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

 From "Schaffer, Mark E" <[email protected]> To <[email protected]> Subject RE: st: RE: xtscc and small samples (equal size T and N) Date Tue, 20 Sep 2011 11:56:02 +0100

```Christina,

Here's one way to think about the cross-sectional dependence issue.

Say you start with simple pooled OLS.  With panel data, you've got reason to think that this is ignoring time-series dependence.  A simple form of time-series dependence is an unobserved effect that is invariant over time (t) and is shared by all the observations in a cross-section group i.  Cross-section fixed effects, i.e., cross-sectional group dummies for each i, address this problem.

Cross-sectional dependence and time dummies are basically the same thing; just swap around the terminology.  You've got reason to think you are ignoring cross-sectional dependence.  A simple form of cross-sectional dependence is an unobserved effect that is invariant across the cross-sections (i) and is shared by all the observations in a time period t.  Time fixed effects, i.e., time dummies for each t, address this problem.

In both cases, you're addressing the problem by assuming a pretty simple form of the dependence.  If you're right, or close, fine.  If there are still forms of time-series or cross-sectional dependence, you'll still have problems.  But with a panel of only 11x11, there is not much room for maneuver.

As for the minimum N or T for asymptotics, that's a question that depends on the estimator, the characteristics of the data, etc. etc.  Sometimes things converge so slowly that thousands of observations aren't "enough" (the example I'm thinking of is weak identification).  On the other hand, sometimes in the time-series world you're lucky enough to have super-consistency, where the order of convergence is O(T), faster than the usual O(sqrt(T)).  But I think the reaction of most people is that 11 isn't going to convince them.

HTH,
Mark

> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of
> christina sakali
> Sent: Tuesday, September 20, 2011 12:13 AM
> To: [email protected]
> 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
>
> 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
>
> On 20 September 2011 00:50, Schaffer, Mark E
> <[email protected]> wrote:
> > Christina,
> >
> > FWIW, I'd be reluctant to follow Sami's advice, for the
> same reasons I gave earlier, and in spite of my soft spot for
> recommendations involving -ivreg2-.  Two-way clustering
> requires asymptotics where both T->infinity and N->infinity.
> 11 is not very far on the way to infinity no matter how you slice it.
> >
> > What about a simple 2-way fixed effects model with both
> group fixed effects and time dummies?  You have 121
> observations, and you're losing 22 dofs to the FEs, so it's
> >
> > --Mark
> >
> >> -----Original Message-----
> >> From: [email protected]
> >> [mailto:[email protected]] On Behalf Of
> >> Sami Alameen
> >> Sent: 19 September 2011 19:46
> >> To: [email protected]
> >> Subject: Re: st: RE: xtscc and small samples (equal size T and N)
> >>
> >> It's up to you but I would use -ivreg2- with two-way
> >> clustering as follow:
> >>
> >> ssc install ivreg2, replace
> >>
> >> use grunfeld
> >>
> >> xi, noomit: ivreg2 invest kstock mvalue i.company, noconst
> >> cluster(company year)
> >>
> >> And igore the irrelevant segments of the output!
> >>
> >> Sami
> >>
> >> On Mon, Sep 19, 2011 at 8:24 PM, christina sakali
> >> <[email protected]> wrote:
> >> > Dear Mark, thanks for the response.
> >> >
> >> > The first two specifications differ only in respect to one
> >> explanatory
> >> > variable, while the third specification includes both these two
> >> > variables from the previous two specifications.
> >> >
> >> > After estimating them with xtreg ..., fe, I checked for
> serial and
> >> > cross-sectional correlation (using -xtregar, ... fe lbi-
> and xtcsd).
> >> > The results indicated NO serial correlation, but the presence of
> >> > cross-sectional dependence.
> >> >
> >> > Moreover, I read in Hoechle (SJ, 2007, p.17) that the
> >> Driscoll-Kraay
> >> > SE have better small sample properties than other more commonly
> >> > employed estimators when cross-sectional dependence is
> >> present, that
> >> > is why I chose to estimate my model with xtscc.
> >> >
> >> > If both xtscc and cluster are not appropriate for a small
> >> sample like
> >> > mine, then  what is the appropriate estimator, when one needs to
> >> > account for the presence of cross-sectional dependence?
> Or should I
> >> > just use -xtreg, ... fe robust-, which only accounts for
> >> > heteroscedasticity?
> >> >
> >> > Any suggestions are greatly appreciated.
> >> >
> >> > On 19 September 2011 19:38, Schaffer, Mark E
> >> <[email protected]> wrote:
> >> >> Christina,
> >> >>
> >> >> You don't tell us how the 3 specifications differ.  It's hard to
> >> >> offer explanations for the differences in results without
> >> this information.
> >> >>
> >> >> That said, it looks like you have a basic problem here.
> >> >>
> >> >> The cluster-robust approach gives you SEs that are robust to
> >> >> arbitrary within-group autocorrelation.  It relies on
> >> asymptotics in
> >> >> which the number of clusters N goes off to infinity.  11
> >> is not very
> >> >> far on the way to infinity.
> >> >>
> >> >> The Driscoll-Kraay SEs implemented by -xtscc- apply the
> >> kernel-robust
> >> >> approach (e.g., Newey-West) to panel data.  It gives you
> >> SEs that are
> >> >> robust to arbitrary common (across-groups) autocorrelated
> >> disturbances.
> >> >> This approach relies on asymptotics in which the number of
> >> >> observations in the T dimension goes off to infinity.  11
> >> is not very
> >> >> far on the way to infinity.
> >> >>
> >> >> Personally, I'd be reluctant to use either of these
> >> approaches with
> >> >> an
> >> >> N=11/T=11 panel.  Maybe others on the list can offer some
> >> suggestions
> >> >> for alternatives.
> >> >>
> >> >> Sorry to sound so negative, but that's how it looks from here.
> >> >>
> >> >> --Mark
> >> >>
> >> >>> -----Original Message-----
> >> >>> From: [email protected]
> >> >>> [mailto:[email protected]] On Behalf
> >> Of christina
> >> >>> sakali
> >> >>> Sent: 19 September 2011 12:44
> >> >>> To: statalist
> >> >>> Subject: st: xtscc and small samples (equal size T and N)
> >> >>>
> >> >>> Hello all,
> >> >>>
> >> >>> I am estimating 3 different specifications of a panel
> >> fixed effects
> >> >>> model with T=N=11. According to Pesaran's test I have found the
> >> >>> presence of contemporaneous correlation in all 3
> specifications.
> >> >>>
> >> >>> I then tried to estimate all 3 specs with both -xtscc ...,
> >> >>> fe- and -xtreg ..., fe cluster(panelvar) -
> >> >>>
> >> >>> When comparing the S.E. produced by the two estimators, I was
> >> >>> surprised to notice the following:
> >> >>>
> >> >>> Although in the first spec, xtscc S.E. were ALL larger
> >> than cluster
> >> >>> S.E., in the other two specs xtscc S.E. were either larger or
> >> >>> smaller than cluster S.E. However the difference was
> rather small.
> >> >>>
> >> >>> What does this indicate for my data and model (when xtscc
> >> produces
> >> >>> both smaller and larger S.E. than cluster in the same
> >> specification)
> >> >>> and which of the two estimates (xtscc or
> >> >>> cluster) should I trust as more appropriate for my model?
> >> >>>
> >> >>> I am using Stata 9.2.
> >> >>>
> >> >>> Any help or suggestions are appreciated.
> >> >>> *
> >> >>> *   For searches and help try:
> >> >>> *   http://www.stata.com/help.cgi?search
> >> >>> *   http://www.stata.com/support/statalist/faq
> >> >>> *   http://www.ats.ucla.edu/stat/stata/
> >> >>>
> >> >>
> >> >>
> >> >> --
> >> >> Heriot-Watt University is a Scottish charity registered
> >> under charity
> >> >> number SC000278.
> >> >>
> >> >>
> >> >> *
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> >> >
> >> > *
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> >
> >
> > --
> > Heriot-Watt University is a Scottish charity
> > registered under charity number SC000278.
> >
> >
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>
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--
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registered under charity number SC000278.

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```