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st: re: question on XTOVERID


From   Kit Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: re: question on XTOVERID
Date   Mon, 22 Mar 2010 10:05:04 -0400

<>
> 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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