Representation of Taste Heterogeneity in Willingness-to-pay Indicators Using Parameterization in Willingness-to-pay Space

Representation of Taste Heterogeneity in Willingness-to-pay Indicators Using Parameterization in Willingness-to-pay Space


S Hess, IVT-ETH Zurich, CH; S Mabit, Technical University of Denmark, DK; S Caussade, Steer Davies Gleave, CL


This paper discusses issues involved in the specification of taste heterogeneity in willingness-to-pay indicators such as the valuation of travel time savings


The calculation of willingness-to-pay (WTP) indicators such as the valuation of travel time savings (VTTS) is one of the most important topics in discrete choice analyses, and the resulting indicators are of crucial importance to transport policy appraisal. Given the significant social and financial considerations in largescale transport schemes, a high level of precision is required in the computation of such indicators. Under the purely hypothetical assumption of a homogeneous population, this can be guaranteed through the use of high-quality data and a detailed model specification. However, in practice, there will be significant variations in sensitivities, and hence WTP indicators, across respondents, and these need to be taken into account. While this has been known all along, and while a number of authors have recently provided in-depth discussions of this issue, there is still a general lack of consensus, and many basic mistakes continue to be made in practice.

Particularly, existing research has often simply looked at the issue from a theoretical perspective, or compared two or three approaches for representing taste heterogeneity in a basic example. What is needed is a largescale comparison of the different approaches, across a host of datasets, including simulated as well as real-world data. This is the topic of the present paper, which also provides a detailed review of existing techniques, and aims to give guidance for good practice.

Existing treatments of taste heterogeneity fall into three main categories, namely (in order of increasing complexity) a) discrete segmentations, b) continuous interactions and c) random variations.

Discrete segmentations form the most basic approach for representing variations in sensitivities across respondents. While straightforward to apply, they lack flexibility as they still assume homogeneity within groups. Additionally, there is the issue of defining the groups, which can be very arbitrary in the case where continuous measures such as income are split into discrete segments.

Continuous interactions can be used to allow for a variation in a given sensitivity as a function of a continuous socio-demographic measure such as income. While offering much more flexibility than discrete segmentations, continuous interactions impose greater estimation cost, and are only used sparsely in practice.

The gains in popularity of mixture models such as Mixed Multinomial Logit (MMNL) have meant that modellers increasingly rely on a purely random representation of taste heterogeneity. While offering very high flexibility, the resulting model structures are not only costly to estimate, but also lead to a number of specification issues, such as the choice of random distribution. While the issue of a choice of distribution does not arise in the case of discrete mixture models, there is now the problem of deciding on a number of support points to be used. Finally, in both cases, there are big issues in interpretation, as it is, without a posterior analysis, not possible to link the taste heterogeneity to socio-demographic information.

The differences in the level of complexity of the three main approaches arise not only in the specification and estimation stages, but also extend to the calculation of WTP measures. Indeed, in the case of deterministic segmentations, the WTP measures can simply be obtained on the basis of a ratio of fixed parameter estimates. In the presence of continuous interactions, these interactions need to be involved in the calculation of the measures. Finally, with the use of mixture models, the measures will often have to be simulated on the basis of a ratio of two randomly distributed coefficients, where special care is required in the case of correlated coefficients. Worryingly, many modellers still make the trivial mistake of calculating WTP indicators simply as the ratio of the means of two randomly distributed coefficients, potentially leading to very biased indicators.

To some extent, the above issues, especially in the case of mixture models, can be alleviated by working directly in WTP space (or log-WTP space) as opposed to preference space. As such, the WTP measures are estimated directly from the models, avoiding a calculation on the basis of independently estimated coefficients. However, while potentially avoiding significant amounts of bias, these approaches are still only used very sparingly.

After an in-depth discussion of the above issues, which also looks at how findings in terms of taste heterogeneity can be masked by the presence of unexplained non-linearities or unmodelled attributes, the paper presents a number of different case studies to support the theoretical claims. The case studies make use of various real-world datasets, including official VOT datasets from a number of European countries, as well as a set of custom-generated synthetic datasets. While the objectives differ slightly depending on the nature of the data, the various case studies all present a comparison of the results in terms of variations in the WTP indicators depending on the treatment of taste heterogeneity, the base specification of the utility function and the decision to work in WTP or preference space. Preliminary results not only support the theoretical claims of the paper in showing significant differences in WTP indicators across modelling approaches, but importantly also indicate significant differences in the conclusions across the various datasets and scenarios used. This not only validates the decision to use a systematic comparison across a large number of datasets but also shows that it is difficult to provide generic guidance other than to advise modellers to use as flexible a modelling approach as possible in conjunction with as a detailed a utility specification as possible.

In closing, the paper also briefly looks at the implications of the results on policy appraisal, such as cost-benefit analysis. Here, it has occasionally been argued that, while different modelling approaches will produce different WTP measures (mean as well as spread), these differences will not actually lead to differences in the conclusions of cost-benefit analyses, and hence different policy decisions. Here, our results are used in conjunction with a few basic hypothetical examples to show the potential extent in the differences in cost-benefit analyses. Again, preliminary results show significant differences which clearly warrant further investigation and show the benefits of using advanced modelling approaches.


Association for European Transport