On Mon, 14 Sep 2020, Adam Elderfield wrote:

"ln (Y/Y(-1)) = coef(1)*(ln(Y(-1))-coef(2)*ln(X(-1)))+coef(3)*ln (Y(-1)/ Y(-2)) + coef(4)*ln(X/X(-1))"

That's what the main difficulty is. At present, we have very good technology for estimating _linear_ simultaneous systems. If we keep within the realm of linearity, simulating from a simultaneous system is trivial if the system is static (just compute the reduced form and you're done) and only slightly more intricate if you have lags (you need to cast the reduced form into a finite-order VAR and use varsimul()).

The real problem is that at present we don't have a way for representing, let alone estimating, systems with nonlinearities, eg something like this:

y_t = a0 + a1 * x_t + u_t
log(x)_t = b0 + b1 * log(y)_t + e_t

First, Jack, sorry, but as a general statement I actually think this is wrong. Gretl can estimate these structural equations already, with TSLS equation-per-equation. Of course that's not the efficient estimator here, and I guess that's what you had in mind. But still it can be done, since both equations are linear by themselves.

Second, a quote from the bimets vignette: "The bimets ESTIMATE() function estimates equations that are *linear* in the coefficients". This is of course not the same as linear in the variables, but still it shows that bimets's scope is somewhat limited, too. Actually, the vignette does not even contain the word "non[-]linear". Another quote: "RESTRICT> is a keyword that can be used to specify *linear* coefficient restrictions".

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.

Cointegration apparently isn't mentioned in the bimets doc, but if you want to deal with it explicitly I think it's pragmatically OK to pre-estimate them somehow (or pre-specify without estimating, since many equilibrium relationships from theory do not really involve any parameters to be estimated). Then you just plug the EC terms into your otherwise stationary partly differenced system, like PcGive/PcFiml did for decades.

...

In fact, we have an expert here among the mailing list members, that is Francesca Di Iorio. Francesca, would you like to comment?

Yes that would be great.

cheers

sven