[Gretl-devel] Re: Simulate simultaneous equation model
Am 14.09.2020 um 17:24 schrieb Allin Cottrell:
On Mon, 14 Sep 2020, Sven Schreiber wrote:
> I'd even say you can go a long way with linear behavioral systems in the
> sense that some variables only appear in logs (including log-differences
> as growth rates) and others only in raw levels (including absolute
> differences, e.g. for interest rates). This would be less general than
> your example above where x and y appear both in levels as well as in
> logs. Then you could estimate it in gretl as a system directly -- OK you
> can't do FIML because the non-linear identities linking the logs and the
> levels are not allowed. But that's not too bad IMHO.
I have the impression it wouldn't be too difficult to support nonlinear
identities (though maybe that's just because I haven't fully thought it
out). It would require extension of the id_atom struct in
lib/src/system.c: besides series ID and "op" (plus/minus) we'd a need a
"transform" element (e.g. log).
That would be nice of course. And indeed I think the most important type
of nonlinear identity are accounting relationships in levels where the
variables in the behavioral equations appear in logs. Like the canonical
exp(l_Y) = exp(l_C) + exp(l_I) + exp(l_G).
However, these things are additively separable; for general
nonlinearities the "atomic" structure with op/varnum/transform wouldn't
be enough. Can't think of a real-world example right now, though.
cheers
sven