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Hello,

I've been estimating VECMs using the VAR object and running a few tests related to the effect of model misspecification using simulated data. In particular, I've been looking at estimating a VECM with 2 cointegration vectors when the simulated data has only 1 cointegrating relationship.

From what I understand of the Johansen Test procedure, the estimated single cointegrating vector should be in the space spanned by the 2 estimated cointegration vectors (since they are just linear combinations of the first 2 eigenvectors of the same matrix). This does not appear to be the case in EViews. I some cases, I get large discrepancies (well beyond what I feel could be explained by floating-point arithmetic error). If I'm missing something here, could someone please let me know.

Thanks,

Could you give an example of a large discrepancy that you're seeing?

I just did a quick test as follows:

Run a cointegration estimation (on random data) with one cointegrating vector, then with two.

Make a new workfile with the three series:
- series01 - the cointegrating vector reported in the rank-1 estimation
- series02 - the first cointegrating vector reported in the rank-2 estimation
- series03 - the second cointegrating vector reported in the rank-2 estimation

I then regressed series01 against series02 and series03 and calculated the residuals. The largest residual in my case was about 7e-15 which is about what I'd expect from rounding error.

So, as far as I can tell, the vector reported in the rank-1 case is a linear combination of the two vectors reported in the rank-2 case as expected.