Censored Regression Models with Unobserved Stochastic Censoring Thresholds

The "Tobit" model is a useful tool for estimation of regression models with a truncated or limited dependent variable, but it requires a threshold which is either a known constant or an observable and independent variable. The model presented here extends the Tobit model to the censored case where the threshold is an unobserved and not necessarily independent random variable. Maximum likelihood procedures can be employed for joint estimation of both the primary regression equation and the parameters of the distribution of that random threshold. The appropriate likelihood function is derived, the conditions necessary for identification are revealed, and the particular estimation difficulties are discussed. The model is illustrated by an application to the determination of a housewife's value of time.