I have a set of predictors in a linear regression, as well as three control variables. The issue here is that one of my variables of interest is only statistically significant if the control variables are included in the final model. However, the control variables themselves are not statistically significant.
Here is how the multicollinearity of all my variables look like (including control variables):
> vif(lm(return ~ EQ + EFF + SIZE + MOM + MSCR + UMP, data = as.data.frame(port.df))) EQ EFF SIZE MOM MSCR UMP 3.687171 3.481672 2.781901 1.064312 1.438596 1.003408 > vif(lm(return ~ EQ + MOM + MSCR, data = as.data.frame(port.df))) EQ MOM MSCR 1.359992 1.048142 1.412658
My variables of interest are EQ, MOM and MSCR, and the control variables are EFF, SIZE and UMP. EQ is only significant if the three control var are included, and becomes insignificant when they are not:
Here are the coefficients (1rst row) and t-stats (2nd row) when control variables are included (notice that EQ is statistically significant)
intercept EQ EFF SIZE MOM MSCR UMP [1,] 0.005206246 -0.006310531 0.0001229055 0.004125551 0.007738259 0.00473377 5.838596e-06 [2,] 1.866628909 -1.746583234 0.0388823612 1.178460997 2.145062820 2.08131100 1.994863e-01
Now, here is the result of the regression when the control variables are excluded (notice that EQ is NOT statistically significant anymore)
intercept EQ MOM MSCR [1,] 0.007313402 -0.002111833 0.007128606 0.00668364 [2,] 2.652662996 -0.595391117 2.036985378 2.80177366
The problem is that when I include my control variables, all my variables of interest are significant, but my control variables are not.
Which variables should I include in my final model? How should I structure my final model then, given the fact that the model will be used for forecasting?