A General Approach to Incorporating Selectivity in a Model

• The impact on the conditional mean of the model of interest will not take the form of an inverse Mills ratio. That is specific to the linear model. (See Terza (1995) for a development in the context of the Poisson regression.) • The bivariate normality assumption needed to justify the inclusion of the inverse Mills ratio in the second model generally does not appear anywhere in the model. • The dependent variable, conditioned on the sample selection, is unlikely to have the distribution described by the model in the absence of selection. That would be needed to use this approach. Note that this even appears in the canonical linear case. The normally distributed disturbance in the absence of sample selection has a nonnormal distribution in the presence of selection. That is the salient feature of Heckman’s development.