On 15/09/2025 21:12, Cottrell, Allin wrote:

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.

Thanks, Allin, this is very nice.

* "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).

Since this matrix lacks an "official" name, I'd suggest we could simply call it "long_run", or something like that.

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

Will do so later today when I get the chance.

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.

I believe this is the right thing to do.

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  Riccardo (Jack) Lucchetti
  Dipartimento di Scienze Economiche e Sociali (DiSES)

  Università Politecnica delle Marche
  (formerly known as Università di Ancona)

  r.lucchetti@univpm.it
  http://www2.econ.univpm.it/servizi/hpp/lucchetti
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