Do emotions matter? Coherent preferences under anchoring and ...

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ECOLOGICAL ECONOMICS 66 (2008) 700– 711705model with anchoring effects that allows us to consider theinterdependencies between the stages in the elicitation process.That is,WTP 1 i¼ A 1 iþ e 1 iWTP 2 i¼ A 2 iþ g i B 1 iþ e 2 iwith g i a½0; 1Š 8i; i ¼ 1; 2;:::nwhere μ i k =α i k +x i k β k (k=1,2) are the linear predictors associatedwith l×1 regression parameter vectors β k and covariate vectorsx i k , α i k is the intercept term, and η i captures the potential existenceof an anchor effect of the first bid on WTP of individual i(Herriges and Shogren, 1996). The linear predictors are linked tothe probability of a positive response by a bivariate normalcumulative distribution (BVN) called the link function. Simultaneitybetween responses is captured by the lower triangle componentof Σ (e.g. σ 2,1 ). This is a model of simultaneous equationswith limited dependent variables (SLDV), which reduces to ageneral triangular system (Zellner, 1971) for complete data sets.3.1. Inconsistency in elicited preferences between answers13 Alternatively, it would allow us to increase the precision of theestimates (lower variance) holding sample size constant.14 The inconsistency between first and second responses leads tothe rejection of the maintained assumption of the restricteddouble bounded model (Hanemann et al. 1991) that the mean andvariances are constant across both bounds, and that the correlationcoefficient between the standard errors is equal to one,which essentially means that WTP i 1 =WTP i 2 . The rejection of thishypothesis implies a reduction in the efficiency gains of thedouble bounded elicitation procedure.15 The number of bounds can be increased successively in theelicitation process, leading to what has been denominated thetriple bounded dichotomous choice model (Langford et al. (1996).Cooper and Hanemann (1995) and Scarpa and Bateman (2000)showed that the efficiency gains are likely to diminish when thenumber of binary steps in the elicitation process is increased.ð1ÞThe main advantage of DBDC over SBDC is that the formerprovides more information on individual's preferences. Hanemannet al. (1991) showed that it leads to more efficient welfareestimates. This additional information may potentially allowthe researcher to conduct studies at a lower cost (smaller samplesizes) while holding the precision of the WTP estimates constant(same variance). 13 However, the DBDC has been questionedbecause of the empirical support to the argument that thedistribution of WTP is incoherent between both steps (e.g. Greenet al., 1998; Cameron and Quiggin, 1994). 14 In other words, themean or median WTP estimated using responses to the firstvaluation question differs empirically from the one estimatedusing the responses to the second question. 15The presence of potential behavioral responses to the followupquestion has been argued in non-market valuation as theprimary explanation of the incoherency between DBDC andSBDC (Alberini, 1995; Carson et al., 2001; Burton et al., 2003;DeShazo, 2002; Bateman et al., 2001). Innovative efforts to modeleconometrically some of the reactions to the second bid offeredcan be found in Cameron and Quiggin (1994), Herriges andShogren (1996), Alberini et al. (1997), Whitehead (2002), Flachaireand Hollard (2006) and Araña and León (2007). Theargumentscommonly raised for explaining these behavioral responsesinclude anchoring effects, strategic behavior, yea-saying, neasaying,uncertainty cost, weighted average, bargaining, guilty/indignation and quality/quantity shift, among others. Forsimplicity, in this paper we focus on the anchoring effects,which can be seen as a general cognitive heuristic implicitlylinked to other behavioral responses.3.2. Anchoring effectsAn empirical result of the DBDC is the fact that, in follow-upquestion the distribution function of WTP could be influencedby precedent stage, implying some type of anchoring effect orbehavioral process (e.g. Herriges and Shogren, 1996; Aadlandand Caplan, 2004). In a general setting, Tversky and Kahneman's(1974) describe the anchoring effect as “the process inwhich people make estimates by starting from an initial valuethat is adjusted to yield a final answer.”Following previous models of DBDC (Herriges and Shogren,1996; Whitehead, 2002), our model collects the influence of thestarting bid amount on WTP in the term η i B i1 . Parameter η imeasures the importance of the anchor effect of the first bidon WTP at an individual level. Thus, the anchoring effecthypothesis may be tested for each individual of the sample byconsidering these two alternatives: H 0 : η i =0; and H 1 : no H 0 .3.3. The econometric modelIn order to estimate the model, we utilize a Bayes approach(Chib, 1992; Albert and Chib, 1993), similar to the one applied byAraña and León (2005). 16 This approach has basically three mainadvantages over standard maximum likelihood estimation: i) itallows for more flexibility and unobserved heterogeneity in themodel through the random parameters specification; ii) itallows for an easy and efficient comparison between modelsthrough the use of the Bayes Factor; iv) it relies on an exacttheory of probability even with small samples, leading to moreaccurate results in this context. The detailed description of theeconometric model and the components of the Bayesianapproach are explained in detailed in the Appendix A.4. ResultsThe estimation of the simultaneous equation model outlinedin the previous section is particularly intended to raise furtherevidence on the anchoring effects produced by the first bidprices offered in the double-bounded dichotomous choicemodel. Although this model centers on anchoring effects, thedata collected in our field experiment also allows us toinvestigate i) the potential relationships between anchoringeffects and the emotional state of the individual, and ii) thepotential relationships between anchoring effects and thescope of the environmental good to be valued, as represented16 In order to test the sensitivity of the results to the econometricapproach, maximum likelihood estimations of a bivariate probitmodel have been carried out. The results show no significantdifferences in terms of the hypotheses proposed in this study.The sensitivity analysis results, data set and the GAUSS programcodes for the Bayesian estimation are available from the authorsupon request.
706 ECOLOGICAL ECONOMICS 66 (2008) 700– 711Table 1 – Estimation results of Bayesian bivariate modelsfor a naïve and anchored individual (posterior standarddeviations in parentheses)Naïve model Anchored modelIntercept 18.9460(4.5615)EIS 12.9748(0.8970)Age −0.2461(0.0463)Log (KIL) 5.1005(1.7401)EDU 0.4274(0.1714)INC 0.0062(0.0018)β 1 β 2 β 1 β 20.7664(3.6249)15.0844(0.6515)−0.2005(0.0353)7.1897(1.3784)0.5997(0.1259)0.0030(0.0014)18.8234(4.4138)12.9463(0.8947)−0.2450(0.0446)5.0873(1.7373)0.4333(0.1683)0.0063(0.0018)0.7878(3.5954)15.0560(0.6486)−0.2006(0.0351)7.1883(1.3571)0.6005(0.1288)0.0030(0.0014)BID 1 – – – 0.2694(0.0379)σ1 13.0619 (0.5807) 13.0302 (0.5603)σ2 11.0802 (0.6310) 11.0647 (0.6313)σ21 70.4236 (8.2962) 59.6298 (10.3180)Mean WTP 19.18 [18.43, 19.98] 19.16 [18.37, 20.01]Marginal likelihood −1113.97 −1057.26by the number of kilometers to be rehabilitated in the policyprogram presented in the market construct.Table 1 shows the estimation results for the simultaneousequation model for two alternative assumptions. Under thenaïve assumption, we omit the bid price from the first response(B i 1 ). Here the anchoring effects are not modeled (Whitehead,2002). The second assumption explicitly considers the bid priceof the first question in the equation for the second response.Anchoring effects as induced by the first bid offered are relevantin this application, as is evident by the significance of the firstbid price in the second equation. This result has been obtainedin most applications of the double-bounded dichotomouschoice format (e.g. Green et al., 1998).The results in Table 1 show also the relevance of some otherexplanatory variables that are significant in explaining WTP atboth stages of the elicitation process. WTP rises with income(INC) and the years of education (EDU), while decreases with theage of the individual (AGE). The significance of these explanatoryvariables can be interpreted as giving support to the constructvalidity of the contingent valuation study that was designed tovalue the rehabilitation of a network of walking paths.But for our purposes, the main variables of interest in theoutput regression of the bivariate model are the emotionalintensity scale (EIS) and the logarithm of the number ofkilometers presented in the valuation task of the contingentvaluation scenario (KIL). 17 These variables are both significantat the 95% level, supporting the following two empiricalresults:logarithmic: when the number of kilometers of the walkingpaths network was increased, mean WTP also increased,but at a decreasing rate. Thus, the scope effect or theabsence of sensitivity to the dimensions of the good to bevalued can be rejected for this particular application.2. The emotional state of the individual played a significantrole on the elicited values of the environmental good inquestion. This relationship was positive, i.e. the higher theemotional state the large becomes WTP.Even though these variables are important for explainingWTP at an aggregate level, they can be also related to thedegree of anchoring which is likely to be found in theelicitation mechanism of the DBDC model. Thus, let usconsider the relationships between the anchoring effectsand i) the scope effect, and ii) the state of emotional loadfacing the individual.4.1. Scope and anchoring effectsIn order to ascertain whether scope effects are also present forthe various anchoring bids utilized in the experiment, Table 2reports the mean WTP for the subsamples of the lowest andhighest bids utilized in the first dichotomous choice question.It can be seen that the size of the walking paths network has asimilar influence on WTP across the lowest and highest bidsoffered to the individuals. This result is similar to the onefound by Ariely et al. (2003) in what these authors called“coherent arbitrariness”. That is, although preferences arelikely to be influenced by initial anchors or bids, they can becoherent in economic terms for the different dimensions ofthe good to be valued. 18However, the scope effect giving support to the coherenceof preferences under anchoring, could be dependent on theemotional status of the individual facing the task of valuingdifferent dimension of a given good. Thus, this potentialrelationship would raise the need to consider the role ofemotions in both the anchoring and scope effects.4.2. Emotional load and anchoring effectsThe extent of the anchoring effects can be also influenced bythe emotional status of the individual. In general, thishypothesis implies that the cognitive aspects of the valuationtask, i.e. the commonly found recurrence to some anchor inorder to base a valuation response, can be influenced by theemotional aspects involved. As can be seen in Table 3, theparameter of the anchoring effect η i is related with the level ofemotional load posed by the individual in the valuation task.The relationship between the anchor parameter η i and theEIS is depicted in Fig. 2. Low and high values of EIS correspondwith significantly high levels of anchoring. This relationship is1. There was significant sensitivity of WTP to the size of theenvironmental good being offered. This relationship was17 After testing for the validity and reliability of the EIS, the PCAreported that a model with only one factor provide the mostsatisfactory solution (e.g. reported Cronbach's alpha was 0.92).18 Ariely et al. (2003) found coherent preferences within individuals,i.e. by asking an individual about various dimensions of agiven good. Since we used split samples for the sizes of thewalking path network, our results can be interpreted as supportingcoherent preferences at an aggregate level, rather than at anindividual one, i.e. at a social welfare function rather than atindividual utility functions.
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