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

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

Roberto,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of Roberto Pannico
> Sent: 09 October 2013 17:15
> To: statalist@hsphsun2.harvard.edu
> Cc: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Tests of overidentifying restrictions with -ivregress-
> 
> Hola Alfonso,
> thank you very much for your answer.
> Actually I have done an endogeneity test of exo4 and this is the result:
> 
> Tests of endogeneity
>   Ho: variables are exogenous
> 
>   Durbin (score) chi2(1)          =  13.8016  (p = 0.0002)
>   Wu-Hausman F(1,5731)            =  13.7747  (p = 0.0002)
> 
> So, it seems that technically the variable is endogenous. The "problem" is
> that theoretically this is impossible: exo4 is the amount of money that a
> country receives from European Union, while the dependent variable of the
> model is the level of support that a citizen give to European Union. And given
> that the amount of money that a country receives is not determined taking
> into account the level of support of its citizens (but the opposite is true),
> theoretically the regressor can not be endogenous.

I am afraid this is a fundamental misunderstanding of what "endogeneity" and "exogeneity" means in the context of econometrics and Sargan/Hansen/Durbin/Wu/Hausman tests.

You have in mind "determined within the system" vs. "determined outside the system", or something like that.  These are perfectly legitimate definitions of endogenous and exogenous.  But that's not what these tests are testing.

In econometrics, "exogenous" means E(Xu)=0.  (You can make it a conditional expectation, you can distinguish between strong and weak exogeneity, etc., it doesn't affect the main point.)  It's easy to think of examples where X is a regressor that is "exogenous" in the way you are using the term ("determined outside the system") but endogenous in the sense that E(Xu) ≠ 0.

Here's an example.  We have a dataset of farms.  X is weather.  It's easy to see that weather is exogenous in the sense that you are using the term - it's determined outside the system, like exo4 in your example.  But it's also easy to see that it can be endogenous in an econometric sense, i.e., E(Xu) is not zero.  The orthogonality condition E(Xu)=0 would fail if there are omitted variables in u which are correlated with weather (like, I don't know, soil quality - I confess I know very little about practical farming - it's just an example).  This makes weather "endogenous" in the econometric sense, even though for most practical purposes (climate change, cloud seeding et al. aside) it's exogenous in a modelling or system sense.

Note that whether or not a regressor is econometrically exogenous depends on the specification of the model (or, if you prefer, what's in u because it's not in the model).  You may be able to come up with a different specification of your model where you have good reasons to think that exo4 is exogenous in the econometric sense.

HTH,
Mark


> Concerning your second questions, when I write
> 
> ivregress 2sls dep (endo endoXexo = instrument1 instrument2
> instrument1#exo instrument2#exo) exo exo1 exo2 exo3 exo4, first
> 
> the command -ivregress- automatically uses all the regressors of the model
> as instrumental variables.
> Finally, I am not sure I understand your last question. Why should I use the
> instruments as explanatory variables in the main model? in any case Stata
> does not allow me doing it. When I write the following model:
> 
> ivregress 2sls dep (endo endoXexo = instrument1 instrument2
> instrument1#exo instrument2#exo) exo exo1 exo2 exo3 exo4 instrument1
> instrument2 instrument1#exo instrument2#eco, first
> 
> Stata gives the following error message
> 
> equation not identified; must have at least as many instruments not in the
> regression as there are instrumented variables
> 
> Any other suggestion?
> Thank you again for your help
> Roberto
> 
> 
> 
> 
> 
> 
> 
> 
> ----- Mensaje original -----
> De: Alfonso S <oneiros_spain@yahoo.com>
> Fecha: Miércoles, Octubre 9, 2013 3:45 pm
> Asunto: Re: st: Tests of overidentifying restrictions with -ivregress-
> 
> > Hola Roberto,
> >
> > my first thought is that exo4 may not be exogenous. Have you done a
> > test of endogeneity? My second question would also be why don't you
> > use all the exogenous variables you have as instruments, and the
> > instruments you are using as explanatory variables as well?
> >
> > Best,
> >
> > Alfonso Sanchez-Penalver
> >
> >
> >
> > On Wednesday, October 9, 2013 7:47 AM, Roberto Pannico
> > <Roberto.Pannico@uab.cat> wrote:
> > 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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