The Role of Constants in WTP Computation
S Hess, ITS, University of Leeds,UK; A Daly, ITS, University of Leeds/RAND Europe, UK; D Hensher, University of Sydney, AU; T Adler, Resource systems Group Inc. US
This paper discusses the role of constants in the computation of WTP measures
Analysts occasionally include dummy terms in a utility specification for alternatives that are in some way different from the remaining alternatives. Common examples include a constant for status quo alternatives, a constant for toll roads (in the case of studies looking at the choice between tolled and untolled options), or a constant for the least expensive alternative (sometimes used in abstract time money trade-offs). In the case where the status quo alternative is a no-fee option, as is often the case in environmental economics studies, the status quo constant additionally plays the role of a free alternative dummy, alongside capturing inertia.
The argument for including toll road dummies or constants for the least/most expensive alternative is that they capture opposition to certain types of alternatives that would otherwise lead to bias in the estimates for the marginal utility coefficients. For toll roads, the constant may also represent effects that are not explicitly included in the utility functions such the inconvenience of stopping at toll plazas or the need to arrange payment for electronic or video tolling. The inclusion of these constants is often supported by high levels of statistical significance. This paper makes the case that their inclusion in the models may conversely lead to bias in the willingness to pay (WTP) measures when not properly accounted for in the WTP calculations.
Indeed, analysts using specifications that include such dummy terms still commonly rely on the simple ratio between the marginal time and cost coefficients when calculating the WTP, even though the value of the dummy (i.e. 0 or 1) is in fact a function of the cost attribute. This equates to an assumption that the dummy term captures only behaviour that would otherwise bias the estimate of the marginal cost coefficient and that this remaining marginal cost coefficient captures all the marginal cost sensitivity.
This is however far from certain. Imagine the case where the interaction between the cost coefficient and the cost attribute is in some way misspecified, for example if the non-linearity in the marginal sensitivities is not captured correctly, or if an incomplete or inaccurate treatment of taste heterogeneity is used (or none at all). It is then conceivable that some of the sensitivities would in fact be captured by the dummy term and the use of the standard WTP calculation would be incorrect. This is especially likely in the case where the inclusion of the dummy variable leads to a strong decrease in marginal cost sensitivity.
Now imagine the case where we have a constant for a free status quo alternative, or a constant for the cheapest option, or a constant for any untolled options. This constant would capture strategic bias against the charged options that would otherwise affect the estimation of the cost coefficient. But similarly, it may in fact capture that part (or all) of the cost sensitivity which relates to the increase from the cheapest (possibly free) alternative to the next least expensive option, with the estimated marginal utility coefficient only dealing with differences between the remaining alternatives. On the other hand, the marginal utility coefficients for the remaining coefficients will still capture the entire variations in those attributes.
The paper shows that the issue in practice is that it is impossible to know what parts of the effects captured by the dummy relate to factors that would otherwise have biased the cost sensitivity upwards and what parts relate to actual cost sensitivity, thus biasing the remaining cost coefficient. We highlight the need for a flexible specification of the utility function to make sure that any dummies aimed at capturing strategic behaviour are not in fact capturing sensitivities that should enter the WTP calculations. We also discuss the possibility of formally modelling extremeness aversion via a contextual concavity model, which takes the attribute value with the lowest part-utility as the reference point and codes the utility of other attribute values as gains against the reference.
Association for European Transport