On Thu, 6 Aug 2009, Allin Cottrell wrote:
On Thu, 6 Aug 2009, Riccardo (Jack) Lucchetti wrote:
> On Wed, 5 Aug 2009, Allin Cottrell wrote:
>>> If the original model was estimated via OLS, the restricted one
>>> could be estimated via NLS.
> An alternative which does away with NLS and the associated potential
> convergence problems is a Wald-type test, that is, a simple application
> of the delta method (see section 5.9 of the manual).
> Basically, all you have to do is write a constraint function
> _row_ vector, which must be 0 under H0 and nonzero under H1. Then, you
> feed it into the nlWald function and you're all set...
This is certainly an elegant approach. In fact, I wonder if it
might be worth offering a semi-automated version as an option to
the existing "restrict" command. That is,
restrict <function-name> --<option-name>
where <function-name> would refer to something like your
somestupidfunction and <option-name> would be something like
"nl-Wald". The place of your "nlWald" function would be taken by
a built-in function that automatically accesses $coeff and $vcv
from the last-estimated model (and deposits $test and $pvalue).
Is this too much like spoon-feeding?
Not at all, if you ask me. In fact it'd be a very valuable addition.
On the other hand, my reading in Greene and Davidson and MacKinnon
(and not, I hasten to say, my own unaided thinking!) leads me to
the idea that such Wald tests are not altogether reliable, since
the result can depend quite sensitively on just how the
restriction is represented.
Yes, this is true. However, it's a finite-sample phenomenon. It's exactly
the same problem you have when you write a GMM orthogonality condition in
two equivalent ways and you end up with widely different estimates. It's a
fact of life, I'm afraid. On the other hand, it's a nice tool to have and
if you feel your sample is too small, you're free to use other approaches.
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche