Censored regression model

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Censored regression models commonly arise in econometrics in cases where the variable of interest is only observable under certain conditions. A 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 for people who are unemployed it is not possible to observe the number of hours they would have worked had they had employment. Still we know age, education and family status for those observations.

A famous model to deal with censored data is the Tobit model as well as variations such as the tobit type II-IV model.

These and other 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.