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Re: st: RE: Panel Data Analysis


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu, Nick Cox <n.j.cox@durham.ac.uk>
Subject   Re: st: RE: Panel Data Analysis
Date   Thu, 15 Apr 2004 22:27:03 +0100 (BST)

Nick, Sukhdev, et al.,

Quoting Nick Cox <n.j.cox@durham.ac.uk>:

> We've seen various versions of this question before, 
> on 29 March and 1 April. 
> 
> On 29 March, I said (among other things) 
> 
> =============
> Having said that, 3 years' worth (or is it 
> 2 years' worth, 1999 and 2001) of data is not much
> basis for fitting a panel model. You're pretty much
> reduced to a cross-sectional study, if I understand 
> you correctly. 
> =============
> 
> As far as I can tell no one else has commented, 
> nor have you replied to this comment. 

OK, I'll have a go.

Short panels are still panels and have their uses.  There are times when 
even just two year's worth of data is a lot more useful than one.

For example, when T=2, fixed-effects estimation is exactly equivalent to 
estimating in first-differences (see Wooldridge's 2002 book, p. 284 and 
292).  Say that the model is one in which each observation (country, in 
Sukhdev's application) has an unobserved characteristic that is time-
invariant and also correlated with the (observed) RHS variables.  Estimate 
in levels and you get inconsistent estimates of the coefficients on the 
regressors; estimate in first-differences and you get consistent estimates.

Wooldridge's book (Econometric Analysis of Cross-Section and Panel Data) 
is very good on this and lots of other related issues; see especially 
chapter 10.

With respect to Sukhdev's specific questions, though, I think Nick is 
right to suggest thinking about the fundamentals first.  Sukhdev has a 2-
year panel and he is interested in explaining GDP growth.  Fixed effects 
is exactly equivalent to estimating in first differences in this case.  
Does he really want to try to explain cross-country *changes* in GDP 
growth, i.e., why GDP growths rates bounce up or down?  This is what FE or 
FD do ... but it may be asking a lot of the data.  Or does he want to try 
to explain variations in cross-country GDP growth rates?  This is what 
cross-section or pooled OLS does ... but then he may have the problem of 
unobserved effects, as noted above.  Does he want to get as efficient 
estimates as possible?  This is obtained by putting some more structure in 
the assumptions about the disturbance term, e.g., estimating a GLS model 
such as random effects ... but as usual, making estimates more efficient 
also makes them less robust to violations of assumptions.

Hope this helps.

--Mark

> 
> I have raised a question, which I now put more 
> strongly: It appears from what 
> you tell us that your dataset is inadequate
> for testing the kind of model you are interested
> in. How do you expect to get a handle on the dynamics
> from two time points? All worries about fixed
> or random effects, autocorrelation, heteroskedasticity,
> etc. are quite secondary until this is answered. 
> 
> Either I am wrong here, in which case tell me
> with a reasoned argument; 
> or you really should be talking this through 
> with an advisor or supervisor. Sorry to 
> be blunt. 
> 
> Nick 
> n.j.cox@durham.ac.uk 
> 
> Sukhdev Kumar
>  
> > I'm pretty new to Stata and I was hoping someone might be 
> > able to help me
> > with a few queries (apologies for the length of the message). I
> have a
> > balanced panel of 78 countries with data for 2 time periods, 
> > 1999 and 2001.
> > I wanted to run the regression whereby the dependent variable 
> > is gdp growth,
> > and the independent variables are aids deaths, literacy rate, 
> > productivity
> > growth and population growth.
> > 
> > I ran xtreg...re i(country) and also xtreg...fe i(country) 
> > followed by the
> > xthausman test. I get the following results.
> > 
> > 
> > Hausman specification test (Warning:  xthausman is no longer 
> > a supported
> > command; use -hausman-.  For
> >  instructions, see help hausman.)
> > 
> >                 ---- Coefficients ----
> >              |      Fixed       Random
> >    gdpgrowth |    Effects      Effects       Difference
> > -------------+-----------------------------------------
> >   aidsdeaths |  -.2627628    -.0446729        -.2180899
> >   prodgrowth |   .5323049     .5334939         -.001189
> >    popgrowth |   .1182492      .307154        -.1889048
> >     literacy |  -.4322142     .0048829        -.4370972
> > 
> >     Test:  Ho:  difference in coefficients not systematic
> > 
> >                  chi2(  4) = (b-B)'[S^(-1)](b-B), S = (S_fe -
> S_re)
> >                            =     5.31
> >                  Prob>chi2 =     0.2569
> > 
> > Both models are quite poor compared to what I expected but I
> don't
> > understand what the above results are telling me - can 
> > anybody help? Can I
> > also test for autocorrelation or heteroskedasticity before 
> > running another
> > model?
> > 
> > As both the fixed effects and random effects models were poor 
> > I also ran the
> > xtgls model with corr(ar1) panel(hetero) force and got much 
> > better results.
> > However, I don't really know whether I should have stated 
> > that the model had
> > both autocorrelation and heteroskedasticity problems (can I 
> > even have ar1
> > seeing as my two time periods do not follow each other?). I 
> > really need to
> > know which model I should use before I go on to run smaller 
> > regressions on
> > samples of my countries.
> > 
> > I'd really appreciate it if somebody could help me with this, and
> I
> > apologise in advance for my lack of expertise in this area!
> 
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> 



Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3008
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes
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