Probit models: Regression parameter estimation using the ML principle despite misspecification of the correlation structure

In this paper it is shown that using the maximum likelihood ML prin ciple for the estimation of multivariate probit models leads to consistent and normally distributed pseudo maximum likelihood regression parame ter estimators PML estimators even if the true correlation structure of the responses is misspeci ed As a consequence e g the PML estimator of the random e ects probit model may be used to estimate the regression parameters of a model with any true correlation structure This result is independent of the kind of covariates included in the model The results of a Monte Carlo experiment show that the PML estimator of the inde pendent binary probit model is ine cient relative to the PML estimator of the random e ects binary panel probit model and two alternative esti mators using the generalized estimating equations approach proposed by Liang and Zeger if the true correlations are high If the true correlations are low the di erences between the estimators are small in nite samples and for the models used Generally the PML estimator of the random e ects probit panel model is very e cient relative to the GEE estimators Therefore if correlations between binary responses cannot be ruled out and the true structure of association is unknown or infeasi ble to estimate the PML estimator of the random e ects probit model is recommended