st: RE: re: question on XTOVERID

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Apostolos,

A quick addendum to what Kit has said: if I'm not mistaken, Baltagi's
textbook on panel data econometrics has a short exposition of the
Hausman-Taylor model and includes a description of what the test of
overidentifying restrictions after a H-T estimation actually tests.

Best wishes,
Mark

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Kit Baum
> Sent: Monday, March 22, 2010 2:05 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: re: question on XTOVERID
> 
> <>
> > I am interesting in performing a Hausman-Taylor estimation 
> in stata (using
> > -xthtaylor command).However, as an attempt to test the 
> assumptions required
> > to get consistent estimators (that the most, except from 
> the endogenous
> > regressors, are not correlated with the time-invariant 
> error term), I did
> > following:
> > xtahylor y x z e f x, endog(z) /// note f, x and z time invariant
> > variables 
> > estimates store xt 
> > xtreg y x e, fe
> > estimates store fe
> > hausman fe xt 
> > In other words, I test the differences between the 
> co-efficients from the
> > two models. If the H0 of no systematic difference was not 
> rejected, the
> > instrumentation of the z variable is sufficient to remove 
> any correlation
> > between the time-ivariant error term and the remaining regressors.
> > I am wondering what the -XTOVERID, after the -xtahylor 
> command, could
> > exactly does? Reading the stata help file, I did not find 
> any specific
> > reference for the case using the command after the xtahylor 
> (except from
> > the calculation of the dof). 
> 
> There are two different sets of assumptions here. If you look 
> at the example in -help xthtaylor-, and rerun that model
> as a FE model, the -hausman- test will not reject its null 
> there either. But that hausman test is run under the 
> maintained hypothesis that the FE model is consistent. If it 
> was consistent, why would you be using an instrumental 
> variables approach such as H-T?
> The hausman test has no power if the maintained hypothesis 
> (that the first model is consistent under H0 and Ha) is violated.
> 
> If you run the example in -help hausman- and then do 
> -xtoverid-, you get a strong rejection of the null that the 
> overidentifying
> restrictions are satisfied. In the case of H-T, the 
> assumption is that some of the variables are correlated with the 
> individual effect (rendering RE inconsistent) but that this 
> can be dealt with using H-T. The second assumption is that ALL of the
> variables are suitably independent of the idiosyncratic error 
> term. This is being tested by -xtoverid-, and the rejection 
> in this case
> means, I believe, that the assumptions required for validity 
> of the H-T estimates are violated. That could be true for many 
> reasons, as in the usual IV case; e.g. omitted variables or 
> wrong functional form.  If you apply -xtoverid- after a RE 
> model, for which the assumption is that X is indep of the 
> individual component, a rejection means that RE assumptions 
> do not hold. 
> I believe the inference here w.r.t. H-T is the same.
> 
> Kit Baum   |   Boston College Economics & DIW Berlin   |   
> http://ideas.repec.org/e/pba1.html
>                               An Introduction to Stata 
> Programming  |   http://www.stata-press.com/books/isp.html
>    An Introduction to Modern Econometrics Using Stata  |   
> http://www.stata-press.com/books/imeus.html
> 
> 
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