[Gretl-users] strange R^2 with TSLS

[Riccardo (Jack) Lucchetti]

On Mon, 10 Dec 2007, John C Frain wrote:

> The constant is by definition uncorrelated with the residual and
> therefore can not be endogenous.

<boring theoretical rant>
The constant cannot by definition be correlated with anything, since it 
has no variance. If what you mean is E(u_t * 1) = 0, that is not true by 
definition, but by hypothesis. To be more specific: in a linear model 
suitable for estimation via tsls it is assumed that E((y - xb)|z) = 0. 
Nothing more, nothing less. 99.9999% of the times it's perfectly natural 
that z includes the constant, but it doesn't _have_ to.

Perhaps the reason why we're all squabbling over this is a difference in 
perception: if one sees tsls as a way to get round the problem of 
endogenous regressors, then, well, there's little more to say. I 
personally tend to see tsls as nothing but a special case of gmm, not 
necessarily tied to a simultaneous system framework, so as far as I'm 
concerned the way you specify your orthogonality relationships is no-one 
else's business.
</boring theoretical rant>

Really, I don't mind either way. Could we go back to serious work now, 
please? :-)

> Measuring R^2 as 1-RSS/TSS will give a different answer in OLS and in
> TSLS which is what one would expect.  Is this, perhaps a more
> appropriate measure of fit for TSLS.  I think that both give the same
> answer in ols.

The equivalent to R^2 that I personally consider most sensible is the one 
proposed by Pesaran & Smith ("A Generalized R^2 Criterion for Regression 
Models Estimated by the Instrumental Variables Method", Econometrica, Vol.
62, pp. 705--10.); however, the one we use in gretl now is reasonably 
established and I don't personally feel the need to change it.


Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche

r.lucchetti at univpm.it
http://www.econ.univpm.it/lucchetti