Truncated regression models are used for data where whole observations are missing so that the values for the dependent and the independent variables are unknown.
Censored dependent variables frequently arise in econometrics.
Data are 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, 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.