The Asymptotic Bias of OLS With Censored Dependent Variables

An interesting result from Greene that I was not previously aware of:

We find that for the case of normally distributed regressors, the slopes in the linear regression of y on x, which are consistently estimated by ordinary least squares, are proportional to the corresponding slopes of the underlying regression relating y*, and x. In this setting, the bias can be "corrected" simply by dividing each OLS slope by the proportion of nonlimit observations in the sample. The other structural parameters can be consistently estimated in similar fashion. - Greene On the Asymptotic Bias of the Ordinary Least Squares Estimator of the Tobit Model Econometrica, Vol. 49, No. 2 (Mar., 1981), pp. 505-513Published