Re: st: Tests of overidentifying restrictions with -ivregress-

[Alfonso S <oneiros_spain@yahoo.com>]

Hi all,

Yes, as Joao and Eric point out the overidentification test only tests whether the additional instruments are valid, and is only valid when there are more instruments than endogenous variables (overidentified case). So as you both mention it is not a test of exogeneity of the instruments, but rather that the additional restrictions we are imposing by having additional instruments are valid.

Having said that, the case that Roberto presents has the same overidentification in both estimations, the only difference is that he augments the specification by adding an additional exogenous variable in his second estimation. Since the instruments (exogenous variables not included as explanatory variables in the second stage) are the same in the first and second specification, that the overidentification test passes in the first and fails to pass in the second strongly suggests that the new variable is endogenous, and thus the orthogonality condition is being violated, because in the first specification the orthogonality condition is being met.

Alfonso



On Tuesday, October 15, 2013 11:05 AM, DE SOUZA Eric <eric.de_souza@coleurope.eu> wrote:
That is why it is called a test of over-identifying restrictions and not a test of exogeneity. Though, you are right that many think it is a test of exogeneity.

Eric

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Santos Silva, Joao M C
Sent: 15 October 2013 16:43
To: statalist@hsphsun2.harvard.edu
Subject: RE: st: Tests of overidentifying restrictions with -ivregress-

Dear All,

I have been following this discussion with interest and I think people tend to read too much into the results of the overid test. Passing the test gives no information on whether the instruments identify the parameters of interest.
I guess this is now a well-known results, but we provide examples in this short paper:  http://bit.ly/18gLPeL

Hope this helps,

Joao

> Dear all,
> I need your help for interpreting some postestimation results of my 
> instrumental variables model. I am using Stata 12.0 and the command - 
> ivregress-. The sintax is the following:
> 
> ivregress 2sls dep (endo endoXexo = instrument1 instrument2 
> instrument1#exo
> instrument2#exo) exo exo1 exo2 exo3, first
> 
> where dep is the dependent variable, endo is the endogenous regressor, 
> exo is an exogenous regressor that I want to interact with the 
> endogenous one, and exo1, exo2, exo3 are other exogenous regressors.
> After running this model I type -estat overid- and I obtain this result:
> 
> 
> Tests of overidentifying restrictions:
> 
> Sargan (score) chi2(2) =  .311939  (p = 0.8556)
> Basmann chi2(2)        =  .310601  (p = 0.8562)
> 
> 
> This should mean that my instruments are not correlated with the error 
> of the main regression and therefore they are valid. Now, I want to 
> add an other exogenous regressor in the main regression, and for this reason I write:
> 
> ivregress 2sls dep (endo endoXexo = instrument1 instrument2 
> instrument1#exo
> instrument2#exo) exo exo1 exo2 exo3 exo4, first
> 
> where exo4 is the new variable that I add to the model. The effect of 
> this new factor on the dependent variable is statistically 
> significant, and it also considerably  reduces the effect of endo. 
> However, when I type again - estat overid-  the result is the following:
> 
> Tests of overidentifying restrictions:
> 
> Sargan (score) chi2(2) =  14.1205  (p = 0.0009)
> Basmann chi2(2)        =  14.0913  (p = 0.0009)
> 
> 
> This means that my instruments are not valid anymore. How it can be possible?
> The error term of the first model should incorporate also the effect of exo4.
> As far as I am aware, if my instruments are not correlated to it (the 
> error term), they can not be correlated with the error term of the 
> second model. I don't know how to interpret these results.....
> Any idea or suggestion?
> Thank you very much for help
> Roberto
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