Thanks Sven, that was helpful. As regards Suspicion 1, unfortunately my restrictions are heavily cross-equation, and non-linear in ways that transforming the variables won't help ... also, I do not care much about testing them. I think the reason non-linear restrictions are not supported in a system is the issue of testing them. How about being able to impose them while losing the ability to test them? Let's say I have complete confidence in my theoretical model...! As regards Suspicion 2, my "solution" makes the definition of the Kalman matrices a bit too long and a little confusing especially when the restrictions are many and more complicated. The issue is that the mle takes the likelihood expression from inside the Kalman bundle, this is why I think It will not work if I try to define a "helper variable" as you write directly inside the mle command block, as we often do in other cases... but maybe it will work regardless. Maybe the following will work <hansl> scalar a11 =0.2 scalar a12 = 0.4 scalar a13 = a11/a12 matrix F' = {a11,a12,a13}  # instead of defining matrix F' = {a11, a12, a11/a12} ... bundle  KF = ksetup(y,H,F,Q) mle logl = ERR ? NA : KF.llt ..... KF.statemat[1,1] = a11 KF.statemat[2,1] = a12 KF.statemat[3,1] = a11/a12 #or alternatively KF.statemat[3,1] = a13 scalar a13 = a11/a12 #end of alternatively ERR = kfilter(&KF) params a11 a12 end mle  --hessian </hansl> Alecos Papadopoulos PhD Athens University of Economics and Business web: alecospapadopoulos.wordpress.com/ skype:alecos.papadopoulos On 5/1/2020 21:55, Sven Schreiber wrote: > Am 05.01.2020 um 02:04 schrieb Alecos Papadopoulos: >> I have the following two suspicions, can somebody please verify/dispel >> them? >> >> 1) In a system of equations, currently I have no way to impose >> non-linear restrictions on the coefficients (like ratios or products of >> coefficients, nothing fancier). Right? Wrong? > > Yes, I think so. (At least that's the documented state.) Of course if > you're happy estimating your system with TSLS, then you can pick out the > equation of interest and you should be able to formulate a restriction > in this single equation. If you aren't thinking of cross-equation > restrictions, that is. > And I guess I don't need to tell you that sometimes you can transfrom > and redefine your regressors to achieve ratios or stuff like that. If > that is feasible in your case, then a LR test might also be viable. > >> >> 2) In using the Kalman filter together with maximum likelihood, consider >> the following detail:  say, in the "obsxmat" matrix there exists a >> coefficient restriction, say a13 = a12/a11 > ... >> scalar a13 = a12/a11 > ... >> If my suspicion is right, then I think I have to define the matrix A by >> >> matrix A = {a11, a12, a12/a11} >> >> so that position a13 is also updated with the MLE estimate. >> >> Right? Wrong? > > This sounds right, but somehow I'm afraid I don't really get your > question, because you already seem to have answered it yourself. > Also, you can have helper variables like a scalar a13 inside your mle > block, which only serve to express the connections of your parameters, > without being params of interest themselves directly. > > cheers > sven > _______________________________________________ > Gretl-users mailing list -- gretl-users(a)gretlml.univpm.it > To unsubscribe send an email to gretl-users-leave(a)gretlml.univpm.it > Website: > https://gretlml.univpm.it/postorius/lists/gretl-users.gretlml.univpm.it/

On Sun, 5 Jan 2020, Alecos Papadopoulos wrote: I may be missing something here, but I think it's the other way round: it's not too difficult just to test nonlinear restrictions on a system; considerably more challenging to impose them on estimation. To test nonlinear restrictions you just need an appropriate estimate of the covariance matrix of the unrestricted parameter estimates and a way of handling derivatives -- either analytically or with the help of gretl's fdjac(). When we estimate a linear system subject to linear restrictions we use the Restricted Least Squares method described by William Greene. It's basically a Lagrangean thing, which involves augmenting the original equations with (linear) equations specifying the restrictions. But if you were to "append" equations representing nonlinear restrictions you'd then have a system of nonlinear equations, and gretl's "system" is not set up to estimate such a thing. As Sven says, you might want to explore GMM for your purpose. Allin