Identifying determinants of willingness to pay

The following section analyses the predictors determining variation in WTP for an increase in Germany’s wolf population. The analysis is based on the theoretical framework developed in Chapter 4 and the methods described in Section 5.4. H1 will be tested on the basis of the first mixed effects model and H2 will be tested by means of the second mixed effects model. Further, the analysis of determinants of WTP will provide insights about H4 with regards to the role of attitudes (note that the role of non-utilitarian and non-consequentialist preferences will be analysed based on the motives).

Table 6-6 presents the regression results of the between-group design.³³ The first column reports the predictor variables (Predictors), followed by the estimated coefficients (Coef.), the associated standard errors (SE), 95% confidence intervals (95% CI), t-statistics (t) and p-values (p). As discussed earlier, the dependent variable (WTP) was log-transformed. Therefore, the last column reports the back-transformed estimated coefficients (back-transf. coef.) representing the proportional change (%) in WTP for each coefficient, all other things being equal. The bottom part of the table summarises measures related to the random effects: the total variance explained by the model (σ²), the variance explained by the random effects (σ²id_group), the ICC, the number of groups (Nid_group), the number of overall observations, the marginal R² (𝑅_𝑚²) and the conditional R² (𝑅_𝑐²). Multicollinearity was not a concern as the VIFs were far below the benchmark of five.

The marginal R² is quite considerable for a contingent valuation study implying that the fixed effects explain almost 53% of variation in WTP. Yet, many predictor variables turned out to be insignificant. In comparison to the predictor variables, the grouping structure was of relatively low importance as suggested by the slightly larger conditional R² (0.556) compared to the marginal R² (0.526) andthe relatively low ICC (0.06). The latter shows that only six percent of the variation in WTP is explained by belonging to a specific group, hence group effects did not play a severe role.

33 Only the robust regressions results will be presented in the following.

Table 6-6 WTP robust mixed effects model regression results: between-group design

In the following, the discussion of predictors follows the categorisation of predictors outlined in the methods (see again Section 5.4.2.7, Table 5-5). Thus, the four relevant categories are:

study design; socio-demographics; connectedness and usage; and attitudes, perception and knowledge.

To begin with, the signs of the significant variables are as expected apart from one exception (att_w_8). All predictors which relate to the experimental design (PE, PM and stage) appear to be insignificant. The non-significance indicates that no significant difference in mean WTP exists between the three valuation methods, implying that the three treatment interventions (citizen-framing, deliberation and moralisation) had no significant effect on WTP in terms of absolute magnitude.

Based on these results, H1 stating that significant differences between the three valuation methods exist cannot be confirmed.

Turning to socio-demographic predictors, mean WTP was more than twice as high for urban residents (urban.residence). Yet, it barely did not achieve the conventional five percent level of significance but is only significant at the ten percent level (p = 0.052). Also donating within the last 12 months (donation) increased mean WTP by 93.5%, being highly significant.

Ownership of a hunting license (either personally or in the household) (hunter) roughly halved mean WTP (significant at five percent level). Dog ownership (dog) was highly significant and WTP was more than twice as high, all other things being equal. Regarding gender (female serving as benchmark) a trend can be seen that mean WTP was around two-thirds smaller for diverse participants, although only significant at a ten percent level. The predictors age and income which are usually expected to determine WTP are non-significant in this study which may be caused by the low variability in both variables due to the experimental design of the study.

Analysing the next category of predictors (connectedness and usage), usage appeared to be irrelevant, whereas reported Inclusion of Nature in Self (INS) is significant at a one percent level. Yet, the effect size (~20% increase) is among the lowest of all significant predictors.

Subjective connectedness to society at large (ICS) was insignificant.

Several predictors referring to attitudes proved significant. The most dominant was the support of establishment of wolves close to the own place of residence implying that participants do not have a NIMBY attitude. This predictor (nimby – no) is highly significant and shows that WTP

is four times higher compared to the case that a NIMBY attitude is held. At a first glance this increase of 405% seems to be quite high, yet, it should be considered that participants having a NIMBY attitude are likely to have a zero or relatively low WTP. Hence, this high proportional increase does not seem unrealistic. In addition, being unsure about the establishment near one’s own residence proved significant at a five percent level and mean WTP was more than twice as high compared to participants with NIMBY attitude. From the set of predictors based on attitudes towards animal species in general (pref_animal and att_sc_1 – att_sc_6) only two turned out to be significant. First, having a strong preference for protection of rare animal species (pref_animal) proved to have a significant effect on WTP with a proportional change of almost 88%. Second, attitudes towards existence rights of animals (att_sc_6) was significant and led to a relative change of 38% in WTP. While the attitude towards wolves as threat for other native species (att_w_8) was expected to have a negative sign, it turned out to have a slight positive effect, although it just did not meet conventional statistical significance (p = 0.053). This may be explained by perceiving this threat as not necessarily negative but as contribution to the natural balance when wolves contribute to nature-management which is usually conducted by forest rangers and hunters.

Half of the specific attitudes towards wolves were significant while the predictors’ directions differ. Attitude towards (or perception of) wolves as beneficial for humans (att_w_4) and attitude towards (or perception of) wolves as competitors for hunters (att_w_5) proved significant at a five percent level. The proportional change of WTP for these predictors is relatively small (13% and 20%) in comparison to other predictors. Surprisingly the predicted sign of att_w_5 is positive. This may be explained by a tendency of negative attitude towards hunting as sport which was occasionally voiced in the group discussions. Highly significant was the measure of attitude towards (or perception of) the historic extinction of wolves (att_w_3), as expected the predicted sign is negative and the proportional change is around 32%. Although this measure is significant, the according general attitude towards mastery of nature in order to meet human needs (att_sc_3) was insignificant. Also, the correlation plot (Figure 6-11) indicates a relatively low correlation between these two predictors (0.12).

Furthermore, the attitude toward impossibility of coexistence of humans and wolves (att_w_1) had a significant negatively effect on mean WTP with a proportional change of 17.3%.

In addition to the full model, two reduced models were estimated. These models also contain the primary variables of interest regarding the method comparison or rather experimental design (PE, PM and stage). Besides these three variables, one submodel contains only the socio-demographic predictor variables (robust model 1 socio) and the other one includes only the predictor variables associated with attitudes, perception, knowledge and connectedness, and usage (robust model 1 attitude).

Source: Own illustration

Only significant correlations with a significance level of p = 0.05 are shown.

Figure 6-11 Correlation plot of numeric predictor variables

Table 6-7 reports the comparison of these models containing the coefficients estimates (Coef.), the standard errors (SE), level of significance (p), the total variance explained by the model (σ²), the variance explained by the random effects (σ²id_group), the ICC, the number of groups (Nid_group), the number of overall observations, and the marginal R² (𝑹_𝒎^𝟐) as well as the conditional R² (𝑹_𝒄^𝟐).³⁴

Overall, the reduced models appear consistent with the full model. Yet, surprisingly income has a negative predicted sign in the socio-demographic submodel, while it was non-significant in the full model. Usually WTP is positively related to income and wealth. In this study this may not hold because firstly, the sample is not representative but was aimed to be homogenous, and secondly, the environmental good may also be perceived as environmental bad. Although, negative perception may be independent of income, the correlation plot (see again Figure 6-11) shows that income is positively correlated with negative attitudes towards wolves. To be precise, income is positively correlated with the attitudes that wolves are a hazard to humans (att_w_6) and a threat for other native species (att_w_8). Further, income is negatively correlated with the consideration of wolves as competitors for hunters (att_w_5) which was found to have a positive effect on WTP. Additionally, income is positively correlated with the general attitude that nature should be mastered to meet human needs (att_sc_3) which was found to have a negative effect on WTP, although insignificant. These correlations further explain the insignificance of the income predictor in the full model, as att_w_5 is significant at the five percent level and att_w_8 at the 10 percent level (almost five percent).

More interestingly, the comparison illustrates that the explanatory power of the attitude model (𝑅_𝑚² = 0.41) is substantially higher than the socio-demographic model (𝑅_𝑚² = 0.16). Hence, variables normally associated with WTP are less important in this model. Yet, this finding should not be overly emphasised, as the socio-demographics were supposed to be relatively homogeneous due to the experimental design. Thus, it would have been surprising if the small variance in socio-demographics had explained a large amount of total variation. Still, the amount of variation explained by the attitude model is considerably high for a valuation study.

Hence, the high relevance of predictors associated with attitudes confirms H4.

34 See Table D-3 and Table D-4 in Appendix D – Supplementary regression results for the complete regression tables of the reduced models, which also report 95% confidence intervals, t-statistics and back-transformed estimated coefficients.

Table 6-7 Comparison of full model’s and submodels’ regression results: between-group design

Robust model 1 Robust model 1 socio Robust model 1 att.

Predictors Coef. SE p Coef. SE p Coef. SE p

Table 6-8 compares the regressions results of the (non-robust) full model, the reduced stepwise regression following the Backward Elimination algorithm and the robust regression.³⁵ In the stepwise results and the robust results, the standard errors are slightly smaller compared to the non-robust full model. Still, the latter suffers from heteroscedasticity. Hence, the results are non-reliable. As mentioned above, the robust mixed effects model does not allow for calculation of log-likelihoods. Thus, the stepwise regression is based on the non-robust full model which suffers from heteroscedasticity. Therefore, also the stepwise regression results should be treated with care, considering also the general criticism of stepwise regressions discussed in Section 5.4.2.

Overall, the stepwise model and the robust model appear consistent, although some deviations exist. The biggest difference between the models appear to be two predictor variables (att_w_1 and att_w_4) that were eliminated in the Backward Elimination process but are significant at the five percent level in the robust model. Further, the NIMBY attitude at level maybe is significant in the robust regression but not in the stepwise model. In contrary, the predictor farmer is significant in the stepwise regression but not in the robust regression. Regarding group specific effects, the ICCs and variance components (σ²id_group) show that in the robust regression the effect size is halved compared to the stepwise model and non-robust model. Also, the residual variance (σ²) is notably smaller.

Still, the comparison illustrates that the differences between the models appear to be minor and may be caused by the presence of heteroscedasticity and potentially influential observations (outliers) in a relatively small sample. For these reasons the robust regression was applied and considered to be most reliable. The comparison confirms overall findings, while the robust regression is more powerful and explains around ten percent more of the total variation in WTP compared to the non-robust regression and the stepwise regression.

35 See Table D-5 in Appendix D – Supplementary regression results for the complete regression table of the reduced stepwise model, which also reports 95% confidence intervals, t-statistics and back-transformed coefficients.

Table 6-8 Comparison of full model’s, stepwise models’ and robust model’s regression results: between-group design

Turning to the analysis of the second model, the regression results of the within-group design are presented in Table 6-9.³⁶ The first column reports the predictor variables (Predictors), followed by the estimated coefficients (Coef.), the associated standard errors (SE), 95%

confidence intervals (95% CI), t-statistics (t), p-values (p) and lastly the back-transformed estimated coefficients (back-transf. coef.). At the bottom of the table measures related to the random effects are summarised: the total variance explained by the model (σ²), the variance explained by the individual-specific random effects (σ²id:id_group) and the group-specific random effects (σ²id_group), the overall ICC and group-specific ICC (ICCid_group), the number of groups (Nid_group) and number of individuals (Nid), the number of overall observations, and the marginal R² (𝑅_𝑚²) and conditional R² (𝑅_𝑐²). Again, multicollinearity was not a concern.

The marginal R² illustrates that the within-group design models’ fixed effects explain around 54% of variation in WTP. Although, only five predictors are significant at the five percent level and three at the ten percent level. The conditional R² appears to be very high with 99.7%

explained variance. So, does that imply any concerns about the model? To answer that question both the random effects as wells as the fixed effects have to be analysed and set in context. The variance explained by the random effects (σ²id:id_group and σ²id_group) and the associated ICC measures illustrate that groups did not have any effect on change in WTP “within” individuals.

Instead, the individual effects are of importance and the stated measurements at the second stage are highly dependent on the ones stated at the first stage.

As mentioned above most of the fixed effects were proven to be insignificant. Most interestingly one interaction of the variables associated with the experimental design is significant at the one percent level: PM:stage. The significant interaction of the deliberative valuation method Preference Moralisation and the stage dummy implies that this method had a significant effect on WTP at the second elicitation. In contrast, Preference Economisation did not have a significant effect on WTP. In case of a significant effect, the predictor stage would have been significant. Nevertheless, the moralisation interventions’ effect is relatively weak, the back-transformed coefficient suggests a relative change in WTP of only 7.3%.

The results suggest that H2 can be confirmed in case of PM but not in case of PE.

36 Again, only the robust regression’s results will be presented in the following.