# Constructing a VECM with a mix of I(0) and I(1) variables

I've been using the Johansen Procedure to check and correct for cointegration in my model, by estimating a VECM instead of VAR. But now I want to estimate a new model, in which I expect the same cointegrated relationships, however, some of my variables are now stationary (because they are one of the former variables, split into growth and decay), is there a way to construct the Error Correction Term and insert it into my differenced data, and then estimate the VECM by ordinary VAR?

And what are the implications of ignoring cointegrated relationships and just estimating the VAR? Is my model subject to bias or inconsistency?

• @EconJohn, I have answered several tightly related questions, have you looked at those? Perhaps one of them could serve as a canonical answer, e.g. this? Nov 10 '17 at 18:00
• @RichardHardy I've searched the site and the rest of the internet high and low for an answer to this specific question. If you can post an answer to this question which is as excellent as your previous answers the bounty is yours. Nov 10 '17 at 18:05
• @EconJohn, let me know if you cannot close it as a dupe, then I may post something similar to the answer linked in my comment in this thread as well. Too bad I am extremely busy these weeks... Nov 10 '17 at 18:14
• @RichardHardy Yeah i cant do it. If you want the SE rep its yours if you post something. I'm not so satisfied with the quality of the answer currently posted (though it does the job) it needs some more details for those new to the topic like myself. Nov 10 '17 at 18:17
• @EconJohn, OK, I will try to do that a little later when I can! Nov 11 '17 at 7:29

## 1 Answer

VECM is a VAR with the (lagged) error correction term. The error correction term is the one you obtained from the cointegrating equation or the long run equilibrium equation. With only two variables, for cointegration, they both need to be I(1). But, with more than two variables, I think it can be a mix of I(0) and I(1). If you mix, you will see that effect in the number of cointegrating equation.

• Thank you for your answer, but not really the one I was looking for. I use the Johansen Procedure to identify the cointegrating relationship(s) with the eigen or trace statistic. And then a command called cajorls() in R to estimate the VECM by OSL. I know the cointegrating rank from my previous analysis, but cannot conduct the same procedure because it assumes all variables to be I(1). How do I go about finding the cointegrating equation? And isn't the ECT a canonical variable I can construct by myself? Apr 20 '13 at 8:20
• In case of multivariate, at least two of the variables need to be I(1), not all. Yes you can. Apr 24 '13 at 13:12