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


From   "Schaffer, Mark E" <[email protected]>
To   "[email protected]" <[email protected]>
Subject   RE: RE: RE: st: Tests of overidentifying restrictions with -ivregress-
Date   Mon, 14 Oct 2013 17:41:02 +0000

Roberto,

> -----Original Message-----
> From: [email protected] [mailto:owner-
> [email protected]] On Behalf Of Roberto Pannico
> Sent: 14 October 2013 16:11
> To: [email protected]
> Subject: Re: RE: RE: st: Tests of overidentifying restrictions with -ivregress-
> 
> Dear Mark,
> thank you again for your explication. It was again really useful.
> You write:
> 
> > The way that I've set it up, the orthogonality condition for the
> > original model means E(Z*e1) = E(Z*e2) + E(Z*exo4) = 0.  E(Z*e2) can
> > be nonzero, and as long as E(Z*exo4) is the opposite sign and the same
> > magnitude, then the orthogonality condition for the original model,
> > E(Z*e1)=0, will be satisfied, but the orthogonality condition for the
> > augmented model, E(Z*e2)=0, will fail.
> 
> This is totally clear. But now I have some doubts on the efficacy of
> overidenfying test in the original model. Following your example, the
> overidentifying test of the original model can say me that  my instrument is
> not correlated with the error term e1. But it can not ensure me that it is not
> correlated with e2 (that is, one of the component of e1). What if in e2 is
> included a variable that is also a determinant of my instrument? Will the
> regression coefficient be biased by this endogenity, or the opposite sign
> correlation  E(Z*exo4) will "correct" the bias? That is, the fact that my
> instrument is correlated with both components of the error term will give the
> same result as it was not correlated with neither of them?

If the orthogonality conditions for your original model, E(Z*e1)=0, are satisfied, then your IV estimates are consistent.  Have a look at any econometrics textbook for a proof.  It doesn't matter if the Zs are correlated with components of e1; all you need is that E(Z*e1)=0 is true for all the Zs.  Whether or not that is plausible is up to you to argue!

--Mark

> thank you again
> Roberto
> 
> Roberto Pannico
> PhD Candidate
> Department of Political Science
> Universitat Autònoma de Barcelona (UAB)
> Edifici B, 08193 Bellaterra, Barcelona, Spain
> Office: B3b/119.1
> Tel. (+34) 93 581 49 73
> [email protected]
> 
> 
> ----- Mensaje original -----
> De: "Schaffer, Mark E" <[email protected]>
> Fecha: Lunes, Octubre 14, 2013 3:19 pm
> Asunto: RE: RE: st: Tests of overidentifying restrictions with -ivregress-
> 
> > Roberto,
> >
> > You write:
> >
> > > The error term
> > > of the second equation should be equal to the error term of the
> > first one,
> > > minus the effect of exo4; if the instruments were not correlated
> > with the
> > > first error, how can be they correlated with the second one?
> >
> > It's possible.  Let me give you a mechanical example.  "Mechanical"
> > means it's an illustration, and there's no economic meaning intended.
> >
> > Call the error term in the original model e1.  The variable exo4 is
> > not in the model, so it's "inside" e1.
> >
> > Call the error term in the augmented model e2.  The variable exo4 is
> > one of the regressors in the augmented model, so it's not "inside" e2.
> >
> > Say that the "true" coefficient on exo4 in the augmented model is 1,
> > just to make the exposition easier.  So a feature of the DGP is that
> > e1 = e2 + exo4.
> >
> > Say that Z is a valid instrument for the original model, so E(Z*e1)=0.
> >
> > Is it possible that Z is not a valid instrument for the new model?
> > That is, is it possible that E(Z*e2) is not zero?  I think so.
> >
> > The way that I've set it up, the orthogonality condition for the
> > original model means E(Z*e1) = E(Z*e2) + E(Z*exo4) = 0.  E(Z*e2) can
> > be nonzero, and as long as E(Z*exo4) is the opposite sign and the same
> > magnitude, then the orthogonality condition for the original model,
> > E(Z*e1)=0, will be satisfied, but the orthogonality condition for the
> > augmented model, E(Z*e2)=0, will fail.
> >
> > Writing this on the fly so caveat emptor, but I think I got that
> > right....
> > --Mark
> >
> > > -----Original Message-----
> > > From: [email protected] [owner-
> > > [email protected]] On Behalf Of Roberto Pannico
> > > Sent: 14 October 2013 11:30
> > > To: [email protected]
> > > Subject: Re: RE: st: Tests of overidentifying restrictions with -
> > ivregress-
> > >
> > > Dear Mark,
> > > thank you very much for your help and for your useful
> > explanation. Actually I
> > > have good reasons for thinking that exo4 is endogenous to the model
> > > because of an omitted variable. What I don't understand is why the
> > > endogeneity of exo4 should cause the invalidity of my
> > instrumental variables.
> > > I will try to explain myself in a better way.
> > > My model 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)
> > >
> > > As far as I understand, this test means that my instruments are
> > valid because
> > > are not correlated with the error term ( and therefore they are not
> > > correlated with the omitted variables that are included in it).
> > Now, I want to
> > > add an other exogenous variable in my 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, meaning that its effect
> > was> included in the error term of the previous regression.
> > 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)
> > >
> > > so, in this case my instruments are not valid anymore, they are
> > correlated> with the error term. I understand that exo4 can be
> > endogenous to the model
> > > and for this reason correlated with the error term, but why this
> > should also
> > > cause the instruments being correlated with the error term? The
> > error term
> > > of the second equation should be equal to the error term of the
> > first one,
> > > minus the effect of exo4; if the instruments were not correlated
> > with the
> > > first error, how can be they correlated with the second one?
> > >
> > > I apologize if I am missing a very obvious point...
> > > Thank you very much for your help
> > > Roberto
> > >
> > >
> > >
> > > Roberto Pannico
> > > PhD Candidate
> > > Department of Political Science
> > > Universitat Autònoma de Barcelona (UAB) Edifici B, 08193 Bellaterra,
> > > Barcelona, Spain
> > > Office: B3b/119.1
> > > Tel. (+34) 93 581 49 73
> > > [email protected]
> > >
> > >
> > > ----- Mensaje original -----
> > > De: "Schaffer, Mark E" <[email protected]>
> > > Fecha: Jueves, Octubre 10, 2013 12:02 pm
> > > Asunto: RE: st: Tests of overidentifying restrictions with -
> > ivregress-
> > >
> > > > Roberto,
> > > >
> > > > > -----Original Message-----
> > > > > From: [email protected] [owner-
> > > > > [email protected]] On Behalf Of Roberto Pannico
> > > > > Sent: 09 October 2013 17:15
> > > > > To: [email protected]
> > > > > Cc: [email protected]
> > > > > 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 <[email protected]>
> > > > > 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
> > > > > > <[email protected]> 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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We invite research leaders and ambitious early career researchers to 
join us in leading and driving research in key inter-disciplinary themes. 
Please see www.hw.ac.uk/researchleaders for further information and how
to apply.

Heriot-Watt University is a Scottish charity
registered under charity number SC000278.


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