A New Shifted Log-Normal Distribution for Mitigating 'exploding' Implicit Prices in Mixed Multinomial Logit Models

This paper introduces a new shifted negative log-normal distribution for the price parameter in Mixed Multinomial logit models. The new distribution, labelled as the u-shifted negative log-normal distribution, has desirable properties for welfare analysis and in particular a point-mass which is further away from zero than the negative log-normal distribution. This contributes to mitigating the 'exploding' implicit prices issue commonly found when the price parameter is specified as negative log-normal and the model is in preference space. The new distribution is tested on 10 stated preference datasets. Comparisons are made with standard alternative approaches such as the willingness-to-pay space approach. It is found that the new u-shifted distribution yields much lower mean marginal WTP estimates compared to the negative log-normal specification (up to 99% lower) and similar to the values derived from a multinomial logit while at the same time fitting the data as well as the negative log-normal specification and much better than the willingness-to-pay space approach