This paper analyzes small sample properties of several versions of z-tests in multinomial probit\udmodels under simulated maximum likelihood estimation. OurMonte Carlo experiments show\udthat z-tests on utility function coefficients provide more robust results than z-tests on variance\udcovariance parameters. As expected, both the number of observations and the number of random\uddraws in the incorporatedGeweke-Hajivassiliou-Keane (GHK) simulator have on average\uda positive impact on the conformities between the shares of type I errors and the nominal significance\udlevels. Furthermore, an increase of the number of observations leads to an expected\uddecrease of the shares of type II errors, whereas the number of random draws in the GHK\udsimulator surprisingly has no significant effect in this respect. One main result of our study\udis that the use of the robust version of the simulated z-test statistics is not systematically\udmore favorable than the use of other versions. However, the application of the z-test statistics\udthat exclusively include the Hessian matrix of the simulated loglikelihood function to estimate\udthe information matrix often leads to substantial computational problems.
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