STATISTICAL-INFERENCE IN THE MULTINOMIAL MULTIPERIOD PROBIT MODEL

Statistical inference in multinomial multiperiod probit models has bee n hindered in the past by the high dimensional numerical integrations necessary to form the likelihood functions, posterior distributions, o r moment conditions in these models. We describe three alternative est imators, implemented using simulation-based approaches to inference, t hat circumvent the integration problem: posterior means computed using Gibbs sampling and data augmentation (GIBES), simulated maximum likel ihood (SML) estimation using the GHK probability simulator, and method of simulated moment (MSM) estimation using GHK. We perform a set of M onte-Carlo experiments to compare the sampling distributions of these estimators. Although all three estimators perform reasonably well, som e important differences emerge. Our most important finding is that, ho lding simulation size fixed, the relative and absolute performance of the classical methods, especially SML, gets worse when serial correlat ion in disturbances is strong. In data sets with an AR(1) parameter of 0.50, the RMSEs for SML and MSM based on GHK with 20 draws exceed tho se of GIBES by 9% and 0%, respectively. But when the AR(1) parameter i s 0.80, the RMSEs for SML and MSM based on 20 draws exceed those of GI BES by 79% and 37%, respectively, and the number of draws needed to re duce the RMSEs to within 10% of GIBES are 160 and 80 respectively. Als o, the SML estimates of serial correlation parameters exhibit signific ant downward bias. Thus, while conventional wisdom suggests that 20 dr aws of GHK is 'enough' to render the bias and noise induced by simulat ion negligible, our results suggest that much larger simulation sizes are needed when serial correlation in disturbances is strung. (C) 1997 Elsevier Science S.A.