@jpfeifer Thanks for clarifying Johannes - appreciated. What I was trying to say is that I believe that first order is actually a bit different from all the others and, numerical inaccuracies aside, sampling / law of large numbers should play no role when computing GIRFs (which is presumably one reason why no one computes them in linear models?).
While I may be missing something, if the linear solution is y(t) = Ay(t-1)+Be(t) and the impulse vector is i(1), then the IRF in period t would be A^(t-1)Bi(1) for every series of shocks e(t) underlying a GIRF. Sure, in practice you’re going to get some numerical inaccuracies and the IRFs corresponding to each shock draw won’t be exactly identical, but that would be only due to numerical imprecision, in contrast to higher orders where base effects matter directly (in any case, the numerical inaccuracies should be much smaller than anything to do with sampling; and I’m not sure the law of large numbers would apply to them…)? Anyway, just so we’re on the same page, and as an aside to the thread topic.
@MichelJuillard Many thanks for looking into this Michel - really appreciated. I guess one of my concerns was whether whatever is causing the IRFs to look a bit off could also show up in standard dynare, given that (if my understanding is correct) the third order algorithms build on those underlying dynare++? Any thoughts on this would be welcome.
Thanks again to both for all your help,
Pawel