@Anastasia items 2 and probably 3 should be different issues. I am not sure I understand the last item. Can you please open two new issues (and remove these two items by editing your post)?
@stepan-a In the auxiliary VAR used to compute PVs we have long-run anchors (trends), and ecm in PAC equation.
As for an example, could you specify what do you need, please? I have a code that estimates a PAC eqn, but I have to adjust this version to make it run in Dynare, so obviously it does not contain neither contemporaneous variables, nor a product of coefficients/negative coefficients. But I can prepare for you a file without those restrictions.
@Anastasia Sorry I have the impression that we are mixing two different things here (so maybe we should have another issue). What I would like to see now an example representative of your auxiliary model, not the PAC equation. When you mention negative coefficient, is it in the auxiliary model or in the PAC equation.
Actually I don't really understand this sign issue. The auxiliary model should not be written with hard coded parameters, but with symbolic parameters that would have to be estimated. So why do you need to write the equations with minus symbols? Even if the estimation is done elsewhere, hard coded parameters should be avoided.
@stepan-a Oh, I totally agree about hard coded parameters. Indeed, our auxiliary model (satellite model as we call it) is estimated with Bayesian technics also with a help of Dynare. It is a structural model, so for example in the IS curve the interest rate will inter directly with a negative sing, as:
y_t = a_1 y_{t-1} - a_2(i_{t-1}-\pi_{t-1})
But as I say, we don't have problems estimating this model. It is done. However we need to use it for PAC estimation, and that's where we stuck.
Shall I send you the codes of the satellite model?
After checking new developments with the 4.8 Dynare version of July, I've noticed the following issues:
When estimating a PAC equation with an exogenous observed variable (EOV), Dynare 4.8 (July) and 4.7(February) give different estimation results. However they give the same outcome without EOV.
In version 4.8 (July) I'am obtaining the same estimation result for a PAC equation, no matter what are the auxiliary equations. Companion matrix though changes every time I change specification of the VAR model. I think this is connected to this problem
https://git.dynare.org/Dynare/dynare/-/issues/1787#note_14703.