The multi-period multinomial Probit model (MMPM) is seen as a flexible tool to
explain individual choices among several alternatives over time. There are two
versions of this model: a) for each individual the covariates for all
alternatives are known and b) for each individual only the parameters of the
alternative which was chosen is known. The main difficulty with the MMPM was
the calculation of the probability for the individual sequence of chosen
alternatives, which requires the computation of the integral over a high
dimensional multivariate Normal density. This remedy was removed by the Smooth
Recursive Conditional (SRC) simulator. Several simulation studies have
investigated the stability of the MMPM estimates with special emphasis to the
number of replications of the SRC routine. In contrast to these studies, which
use the case of alternative specific covariates, we use the case of the
individual specific covariates. We conclude that the MMPM with individual
specific covariates is only weakly identified, generalizing Keane’s (1992)
result for the one period case. As a consequence the maximization of the
simulated likelihood often converges to a singular covariance structure so
that the SRC-routine stops iterating. This feature cannot be avoided by
increasing the number of replications in the SRC-routine. The percentage of
these failures rapidly increases with the number of alternatives