Simulated classical tests in the multiperiod multinomial probit model

This paper compares different versions of the simulated counterparts of the Wald test, the score test, and the likelihood ratio test in the multiperiod multinomial probit model. Monte Carlo experiments show that the simple form of the simulated likelihood ratio test delivers the most favorable test results in the five-period three-alternative probit model considered here. This result applies to the deviation of the frequency of type I errors from the given significance levels as well as to the frequency of type II errors. In contrast, the inclusion of the quasi maximum likelihood theory into the simulated likelihood ratio test leads to substantial computational problems. The combination of this theory with the simulated Wald test or the simulated score test also produces no general advantages over the other versions of these two simulated classical tests. Neither an increase in the number of observations nor a rise in the number of random draws in the considered GHK simulator systematically lead to a more precise conformity between the frequency of type I errors and the basic significance levels. An increase in the number of observations merely reduces the frequency of type II errors.