Dear Mark and Rodrigo,
sorry, I was a few days out of office, but sure, the discussion certainly
gave me some new insights. I will inspect my data again (I suspect the odd
estimates come from weak instruments, since some variables are indeed hardly
time-varying) and try to do the HAC in the most appropriate way based on the
amount of heteroskedasticity I have in the data.
Thank you both very much again! Your comments are highly appreciated.
Cheers,
Julia
> --- Ursprüngliche Nachricht ---
> Von: "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
> An: <statalist@hsphsun2.harvard.edu>
> Betreff: RE: st: RE: Hausman taylor
> Datum: Tue, 2 May 2006 23:32:35 +0100
>
> Rodrigo, Julia,
>
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> > Rodrigo A. Alfaro
> > Sent: 02 May 2006 22:16
> > To: statalist@hsphsun2.harvard.edu
> > Subject: Re: st: RE: Hausman taylor
> >
> > Mark
> >
> > I rechecked my comments and found that you are right. GLS is
> > still a consistent (inefficient and noisy) estimator under
> > het/auto then your solution is valid. But let me compare the
> > procedures in word: (1) yours controls for the RE (w/wrong
> > weights) then applies IV to obtain the third-round
> > coefficients and uses robust std errors and (2) mine stops HT
> > at step 2 and uses robust std error (keeping in mind the fact
> > that IV coefficient were obtained in a second round). After
> > our discussion both procedures are consistent and efficient,
> > but numerically will give us different results in
> > coefficients as well std-errors. Very interesting. I have 2
> > more comments about your procedure: (1) it needs needs (as same as
> > HT) some (extra) exogeneity in time-variant variables (to do
> > the last IV procedure) and (2) it generates some extra noise to the
> > variables computing a wrong GLS factor.
>
> Rodrigo - we don't know which estimator is more "noisy". It all depends
> on the het./AC. If, say, heteroskedasticity exists but is very small,
> then HT will be almost efficient and probably better than stopping after
> step 2. If the heteroskedasticity is huge, then all bets are off and
> stopping after step 2 is probably a better idea. But we should continue
> this off-list.
>
> Julia - did this debate help?? This was your question to start with!
>
> Cheers,
> Mark
>
> >
> > Rodrigo.
> > PS: We can continue the discussion off the list if you want.
> >
> > ----- Original Message -----
> > From: "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
> > To: <statalist@hsphsun2.harvard.edu>
> > Sent: Tuesday, May 02, 2006 12:35 PM
> > Subject: RE: st: RE: Hausman taylor
> >
> >
> > Rodrigo,
> >
> > > -----Original Message-----
> > > From: owner-statalist@hsphsun2.harvard.edu
> > > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> > > Rodrigo A. Alfaro
> > > Sent: 02 May 2006 16:12
> > > To: statalist@hsphsun2.harvard.edu
> > > Subject: Re: st: RE: Hausman taylor
> > >
> > > Mark,
> > >
> > > This is very interesting discussion. My point is that under
> > > autocorrelation and/or heteroskedasticity you cannot generate
> > > consistent estimator for variance of the error term,
> > > therefore the GLS transformation applied in the last step of
> > > original-HT is wrong. For this reason, I cannot see that the
> > > coefficients of modified-HT can be consistent, based on that
> > > in your suggestion is still using the wrong GLS
> > > transformation.
> >
> > I agree, this is interesting. But I am pretty sure that the
> > HT coefficients
> > are consistent in the presence of het. or AC. Here are two reasons:
> >
> > 1. The GLS transform used is a weighted average of the
> > within and between
> > estimators (HT, p. 1381). A weighted average of two
> > consistent estimators
> > will be consistent (except perhaps in special cases constructed by
> > specialists, i.e., not me).
> >
> > 2. In the standard random effects estimator, in the presence
> > of het./AC,
> > you also cannot obtain a consistent estimator for the
> > variance of the error
> > term - just as you say for HT. The GLS transform applied to
> > get the random
> > effects estimator is therefore "wrong" - but only in the
> > sense that it isn't
> > an *efficient* estimator. It's still consistent. That's why various
> > textbooks (e.g., Wooldridge 2002) point out that one can use the
> > cluster-robust covariance estimate to get consistent SEs for
> > the random
> > effects estimator even in the presence of het./AC. The same
> > argument should
> > [sic!] apply to HT, no?
> >
> > > Mind that original-GLS transformations uses
> > > the variance of the residual as a scalar and now it is an
> > > unknown matrix.
> > >
> > > As I said early, coefficients on the previous steps are
> > > consistent, but inefficient. Indeed, the section 2.3 in the
> > > paper is called "Consistent but Inefficient Estimation". I
> > > think that the Julia's problem can be solved but keeping the
> > > FE (time-variant variables) and IV (time-invariant variables)
> > > coefficients and generating a non-parametric std error as
> > > Newey-West procedure does.
> >
> > This is a good idea. Another way to put it would be to say
> > that the last
> > step of HT generates efficient estimators of the coefficients
> > only under
> > homoskedasticity. If this assumption fails, then HT is
> > consistent but not
> > efficient (my point above). In that case, the HT approach of
> > GLS loses its
> > main attraction, and so why bother doing it - just stop at
> > the previous
> > stage, with the within and between estimators. Julia can do
> > this by hand.
> >
> > Cheers,
> > Mark
> >
>
>
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