Am 31.01.2019 um 16:07 schrieb Reynaldo Senra:

Dear Sven,

Very much thank you for the quick response.

Yes I know they are different. Maybe I was not clear with my message. R reports critical values and gretl p-values. The problem is that the critical values in R indicated 1 cointegration vector but the p-values in Gretl indicated 2. That is the problem. Logically, I expected no discrepancy

Ah OK, I see. Right now I don't know a full answer to the question, but it certainly should be clarified. From the ca.jo documentation (in R / urca package I think) it appears that he uses the Osterwald-Lenum 1992 critical values. Gretl, in contrast, uses a later paper by Doornik (1998) (check the help for coint2).

Also it seems that somebody else had a very similar question comparing ca.jo and Python's statsmodels:
https://github.com/statsmodels/statsmodels/issues/5355

That thread also seems to end without a real answer. Is Osterwald-Lenum obsolete?

thanks,
sven