[Gretl-devel] RFC: $sigma & co.

[Sven Schreiber]

Am 01.05.2008 14:03, Riccardo (Jack) Lucchetti schrieb:
> On Thu, 1 May 2008, Sven Schreiber wrote:
> 
>> Am 01.05.2008 12:54, Riccardo (Jack) Lucchetti schrieb:
>>
>>>
>>> Moreover, we have a slight inconsistency in the way we compute 
>>> things: $sigma uses the asymptotic formula (ie, E'E over T), while in 
>>> the displayed equations we use degrees-of-freedom corrected figures 
>>> for standard errors. I'm not overly bothered by this, but some may. 
>>
>> What about $sigma in other contexts, is that asymptotic or 
>> dof-corrected? I think that should be made consistent.
> 
> I'm all for consistency in general, but this case is difficult. In OLS 
> estimation, for example, SSR/T and SSR/(T-k) are both consistent, but 
> the latter has the additional small advantage of being unbiased under 
> certain conditions, so that's traditionally what people use. I 
> personally think it's rather silly to worry about this when you have a 
> decent sample size; if you don't, well, I doubt very much you should be 
> doing inference _at all_.
> 
> In other contexts, Tobit models for example, you simply don't have a 
> choice. In my view, the really important thing is that you know which 
> formula is used in each case, so that if you feel like re-computing 
> $sigma to your taste, you have the tools to do it.
> 

I just meant "consistent definition" across the various contexts of 
$sigma, not consistent in the statistical sense. So if you are saying 
$sigma for Tobit models is w/o dof correction out of necessity but for 
OLS it currently is dof-corrected, then I would suggest the rule: 
"$sigma has a dof correction if at all feasible". That would mean dof 
correction for the VAR/VECM $sigma. BTW, I remember we had a discussion 
in the context of the vcv of the betas in the VECM, but I don't remember 
the result. Is there a dof correction there in the end? (I know I know 
it's probably in the manual...)

cheers,
sven