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RE: st: RE: xtscc and small samples (equal size T and N)


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: xtscc and small samples (equal size T and N)
Date   Tue, 20 Sep 2011 14:23:34 +0100

Christina,

With respect to your last point, you might actually be OK here.

Stock & Watson show that the standard Eicker-Huber-White-robust VCV is biased with small-N large-T panels.  But if you check the paper (eqn 5), you'll see that the bias term has a 1/(T-1) in front of it.  In other words, the bias is decreasing in T.  In your case, T=11 may be enough for you to justify using the standard het-robust VCV.

There is an as-yet undocumented option in -xtivreg2-, sw, that implements the Stock-Watson correction to the standard het-robust VCV.  (It's still not documented because I haven't yet verified it against a published output or another package.)  If the sw option gives you SEs that are similar to the standard het-robust SEs, you've got grounds to believe that T is indeed large enough to justify using the latter.

HTH,
Mark

NB: If anyone can point me to an example of Stock-Watson SEs that I can try to replicate, I'd be most grateful.

References:

Stock & Watson (2008), http://www.princeton.edu/~mwatson/papers/ecta6489.pdf

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> christina sakali
> Sent: 20 September 2011 13:17
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: xtscc and small samples (equal size T and N)
> 
> Dear Gordon, thanks for the response.
> 
> From your as well as Mark's suggestions, I get the idea that 
> perhaps the simple two way fixed effects model is the most 
> appropriate choice for my data, although I do understand than 
> none of the options is ideal with such a small panel sample.
> 
> In other, previous papers with similar sample sizes and 
> topic, I have seen that they usually either go for a simple 
> one or two way fixed effects model or rely on simple robust 
> SE such as White SE. However I am aware that Stock and Watson 
> (2008) showed that these are inconsistent, so this option is 
> also ruled out for my data..
> 
> On 20 September 2011 13:29, Gordon Hughes <G.A.Hughes@ed.ac.uk> wrote:
> > You will probably get almost as many views about what constitutes 
> > large T and/or large N as the number of people you consult.  The 
> > answer is very dependent upon the type of data which you are 
> > analysing, because panel data comes in many different 
> forms.  However, 
> > as Mark says, no one would believe that 11 gets close.
> >
> > For -xtscc- you are dealing with large T asymptotics, so 
> the reference 
> > point would be time series asymptotics.  If you have annual data I 
> > doubt whether anyone would rely on large T results for T 
> much below 30 
> > and some might be much stricter.  The problem, of course, 
> is that many 
> > panel datasets don't meet that criterion, in which case you have to 
> > start to think carefully about what you are trying to 
> estimate.  That 
> > is the point which underlies Mark's original suggestion.  Your 
> > response indicates that you may be trying to get too much 
> out of some rather noisy - or complex - data.
> >
> > Gordon Hughes
> > g.a.hughes@ed.ac.uk
> >
> > =====================================
> >
> > Date: Tue, 20 Sep 2011 02:12:43 +0300
> > From: christina sakali <christina.sakali@googlemail.com>
> > Subject: Re: st: RE: xtscc and small samples (equal size T and N)
> >
> > Dear Mark, thanks a lot for the advice and recommendations.
> >
> > I am a bit reluctant to go for just the simple 2-way fixed effects 
> > model, since after implementing the necessary tests, I have 
> found that 
> > my residuals suffer from both heteroscedasticity and 
> cross-sectional 
> > dependence, so I am looking for an estimator to account for both of 
> > these problems.
> >
> > Does the inclusion of time fixed effects correct for 
> > heteroscedasticity and/or cross-sectional dependence and 
> how exactly 
> > is this achieved? (or can you suggest some reference where 
> I can find 
> > some more information on this issue).
> >
> > Can you also please clarify this for me: What is the 
> minimum (more or
> > less) sample size required for the use of estimators that rely on 
> > large T and N asymptotics?
> >
> > Thank you again.
> >
> > Christina
> >
> >
> > *
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> >
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