Censored regression model

Censored regression models commonly arise in econometrics in cases where data is only available on observations where the variable of interest is positive. The most common example is labor supply. Data is frequently available on the hours worked by employees, and a labor supply model estimates the relationship between hours worked and characteristics of employees such as age, education and family status. However, the results of such estimates, undertaken using linear regression will be biased by the fact that people who have chosen not to work, or have not gained employment.

A famous example is the Tobit model but also the tobit type II-IV model.

Censored regression models are often confused with truncated regression models. Truncated regression models are used for data, where whole observations are missing so that the value for the dependent and the independent variable is unknown. Censored regression models are used for data, where only the value for the dependent variable (hours of work in the example above) is unknown while the value of the independent variable (age, education, family status) is still available - just a a censored letter or newspaper where some words are blackened out but other words are still readable.

Censored regression models are usually estimated using likelihood estimation. The general validity of this approach has been shown by Schnedler (2005) who also provides a method to find the likelihood for a broad class of applications.

• Schnedler, Wendelin (2005). "Likelihood estimation for censored random vectors". Econometric Reviews 24 (2),195–217.