A new empirical approach for mitigating exploding implicit prices in mixed multinomial logit models

Abstract

This paper introduces a new shifted negative log-normal distribution for the price parameter in mixed multinomial logit models. The new distribution, labeled as the μ-shifted negative log-normal distribution, has desirable properties for welfare analysis and in particular a point mass that 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 five stated preference datasets. Comparisons are made with standard alternative approaches such as the willingness-to-pay (WTP) space approach. It is found that the μ-shifted distribution yields substantially lower mean marginal WTP estimates compared to the negative log-normal specification and similar to the values derived from models estimated in WTP-space with flexible distributions, while at the same time fitting the data as well as the negative log-normal specification.