Tobit model

The tobit model a statistical procedure proposed by James Tobin (1958).

In this model the dependent variable $y_{i}$ is censored:

$y_{i}={\begin{cases}y_{i}^{*}&{\textrm {if}}\;y_{i}^{*}>0\\0&{\textrm {if}}\;y_{i}^{*}\leq 0\end{cases}}$

where $y_{i}^{*}$ is a latent variable that cannot be observed:

$y_{i}^{*}=\beta x_{i}+u_{i}$

While an ordinary least squares estimator of $\beta$ is biased, a special maximum likelihood estimator for this model is unbiased.