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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 15:15:32 +0100

Christina,

The factor in front of bias term in eqn 5 is 1/(T-1).  As T gets bigger, this term gets smaller.  For T=11, the bias term is being multiplied by 1/10, i.e., by 0.1.

-xtivreg2-, like -ivreg2-, can estimate straight OLS as well as IV.  The underlying logic is GMM.  OLS, IV, FE, RE, etc., are all GMM estimators.

--Mark

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> christina sakali
> Sent: 20 September 2011 15:03
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: xtscc and small samples (equal size T and N)
> 
> Mark, this is very useful information.
> 
> Can you please clarify what exactly you mean by "the bias is 
> decreasing in T". To me this sounds like the bias is 
> decreasing when T is decreasing, but then you say that T=11 
> may be large enough to justify using the standard het-robust 
> VCV, so I am not sure I completely get what you mean.
> 
> Also, xtivreg works with instrumental variables, will I be 
> able to implement it with my data?
> 
> On 20 September 2011 16:23, Schaffer, Mark E 
> <M.E.Schaffer@hw.ac.uk> wrote:
> > 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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