Multinomial Probit : Probability Simulators and Identification

The paper introduces four unbiased probability-simulators which produce continuous (simulated) log-likelihood functions with almost everywhere continuous derivatives. Identification conditions are derived which show that in the presence of intercepts in the latent utilities, then the shocks' variance-covariance matrix must be fixed in order to attain exact-identification. Monte Carlo simulations illustrate unbiasedness and relative efficiency of the proposed simulators and confirm the predicted under- and exact-identification of representative parameterizations. A previous study on the relation between movie attendance and violent crimes is reconsidered in the multinomial probit framework