Hi all cointegration aficionados, this is the attempt to summarize and clarify some confusion that seems to exist about the meaning of the choices for deterministics in a VECM (including the Johansen test setup) in gretl and other software, related or unrelated. This is going to be a bit long, but hopefully clear. Feel free to correct me about the situation in R further down. First, gretl's 'vecm' and 'coint2' commands use the widely known "five cases", same as in most other software including for example Eviews and I think also Stata: ['coint2' might get an alias name soon, but the workings will stay the same] 1/nc: no constant at all - 2/rc: restricted constant (only in the EC term) - 3/uc: unrestricted constant (to model a trend component in the data but not in the EC term) - 4/crt: unrestr.const plus a trend term restricted to the EC term - 5/ct: both unrestr.const and unrestr.trend. Cases 2,3,4 are by far the most relevant for applications. Second, comparison with R/urca: I'm not an expert for this R package, but it became clear recently that its labels have a different meaning, in my view a little misleading. Its "no constant" case is _not_ case 1. Instead it seems to mean, "let's not put a constant specifically into the EC term (but of course we'll need one in the overall system)". So "no constant" in R/urca apparently corresponds to case 3. [The question of the inference in the rank test is then a little more complicated and we had a thread about that recently, which I won't repeat here.] "Constant" in R/urca seems to be case 2, and "trend" would be case 4. Thirdly, I have (together with original code author Andreas Noack Jensen) a function package "coint2rec" for gretl with which you can do stability analysis of the cointegration structure in a VECM. Only the cases 'nc','rc,' and 'crt' are implemented there, so cases 1,2,4 in the numbering above. There is a reason for this coming from the statistical theory, namely that these setups yield so-called "similar" tests. In particular, you cannot directly choose the popular case 3/uc. What might be confusing is that in coint2rec the codes are also numbered consecutively from one to three, but the last of those cases is not number 3 (uc) in the "usual" terminology. (Instead, I repeat, it is case 4/crt.) Follow-up question: What do you do if your model is 3/uc but you want to use coint2rec? Well, you would have to move temporarily to the more general model case 4/crt. In theory, you would estimate the cointegration rank with case 4/crt, conduct the stability analysis with coint2rec with case 4/crt (where it has code number 3), and if it's stable then test (with gretl) whether you can exclude the trend from the EC term. [In practice, things usually do not go so smoothly, but that's our common problem as econometricians...] Finally, a note about another related package from Andreas and me, "johansensmall" for small-sample inference on the rank test. There you have the standard cases 1 to 4 available, but not the rare case 5. (And in case you want the Bartlett correction case 3/uc is also not there, for the same theoretical reason as in coint2rec.) HTH Sven