A note on the Tobit model in the presence of a duration variable

The Tobit model (censored regression model) is an important basic model appearing in many applications in economics. In this paper we consider a duration Tobit model in which a duration variable which counts the number of times the data is being censored is included as a covariate. We show that in this case, the dependent variable eventually becomes degenerate, which makes the asymptotic Fisher information matrix singular, rendering the standard methods of asymptotic inference inapplicable. We provide a simulation study and an empirical application to support our results.