Identification by non-linearity in censored regression models
A Monte Carlo framework confirms that separate sources of variation in the selection and regression equations improve the precision of the HL estimator. Even so, the HL estimator does not provide an unequivocal mean square error improvement upon subsample OLS in small samples. The HL estimator controls for selectivity bias, but suffers a loss in precision relative to subsample OLS. Additionally, there is little advantage to mis-specifying the equations when separate regressors are unavailable. The consistency of the HL estimator is traded for, at best, a modest MSE improvement that is contingent on the unknown parameters.
monte carlo mean square error selectivity bias tobit model colinearity specification error