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

- Including duration variables in Tobit models may lead to degenerate dependent variables.
- This implies that asymptotic inference based on the Fisher information matrix is invalid.
- We provide a simulation study and an empirical application to support our results.

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.