This paper analyzes the consistency properties of classical estimators for limited dependent variables models, under conditions of serial correlation in the unobservables. A uniﬁed method of proof is used to show that for certain cases (e.g., Probit, Tobit and Normal Switching Regimes models, which are normality-based) estimators that neglect particular types of serial dependence (speciﬁcally, corresponding to the class of “mixing” processes) are still consistent. The same line of proof fails for the analogues to the above models that impose logistic distributional assumptions, thus indicating that normality plays a special role in these problems. Sets of Monte-Carlo experiments are then carried out to investigate these theoretical results.
Hajivassiliou, Vassilis A., "Temporal Dependence in Limited Dependent Variable Models: Theoretical and Monte-Carlo Results" (1986). Cowles Foundation Discussion Papers. 1046.