When does Heckman’s two-step procedure for censored data work and when does it not?

Heckman’s two-step procedure (Heckit) for estimating the parameters in linear models from censored data is frequently used by econometricians, despite of the fact that earlier studies cast doubt on the procedure. In this paper it is shown that estimates of the hazard h for approaching the censoring limit, the latter being used as an explanatory variable in the second step of the Heckit, can induce multicollinearity. The influence of the censoring proportion and sample size upon bias and variance in three types of random linear models are studied by simulations. From these results a simple relation is established that describes how absolute bias depends on the censoring proportion and the sample size. It is also shown that the Heckit may work with non-normal (Laplace) distributions, but it collapses if h deviates too much from that of the normal distribution. Data from a study of work resumption after sick-listing are used to demonstrate that the Heckit can be very risky.