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. 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. The complication is the std-error for IV will be downward
bias if you don't apply a correction for the fact that left-hand-side
variable used in the second step is generated using FE coefficient.
In addition, other reasons can be the causes of Julia's results: (1) HT
procedure leaves discretion to the researcher to choose the endogenous
variable, one can try different specifications based on the theorical
support of the model, (2) HT requires correlation between Z1 and Z2 subsets,
additional instruments could improve the results if the correlation is low,
but one needs to write the program (like Mark suggestion) to include the
possibility of more variables and (3) some time-variant variables have slow
time-variation. One could check if this is your case using -xtsum- and
looking the within and between std deviations. I don't know how to solve the
last one, if someone knows some reference I will appreciate that.
Rodrigo.
----- Original Message -----
From: "Schaffer, Mark E" <[email protected]>
To: <[email protected]>
Sent: Tuesday, May 02, 2006 9:53 AM
Subject: RE: st: RE: Hausman taylor
Rodrigo,
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of
> Rodrigo A. Alfaro
> Sent: 02 May 2006 14:31
> To: [email protected]
> 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" <[email protected]>
> To: <[email protected]>
> Sent: Monday, May 01, 2006 5:47 PM
> Subject: RE: st: RE: Hausman taylor
>
>
> Julia,
>
> > -----Original Message-----
> > From: [email protected]
> > [mailto:[email protected]] On Behalf Of
> Julia Spies
> > Sent: 29 April 2006 10:20
> > To: [email protected]
> > 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
> >
> > > --- Urspr�ngliche Nachricht ---
> > > Von: "Schaffer, Mark E" <[email protected]>
> > > An: <[email protected]>
> > > Betreff: RE: st: RE: Hausman taylor
> > > Datum: Sat, 29 Apr 2006 07:39:07 +0100
> > >
> > > Julia,
> > >
> > > > -----Original Message-----
> > > > From: [email protected]
> > > > [mailto:[email protected]] On Behalf Of Julia
> > > > Spies
> > > > Sent: 28 April 2006 23:51
> > > > To: [email protected]
> > > > 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
> > > >
> > > >
> > > > > --- Urspr�ngliche Nachricht ---
> > > > > Von: "Schaffer, Mark E" <[email protected]>
> > > > > An: <[email protected]>
> > > > > Betreff: st: RE: Hausman taylor
> > > > > Datum: Fri, 28 Apr 2006 22:51:29 +0100
> > > > >
> > > > > Julia,
> > > > >
> > > > > > -----Original Message-----
> > > > > > From: [email protected]
> > > > > > [mailto:[email protected]] On
> > Behalf Of Julia
> > > > > > Spies
> > > > > > Sent: 28 April 2006 12:48
> > > > > > To: [email protected]
> > > > > > 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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