Indeed, numerous issues were encountered when estimating a latent class
random parameter logit using our data. Such model has been shown to report more reliable price
non-attendance rates. As a result, we could not precisely state which one of the five samples created
is the more suitable for policy analysis. Future research on this topic will hence include the use of
more robust models for identifying price non-attendants as well as the use of specific survey design
in order to better identify the reasons for not attending the price coefficients.
References
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Non-attendance in Choice Experiments. Environmental and Resource Economics 54, 333-359.
Campbell, D., Hensher, D.A., Scarpa, R., 2012. Cost thresholds, cut-offs and sensitivities in stated
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Collins, A.T., Rose, J.M., Hensher, D.A., 2013. Specification issues in a generalised random parameters
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V.S., Gaillard, D., 2014. Erosive runoff events in the European Union : using discrete choice
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http://economics.ca/cree/2013/papers/032.pdf
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21
Extended non-attendance model
Restricted
nonattendance
model
Table 1
Class structure
Agriculture
Infrastructure
Communication
Price
Class1
β1
β2
β3
β4
Total Attendance
Class2
β1
β2
β3
0
Price Non-Attendance
Class3
0
0
0
β4
ANA1
Class4
0
β2
β3
β4
ANA2
Class5
β1
0
β3
β4
ANA3
Class6
β1
β2
0
β4
ANA4
Class7
0
β2
β3
0
ANA5
Class8
β1
β2
0
0
ANA6
Class9
0
0
0
0
Total Non-Attendance
22
Table 2
ANA model results
Latent class models
Restricted model
Extended model
Coeff.
Std. Err.
P-value
Coeff.
Std. Err.
P-value
agriculture
2.108
0.099
0.000
6.636
0.430
0.000
infrastructure
2.124
0.101
0.000
5.806
0.396
0.000
communication
1.213
0.082
0.000
5.006
0.431
0.000
price
-0.188
0.009
0.000
-0.422
0.034
0.000
asc
-0.202
0.176
0.251
0.093
0.173
0.000
n
LL
AIC
AIC/n
11142
11142
-1792.918
-1632.953
3619.8
3291.9
0.325
0.295
Average class membership probabilities
probability
95% Conf. Int.
probability
95% Conf. Int.
Class1
0.133
0.077
0.181
0.053
0.029
0.078
Class2
0.371
0.341
0.444
0.092
0.062
0.122
Class3
0.495
0.406
0.549
0.489
0.446
0.532
Class4
0.061
0.033
0.089
Class5
0.025
0.010
0.039
Class6
0.019
-0.004
0.042
Class7
0.066
0.036
0.096
Class8
0.124
0.088
0.160
Class9
0.070
0.046
0.095
Class membership probability model for the restricted
model
Class2
Class3
Coeff.
Coeff.
Std. Err.
P-value
Std. Err.
P-value
constant
0.136
0.407
0.738
1.769
0.390
0.000
info_att
-0.678
0.329
0.040
-1.070
0.330
0.002
difficult
0.469
0.432
0.278
-0.248
0.419
0.553
study_level
0.099
0.115
0.390
-0.237
0.114
0.038
know
1.141
0.665
0.086
0.890
0.654
0.174
understanding
0.772
0.322
0.014
0.416
0.295
0.158
Class1
base outcome
0.000
23
Table 3
Descriptive statistics
Full sample
Variable
urban
female
age
know
info_att
study_level
household_size
difficult
protester
understanding
Description
urban respondents = 1, 0 else
female respondents equal 1, 0 else
age in years
respondents who prove to know about erosive
runoff = 1, 0 else
respondents who stated to look for information
on erosive runoff on their own = 1, 0 else
years of study after highschool
number of persons living in the household
respondents who stated to have difficulties
answsering the questions = 1, 0 else
respondents identified as protesters = 1, 0 else
respondents who understood the survey rules the
first time they were explained = 1, 0 else
S1
S2
S3
Smean
Sprotest
Mean
Mean
Mean
Mean
Mean
Mean
(Std. Err.)
(Std. Err.)
(Std. Err.)
(Std. Err.)
(Std. Err.)
(Std. Err.)
0.449
0.461
0.475
0.495
0.505
0.439
(0.497)
(0.498)
(0.499)
(0.5)
(0.5)
(0.496)
0.544
0.541
0.536
0.543
0.548
0.540
(0.498)
(0.498)
(0.498)
(0.498)
(0.497)
(0.498)
49.300
49.498
50.044
50.246
50.153
48.648
(16.938)
(17.134)
(17.153)
(17.331)
(17.303)
(17.184)
0.105
0.091
0.092
0.092
0.087
0.103
(0.306)
(0.288)
(0.29)
(0.289)
(0.282)
(0.304)
0.161
0.161
0.157
0.152
0.153
0.181
(0.368)
(0.367)
(0.364)
(0.359)
(0.361)
(0.385)
2.531
2.489
2.461
2.398
2.384
2.639
(1.209)
(1.201)
(1.207)
(1.191)
(1.19)
(1.230)
2.71
2.661
2.625
2.580
2.571
2.731
(1.265)
(1.24)
(1.247)
(1.258)
(1.237)
(1.262)
0.155
0.161
0.145
0.135
0.125
0.165
(0.362)
(0.367)
(0.352)
(0.342)
(0.331)
0.297
0.329
0.368
0.421
0.469
(0.371)
0
(0.457)
(0.47)
(0.482)
(0.493)
(0.499)
0
0.773
0.767
0.745
0.739
0.738
0.772
(0.418)
(0.422)
(0.435)
(0.438)
(0.439)
(0.419)
n=11142
n=10044
n=8928
n=7812
n=7020
n=7830
24
Min. Max.
0
1
0
1
0
92
0
1
0
1
1
6
1
7
0
1
0
1
0
1
Table 4
Multinomial logit model results
Full sample
Std.
Coef.
Err.
Coefficient
S1
P>z
Coef.
S2
S3
Std.
Err.
P>z
Coef.
Std.
Err.
P>z
Coef.
Smean
Std.
Err.
P>z
Sprotest
Coef.
Std.
Err.
P>z
Coef.
Std.
Err.
P>z
Mean
asc
-1.972
0.098
0.000 -1.749
0.107
0.000
-1.443
0.122
0.000 -1.107
0.148
0.000
-1.295
0.198
0.000
-1.591
0.107
0.000
agriculture
1.124
0.062
0.000
1.081
0.069
0.000
0.814
0.078
0.000
0.583
0.095
0.000
0.601
0.124
0.000
1.377
0.09
0.000
infrastructure
1.205
0.062
0.000
1.110
0.069
0.000
1.210
0.081
0.000
0.918
0.098
0.000
0.749
0.126
0.000
1.472
0.07
0.000
communication
0.597
0.060
0.000
0.675
0.067
0.000
0.508
0.077
0.000
0.485
0.095
0.000
0.617
0.124
0.000
0.725
0.067
0.000
price
-0.038
0.002
0.000 -0.055
0.003
0.000
-0.0743
0.004
0.000 -0.098
0.005
0.000
-0.119
0.008
0.000
-0.046
0.003
0.000
LL
-6057.797
-5185.278
-4289.06
-3345.476
-2603.615
-4505.197
N
11142
10044
8928
7812
7020
7830
AIC
12125.59
10380.56
8588.011
6700.951
5217.23
9020.393
BIC
12162.19
10416.63
8623.496
6735.768
5251.513
9055.222
AIC/n
1.088
1.033
0.961
0.857
0.743
1.152
25
Table 5
Mixed logit model results
Full sample
Coefficient
S1
S2
S3
Smean
Sprotest
Coef.
Std. Err.
P>z
Coef.
Std. Err.
P>z
Coef.
Std. Err.
P>z
Coef.
Std. Err.
P>z
Coef.
Std. Err.
P>z
Coef.
Std. Err.
P>z
asc
1.577
0.414
0.000
-4.991
0.598
0.000
-0.115
0.424
0.786
-5.921
0.794
0.000
-3.029
0.695
0.000
3.205
0.472
0.000
agriculture
2.225
0.194
0.000
1.895
0.187
0.000
1.885
0.208
0.000
1.101
0.246
0.000
1.089
0.311
0.000
2.341
0.214
0.000
infrastructure
2.397
0.178
0.000
2.109
0.165
0.000
2.297
0.218
0.000
1.851
0.214
0.000
1.897
0.285
0.000
2.504
0.191
0.000
communication
1.328
0.162
0.000
1.411
0.186
0.000
1.373
0.187
0.000
1.281
0.244
0.000
1.741
0.323
0.000
1.446
0.181
0.000
price
-2.309
0.17
0.000
-1.985
0.097
0.000
-0.701
0.097
0.000
-1.501
0.076
0.000
-0.624
0.118
0.000
-2.161
0.121
0.000
asc
11.004
0.963
0.000
11.321
0.956
0.000
6.167
0.549
0.000
7.724
0.767
0.000
5.787
0.675
0.000
4.486
0.523
0.000
Agriculture
2.040
0.213
0.000
1.929
0.219
0.000
1.551
0.248
0.000
2.120
0.309
0.000
2.272
0.353
0.000
2.211
0.22
0.000
infrastructure
1.361
0.201
0.000
1.028
0.202
0.000
0.987
0.261
0.000
-0.944
0.331
0.004
0.667
0.277
0.016
1.33
0.22
0.000
communication
0.113
0.311
0.716
0.526
0.344
0.126
0.264
0.227
0.245
-0.183
0.453
0.686
-0.707
0.358
0.049
-0.198
0.263
0.450
price
2.597
0.17
0.000
1.014
0.055
0.000
1.481
0.107
0.000
-0.103
0.071
0.140
0.783
0.068
0.000
2.336
0.181
0.000
Mean
Std. Dev.
LL
-1604.602
-1359.601
-1098.454
-813.919
-584.562
-1364.855
N
11142
10044
8928
7812
7020
7830
AIC
3229.204
2739.202
2216.9079
1647.838
1189.125
2749.71
BIC
3302.389
2811.349
2287.8774
1717.472
1257.691
2819.368
AIC/n
0.289
0.272
0.248
0.211
0.169
0.351
26
Table 6
WTP estimates (in euros per year)
Multinomial logit model
Agriculture
Infrastructure
Full sample
S1
S2
S3
Smean
Sprotest
Mean
29.56
19.47
10.95
5.92
5.03
29.37
Std. Err.
2.73
1.66
1.18
1.01
1.09
2.42
Mean
31.68
20.01
16.13
9.32
6.26
31.39
Std. Err.
2.87
1.69
1.36
1.1
1.13
2.53
Mean
15.71
12.17
6.83
4.92
5.16
15.47
1.96
1.39
1.09
0.99
1.09
1.76
Full sample
S1
S2
S3
Smean
Sprotest
Communication Std. Err.
RPL model
Mean
Agriculture
Infrastructure
626.31
22.95
11.38
4.92
2.76
367.35
15179.87
50.33
39.22
9.58
8.24
8735.86
Mean
666.51
25.59
13.67
8.35
4.81
345.72
Std. Err.
8912.4
39.39
41.85
4.37
4.97
4460.18
Mean
356.72
17.14
8.23
5.77
4.44
188.62
4319.57
24.77
22.66
1.02
4.76
2388.56
Std. Err.
Communication Std. Err.
27