Discrete Choice Models in Preference Space and Willingness-to Pay Space

In models with unobserved taste heterogeneity, distributional assumptions can be placed in two ways: (1) by specifying the distribution of coefficients in the utility function and deriving the distribution of willingness to pay (wtp), or (2) by specifying the distribution of wtp and deriving the distribution of coefficients. In general the two approaches are equivalent, in that any mutually compatible distributions for coefficients and wtp can be represented in either way. However, in practice, convenient distributions, such as normal or lognormal, are usually specified, and these convenient distributions have different implications when placed on wtp's than on coefficients. We compare models that use normal and lognormal distributions for coefficients (models in preference space) with models using these distributions for wtp (models in wtp space). We find that the models in preference space fit the data better but provide less reasonable distributions of wtp than the models in wtp space.