Allin,
Many thanks for your prompt replies. Your point about the ill-conditioned
instrument matrix makes perfect sense (I'd wondered why the info criteria were
showing "1.#INF00").
I've tested the latest cvs with the following model
X = {const black ed76 smsa76 south76 exp76}
Z = {const black age76 smsa66 south66 nearc4b}
The weak instrument test is still sensitive to the order of the instruments --
when it is there, only the minimum eigenvalue is reported. That would seem to
work as a "flag" that something's wrong.
If I change the instrument list to
Z = {const black age76 smsa76 south76 momed daded},
all three tests (Hausman, Sargan and weak instruments) are reported, although
the latter starts off with
Weak instrument test -
Cragg-Donald minimum eigenvalue = 195.731
Critical values for TSLS bias relative to OLS:
bias 5% 10% 20% 30%
value 0.00 0.00 0.00 0.00
(I'm not familiar with this form of the test, so maybe those 0's are what
they're supposed to be).
I'm still not sure about the df in the Hausman test though. In the last model
it seems to me that this should be 2, not 1. There's no issue of collinearity
that I can see (though rcond(Z'Z) = 5.6e-006), and we're asking about the
exogeneity of 2 variables. I don't want to belabor this -- I know there are
lots of ways of computing the test, but so far I haven't found one that uses (#
endog variables)-1 (though I see how that could/should happen with collinear
variables).
I'm willing to be enlightened or persuaded though...
PS
-----Original Message-----
From: gretl-users-bounces(a)lists.wfu.edu
[mailto:gretl-users-bounces(a)lists.wfu.edu] On Behalf Of Allin Cottrell
Sent: Tuesday, April 20, 2010 11:10 PM
To: Gretl list
Subject: Re: [Gretl-users] tsls tests
On Tue, 20 Apr 2010, Allin Cottrell wrote:
> On Tue, 20 Apr 2010, Summers, Peter wrote:
>
> > First, in a model with k (potentially) endogenous regressors,
> > gretl seems to use k-1 degrees of freedom for the Hausman test
> > rather than k. My impression is that gretl uses the "variable
> > addition" form (eg, Greene p. 323), is that right? If so,
> > shouldn't the the df be k?
>
> I'm going to defer on that one for now, but address the next
> point.
Ready to answer this one: It depends. The degrees of freedom
equals the difference between the number of regressors in the
unrestricted and restricted regressions, which may or may not
equal the 'k' you're talking about. In the model you describe one
"hat variable" is dropped from the the unrestricted regression due
to exact collinearity.
As for the presence/absence of the weak instruments test depending
on the ordering of the variables, clearly that shouldn't happen.
I've committed a change to CVS which I think ensures that you'll
never see broken "weak instruments" output if the matrix of
instruments is too close to rank deficiency. We should probably
print a warning in such a case but I haven't put that into CVS
yet.
Allin Cottrell
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