Tobit model

The Tobit model is a returning to James Tobin econometric model for analyzing limited dependent variables ( censored variable ). Since the dependent variable exists only in a certain range of values, standard regression coefficients are not the best estimator, so that the estimator must be corrected. This correction is implemented in the Tobit model.

Model

With the Tobit model, the relationship between a non -negative dependent variable and an independent variable ( or a vector ) is described. The model assumes that there is a latent ( ie unobservable ) variable. This variable is a linear function of a parameter (or vector) of the relationship between the independent variable determined as a linear regression ( or vector ) and the latent variables.

In addition, there is a normal distribution error term in order to detect random influences on this connection.

The observable variable is by definition equal to the latent variable whenever the latent variable is greater than zero. Otherwise it is zero.

Wherein a latent variable representing:

Parameter estimation

If the connection parameters via a conventional regression of the observed variable is estimated, the resulting ordinary least squares estimator inconsistent. Amemiya (1973 ) has shown that the likelihood estimator, which was proposed by Tobin for this model is consistent.

Generalization

The Tobit model is a special case of a censored regression model because the latent variable can not always be observed, while the independent variable is observable. A common variant of the Tobit model is to restrict a variable to a nonzero value:

Another example is the limitation to a value above.

Another model results when the same is limited from above and from below.

Such generalizations are also typically referred to as Tobit models. Depending on where and when the restriction is done, results in further variants of the Tobit model. Takshi Amemiya classified these variants into five categories ( Tobit type I Tobit type V), where Tobit type I represents the model described above. Schnedler provides a general formula to achieve consistent probability estimates for these and other variants of the Tobit model.