In running any regression on demand based on parameters derived from theory, I'm having some confusion in some order of operations when the results come out inconsistent.
For instant in the case of multi-collinearity and having to drop parameters -- what is the case when parameters of equal importance to theory (like price's) have perfect collinearity? They can't be indexed or made into any ratio, so must be dropped.
My default is to discriminate between the parameters on their explanatory power -- R squared. But what about F-test of significance? If one is higher R than the other but may be nullified by the insignificant F test. Would the 'normal' protocol still be to include the parameter that results with that same higher R-squared despite the F-test being insignificant. -- Or is it even not possible given the parameters are in the same model the F-test is being ran on?