[Gretl-users] Re: System of Equations and Kalman/MLE - two suspicions
On Sun, 5 Jan 2020, Alecos Papadopoulos wrote:
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?
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