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Why Not Allow Individuals to Rank Freely?
A Scaled Rank-Ordered Logit Approach Applied to
Waste Management in Corsica
Olivier Beaumais, Anne Casabianca, Xavier Pieri, Dominique Prunetti
UMR CNRS 6240 LISA; Università di Corsica - Pasquale Paoli;
Campus Mariani, BP 52, 20250 Corte, France.
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September 2014
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Abstract
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Since the introduction of the rank-ordered logit model in the eighties, the cognitive e¤ort involved in a
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ranking task has been the source of concerns. Despite the fact that the rank-ordered logit model provides
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e¢ ciency gains, when compared to the basic multinomial logit model, respondents may not all be able to
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provide a reliable full ranking of the alternatives they face. Unreliable or ’noisy’rankings result in estimate
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biases, so that it has even been suggested that only the …rst three ranks to be used for estimation. In order
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to deal with that ranking capabilities issue, we propose a survey design which allows the respondents to
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provide freely incomplete rankings in accordance with their actual heterogeneous ranking capabilities.
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Using the full-ranking of the alternatives and the accurate sub-ranking of the alternatives, we …rst
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estimate a basic rank-ordered logit model. After testing for heteroscedasticity, we also estimate an
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heteroscedastic rank-ordered logit à la Hausman and Ruud, 1987, and introduce a new scaled rank-ordered
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logit which allows us to model further the sources of heteroscedasticity in the data. The methodology
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is applied to the issue of waste management in Corsica. Using rankings of waste management options
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given by a representative sample of the Corsican population (530 respondents) we provide estimates of
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the willingness-to-pay for various options of waste management calculated from models estimated on
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the full-ranking and on the sub-ranking data. We …nd strong evidence that estimations on the full-
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ranking data set and on the accurate sub-ranking data set di¤er widely. Allowing individuals to provide
Corresponding author: olivier.beaumais@univ-rouen.fr
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freely incomplete rankings eliminates a large part of the heteroscedasticity stemming from heterogeneous
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ranking capabilities.
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Introduction
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As recalled by Hoyos (2010), the econometrics of choice experiment is mainly based on the multinomial logit
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model and its extensions. Amongst the extensions of the multinomial logit model, the rank-ordered logit
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model has proven to provide e¢ ciency gains as an appropriate tool for analyzing ranking data obtained by
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asking the respondents to a choice experiment to rank various alternatives instead of simply choosing the
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one they consider to be the best. However, since the introduction of the rank-ordered logit model (Beggs et
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al., 1981, Chapman and Staelin, 1982) the cognitive e¤ort involved in a ranking task has been the source
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of concerns. Respondents probably do not rank accurately from top to bottom and are suspected to pay
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more attention to their top preferred alternatives, so that a full-ranking data set probably includes ’noisy’
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(Chapman and Staelin, 1982) information which can bias the estimates. Thus, it is likely that only the …rst
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few ranks provide reliable information for the estimation. As a consequence, Chapman and Staelin (1982)
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suggest using the …rst three ranks, taking into account a trade-o¤ between improvements in the precision
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of the parameter estimates and the e¤ect of the inclusion of ’noisy’observations (i.e. non-reliable ranking
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information). They also suggest asking the respondents to provide ratings of the alternatives, arguing that
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it may allow them to give tied ratings (instead of full rankings) more easily. Hausman and Ruud (1987)
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propose a heteroscedastic rank-ordered model where ranks receive weights (scaling parameters) that "allow
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the variance of the lower ranks to be di¤erent from those in the higher ranks". However, in Chapman and
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Staelin (1982) so as in Hausman and Ruud (1987) estimations are run over the same ranking range for each
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respondent. Ben Akiva et al. (1992) explore further the reliability of preference ranking data. They estimate
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heteroscedastic rank-ordered logit models in which heteroscedasticity depends on the ranking depth along
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with rank-ordered logit models that attempt to capture the e¤ects of actual choices and/or of the survey
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design on the parameter estimates. They conclude that estimations from full-ranking data su¤er from
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biases which cannot be fully corrected by observed and unobserved heteroscedastic model speci…cations.
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Also dealing with the cognitive task of ranking multiple alternatives, Van Ophem et al. (1999) design a
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questionnaire where the respondents …rst choose the 16 most preferred from 32 o¤ers of …ctitious classical
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concerts, then select the 8 most preferred from the 16 classical concerts selected in the …rst step, and …nally
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fully rank the resulting 8 o¤ers. They argue that such a design is more manageable than a design where the
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respondents are asked to rank all the alternatives and show that the additional information provided by the
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ranking of the 8 preferred o¤ers clearly yields more e¢ cient estimates of the parameters of their model.
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Recent developments in the …eld of discrete choice experiment focus on ways to lessen the cognitive e¤ort
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involved in a ranking task. Scarpa et al. (2011) argue that a best/worst approach provide high quality
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ranked-ordered data. A best/worst elicitation format consists in asking the respondents to state which
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alternative they think is the best, and which alternative they think is the worst, out of the initial choice set.
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Then, they perform the same task on the choice set obtained by withdrawing the …rst two choices from the
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initial choice set and so on, until they have ranked all the alternatives. Estimating heteroscedastic ranked-
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ordered logit models, Scarpa et al. (2011) …nd that the iterated best/worst elicitation format facilitates the
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respondents’ranking task and hence provides better data and welfare estimates.
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Likewise, in order to cope with the heterogeneous ranking capabilities, Fok et al. (2012) propose a latent-
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class rank-ordered model which describes endogenously the ranking ability of the individuals. According to
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their approach, the respondents belong to latent segments which capture the unobserved ranking capabilities.
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The latent-class rank-ordered model allows to use all the rankings provided by the respondents and to reveal
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their ability to rank. Using Monte-Carlo simulations, Fok et al. (2012) show that the latent-class rank-
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ordered model provide e¢ ciency gains compared to the standard multinomial model when at least some
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respondents are able to rank1 . However, they also conclude that: "In our approach the ranking ability is
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considered to be unobserved. One can imagine a survey design in which respondents are asked to rank only
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those options that they are able to rank. In such a survey the ranking ability would actually be observed."
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Indeed, when the survey design allows to observe the ranking capability of each individual, the use of the
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latent-class rank-ordered model proposed by Fok et al. (2012) has no motivation.
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It should be noted that rank-ordered data have also been compared to data stemming from other elici-
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tation formats, in the conjoint analysis/choice experiment literature. Boyle et al. (2001) use a split-sample
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approach to assess whether recoding ratings to ranks or to a ’choose one’format results in di¤erent valua-
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tions. After concluding that these three formats probably give di¤erent valuation results, they recommend
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not to recode ratings to ranks or to ’choose one’, but assessing the ranking capability of the respondents is
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beyond the scope of their work.
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So far, and surprisingly enough, the literature devoted to the ranking capability issue rests on survey
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designs that force the respondents to provide a full preference ranking of a given set of alternatives. Then,
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sophitiscated econometric methods are invoked in order to capture the heteroscedastic nature of the data
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generated.
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As an exception, in her paper on the valuation of a nature reserve, Baarsma (2003) proposes a survey
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design that includes three valuation questions: the …rst valuation question asks individuals to rank six cards,
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the second valuation question asks individuals to rate the same cards and the third valuation question asks
1 Yoo and Doiron (2013) develop a model, the latent-class heteroskedastic rank-ordered model, that nests both the models of
Hausman and Ruud (1987) and Fok et al. (2012). For now, their model has been estimated on data from a choice experiment
in which nursing students have too rank hypothetical nursing jobs.
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individual which of the six cards (none, the …rst one, ..., all six) is/are the most acceptable to them. She
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…nds that the three elicitation formats give quite similar valuation results but the ranking capability of the
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respondents is beyond the scope of her work so that, from this point of view, she does not exploit the richness
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of her data. As we argue further below, we suggest that a survey design à la Baarsma (2003) may provide
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the information necessary to overcome the ranking capability issue. The main idea is to cross-compare the
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answers to a series of ranking tasks, including a ranking task which allows the respondent to provide freely
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incomplete rankings, in order to assess precisely the e¤ect of the heterogeneous ranking capabilities of the
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respondents on the estimates.
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Our methodology is illustrated with a multi-attribute stated preference survey focused on solid waste
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management in Corsica. Although some studies have employed choice experiment to study preferences
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relative to solid waste management in big countries, none of these have focused on a small island like Corsica
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characterized by the pressure of tourism and scarcity of usable land. Recent attempts to comply with
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French law and European directives on waste management have resulted in con‡icts between environment
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and development, leading the local authorities to abandon an incinerator project without proposing any
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other solution, despite the fact that the status quo could undermine the bedrock of the whole economy.
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Thus, one of the motivations of the choice experiment we report in this paper was to provide up-to-date
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information to the decision makers on the individuals’preferences regarding waste management options. In
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particular, we compare rural and urban preferences for solid waste management options characterized by
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their environmental impacts and the time spent on sorting and cleaning waste.
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The rest of the paper is organized as follows. Section 2 o¤ers a brief review of the choice experiment
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literature in the …eld of waste management. Section 3 gives a quick inventory of solid waste management
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programs in Corsica. Section 4 presents the econometric strategy, the survey design and its implementation.
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Section 5 discusses the empirical results, beginning with the assessment of the actual heterogeneous ranking
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capability of the respondents. Section 6 concludes and proposes future directions as well as some policy
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implications of the study.
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2
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Although recent surveys of literature have underlined the growing interest in environmental studies based
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on choice experiment (Alriksson and Öberg, 2008; Hoyos, 2010), very few of the papers reviewed deal with
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solid waste management issues.
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Choice experiment and waste management: what do we know?
As far as we know, Garrod and Willis (1998) are the …rst authors to apply choice experiment to solid
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waste management. Using a multinomial logit model allows them to determine marginal willingness-to-
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pay to reduce noise, odor and dust from a land…ll site in the North-East of England. They implement an
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elicitation method in two steps. In the …rst step, respondents are asked to make a choice between two cards
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(alternatives). In the second step, they are asked to make another choice between the chosen card and two
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new cards. As in Garrod and Willis (1998), the majority of choice experiment studies used for valuing
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waste management externalities are based on the basic multinomial logit model and a simple choice task
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consisting in asking respondents to choose the best alternative within sets of cards. This choice task can
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consist in choosing one of two cards including status quo (Jamal, 2006 in Malaysia; Jin et al., 2006). The
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choice can also be made between two cards and an opt-out option as in Karousakis and Birol (2008). Using
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pair-wise choice experiment they estimate the households’willingness-to-pay for speci…c kerbside recycling
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services in London. In some studies, the choice has to be made between three cards including status quo (Pek
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and Jamal, 2011 in Malaysia examining a labelling e¤ect for solid waste management options on choice) or
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between three cards plus an opt-out option (Sasao, 2004a, 2004b in Japan). Caplan et al. (2007) use a simple
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logit model, a binary-choice logit model2 . In their study in Cache County (Utah), respondents are asked to
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make four choices within sets of two cards. The method allows the authors to conduct compensation tests
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between host and non-host communities. Two studies however use a probit model. Sakata (2007) estimates
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a multinomial probit model3 to assess the residents’ utility for waste collection methods in Japan. Using
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pair-wise choice experiment Nakatani et al. (2008) estimate on the basis of an ordered probit model the
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households’ willingness-to-pay for municipal solid waste management options in Kawasaki City (Japan).
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They notably report existence of respondents with dominant strategies. As far as we know, Caplan et
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al. (2002) is the unique contribution employing a ranked-ordered logit model in the …eld of solid waste
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management studying the willingness-to-pay for curbside waste disposal options in Ogden (Utah). The
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authors use a survey where respondents are asked to rate a status quo option and two di¤erent options
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(same two options for all individuals) in terms of curbside trash-separation services provided and price
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attributes.
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This brief review of the literature shows that the econometrics of choice experiment applied to the
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valuation of waste management externalities is mainly based on the multinomial logit model and rarely on
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its extensions, especially on the rank-ordered logit model. Before turning to theoretical considerations, the
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next section provide more information on the survey area.
2 On the basis of the binary-choice probit model used by Bre- e and Rowe (2002) in a study addressing PCB-cased natural
resource losses in Green Bay, Wisconsin.
3 Arguing the fact that this model permits to relax the restriction imposed by the multinomial logit model which requires the
assumption of independence from irrelevant alternatives. Indeed, he argues that "[...] IIA assumption is a very strong restriction
when using CA in policy studies."
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3
A quick inventory of the solid waste management programs in
Corsica
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The French island of Corsica lies in the Northern Mediterranean, only 7 miles north of the Italian island
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of Sardinia. It has a land area of 3,350 square miles, and a permanent population of 305,674 in 20094 ,
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making for a rather low population density of 83 inhabitants per square mile. However, tourism in Corsica is
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signi…cant, if seasonal: the island receives almost 2.5 million tourists annually, with a peak of around 450,000
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visitors in the month of August alone. Though some studies have employed choice experiment to study
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preferences relative to solid waste management in big countries, none of these have focused on a small island
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like Corsica characterized by the pressure of tourism and scarcity of usable land. Like other mediterranean
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islands, the Corsican economy is mainly based on tourism, which is driven by remarkable amenities and
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also has signi…cant e¤ects on the share of the construction sector in the local gdp. Thus, as solid waste
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management programs impact these amenities, their design has been, and still is, the source of concerns and
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con‡icts in Corsica. As other French regions, Corsica had to de…ne its "Household and Assimilated Waste
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Disposal Interdepartmental Plan"5 . This Plan, implemented by the Corsican Environment Agency (O¢ ce
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de l’Environnement de la Corse), had to set technically and economically achievable targets of recycling
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and recovery, as long as to determine facilities requirements and timeliness. It was established in a context
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where available data report that Corsica was not in compliance with French and European institutional
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framework6 . 315,000 tones of household and assimilated waste were produced in 2008 in Corsica: 145,000
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tonnes were strictly household solid waste. This corresponds to 402 kg/yr per capita, while the French average
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is 360 kg/yr per capita. A signi…cant part of this overproduction is due to the importance of the tourism
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industry in the Corsican economy. Indeed, the quantities of waste (broadly de…ned) are respectively 58.5
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kg/month per capita during tourist season (base: 360,000 inhabitants) and 51.3 kg/month per capita for
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the rest of the year (base: 304,000 inhabitants), (SYVADEC, 2009). 7.3% of the household and assimilated
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waste were separated and 79% were treated in controlled land…lls7 . Some of these controlled land…lls, still
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in operation, are non-standard and some reached a saturation threshold. For sanitary reasons and to meet
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current legislation, it was decided to built an incinerator in a rural area of the center of Corsica. This project
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has met sti¤ opposition from various associations and civic society representatives (aggregated in a collective
4 INSEE
(French National Institute of Statistics and Economic Studies), General Census of Population 2009.
PIEDMA (2002). Revision of this Plan starded in June 2009 and should have been achieved before May, the 17, 2012.
6 Thereby, French law on waste from July 12, 1993 de…nes new principles relative to national solid waste management. Among
these, a priority on valorization and the end of uncontrolled land…lls. "Voynet Circular" from 1998 set a recovery target of 50%
of all waste collected.
7 Cf. SYVADEC (2009), it has to be noted that the destination of 13% of these solid waste is unknown!
5 Cf.
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action group named "Against Corsican Incinerator"). This opposition was based on three arguments: the
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oversize and the inadequacy of this technological solution regarding the size of the island’s population and
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its geographical characteristics, the cost of the project and, mainly, the potential environmental and health
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impacts. In light of the protest against the project, it was …nally canceled in July 31, 2007 and no other
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alternative solid waste management plan has been decided to date.
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Thus, one of the motivations of the choice experiment we report in this paper was to provide up-to-date
7
information to the decision makers on the individuals’preferences regarding waste management options. In
8
particular, we compare rural and urban preferences for solid waste management options characterized by
9
their environmental impacts and the time spent on sorting and cleaning waste8 .
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4
Econometric strategy, survey design and data collection
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Because of the recent opposition to a particular solid waste disposal technology (the incinerator), it seemed
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inappropriate to use an approach focusing on a particular new waste disposal technology. Instead, it seemed
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more appropriate to present generic waste disposal technology alternatives in order to allow the identi…cation
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of the trade-o¤s between various waste management attributes. In such a context, discrete choice experiment
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appears to be the most relevant approach. As Hoyos (2010) recalls, various elicitation formats have been
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proposed within the discrete choice experiment methodology. The most common approach probably consists
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in asking the respondents to choose their most preferred option amongst a set of mutually exclusive alter-
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natives which provides one-choice data which are usually analyzed using the well-known multinomial logit
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model and its extensions. When respondents are asked to rank the alternatives they face instead of choosing
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their most preferred one, this provides rank-ordered choice data which are commonly analyzed using the
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little less-known rank-ordered logit model.
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4.1
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Like the multinomial logit model, the rank-ordered logit model (or exploded logit model) rests on the random
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utility model (Caplan et al., 2002). Since the model was independently proposed by marketing researchers
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(Chapman and Staelin, 1982) and by econometricians (Beggs et al., 1981) it has been used in many …elds
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including environmental economics and waste management.
The rank-ordered logit model
8 Bergmann et al. (2008) report sensibly di¤erent preferences between urban and rural dwellers but for energy projects in
Scotland. Sasao (2004b) includes this comparison but for a particular waste management disposal technology (land…ll) and
regarding di¤erent attributes (namely, geographical origin of waste, area of deforestation, proximity with sources of drinking
water, distance from respondent’s house) from the ones considered in this paper.
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Each respondent i faces a choice set consisting in J alternatives, which are characterized by attributes.
2
Following partially the notations from Fok et al. (2012), let yij denotes the rank given by respondent i
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to alternative j. The vector yi = (yi1 ; :::; yiJ )0 corresponds to the full ranking. Respondent ranks the
4
alternatives according to the level of utility that these provide. For each respondent i, the utility associated
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with each alternative j is Uij which is assumed to be the sum of a deterministic component Vij and a random
6
component
ij .
That is:
Uij = Vij +
7
The
ij ’s
(1)
ij
are independent and identically distributed with a type I extreme value distribution. Further0
0
8
more, Vij can be modeled as Vij =
9
describe the alternatives, and the wij contains interaction variables between the respondents characteristics
10
11
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zj +
wij where the zj vector contains variables (attributes) that
(gender, age, etc.) and the zj variables.
Given these assumptions, the likelihood of a given ranking for a single respondent i is given by (Allison
and Christakis, 1994):
Li =
2
3
J 6
7
Y
exp(Vij )
6
7
6 J
7
P
4
5
j=1
ijk exp(Vik )
(2)
k=1
13
where
ijk
= 1 if yik
yij , and 0 otherwise. As explained by Chapman and Staelin (1982), this likelihood
14
is strictly equivalent to the likelihood implied by a series of sequential choices with each choice governed
15
by a logit model, where the respondent …rst chooses his/her more preferred alternative among the entire
16
set of alternatives, then the most preferred alternative among the remaining set of J
17
so on. Thus, the rank-ordered model may be estimated via a conditional logit model over what Chapman
18
and Staelin (1982) call the ’exploded choice sets’or the ’exploded choice observations’: each individual rank
19
ordered choice set can be decomposed (exploded) into J
20
estimation.
21
i=1 j=1
23
1 choice sets or choice observations used for
Furthermore, for a sample of n respondents, the log likelihood is simply given by:
Ji
n X
X
22
1 alternatives and
exp(Vij )
Ji
n X
X
i=1 j=1
log
"
Ji
X
k=1
ijk
#
exp(Vik )
Note that, following Allison and Christakis (1994), we allow the depth of the ranking (Ji , 1
(3)
Ji
J)
to vary across respondents. In other words, we allow for incomplete rankings. It should be underlined, as
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…rst pointed out by Allison and Christakis (1994), that the estimation of the rank ordered model can also
2
be accomplished by partial likelihood procedures in the spirit of the survival analysis. To be more speci…c,
3
a higher rank for an alternative may be interpreted as a higher rate of failure in the basic Cox regression
4
model. As modern econometrics packages usually include commands to estimate conditional logit models
5
and Cox regression models, the estimation of a rank-ordered model can be routinely accomplished9 .
6
It should be also noted that the previous likelihood function could be more generally written as:
Ji
n X
X
exp( Vij )
i=1 j=1
7
where
Ji
n X
X
log
i=1 j=1
"
Ji
X
ijk
k=1
#
exp( Vik )
(4)
is a positive scale parameter, inversely proportional to the error variance
2
and usually nor-
8
malized to the unity. Relaxing the assumption that the error variance is constant across individuals allows
9
to specify a wide class of rank-ordered logit model.
10
11
First, the basic heteroscedastic rank-ordered logit model assumes that the scale parameter varies across
individuals as follows:
= exp( 0 xi )
(5)
where xi is a vector of individual speci…c variables, and
is a vector of parameters which re‡ects the
i
12
13
in‡uence of those individual speci…c variables on the error variance. Within the context of a stated preference
14
survey, xi can include variables that capture design e¤ects, order e¤ects or ranking e¤ects (see Ben Akiva et
15
al., 1992; Caussade et al., 2005; Scarpa et al., 2011).
16
Second, in the spirit of recent developments in the choice experiment literature (Fiebig et al., 2010; Greene
17
and Hensher, 2010) and in order to explore further the ranking capability issue, we propose to extend the
18
basic heteroscedastic model to a scaled rank-ordered logit model. The basic idea is to allow observed and
19
unobserved heterogeneity in the scale parameter. If we considered only unobserved heterogeneity, the scale
20
parameter would be written as:
i
21
22
where
i
2
= exp(
is random variation across individual,
i
=2 +
i)
N (0; 1) and the constant
(6)
2
=2 is chosen so that
E[ i ] = 1 (see Fiebig et al., 2010; Greene and Hensher, 2010).
9 Econometrics softwares usually provide speci…c commands to estimate rank-ordered models, but these commands rests
ultimately on a conditional logit likelihood (see the package mlogit in R, see Croissant, 2012) or a partial likelihood procedure
(see rologit in Stata).
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Combining observed and unobserved heterogeneity leads to the following speci…cation of the scale parameter:
i
3
To sum up, with
= 0 and
2
=2 +
i
+ 0 xi )
(7)
= 0, the scaled rank-ordered logit model reverts back to the rank-ordered
4
logit model; with
5
model. The rank-ordered logit model and the heteroscedastic rank-ordered logit model are estimated using
6
maximum likelihood, whereas the scaled rank-ordered logit model is estimated using simulated maximum
7
likelihood.
8
9
= 0 and
= exp(
6= 0, this encompassing model collapses to the heteroscedastic rank-ordered
As shown in the next section, our choice survey was speci…cally designed to assess the implications of
heterogeneous ranking capabilities.
10
4.2
Survey design and data collection
11
Attributes of the choices and their corresponding levels were derived from the literature on waste manage-
12
ment, pretest studies and focus group. This step permits to exclude some previously considered attributes
13
regarding environmental impacts as irrelevant or involving task complexity and cognitive burden to respon-
14
dents10 , in line with the most recent advances in choice experiment (Caussade et al., 2005; Scarpa et al.,
15
2011) which are strongly in favor of a reasonable number of attributes and alternatives. We used a change
16
in the current annual waste fee per household11 as payment vehicle as it appears to be the natural extension
17
of the actual tax payment for disposal services. Attributes and levels …nally selected given the con‡ict over
18
the incinerator and the aims of local authorities are presented in Table 1.
Attribute
FAC1
FAC2
FAC3
Table 1: Attributes and their levels
Description
Categorical variable (1-5) co ding the p ollution im pact
Levels
Degradation: Very High - High
(environm ental degradation and health e¤ects)
Interm ediate - Low - Very Low
Categorical variable (1-5) co ding tim e households
M ore than 30 m in. - 20 to 30 m in.
weekly sp end on sorting and cleaning waste
10 to 20 m in. - less than 10 m in. - None
Change in annual waste fee p er household
-40e; -20e; 0e; +20e; +40e
19
1 0 The impacts of waste disposal technologies were initially divided in three components: nuisance from collecting waste,
pollution, and toxicity.
1 1 TEOM: French waste fee.
11
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
1
Each of the levels taken by attribute F AC1 which codes the pollution impact, i.e. the environmental
2
and health e¤ects, was precisely described to the respondents during the administration of the survey. To
3
be more speci…c, the pollution impact attribute was presented from "Very Low" to "Very High" using an
4
incremental formulation, as shown in Table 2, so that every respondent values the same good.
Levels/Impacts
Very Low
Low
Table 2: Description of attribute FAC1
Description
M ild noise or visual nuisances (e.g. noise due to garbage trucks, visual p ollution caused by plastic bags)
Previous level (Very Low) + low im pact p ollution (no health e¤ects)
Interm ediate
Previous level (Low) + disturbing p ollution
High
Previous level (Interm ediate)+health im pacts
Very High
Previous level (High)+heavy visual and o dor nuisances
5
6
A large number of unique solid waste disposal technology service descriptions can be constructed from
7
this number of attributes and levels. Given our 53 factorial structure, we constructed a design in 40 choice
8
sets of 6 cards12 . Table 3 gives an example of a card.
Table 3: An example of a card
Situation 1
Pollution impact
Time weekly spent on
Change in the annual
sorting and cleaning waste
waste fee
more than 10 min.
-20e
High degradation
9
10
The …nal survey was conducted face-to-face by six well-trained interwievers. They surveyed a represen-
11
tative sample of the Corsican population (530 respondents) in November and December 2008. Respondents
12
were selected by strati…ed random sampling based on parameters of age, sex, population and location (IN-
13
SEE, General Census of Population 1999).
14
Survey implementation consisted of three steps. The …rst step gave a presentation of the current situation
15
of solid waste management in Corsica, a description of the various solid waste disposal technologies available
16
and an explanation of the aims of the study. The current situation was presented in terms of annual
17
volume of solid waste produced in Corsica, actual solid waste management used and health risks associated
18
and, …nally, requirements of compliance with institutional framework. Solid waste management options
1 2 Theory and methods regarding the construction of optimal stated choice experiments are fully described in Street and
Burgess, 2007.
12
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
1
were then discussed on the basis of a presentation of their relative advantages and disadvantages regarding
2
environmental impacts and health risks associated, potential for energy production and necessity to spent
3
time on sorting and cleaning waste. Four possible solid waste management options were described aloud
4
to each respondent: sanitary land…lling, incineration, sorting and recycling, composting. This …rst stage of
5
presentation ended with a description of the three attributes used and a presentation of the levels of these
6
attributes. All the information was read aloud during the questionnaire administration.
7
During the second step, each respondent was presented with one of the 40 choice sets of 6 cards and a list
8
description of the levels of the three attributes. On this basis, each respondent was asked to perform three
9
ranking tasks. Finally, in the third step, socio-demographic data about the respondents were collected13 .
10
Regarding the second step, we incorporated an opt-out option allowing the respondent to not choose any
11
of the alternatives in the choice set. This opt-out option can be considered as a status quo option and allows
12
to compute welfare measures consistent with demand theory14 , although it could also be considered simply
13
as a way-out for individuals reacting to the cognitive burden associated to choice experiment (see Caussade
14
et al., 2005).
15
16
As stated above, the design of the three ranking tasks was inspired by Baarsma (2003). The …rst ranking
task was simply:
17
Ranking task 1: Please rank the previous cards according to your preferences, with one (1)
18
being most desirable and six (6) being least desirable
19
20
Two follow-up ranking tasks were asked which generate relevant information to assess the actual ranking
capabitity of the respondents:
21
Ranking/Rating task 2: Please rate the previous cards (from 0 to 10), 10 being the ideal
22
situation and 0 the worst possible situation
23
Ranking task 3: Could you please now state which of the previous ranked six cards is/are
24
acceptable to you (meaning the policy measure(s) you are really willing to see implemented)
25
To be more speci…c, ranking task 3 was a single question composed of seven items (choices): only the …rst
26
card, the …rst and the second cards ... all six cards, and the opt-out answer: none of these cards. Ranking
1 3 The following individual-speci…c variables have been used: Gender (male; female); Age of the respondent; Municipality
of residence (postal code); House type (individual house; apartment); Occupational status (owner; non owner); Knowledge
of actual garbage fee (yes; no); Household composition (number of household members by age); Socio-professional categories
(CSP in INSEE terminology); Activity sector; Education of respondent; Income (total household income); Preferred solid waste
disposal technology; Actual time (mins) weekly spent on sorting and cleaning waste; Opposition to waste treatment plant (yes;
no); SWM as a societal issue (yes; no); Belonging to an environmental association (yes; no).
1 4 See, amongst others, Louviere et al. (2000), Boyle et al. (2001) and Bridges et al. (2011).
13
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
1
task 1 corresponds to the full-ranking tasks. Ranking task 3 asks the respondent to perform a sub-ranking
2
tasks so that she/he reveals her/his actual ranking capability for the current survey. Stated di¤erently,
3
ranking task 3 allows the respondent to extract freely incomplete rankings, from her/his initial full-ranking,
4
strictly in accordance with her/his ranking capability. Ratings resulting from question 2 can be recoded to
5
ranks in order to assess the consistency of the answers to question 1 and question 3, as shown in the next
6
section.
7
5
8
5.1
9
From the initial data set of 530 respondents, observations were excluded when:
Empirical results
A close inspection of the outcome of the three ranking tasks
10
the gender was not mentioned (two cases deleted),
11
the respondent’s location (rural/urban) was not available (four cases deleted),
12
the full-ranking task was not reported properly (three cases deleted).
13
Which leaves us with a data set of 521 respondents. Amongst them 26 (about 5%) chose the opt-out
14
item from the valuation question 3. In their choice experiment study on forest management practices in
15
Maine, using an opt-out question, Boyle et al. (2001) …nd that only 8% of the respondents would not choose
16
any of the four alternatives (four forest management plans) they face. They argue (Footnote 7, p. 450)
17
that this arises because of the general dissatisfaction with the status quo of forest management in Maine.
18
Unfortunately, Baarsma (2003) does not provide information about the distribution of answers to the opt-out
19
question of her survey. The low percentage of individuals choosing the status quo in our study re‡ects the
20
fact that people in Corsica are aware of the negative externalities associated with the status quo of waste
21
management on their island, and thus vote for a change. This low percentage also re‡ects the fact that the
22
controversial incinerator project was probably rejected because it was perceived as a "take it or leave it"
23
only option.
24
25
Recoding ratings to ranks gives us the possibility to assess the actual ranking capabilities of the individuals.
26
Firstly, out of the 521 cases, only three respondents used ties in their ratings and no one in its rankings.
27
Boyle et al. (2001) …nd numerous ties in the rating data of their study, but not in their ranking data,
28
whereas other studies (Alwin and Krosnick, 1985) …nd ties in their ranking data. Although no directions
14
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
1
were given to respondents about the use of ties, we would have expected to get more respondents using ties,
2
but it seems that they have carefully distinguished between alternatives for the ranking and for the rating
3
questions. Thus, it o¤ers rather some evidence that the elicitation task was not a¤ected by fatigue.
4
Secondly, out of the 521 cases, 20 respondents (about 3.8% of the respondents) gave inconsistent answers
5
in the sense that their ratings (valuation question 2), recoded to ranks, were not the same as their full-
6
rankings (valuation question 1). Three of these 20 ’inconsistent’cases present ties, as explained just above.
7
The rest of these ’inconsistent’cases exhibit di¤erences in the ranks given to the less-preferred alternatives,
8
mainly for ranks deeper than 315 . It should be noted that the 26 respondents who chose further the opt-out
9
item in the valuation question 3 all gave consistent recoded ratings and full-ranking, so that we can infer
10
that their opt-out choice was not some kind of protest response.
11
Thirdly, the sub-ranking (valuation question 3) is found fully consistent with the recoded ratings. This
12
gives us strong evidence, coupled with the previous …ndings, that the sub-ranking derived from the valuation
13
question 3 provides accurate data in accordance with the actual ranking capabilities and the underlying
14
preferences of the individuals. Table 4 presents the distribution of the ranking depth in the sample, that is
15
the ranking capability stated by the individuals when they perform the third ranking task. For example, if
16
an individual stated, in response to ranking task 3, that only the …rst and second cards were acceptable to
17
her/him, then her/his ranking depth is 2. Notice that Section 5.3 o¤ers another interpretation of ranking
18
task 3, in which the ranking of the status quo is explicitly taken into account.
Table 4: Ranking Depth
Depth Frequency Percentage
None
26
4.99
1
134
25.72
2
207
39.73
3
120
23.03
4
28
5.37
5
6
1.15
19
20
From Table 4, two main results are worth noting. First, none of the respondents gave a full rank of the
21
alternatives, that is, agreed to rank the six alternatives. Second, the distribution of the ranking depth over
22
the sample is clearly heterogeneous. Thus choosing the same ranking depth (for example a ranking depth
23
of three, as recommended by Chapman and Staelin, 1982) for each individual over the whole sample will
1 5 Which is in line with the recommendation of Chapman and Staelin (1982) to use the …rst three ranks of rank-ordered data
for estimation.
15
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
1
certainly lead to the inclusion of ’noisy’observations and thus will bias estimations. As we have checked the
2
consistency of the rankings stated by the respondents in response to the three ranking tasks, the next step
3
is to compare the estimation using the full-ranking data and the (observed) accurate sub-ranking data.
4
Since the 26 individuals who chose the opt-out item in the valuation question 3 do not contribute to
5
the likelihood function of the rank-ordered logit model (see, e.g., Allison and Christakis, 1994), they were
6
excluded from our …nal estimation data set (495 respondents).
7
5.2
8
Table 5 …rst presents two basic rank-ordered models. The full-ranking model is estimated from the full-
9
ranking data provided by the respondents. The sub-ranking model is estimated from the sub-ranking data
10
Estimation results
which re‡ects the actual heterogeneous ranking capabilities of the respondents.
11
12
First, it should be noted that the attribute F AC1 (impact level of the waste management) was dis-
13
cretized. Curiously, although attributes are often, if not always, coded as categorical variables, they are
14
rarely discretized for estimation purpose. However, discretizing the variable F AC1, which is at the center
15
of our analysis, gives us the opportunity to capture subtle details of individuals preferences. Keeping in
16
mind that the reference category is ’Very High Degradation’the signs of the coe¢ cients associated with the
17
F AC1 items are positive, meaning that individuals do value the reduction of waste externalities. Here a
18
…rst di¤erence appears when comparing the full-ranking model with the sub-ranking model: the coe¢ cient
19
of the ’High Degradation’item of F AC1 is found signi…cant in the full-ranking model whereas it is not in
20
the sub-ranking model16 . Using the sub-ranking data tells us that individuals do not distinguish ’Very High’
21
and ’High’degradation, whereas the opposite may have been wrongly concluded from the full-ranking data.
22
As expected, the sign of the coe¢ cient of F AC2 is positive and signi…cant: the rank of a card decreases
23
with the time spent sorting and cleaning waste, or, stated di¤erently, individuals value positively the time
24
devoted to sorting and cleaning waste.
25
26
Likewise, the coe¢ cient associated with F AC3 is negative and signi…cant. The change in the waste fee
plays its expected role in the ranking of waste management policies.
27
Three individual characteristics were found signi…cant17 in interaction with the attributes’levels. Urban
28
respondents (51% of the sample) tend to be less sensitive to the degradation level (negative and signi…cant
1 6 In
both the models, the hypothesis of equality of the coe¢ cients of the various items of F AC1 is strongly rejected:
= 262:36 for the full-ranking model and 2 (3) = 196:37 for the sub-ranking model.
1 7 Joint tests where conducted to check the in‡uence of these characteristics on the rankings. Other speci…cations including
individual characteristics such as gender, revenue, etc. were tested, without any success.
2 (3)
16
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
Table 5: Rank-ordered logit models
Variable
Intercept
FAC1 a (high)
FAC1 (intermediate)
FAC1 (low)
FAC1 (very low)
FAC2 b
FAC3 c
Urban Dweller
FAC1
FAC2
FAC3
Owner
FAC1
FAC2
FAC3
Full-Ranking Model
Coe¢ cient
p-value
(standard-error)
1.250
(0.116)
2.397
(0.149)
3.260
(0.187)
4.038
(0.227)
0.188
(0.036)
-0.490
(0.038)
0.000
0.000
0.000
0.000
0.000
0.000
-0.064
(0.064)
-0.114
(0.042)
0.085
(0.044)
0.315
0.147
(0.064)
0.004
(0.043)
-0.010
(0.044)
0.022
0.008
0.052
0.909
0.821
Know ledge of the waste fee
FAC1
Sub-Ranking Model
Coe¢ cient
p-value
(standard-error)
0.155
(0.177)
0.679
(0.182)
1.531
(0.207)
2.762
(0.250)
0.314
(0.056)
-0.803
(0.063)
0.000
0.000
0.000
0.000
0.000
-0.153
(0.066)
-0.121
(0.066)
0.233
(0.069)
0.025
0.187
(0.068)
-0.054
(0.066)
0.009
(0.068)
0.006
-0.090
0.246
-0.102
(0.077)
(0.081)
FAC2
-0.019
0.710
-0.058
(0.051)
(0.077)
FAC3
0.082
0.130
0.251
(0.054)
(0.082)
Cases
495
Cases
LogLik
-2,258.65
LogLik
LR 2(15)
1,996.15
LR 2(15)
a Pollution impact (level) - reference category is ’Very High Degradation’
b Weekly time on sorting and cleaning waste
c Raise in annual waste fee per household
17
0.383
0.070
0.001
0.419
0.891
0.209
0.449
0.002
495
-1,188.95
1,067.95
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
1
coe¢ cient of attribute F AC1), less sensitive to the time burden (negative and signi…cant coe¢ cient of
2
attribute F AC2), but also less sensitive to the monetary incentive (which could be interpreted as a revenue
3
e¤ect). Again, the comparison between the full-ranking model and the sub-ranking model shows that the
4
…rst e¤ect signi…cantly holds only for the second model. The result that urban respondents tend to be less
5
sensitive to the time burden of sorting and cleaning waste receives no straightforward interpretation: it may
6
mean that urban respondents value less the time devoted to waste than rural respondents, probably because
7
waste collection services are better designed in urban areas in Corsica (collection schedules, extra pick-ups,
8
etc.).
9
Homeownership (60% of the respondents own their home) in‡uences positively the perception of the
10
degradation level. Homeowners certainly pay more attention to the reduction of waste externalities because
11
these are known to impact negatively the real estate market and thus the value of their home.
12
Finally respondents who state that they know their actual waste fee (16% of the sample) do also react
13
more strongly to the monetary incentive. This result holds only for the sub-ranking model which shows
14
again that taking into account the heterogeneous ranking capabilities leads to di¤erent results. Thus, before
15
calculating welfare variations, we …rst need to address the following question: do the estimates from both
16
the models di¤er?
17
To answer this question, we …rst perform a Hausman test to compare the full-ranking and the sub-ranking
18
models: under the null hypothesis (H0: choosing the second best alternative is determined with the same
19
decision weight as the best, etc.), the full-ranking estimator is e¢ cient and consistent and the sub-ranking
20
estimator is consistent, but uses less information and is not e¢ cient. This Hausman test clearly rejects the
21
null-hypothesis (
22
in the coe¢ cients.
2
(15) = 6716:16) calling for further investigation of the sources of systematic di¤erences
23
As stated above, the scaled rank-ordered logit model, both in constrained and unconstrained form, o¤ers
24
us a powerful tool to investigate the e¤ects of heterogeneous ranking capabilities. We recall (see above) that
25
the scaled rank-ordered logit model assumes that the scale parameter is written as:
i
= exp(
2
=2 +
i
+ 0 xi )
(8)
26
We now have to speci…cy how the observed heterogeneity is captured, i.e., the variables included in vector
27
xi . Given that we focus on the ranking capability issue, that we want to assess rank order e¤ects, and to be
28
29
in line with the seminal work of Hausman and Ruud (1987), as well with the work of Ben Akiva et al. (1992),
JX
i 1
we set 0 xi =
k where each parameter k is associated with a dummy coded indicator-function (Scarpa
k=1
18
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
1
et al., 2011) that denotes that the choice is made from choice set k in the exploded logit representation of
2
the rank-ordered logit model and Ji = maxi Ji . For example, the full-ranking data is exploded into …ve
3
choice sets, choice set 1 corresponding to the most prefered choice amongst the six alternatives, choice set
4
2 corresponding to the most prefered choice amongst the …ve remaining choices, etc. Obviously one of the
5
k
has to be normalized to zero; again in line with Hausman and Ruud (1987), we set
6
k
captures the rank e¤ect of rank k, on the individual scale parameter
7
i.
Ji 1
= 0. Thus,
Given our speci…cation, and
putting aside the unobserved heterogeneity ( ) for the sake of clarity, the contribution of rank 1 choices to
8
i
9
Ji
is simply exp( 1 ), the contribution of rank 2 choices to
1 choices to
i
is exp(
Ji 1 ).
i
is exp( 2 ) ... and the contribution of rank
If the top choices are more precise (rank 1 choices are more precise
10
than rank 2 choices, which are more precise than rank 3 choices, etc.), as the scale parameter is inversely
11
related to the error variance, we expect a scale parameter decreasing in the rank, i.e., given our speci…cation,
12
1
>
2
> ::: >
Ji 1
= 0 (Hausman and Ruud, 1987, p. 98-99).
13
At this point of our analysis, we can re…ne our initial question regarding systematic di¤erences in the
14
estimates. First, do both the full-ranking and the sub-ranking models exhibit rank order e¤ects? Second,
15
do both the full-ranking and the sub-ranking models exhibit observed and unobserved heterogeneity.
To answer these questions, we estimate two models: a heteroscedastic rank-ordered logit model (H-ROL;
16
17
imposing
= 0) and a scaled rank-ordered logit model (S-ROL)18 .
18
Estimates of the H-ROL models are reported in Table 6. Estimates are qualitatively the same as those
19
in Table 5. A likelihood ratio test for null-hypothesis of no heteroscedasticity is reported at the bottom of
20
the Table 6. It shows that the full-ranking data are found to be heteroscedastic, whereas the sub-ranking
21
data are not (
22
k ’s
23
1
2
(4)
= 131:01 and
2
(3)
= 6:79, respectively). This result is consistent with the fact that the
are signi…cant in the full-ranking model, but are not signi…cant in the sub-ranking model. As expected,
>
2
> ::: >
5
= 0 which shows that when respondents are forced to rank all the alternatives, they do it
24
less and less precisely. On the contrary, when we estimate the model on the sub-ranking data, taking into
25
account the heterogeneous ranking capabilities of the individuals, allowing them to choose the alternatives
26
that they really want to rank, we do not …nd any rank e¤ects. From one choice to another, the coe¢ cients
27
are found to be stable.
28
29
The results from the S-ROL models (Table 7) supports further this striking result. Again the results are
qualitatively the same as the results from the basic rank-ordered logit (ROL) and H-ROL models.
1 8 The
estimations were run using NLOGIT 5 (Greene, 2013). 50 Halton draws when estimating the S-ROL models.
19
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
Table 6: Heteroscedastic Rank-ordered logit models
Variable
Intercept
FAC1 a (high)
FAC1 (intermediate)
FAC1 (low)
FAC1 (very low)
FAC2 b
FAC3 c
Urban Dweller
FAC1
FAC2
FAC3
Owner
FAC1
FAC2
FAC3
Know ledge of the waste fee
FAC1
Full-Ranking Model
Coe¢ cient
p-value
(standard-error)
2.500
(0.280)
5.383
(0.564)
7.591
(0.776)
9.326
(0.958)
0.415
(0.079)
-0.975
(0.110)
0.000
0.000
0.000
0.000
0.000
0.000
-0.147
(0.153)
-0.291
(0.088)
0.211
(0.093)
0.339
0.411
(0.158)
0.027
(0.084)
-0.098
(0.093)
0.009
-0.268
(0.186)
-0.032
(0.096)
0.176
(0.112)
0.001
0.024
0.742
0.293
0.149
Sub-Ranking Model
Coe¢ cient
p-value
(standard-error)
0.170
(0.199)
0.760
(0.284)
1.746
(0.518)
3.086
(0.844)
0.342
(0.104)
-0.876
(0.233)
0.394
0.008
0.001
0.000
0.001
0.000
-0.181
(0.090)
-0.127
(0.079)
0.259
(0.099)
0.044
0.214
(0.091)
-0.054
(0.073)
0.014
(0.076)
0.020
0.111
0.009
0.459
0.848
-0.108
(0.094)
-0.060
(0.085)
0.267
(0.112)
0.250
1.142
0.000
0.136
(0.112)
(0.264)
1.096
0.000
0.149
2
(0.114)
(0.267)
0.655
0.000
-0.184
3
(0.111)
(0.276)
0.499
0.000
4
(0.115)
Cases
495
Cases
LogLik
-2,193.15
LogLik
LR 2(4)
131.01
LR 2(3)
a Pollution impact (level) - reference category is ’Very High Degradation’
b Weekly time on sorting and cleaning waste
c Raise in annual waste fee per household
0.607
FAC2
FAC3
0.738
0.117
0.483
0.017
Observed heterogeneity
1
20
0.577
0.504
495
-1,185.56
6.79
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
Table 7: Scaled Rank-ordered logit models
Variable
Intercept
FAC1 a (high)
FAC1 (intermediate)
FAC1 (low)
FAC1 (very low)
FAC2 b
FAC3 c
Urban Dweller
FAC1
FAC2
FAC3
Owner
FAC1
FAC2
FAC3
Know ledge of the waste fee
FAC1
Full-Ranking Model
Coe¢ cient
p-value
(standard-error)
4.597
(0.749)
9.768
(1.539)
13.571
(2.162)
16.356
(2.670)
0.675
(0.145)
-1.536
(0.260)
0.076
(0.435)
-0.560
(0.155)
0.332
(0.174)
0.623
(0.439)
0.064
(0.127)
-0.114
(0.165)
0.000
0.000
0.000
0.000
0.000
0.000
0.861
0.000
0.056
0.156
0.614
0.489
Sub-Ranking Model
Coe¢ cient
p-value
(standard-error)
0.146
(0.148)
0.568
(0.169)
1.259
(0.236)
2.274
(0.348)
0.254
(0.056)
-0.665
(0.098)
0.325
0.001
0.000
0.000
0.000
0.000
-0.131
(0.058)
-0.100
(0.056)
0.205
(0.060)
0.025
0.159
(0.058)
-0.047
(0.055)
0.011
(0.057)
0.007
0.074
0.001
0.394
0.837
-0.080
(0.068)
-0.040
(0.064)
0.213
(0.071)
0.243
-0.350
(0.164)
-0.170
(0.143)
-0.241
(0.145)
-
0.033
-0.087
0.716
0.000
(0.203)
(0.064)
Cases
495
Cases
LogLik
-2,150.92
LogLik
a Pollution impact (level) - reference category is ’Very High Degradation’
b Weekly time on sorting and cleaning waste
c Raise in annual waste fee per household
0.667
FAC2
FAC3
-0.624
(0.529)
-0.084
(0.139)
0.345
(0.186)
0.238
1.534
(0.153)
1.420
(0.154)
0.694
(0.147)
0.425
(0.147)
0.000
0.544
0.064
0.530
0.003
Observed heterogeneity
1
2
3
4
0.000
0.000
0.004
0.235
0.097
-
Unobserved heterogeneity
21
495
-1,186.16
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
Table 8: Information criteria
Full-Ranking Models
ROL
H-ROL
N. of parameters
15
19
LogLik
-2258
-2193
BIC
4634
4534
CAIC
4649
4553
1
2
Sub-Ranking Models
ROL
H-ROL
S-ROL
15
18
19
-1188
-1185
-1186
2482
2496
2504
2497
2514
2523
S-ROL
20
-2150
4458
4478
The S-ROL full-ranking model shows strong evidence of both observed and unobserved heterogeneity: the
k ’s
are still signi…cant, following the expected pattern, and the
parameter, which captures the unobserved
3
heterogeneity, is highly signi…cant. As for the H-ROL model, the estimation of the S-ROL sub-ranking model
4
does not reveal any scale heterogeneity stemming from the data.
5
As Fiebig et al. (2010) recommend it, we use information criteria (Bayesian (BIC) and Consistent Akaike
6
(CAIC)) to compare the models estimated on the same data set (Table 8). According to the BIC and the
7
CAIC, the S-ROL model clearly …ts better the full-ranking data. According to the same criteria, however, the
8
basic ROL model performs better than its heteroscedastic counterparts when it comes with the sub-ranking
9
data.
10
Taken together these results allow us to calculate welfare changes.
11
As it is well known from the literature, measures of compensating variation can be simply derived from
12
multinomial or rank-ordered logit model. Turning back to the deterministic component of the utility equation:
Vij =
13
zj +
0
wij
(9)
The compensating variation associated with a change in an attribute k is given by:
CV
14
0
where
e
k
=
k
zk + k wik
e + e wie
(10)
is the coe¢ cient of the monetary incentive/attribute (change in the waste fee),
15
coe¢ cient of attribute k,
16
involving attribute k and
17
level of attribute k,
18
e and
19
attribute.
e
zk is the change in the level of attribute k,
k
k
is the
is a vector of interaction coe¢ cients
wik is the change in the interaction variables consistent with the change in the
is a vector of interaction coe¢ cients involving the monetary attribute F AC3 denoted
wie is the change in the interaction variables consistent with the change in the level of the monetary
20
As the information criteria led us to select the S-ROL full-ranking model and the ROL sub-ranking
21
model, we provide in Table 9 welfare variations calculated only from these models. As written above, the
22
discretization of the F AC1 variable permits the calculation of detailed WTP for the reduction of waste
22
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
Table 9: Compensating Variation - annual WTP (e)a
Full-Ranking Model (S-ROL)
Sub-Ranking Model (ROL)
High Degradation
e2.99 [2.50,3.47]
(p-value: 0.000)
e0.19 [-0.23,0.62]
(p-value: 0.381)
e6.35 [5.48,7.22]
(p-value: 0.000)
e0.84 [0.40,1.28]
(p-value: 0.000)
e8.83 [7.68,9.97]
(p-value: 0.000)
e1.90 [1.38,2.42]
(p-value: 0.000)
e10.64 [9.25,12.03]
(p-value: 0.000)
e3.43 [2.78,4.08]
(p-value: 0.000)
a
For a change in environmental degradation compared
to the reference level (Very High Degradation).
95% con…dence bounds are provided in brackets (delta method).
p-values refer to the point estimates.
1
externalities (environmental and health impacts). Point estimates reported in Table 9 (with no interaction
2
e¤ects) for the full-ranking model and the sub-ranking model di¤er in magnitude and estimation on the
3
sub-ranking data show that individuals are not willing to pay for a ’High Degradation’compared to a ’Very
4
High Degradation’. From these data, re‡ecting actual ranking capabilities of the respondents, signi…cant
5
and positive WTP are only found for waste management options that really depart from negative impacts.
6
Beyond the point estimates, careful attention has to be paid to the con…dence intervals. Again, comparing
7
con…dence intervals obtained with both the models, shows that these con…dence intervals do not overlap thus
8
con…rming strong di¤erences between the S-ROL full-ranking model and the ROL sub-ranking model. As
9
the ROL sub-ranking model gives more conservative welfare measures and also as we have shown that there
10
is no heteroscedasticity in the data when the heterogeneous ranking capability of the respondents is taken
11
into account, we suggest that the welfare measures calculated from the ROL sub-ranking model are more
12
reliable than those calculated from the S-ROL full-ranking model. However, one could argue that ranking
13
task 3 could be interpreted di¤erently than the way we do it in Section 4.2.
14
5.3
15
So far, and in line with what can be found in the seminal as well as in the recent literature (Chapman and
16
Staelin, 1982; Fok et al., 2012), we have indeed considered that unranked alternatives are less preferred than
17
the ranked alternatives, without making any assumption regarding the ordering of the unranked alternatives.
18
What if we assume, instead, that ranking task 3 implies that the status quo is actually ranked immediately
19
after the last ranked alternative derived from ranking task 3? For example, if an individual states a ranking
20
depth of 2, then the status quo is assumed to be ranked 3, more preferred than the remaining unranked
An alternative speci…cation
23
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
1
alternatives19 .
2
Testing this alternative speci…cation requires …rst to recall that the status quo was described, during
3
the administration of the questionnaire, in terms of the following levels of the three attributes: Very high
4
Degradation (F AC1), no change in the time devoted to recycling (F AC2), and no change in the waste fee
5
(F AC3). Notice that the questionnaire included a question regarding the actual time weekly devoted to
6
recycling by the respondents (about 41% of the respondents stated that they did not devote anytime to
7
recycling). As the status quo is now explicitly considered, we also have to introduce an alternative speci…c
8
constant (ASC) which takes a value of one when the status quo is chosen and a value of 0 otherwise. The
9
ASC is usually introduced, in the choice experiment literature, to control for a potential status quo bias (see
10
Crastes et al., 2014). More generally, the ASC will capture intangible aspects of the status quo, including,
11
when relevant, protest behavior, design e¤ects, fatigue e¤ects, etc. (see Fiebig et al., 2010 for an insightful
12
discussion on ASCc). Then we follow the same econometric strategy as in Section 5.2, estimating a basic
13
ROL model, a H-ROL model and a S-ROL model on the alternative sub-ranking data. Table 10 compares the
14
initial sub-ranking model with the alternative sub-ranking model. Estimates are quite similar, except that
15
the ASC coe¢ cient is found highly signi…cant and positive, which is not surprising given that the assumption
16
regarding the ranking of the status quo weighs heavily in favor of the status quo. Indeed, referring back to
17
Table 4 above, 134 individuals are now considered to rank the status quo 2, 207 to rank it 3 and so on. We
18
should nonetheless keep in mind that only 26 respondents actually chose the opt-out option.
19
Table 11 reports the estimates of the H-ROL and S-ROL models on the alternative sub-ranking data.
20
Again, and in both models, the ASC coe¢ cient is highly signi…cant and positive, capturing the e¤ect of our
21
assumption regarding the ranking of the status quo. Estimation of the H-ROL shows that, contrary to the
22
sub-ranking data, the alternative sub-ranking data are clearly heteroscedastic: a likelihood ratio test leads
23
to the rejection of the null-hypothesis of no heteroscedasticity (
24
and positive.
25
However, the
k ’s
2
(4)
= 84:46), whereas the
do not exhibit a clear pattern: a one-sided test of
2
(1)
>
1
gives a p-value of 0.994,
2
(1)
is
27
to these test results, second choices would be more precise than other choices, …rst and third choices would
28
be similarly precise, and fourth choices would be the less precise. But, given that the alternative sub-ranking
29
data set results from an assumption regarding the ranking of the status quo, and does not stem from an
30
actual behaviour of the respondents, such an interpretation remains quite hazardous.
4
(
1
not statistically di¤erent from
31
= 1:02) and is statistically di¤erent from
are signi…cant
26
3
(
2
k ’s
= 10:55). According
Also, the S-ROL model was found to be unstable: we were not able to estimate a model with both
1 9 We
thank the Editor for suggesting us this alternative interpretation.
24
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
Table 10: Rank-ordered logit models
Variable
ASC
Intercept
FAC1 a (high)
FAC1 (intermediate)
FAC1 (low)
FAC1 (very low)
FAC2 b
FAC3 c
Urban Dweller
FAC1
FAC2
FAC3
Owner
FAC1
FAC2
FAC3
Sub-Ranking Model
Coe¢ cient
p-value
(standard-error)
-
0.155
(0.177)
0.679
(0.182)
1.531
(0.207)
2.762
(0.250)
0.314
(0.056)
-0.803
(0.063)
0.383
0.000
0.000
0.000
0.000
0.000
-0.153
(0.066)
-0.121
(0.066)
0.233
(0.069)
0.025
0.187
(0.068)
-0.054
(0.066)
0.009
(0.068)
0.006
0.070
0.001
0.419
0.891
Know ledge of the waste fee
FAC1
Alternative Sub-Ranking Model
Coe¢ cient
p-value
(standard-error)
1.688
0.000
(0.135)
0.284
(0.172)
0.599
(0.168)
1.705
(0.178)
2.971
(0.201)
0.242
(0.048)
-0.804
(0.056)
0.000
0.000
0.000
0.000
0.000
-0.083
(0.043)
-0.066
(0.054)
0.224
(0.060)
0.057
0.059
(0.044)
-0.059
(0.054)
-0.003
(0.061)
0.174
-0.102
0.209
-0.032
(0.081)
(0.053)
FAC2
-0.058
0.449
-0.020
(0.077)
(0.067)
FAC3
0.251
0.002
0.176
(0.082)
(0.079)
Cases
495
Cases
LogLik
-1,188.95
LogLik
LR 2(15)
1,067.95
LR 2(16)
a Pollution impact (level) - reference category is ’Very High Degradation’
b Weekly time on sorting and cleaning waste
c Raise in annual waste fee per household
25
0.099
0.222
0.000
0.279
0.961
0.548
0.759
0.026
495
-1,747.41
1,258.76
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
Table 11: Alternative Heteroscedastic and Scaled Rank-ordered logit modelsd
Variable
ASC
Intercept
FAC1 a (high)
FAC1 (intermediate)
FAC1 (low)
FAC1 (very low)
FAC2 b
FAC3 c
Urban Dweller
FAC1
FAC2
FAC3
Owner
FAC1
FAC2
FAC3
Know ledge of the waste fee
FAC1
FAC2
FAC3
H-ROL
Coe¢ cient
p-value
(standard-error)
5.360
0.000
(0.720)
0.457
(0.487)
1.337
(0.467)
4.000
(0.583)
7.213
(0.823)
0.529
(0.128)
-1.917
(0.230)
0.348
0.004
0.000
0.000
0.000
0.000
-0.164
(0.097)
-0.042
(0.132)
0.536
(0.159)
0.093
0.120
(0.100)
-0.179
(0.139)
0.032
(0.152)
0.230
0.747
0.001
0.200
0.830
-0.002
(0.119)
0.187
(0.176)
0.400
(0.211)
0.986
1.139
(0.130)
1.437
(0.164)
1.017
(0.164)
0.666
(0.173)
-
-
S-ROL
Coe¢ cient
(standard-error)
1.688
(0.135)
0.284
(0.172)
0.599
(0.168)
1.706
(0.178)
2.972
(0.201)
0.242
(0.048)
-0.804
(0.056)
p-value
0.000
0.098
0.000
0.000
0.000
0.000
0.000
-0.083
(0.043)
-0.066
(0.054)
0.225
(0.060)
0.057
0.059
(0.044)
-0.059
(0.055)
0.002
(0.061)
0.176
0.22
0.001
0.278
0.962
-0.032
(0.053)
-0.021
(0.067)
0.176
(0.079)
0.551
0.000
-
-
0.000
-
-
0.000
-
-
0.000
-
-
0.288
0.059
0.757
0.026
Observed heterogeneity
1
2
3
4
Unobserved heterogeneity
-0.024
(0.077)
Cases
495
Cases
LogLik
-1,705.18
LogLik
a Pollution impact (level) - reference category is ’Very High Degradation’
b Weekly time on sorting and cleaning waste
c Raise in annual waste fee per household
d As stated in the text, the unconstrained model failed to converge
26
0.753
495
-1,147.36
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
Table 12: Information criteria
Alternative Sub-Ranking Models
ROL
H-ROL
S-ROL
N. of parameters
16
20
17
LogLik
-1747
-1705
-1747
BIC
3612
3557
3619
CAIC
3628
3577
3636
1
observed and unobserved heterogeneity. To be more precise, when
and
were both left free, the model
2
failed to converge, although various vectors of initial values, more simple speci…cations, etc., were tested.
3
Moreover, a simple S-ROL model does not reveal any scale heterogeneity related to the alternative sub-
4
ranking data (the
5
model …ts better the alternative sub-ranking data (see Table 12).
parameter is not signi…cant). Finally, according to BIC and CAIC criteria, the H-ROL
6
At this point, it would be very interesting to assess which of the interpretations of ranking task 3 is the
7
best, using an appropriate test to compare the ROL sub-ranking and the H-ROL alternative sub-ranking
8
models. However, by construction the choice sets associated with the sub-ranking and the alternative sub-
9
ranking data are di¤erent, so that it rules out the possibility to run a test like the Vuong test (Vuong, 1989),
10
or the Clarke test (Clarke, 2007) which can both be used to assess which of two nonnested models is closer
11
to the true model, but which also both require that the models to be compared are …tted using exactly the
12
same set of response values. One relevant way to deal with the interpretation of ranking task 3 would be to
13
modify the survey design and to use a split sample approach, in order to rigorously analyze data obtained
14
from alternative formulations of "ranking task 3 like" questions. Given our survey design, and considering
15
that the sub-ranking data are not found to be heteroscedastic, we advocate that the basic ROL sub-ranking
16
model provides relevant welfare estimates. Allowing the respondents to rank freely is a good way to address
17
the ranking capability issue while at the same time collecting more information by individual.
18
6
19
Since the introduction of the rank-ordered logit model in the 1980s as an appropriate tool for analyzing
20
ranking data, the ranking capability of the respondents has been a source of concerns. Extensions of the
21
rank-ordered logit model continue to be proposed, through heteroscedastic and/or latent class models which
22
seeks to capture the implicit heterogeneous ranking capabilities of the individuals.
Conclusions
23
In this article, we propose to address the ranking capability issue through the survey design: appropriate
24
valuation and follow-up questions allow to obtain data which re‡ect the actual heterogeneous ranking capa-
25
bilities of the individuals. Taken together, the results of our analysis suggest that the scale heterogeneity,
27
W h y N o t A llo w In d iv id u a ls t o R a n k Fr e e ly ? A S c a le d R a n k -O r d e r e d L o g it A p p r o a ch A p p lie d t o W a s t e M a n a g e m e n t in C o r s ic a
1
observed and unobserved, vanishes when the respondents are left free to rank a number of alternatives which
2
is stricly in accordance with their heterogeneous ranking capabilities and their preferences.
3
We …nd that WTP estimates on the ’noisy’full-ranking data do di¤er signi…cantly from WTP estimates on
4
the accurate sub-ranking data: for instance, total WTP estimations (based on 129,000 Corsican households,
5
INSEE, 2009) for a very low impact are e1,372,560 and e442,470 respectively for full-ranking (S-ROL model)
6
and sub-ranking data (ROL model). As the acceptability of policy measures is also of great concern to public
7
decision makers, the need for reliable information is obvious.
8
Regarding waste management on the ’Island of Beauty’(Corsica), we …nd that people are not satis…ed
9
with the status quo. Homeowners and urban dwellers are found to be more willing to pay for the reduction
10
of waste externalities. We also …nd that individuals who are aware of the waste fee are more likely to accept
11
a rise in the waste fee, and hence show a greater willingness-to-pay for the reduction of waste externalities.
12
Although only 16% of the respondents stated that they knew how much they pay for waste management,
13
this …nding suggests that the fee is perceived as a legitimate tool for covering waste management costs.
14
According to our study, a rise of about 10% of the actual waste fee should be acceptable.
15
To conclude, the empirical results presented in this article may be data speci…c. However, the pro-
16
posed methodology is relevant to any ranking data and could be used to assess the advantages of recent
17
developments in the choice experiment literature, such as the best-worst preference elicitation approach.
18
19
20
21
22
23
24
25
26
27
28
29
30
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