On the Asymptotic Properties of Estimators of Models Containing Limited Dependent Variables

For the Tobit model with independent observations, Amemiya 1 has established the strong consistency and asymptotic normality of a stationary point, 9, of the log-likelihood. The likelihood for dependent observations may be computationally intractable, so the behavior of 9 in the presence of serially correlated observations is of interest. Under a relaxation of Amemiya's assumption of independence, we prove that 9 is strongly consistent and asymptotically normal, and give an expression for the limiting covariance matrix.