Missing independent variable on main equation in sample selection model may incorrectly remove valid observations on selection equation


If you specify a sample selection model and the following conditions are met:

  1. missing values on some independent variables on the main equation where the dependent variable is observed only at certain levels of the selection variable
  2. missing values appear on observations when the selection variable is not being selected
  3. independent variables with missing values do not appear on the selection equation in the model

then these observations are incorrectly excluded in the selection equation and the discrete response profile for the discrete dependent variable on the selection equation will contain incorrect frequency count and percent information. The total frequency count will not sum up to total number of all valid observations on the selection equation and the percent for all levels of the selection variable will not sum up to 100.

To circumvent the problem when the selection variable is not being selected, replace missing values on the independent variables in the main equation with arbitrary values. Then these observations will not be excluded from the analysis in the selection equation and the arbitrary values will not affect estimation since these values do not enter the log likelihood function when the selection variable is not being selected.