[Gretl-users] R: Restriction on model coefficients
Thank you Sven for your advice!
Indeed I think the Riccardo solution is econometrically appropriate, but I
need an easier one.
I have already tried the restriction command, but I did not get how to
impose the restriction and then launch the estimation. For just one equation
the guide says that the restriction is applied to the estimation (already
run) of the equation.
So in theory:
1) you run the equation estimation (in my case with 2sls)
2) you put the restriction
3) it tests the coefficient restriction b3=[a1/(1-a2)](1-b2)-b1, using the
estimates coming from the "a" equation (already estimated), and the b1 and
b2 estimates coming from the estimation of the "b" equation (the one
estimated in point 1).
Instead, I need that in the estimation of the equation (the one estimated in
point 1), the coefficients would be estimated using the restriction, that is
using the restriction during the estimation.
I hope to have been enough clear.
Thank you.
-----Messaggio originale-----
Da: gretl-users-bounces(a)lists.wfu.edu
[mailto:gretl-users-bounces@lists.wfu.edu] Per conto di Sven Schreiber
Inviato: giovedì 4 febbraio 2016 19:12
A: gretl-users(a)lists.wfu.edu
Oggetto: Re: [Gretl-users] Restriction on model coefficients
Am 04.02.2016 um 16:57 schrieb Riccardo (Jack) Lucchetti:
On Thu, 4 Feb 2016, Carlo Maria Petrangelo wrote:
> Hello everyone,
>
> I need to estimate an equation with tsls. This equation has a
> restriction on parameters. The restriction has inside itself values
> coming from the estimation parameters of another equation and it is
> the following:
> b3=[a1/(1-a2)](1-b2)-b1, on which "a" indicate a parameter of the
> first equation (already estimated) and "b" indicate a parameter of
> the second equation (which has to be estimated with tsls) and the
> numbers indicate the parameter associated to a regressor.
>
> How can I estimated the second equation once I have estimated the first.
Premise: for this kind of things, your best bet is ALWAYS two estimate
the two equations jointly. Otherwise, you have to make a few
adjustments to you standard errors which are not only boring to
compute, but also prone to sizeable finite-sample bias.
While Jack's answer is econometrically the proper one, it could be that it's
not the one you wanted to hear. If you could live without the correct
standard errors and are really only interested in the point estimates, then
technically it's easy to save (or write down) the values
a1 and a2 and plug them into the restriction concerning b1 and b2,
especially since that restriction seems to be linear, given a1 and a2.
So, please read the documentation of the "restrict" command, and report back
if anything remains unclear.
good luck,
sven
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