Simulated z-Tests in Multinomial Probit Models

Within the framework of Monte Carlo experiments, this paper systematically compares different versions of the simulated z-test (using the GHK simulator) in oneand multiperiod multinomial probit models. One important finding is that, in the flexible probit models, the tests on parameters of explanatory variables mostly provide robust results in contrast to the tests on variance-covariance parameters. Overall, neither the amount of random draws in the GHK simulator nor the choice of a certain version of the simulated z-test have a strong influence on the test results. This finding refers to the conformity between the shares of type I errors and the basic significance levels as well as to the number of type II errors. In contrast, the number of type II errors in the simulated z-tests on variance-covariance parameters is reduced by increasing the sample size. Effects of misspecifications on simulated z-tests only appear in the multiperiod multinomial probit model. In this case, the inclusion of the concept of the quasi maximum likelihood theory in the simulated z-test provides comparatively more favourable results. ∗I would like to thank Axel Börsch-Supan, Elke Eberts, Angelika Eymann, Klaus Winckler and Thomas Zwick as well as the discussion partners Bernd Fitzenberger, Olaf Hübler, Winfried Pohlmeier, Gerd Ronning and the participants of the ”DStatG-Nachwuchs-Workshop: Mikroökonometrie” in Blaubeuren for their useful comments.