Multinomial probit model estimation: computational procedures and applications

The multinomial probit (MNP) model offers a rather general and flexible framework for the analysis of discrete choices obtained from panel data and the specification of models with general error structures. However, this flexibility of specification has come at a relatively high price in terms of difficulty of computing maximum likelihood estimates ofthe model parameters and evaluating the associated choice function. This paper presents a new procedure for the estimation of MNP models, motivated primarily by the advances that have taken place in terms of computing environments and capabilities. The procedure derives its efficiency from execution in a parallel computing environment (CRAY YMP/8) and its accuracy from the use of better (but otherwise more computationally intensive) mathematical procedures. The paper also discusses and compares alternative nonlinear optimization procedures to search for the parameter values that maximize the likelihood function, in connection with Monte Carlo evaluation of the likelihood of each observation. The results are also compared to those obtained using the Clark approximation to evaluate the choice probabilities. (A)