A tobit model with garch errors

In the context of time series regression, we extend the standard Tobit model to allow for the possibility of conditional heteroskedastic error processes of the GARCH type. We discuss the likelihood function of the Tobit model in the presence of conditionally heteroskedastic errors. Expressing the exact likelihood function turns out to be infeasible, and we propose an approximation by treating the model as being conditionally Gaussian. The performance of the estimator is investigated by means of Monte Carlo simulations. We find that, when the error terms follow a GARCH process, the proposed estimator considerably outperforms the standard Tobit quasi maximum likelihood estimator. The efficiency loss due to the approximation of the likelihood is finally evaluated.