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RE: st: RE: Hausman taylor


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: Hausman taylor
Date   Tue, 2 May 2006 14:53:05 +0100

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 14:31
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: Hausman taylor
> 
> Dear Mark and Julia,
> 
> HT does not generate consistent estimators for the presence 
> of autocorrelation and/or heteroskedasticity. Section 2.3 of 
> the paper gives you consistency analysis. As you can see the 
> consistent std errors are based on homoskedastic case.

The key question is the consistency of the coefficient estimates.  The SEs are, of course, inconsistent - I think that's why Julia is interested dealing with the heteroskedaticity and AC problem.  But if the coefficient estimates are consistent, then the procedure I outlined below ought to generate consistent SEs.

It's just like standard random effects GLS.  The coefficient estimates are consistent but inefficient in the presence of heteroskedasticity or autocorrelation, but the usual GLS SEs are not consistent.  Using cluster-robust SEs then solves the problem of obtaining consistent standard errors for a standard random effects estimation.

I *think* same reasoning carries through with HT....

--Mark

> 
> In other words, you have to work with fixed-effects 
> estimators and IV-between-effects estimators, steps 1 and 2. 
> The goal is to build a HAC for this estimators. Note IV were 
> generated using FE, then the variance has to control for that.
> 
> Best, Rodrigo.
> 
> 
> ----- Original Message -----
> From: "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
> To: <statalist@hsphsun2.harvard.edu>
> Sent: Monday, May 01, 2006 5:47 PM
> Subject: RE: st: RE: Hausman taylor
> 
> 
> Julia,
> 
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Julia Spies
> > Sent: 29 April 2006 10:20
> > To: statalist@hsphsun2.harvard.edu
> > Subject: RE: st: RE: Hausman taylor
> >
> > Sorry, what I meant was the the overid test stats is not
> > significant and running a hausman test to compare HT with GLS
> > is significant. I just mixed it up. Apologies!
> >
> > 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: Sat, 29 Apr 2006 07:39:07 +0100
> > >
> > > Julia,
> > >
> > > > -----Original Message-----
> > > > From: owner-statalist@hsphsun2.harvard.edu
> > > > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Julia
> > > > Spies
> > > > Sent: 28 April 2006 23:51
> > > > To: statalist@hsphsun2.harvard.edu
> > > > Subject: Re: st: RE: Hausman taylor
> > > >
> > > > Dear Mark,
> > > >
> > > > with "improving the model" I mean that the 
> over-identification test
> > > > statistic comparing the FE model (I use areg with the cluster()
> > > > option, since i identified autocorr. and 
> heteroskedasticity) with
> > > > the HT estimation is significant, which means - if I 
> understand it
> > > > correctly - that the correlation between the 
> explanatory variables
> > > > and the individual effects has been removed by the 
> instrumentation.
> > >
> > > Apologies if I am misunderstanding what you have 
> reported, but it's
> > > the other way around.  A large and significant overid 
> stat is evidence
> > > AGAINST your HT estimate.  As usual with IV estimation, 
> under the null
> > > that the orthogonality conditions are statisfied (the 
> instruments are
> > > "valid"), the overid stat is distributed as chi-sq.  A 
> big stat and
> > > rejection of the null
> > > suggests that your orthogonality conditions are not 
> satisfied, i.e.,
> > > the instruments are not valid, i.e., your HT estimation 
> is misspecified.
> > >
> > > --Mark
> > >
> > > > Of course, since I have the odd parameter estimates in the
> > > > instrumented time-invariant variables (which cannot be 
> estimated in
> > > > the FE model), they don't enter the over-identification test.
> 
> I'm not sure this is quite right.  Hausman-Taylor (1981, p. 
> 1389) say that 
> "_all_ of the exogeneity information about X and Z is subject 
> to test by 
> this procedure" [emphasis in the original], meaning the 
> overid test they 
> give in their equation (2.2).  Even though they aren't used 
> to calculate the 
> test statistic, all the orthogonality conditions are part of 
> the null, or so 
> they say.
> 
> > > > My question therefore was whether autocorr. and 
> heteroskedasticity
> > > > could produce these very high estimates or whether someone could
> > > > think of any other source for the problem, and how I 
> can correct for
> > > > it in the HT estimation.
> 
> I am not sure, but the HT estimation may generate consistent 
> parameter 
> estimates even in the presence of autocorrelation and 
> heteroskedasticity, 
> and the problem may be that the var-cov estimate is wrong.  
> This needs 
> checking, but if so, then you could address the problem by using 
> cluster-robust standard errors.  This would give you SEs that 
> are robust to 
> arbitrary autocorrelation and heteroskedasticity.
> 
> Unfortunately, -xthtaylor- doesn't support the -cluster- 
> option.  This be 
> might deliberate (i.e., the Stata programmers know that HT 
> won't generate 
> consistent parameter estimates in the presence of AC or het), 
> or it might 
> not.  If not, then you could consider making a copy of 
> -xthtaylor-  (call 
> it, say -xthtaylor2-) and editing it so that it forces cluster-robust 
> standard errors.  The way to do this is to go to the block that says
> 
> /* Hausman-Taylor estimator */
> 
> A few lines under that is a call to regress, using the 
> old-fashioned syntax 
> (IVs in parentheses) for an IV estimation.  You would add a 
> cluster option 
> to that line.  It's currently
> 
> reg `yvar_g' `list_g' `g_cons'  /*
> */ (`xvar1_dm' `xvar2_dm' /*
> */ `xvar1_m' `zvar1' `g_cons') `wtopt' /*
> */ if `touse', nocons
> 
> and you would change this to
> 
> reg `yvar_g' `list_g' `g_cons'  /*
> */ (`xvar1_dm' `xvar2_dm' /*
> */ `xvar1_m' `zvar1' `g_cons') `wtopt' /*
> */ if `touse', nocons cluster(`ivar')
>                             ^^^^^^^^^^^^^^^
>                             ^add this bit^
> 
> You would also need to change the line at the top of the file from
> 
> program  xthtaylor, eclass byable(recall) sort
> 
> to
> 
> program  xthtaylor2, eclass byable(recall) sort
> 
> Might work.  Worth a thought, anyway.
> 
> HTH.
> 
> Cheers,
> Mark
> 
> > > > Sorry for not making my point clear in the first e-mail. I will
> > > > definitely try out Rodrigo's suggestions. Thank you 
> very much for
> > > > the advice!
> > > >
> > > > Best regards,
> > > > Julia
> > > >
> > > >
> > > > > --- Ursprüngliche Nachricht ---
> > > > > Von: "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
> > > > > An: <statalist@hsphsun2.harvard.edu>
> > > > > Betreff: st: RE: Hausman taylor
> > > > > Datum: Fri, 28 Apr 2006 22:51:29 +0100
> > > > >
> > > > > Julia,
> > > > >
> > > > > > -----Original Message-----
> > > > > > From: owner-statalist@hsphsun2.harvard.edu
> > > > > > [mailto:owner-statalist@hsphsun2.harvard.edu] On
> > Behalf Of Julia
> > > > > > Spies
> > > > > > Sent: 28 April 2006 12:48
> > > > > > To: statalist@hsphsun2.harvard.edu
> > > > > > Subject: st: Hausman taylor
> > > > > >
> > > > > > Dear all,
> > > > > >
> > > > > > I'm quite a beginner with Stata and i'm trying to 
> run a Hausman
> > > > > > taylor regression. However, taking some (plausible) 
> time-invariant
> > > > > > variables as endogeneous results in outrageous 
> parameter estimates
> > > > > > for these variables.
> > > > > > Nevertheless, the over-identification test suggests that
> > > > > > instrumenting these variables has improved the model.
> > > > >
> > > > > This sounds odd ... what do you mean by "improving the model"?
> > > > >
> > > > > --Mark
> > > > >
> > > > > > Does
> > > > > > anyone have an idea what the problem could be? I
> > > > > > understand there is no option to correct for 
> heteroskedasticity 
> > > > > > and
> > > > > > autocorrelation.
> > > > > > Does anyone know how to do it manually?
> > > > > >
> > > > > > Cheers,
> > > > > > Julia
> 
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