Efficient estimation of probit models with correlated errors

Maximum Likelihood (ML) estimation of probit models with correlated errors typically requires high-dimensional truncated integration. Prominent examples of such models are multinomial probit models and binomial panel probit models with serially correlated errors. In this paper we propose to use a generic procedure known as Efficient Importance Sampling (EIS) for the evaluation of likelihood functions for probit models with correlated errors. Our proposed EIS algorithm covers the standard GHK probability simulator as a special case. We perform a set of Monte Carlo experiments in order to illustrate the relative performance of both procedures for the estimation of a multinomial multiperiod probit model. Our results indicate substantial numerical efficiency gains for ML estimates based on the GHK–EIS procedure relative to those obtained by using the GHK procedure.