Approximation and Simulation of the Multinomial Probit Model: An Analysis of Covariance Matrix Estimation

The multinomial probit (MNP) model is a primary application for combining simulation with estimation. Indeed, McFadden (1989) featured the MNP model in his seminal paper. As random utility model, the MNP model offers a highly desirable flexibility in substitution among alternatives that its chief rival, the multinomial logit model, fails to possess. The unrestricted character of the variance matrix in the multivariate normal distribution that underlies probit cannot be produced by logit, even in its generalized extreme value forms. As experience with the MNP model has developed recently, researchers have developed an appreciation for the practical difficulties that estimation with simulation presents. McFadden & Ruud (1994) give a general description, analyzing some of the generic problems with the methods of simulated moments and maximum simulated likelihood. In this paper, we draw on their analysis to develop a new estimation strategy for the MNP model based on the method of simulated moments. ∗I am indebted to Kenneth Train for discussions about many topics related to the material in this paper. He helped me particularly with the history of the random parameters logit model. He has not even seen this paper yet, so he cannot be held responsible for its contents.