Instability in mixed logit demand models

When a mixed logit demand model is used to estimate market-clearing prices, the high influence of the left tail of the random price coefficient can lead to numerical and statistical instability. I show this is an issue with any mixing distribution whose price coefficient is not bounded away from zero. I give conditions under which market equilibrium prices implied by mixed logit models exist, and show they are satisfied for lognormal mixing and some cases of truncated normal mixing. However, even when market equilibria exist, these models can be unstable and produce statistically unreliable and economically implausible conclusions.