Why scoring functions cannot assess tail properties

Motivated by the growing interest in sound forecast evaluation techniques with an emphasis on distribution tails rather than average behaviour, we investigate a fundamental question arising in this context: Can statistical features of distribution tails be elicitable, i.e. be the unique minimizer of an expected score? We demonstrate that expected scores are not suitable to distinguish genuine tail properties in a very strong sense. Specifically, we introduce the class of max-functionals, which contains key characteristics from extreme value theory, for instance the extreme value index. We show that its members fail to be elicitable and that their elicitation complexity is in fact infinite under mild regularity assumptions. Further we prove that, even if the information of a max-functional is reported via the entire distribution function, a proper scoring rule cannot separate max-functional values. These findings highlight the caution needed in forecast evaluation and statistical inference if relevant information is encoded by such functionals.Comment: 18 page

On the decomposition of Generalized Additive Independence models

The GAI (Generalized Additive Independence) model proposed by Fishburn is a generalization of the additive utility model, which need not satisfy mutual preferential independence. Its great generality makes however its application and study difficult. We consider a significant subclass of GAI models, namely the discrete 2-additive GAI models, and provide for this class a decomposition into nonnegative monotone terms. This decomposition allows a reduction from exponential to quadratic complexity in any optimization problem involving discrete 2-additive models, making them usable in practice

Do scenario context and question order influence WTP? The application of a model of uncertain WTP to the CV of the morbidity impacts of air pollution

This paper presents a general framework for modelling responses to contingent valuation questions when respondents are uncertain about their ‘true’ WTP. These models are applied to a contingent valuation data set recording respondents’ WTP to avoid episodes of ill-health. Two issues are addressed. First, whether the order in which a respondent answers a series of contingent valuation questions influences their WTP. Second, whether the context in which a good is valued (in this case the information the respondent is given concerning the cause of the ill-health episode or the policy put into place to avoid that episode) influences respondents’ WTP. The results of the modelling exercise suggest that neither valuation order nor the context included in the valuation scenario impact on the precision with which respondents answer the contingent valuation questions. Similarly, valuation order does not appear to influence the mean or median WTP of the sample. In contrast, it is shown that in some cases, the inclusion of richer context significantly shifts both the mean and median WTP of the sample. This result has implications for the application of benefits transfer. Since, WTP to avoid an episode of ill-health cannot be shown to be independent of the context in which it is valued, the validity of transferring benefits of avoided ill-health episodes from one policy context to another must be called into question