And because thou wast acceptable to God, it was necessary that temptation should prove thee. And now the Lord hath sent me to heal thee … — Tobit 12:13.
This week I wanted to discuss tobit estimators. In case you are not familiar with it, Wiki describes the tobit estimators (people say tobit “models,” but I don’t like calling estimators models, which confuses theory with empirics a bit too much for my taste) as
a statistical model proposed by James Tobin (1958) to describe the relationship between a non-negative dependent variable Y and an independent variable X. The term tobit was derived from Tobin’s name by truncating and adding -it by analogy with the probit model.
The model supposes that there is a latent (i.e. unobservable) variable Y*. This variable linearly depends on X via a parameter (vector) b which determines the relationship between the independent variable (or vector) X and the latent variable Y* (just as in a linear model). In addition, there is a normally distributed error term U to capture random influences on this relationship. The observable variable Y is defined to be equal to the latent variable whenever the latent variable is above zero and zero otherwise.
There are many types of tobits–Wiki lists five, which are such that
