The stability of simulation based estimation of the multiperiod multinominal probit model with individual specific covariates

Abstract

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.