On Wed, 29 Aug 2012, Jan Tille wrote:
> Dear gretl users,
>
> first of all let me thank you, that you have already provided me with
> solutions on other topics. Unfortunately, I need your help again.
No problem, that's what the mailing list is for.
> The problem I am now trying to solve is the following.
[... rolling regression with constraints ...]
IMHO, your problem can be solved, once it's stated less ambiguously. Allow
me to explain (and to apologise in advance for being pedantic).
Suppose you have 3 regressors instead of 10. Then you have
y_t = b0 + x_{1t} b1 + x_{2t} b2 + x_{3t} b3 + u_t
Let's call this model U (for unrestricted). Once you impose the
restriction b1+b2+b3=1, you can write the same model as
y_t - x_3 = b0 + (x_{1t} - x_{3t}) b1 + (x_{2t} - x_{3t}) b2 + u_t
Call this model R (restricted). Running OLS on model R, you get exactly
the constrained estimates you're after. Then, you can recover you estimate
of b3 as 1 - b1 - b2 and compute its standard error as sqrt(V(b1+b2)),
which is easy to do.
Do you want to NOW drop those coefficients whose t-statistic is less than
a predefined threshold? But in this case, the remaining ones won't sum to
1 anymore.
Or perhaps, you want run model R, trim it to your liking and then compute
b3 as 1 - (sum of surviving betas). But then, what guarantee do you have
that that b3 will itself be significant? Because if it isn't, you have the
option of dropping it (and have the sum being different from 1) or keeping
it (but why should you treat b3 specially?).
Or maybe you want to run model U first, drop the "excess" variables and
then force the coefficients to sum to 1? Because in this case, you have no
guarantee that the surviving coefficients will be "significant" (whatever
that means).
I don't mean to be patronizing, but I think that before you think of the
hansl syntax to do what you want, you should think a little harder about
what you actually want! :)
--------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
--------------------------------------------------
