Re: [Gretl-users] Thanks on Allison's alternative Hausman test / No joy on PCSEs
On Thu, 27 Dec 2012, Clive Nicholas wrote:
> On Thu, 27 Dec 2012, Riccardo (Jack) Lucchetti replied:
>
> [...]
>> When you write restrictions for the "restrict" command, no
coefficients
> must
>> appear on the right-hand side of the equality. This is stated in the
>> documentation.
>>
>>> Test statistic: F(3, 1016) = 3.27298, with p-value = 0.0205637
>>>
>>> This test would appear to comprehensively reject the RE model in favour
> of
>>> retaining the FE model. Or does it? Is this an acceptable test in place
> of
>>> the Wald test for jointly equal parameters that I can't run in -gretl-?
>
Allin Cottrell wrote:
> I'd just add to Jack's reply: this _is_ a Wald test for
> jointly equal parameters (the F-form of the test). If you
> multiply the test statistic by 3 and refer it to the
> chi-square(3) distribution you get the same p-value as given
> above.
Excellent stuff - I thought I was on the right track! Nice to be able to
deploy some correct logic for once.
Thanks for pulling me up on not reading the documentation, but in my
defence: (a) I've only just installed -gretl-; (b) it's Christmas, so I've
not had much of a chance to peruse what is a very large users' guide; and
(c) I did look at the program help on restrictions (although clearly
they're not as comprehensive as that laid out in the guide).
If I may, I had another quick query about panel-corrected standard errors.
I'm delighted you've included them in -gretl-, but I've had no luck in
fitting any fixed-effect models with PCSEs (N=47, T=36, NT=795, with ten X
variables; all bar the first and last of the time dummies were included;
there was no lagged dependent variable). Every time I do, the model does
run, but with the message "Could not compute Beck-Katz errors". I'm sure
the reasons for not doing so are valid, but no reason was given at all.
Beck-Katz does:
Var(b) = A^{-1} W A^{-1}
where A = \sum_{i=1}^n X'_i X_i,
W = \sum_{i=1}^n \sum_{j=1}^n \sigma_{ij} X'_i X_j
and \sigma_{ij} is estimated as (1/T) \sum_{t=1}^T e_i e_j,
with the e's being OLS (or fixed effects) residuals.
The trouble is there's no guarantee that W (which is supposed
to be a variance measure) is positive definite in unbalanced
panels; if it's not, we "fail".
Also, which standard errors are reported instead?
The "classical" ones. If the Arellano method is used you'll
see "Robust (HAC) standard errors".
Allin Cottrell