Difference or not to difference variable in VAR

[BinhPham]

Hi Tom,

You mentioned that variables should not be differenced as the transformation results in the lost information. But, I see many papers do or don't with very little explanation. If I estimate a VAR with mixed I(1) and I(0) without any transformation then it has been seen that the IRFs of I(1) variables are identical with that accumulated IRFs of the corresponding transformed variables.

So, what are the main points to justify difference or not to difference? (of course, Yoda - Yamamoto say we can augment an extra lag, but you commented that the true p is really unknown so that this trick will not always true). In the case, all I(1) are not cointegrated should we do difference?

Many thanks your help,
Best

[TomDoan]

Hi Tom,

You mentioned that variables should not be differenced as the transformation results in the lost information. But, I see many papers do or don't with very little explanation. If I estimate a VAR with mixed I(1) and I(0) without any transformation then it has been seen that the IRFs of I(1) variables are identical with that accumulated IRFs of the corresponding transformed variables.

They won't be "identical", but they should be similar if the series aren't cointegrated.

So, what are the main points to justify difference or not to difference? (of course, Yoda - Yamamoto say we can augment an extra lag, but you commented that the true p is really unknown so that this trick will not always true). In the case, all I(1) are not cointegrated should we do difference?

If the series are seen to be I(1) and (clearly) aren't cointegrated, and you're mainly interested in growth rates, then there is no real harm in differencing. The result runs both ways: the differenced regression is asymptotically equivalent to the levels regression. Note that that's three conditions that need to be met. Given that there is also little harm in running this in levels (unless the data set is short) if you have any doubt, you should leave it in levels.

[BinhPham]

Many thanks Tom! It's clear to me now.