A new approach to specify and estimate non-normally mixed multinomial probit models

The current paper proposes the use of the multivariate skew-normal distribution function to accommodate non-normal mixing in cross-sectional and panel multinomial probit (MNP) models. The combination of skew-normal mixing and the MNP kernel lends itself nicely to estimation using Bhat’s (2011) maximum approximate composite marginal likelihood (MACML) approach. Simulation results for the cross-sectional case show that our proposed approach does well in recovering the underlying parameters, and also highlights the pitfalls of ignoring non-normality of the continuous mixing distribution when such non-normality is present. At the same time, the proposed model obviates the need to assume a pre-specified parametric distribution for the mixing, and allows the estimation of a very flexible, but still parsimonious, mixing distribution form.

► The mixed MNL model has been widely used, with a normal continuous mixing distribution.
► Non-normal continuous mixing is important to consider, but leads to estimation difficulties.
► We combine an MNP kernel with skew-normally distributed mixing to consider non-normality.
► The resultant model lends itself nicely to MACML estimation.
► The proposed model is a completely new way of introducing non-normal mixing.