Question

Why is it necessary to avoid regressions which have omitted variables due to collinearity?

Answer 1

If Stata is eliminating variables due to colinearity, then there is simply no mathematical possibility of estimating the effects of all of those variables. This is not peculiar to Stata: it is mathematics and you will run into the same thing with any statistical package (although a different statistical package might omit different variables.) Whether you want to ignore them or not, you have no choice in the matter.

What you do have choice over is which variables to omit. So the first thing you need to do is to determine which variables are involved in the colinear relationship(s). For each of the omitted variables, you can run a regression with that variable as the outcome and all the other predictors from the original model as predictors. That will come out with an R² = 1 (or within rounding error of 1) and the coefficients will show you which variables are colinear. You can then decide which among those variables you prefer to omit if you want to keep the one that Stata omitted.