infonet-economy

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