Re: [Gretl-devel] restrict after GMM

On Thu, 31 Jan 2008, Sven Schreiber wrote: The same applies to mle. It seems quite clear to me that only the --wald form should be allowed (in these cases, automatic estimation of the restricted model would involve quite a bit of work). I guess in principle this could be done, once we overcome a slight problem of notation: we may adopt a convention by which b3 is $coeff[3] and so on, like we do with, say, ols. Note, however, that this may be confusing in some cases, since gmm & mle allow you to put your parameters under arbitrary names. Example (admittedly a bit contrived): <script> nulldata 100 x = normal() y = x + normal() ols y 0 x scalar b1 = 0 scalar b2 = 0 matrix W = I(2) series e gmm e = y - b1 - b2*x orthog e ; const orthog e ; x weights W params b2 b1 end gmm </script> If, at this point, you were allowed to test a restriction for "b1 = 0", you wouldn't be testing the hypothesis of zero intercept, but rather of zero slope, since $coeff[1] is the _slope_, but comes first in the ordering of the "params" statement. On the other hand, a Wald-type statistic for restrictions of the kind $R \theta = d$ can be computed quite easily, considering that after gmm you _do_ have the $coeff and $vcv accessors ready to use. Example: <script> function Wald_type(matrix b, matrix V, matrix R, matrix d) matrix num = R*b - d matrix den = invpd(qform(R,V)) scalar wt = qform(num', den) return scalar wt end function </script> But I agree that having "restrict" work after gmm/mle would be nice. Actually, if we decide to devote some time to "restrict", it'd be rather cool to handle nonlinear constraints via the delta method. The problem is, this would probably force us introduce a few backward-incompatible changes. Riccardo (Jack) Lucchetti Dipartimento di Economia Università Politecnica delle Marche r.lucchetti(a)univpm.it http://www.econ.univpm.it/lucchetti