How to handle a structural break of only one variable in a VAR model? I am estimating a VAR-model with two variables: GDP real and Investments. Investments has a structural break, GDP real not.
As I understood it is only possible to add a dummy variable to both equations, not only to one. Is this correct and would this also be correct in this case ?
Thanks in advance
 A: You can implement the two equations of the VAR model manually as two linear regressions, then you are free to choose what to put in each of them.
Alternatively, you can try adding a dummy to both equations and subsequently restricting its coefficient to zero in the equation where you think it should be zero. (You could even test whether it is really zero.)
If that is not possible in your favorite software, perhaps including an irrelevant dummy would not be so bad. If the dummy is truly irrelevant, its coefficient estimate should be close to zero, and the other estimates should not be affected much (inclusion of an irrelevant variable is known to increase the variance of estimators but it does not bias them).
Yet another alternative is to adjust investments for a structural break in an auxiliary regression on the dummy variable and then use the adjusted variable in the VAR. This would lead to some additional uncertainty in parameter estimates that will not be visible in the VAR model output, though.
