Hi all, I would like to retrieve the long-run impact matrix, called "C" in Johansen's jargon. After estimating a vecm, there is item "C". Is this object the matrix I am looking for (I could not find anything in the docs)?

Furthermore, in a recent paper by Juselius, she reports standard errors for C. Is this information also stored in the system bundle?

Am 14.09.2025 um 12:29 schrieb Riccardo (Jack) Lucchetti: > On 13/09/2025 14:52, Artur T. wrote: >> >> I would like to retrieve the long-run impact matrix, called "C" in >> Johansen's jargon. >> >> After estimating a vecm, there is item "C". Is this object the >> matrix I am looking for (I could not find anything in the docs)? > > No, that's the Cholesky factor of the residual covariance matrix. > >> >> Furthermore, in a recent paper by Juselius, she reports standard >> errors for C. Is this information also stored in the system bundle? >> > That matrix is referred to with different letters in different > sources. For example, Kilian & Lütkepohl use the letter $\Xi$. Its > calculation is not very difficult, given the information contained in > the $system bundle you get out of the "vecm" command. Its asymptotic > distribution, however, is a bit more intricate. It was derived by > Paolo Paruolo in https://www.jstor.org/stable/pdf/3532701.pdf., but > you can also find it in Søren's 1995 OUP book (section 13.5). > > A function package doing all this would be very welcome 😉 > Ahem, I'm pretty sure that at least some of that stuff is in our SVAR addon, no? Please check out the "lrmat" object in the model bundle after estimating the VECM not with gretl's core vecm command, but with the addon. See also appendix D of the SVAR documentation, along with section 7 there. Of course that's for identified shocks, even if the identification is simple like Choleski. If you really want to have the impact matrix of the reduced-form errors, it's a bit different. I don't remember what's in SVAR for this. Maybe it could also be "tricked" into interpreting the reduced-form innovations as the structural ones. (BTW, it seems that in the current SVAR doc we have a bunch of superfluous literal backslash characters appearing. I guess that's fallout from the attempt to have searchable underscore characters from a while ago.)

In gretl git, I've added a couple of elements to the vecm_info bundle inside the $system bundle that can be retrieved after estimation of a cointegrated VAR.

* "JC": the matrix that Johansen refers to as 'C' (and that Artur was interested in), namely C = \beta_{\perp} (\alpha_{\perp}' \Gamma \beta_{\perp})^{-1} \alpha_{\perp}' (1995, page 49).

I'd appreciate it if anyone can check the correctness of these results!

In particular I'm assuming that when \beta has more rows than \alpha (because some deterministic and/or exogenous terms are restricted to the cointegration space), the "beta" that enters the "JC" formula should just be the first p rows of what we're calling beta in gretl (where p is the number of endogenous variables). Otherwise the formula Johansen gives for C doesn't work.

> In gretl git, I've added a couple of elements to the vecm_info bundle > inside the $system bundle that can be retrieved after estimation of a > cointegrated VAR. > > * "Gamma": the matrix formed as (identity matrix minus the summation > of the per-lag \Gamma_i matrices in the short-run dynamics) -- see > Johansen (1995) page 45 -- and

> * "JC": the matrix that Johansen refers to as 'C' (and that Artur was > interested in), namely C = \beta_{\perp} (\alpha_{\perp}' \Gamma > \beta_{\perp})^{-1} \alpha_{\perp}' (1995, page 49).

> I'd appreciate it if anyone can check the correctness of these > results! In particular I'm assuming that when \beta has more rows than > \alpha (because some deterministic and/or exogenous terms are > restricted to the cointegration space), the "beta" that enters the > "JC" formula should just be the first p rows of what we're calling > beta in gretl (where p is the number of endogenous variables). > Otherwise the formula Johansen gives for C doesn't work.