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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   Mon, 1 May 2006 22:47:21 +0100

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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