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# Re: Antwort: Re: Antwort: Re: Antwort: Re: RE: st: Spurious inference from endogeneity tests

 From "Justina Fischer" To statalist@hsphsun2.harvard.edu Subject Re: Antwort: Re: Antwort: Re: Antwort: Re: RE: st: Spurious inference from endogeneity tests Date Mon, 23 Jan 2012 16:18:57 +0100

```Hi Andreas

1) true. This is why you should always consult several test stats (incl. t-stats, F-stats, Shea R2, robust-to-weak instr. stats, etc.) to get an overall picture. Selecting instruments is a hard and complex business...

2) reduncancy tests make only sense when you have managed to select good instruments (it is based on the Sargan/Hansen-J test, if I recall well -> consult ivreg2 help file).

3) practice shows it is in most cases to have no of instruments > endogenous regressors, but not too many in absolute number. For one endogenous regressor, I usually try to find three instruments. You can increase the number of instruments artificially by doing some non-linear stuff, e.g. using a quadratic term.

Best,
justina

-------- Original-Nachricht --------
> Datum: Mon, 23 Jan 2012 15:59:27 +0100
> Von: andreas.zweifel@uzh.ch
> An: statalist@hsphsun2.harvard.edu
> Betreff: Antwort: Re: Antwort: Re: Antwort: Re: RE: st: Spurious inference from endogeneity tests

> Hi Justina,
>
> thank you for the intuitive ideas with respect to the quality of the
> instruments.
>
> So I was wrong with my notion that one should have as many instruments as
> endogenous variables in the regression. But I can tell you that I have
> already tested my model with one endogenous regressor under overidentification,
> that is with a whole set of instruments. The Sargan test statistic using
> -ivreg2- (or -ivreg28- in Stata8) is clearly not significant then, so the
> null that the instruments are exogenous cannot be rejected. However, I fear
> that this is weak evidence especially for my setting, because
>
> 1) To my knowlegde, Sargan only allows to test whether the instruments are
> *jointly* exogenous. It does yield no information about the strength of
> one single instrument.
>
> 2) Using the -redundant- option in -ivreg2-, I get contradictory results.
> I tried a sensitivity test with a varying number of possibly good
> instruments and control variables to find the following: Virtually every instrument
> candidate yields a more or less significant p-value for the redundancy test
> if combined with many
> other excluded instruments but few control variables. But reducing the
> number of instruments or increasing
> the number of controls in the regression model, the remaining instruments
> seem to become more redundant as well.
> I don't know what is to be held of an instruments relevance test which
> reacts thus sensitively to minor changes in the model specification.
>
>
> Best,
> Andreas
>
> -----owner-statalist@hsphsun2.harvard.edu schrieb: -----
> An: statalist@hsphsun2.harvard.edu
> Von: "Justina Fischer"
> Gesendet von: owner-statalist@hsphsun2.harvard.edu
> Datum: 21.01.2012 01:35
> Betreff: Re: Antwort: Re: Antwort: Re: RE: st: Spurious inference from
> endogeneity tests
>
> HI Andreas,
>
> there are no 'right' instrumentsas such: there are only good ones (valid,
> strong) and bad ones. Imagine ´good´ and ´bad´ being on a continuous
> scale: most instruments are somwhere on this scale, but rarely at the
> extreme.
>
> now to the Sargan:
> "The Sargan test statistic [...] [is] under the null that the error term
> is uncorrelated with the instruments."
> source: http://en.wikipedia.org/wiki/Instrumental_variable
>
> so you want a p-value > 0.10
>
> no rejection is what you want: the null means you have good instruments.
>
> I recommend to use ivreg2 whih allows you to test the redundany of
> instruments.
>
> Best
> Justina
>
>
> -------- Original-Nachricht --------
> > Datum: Fri, 20 Jan 2012 21:22:54 +0100
> > Von: andreas.zweifel@uzh.ch
> > An: statalist@hsphsun2.harvard.edu
> > Betreff: Antwort: Re: Antwort: Re: RE: st: Spurious inference from
> endogeneity tests
>
> > Hi
> >
> > I think you are quite right, and my intuition also tells me something
> > else. Let's assume I have only one endogenous regressor,
> > but more than one instrument candidates since there is no theoretical
> > foundation for choosing the 'right' instruments for the
> > endogenous variable. If I include all of these instruments and the
> > -overid- test statistic is still not significant, there is
> > likely something wrong with the instruments. This is because theory
> claims
> > that one instrument should suffice here, and each
> > additional instrument included merely increases the standard deviation
> of
> > the IV estimator. As a consequence, the model must
> > be overidentified from a theoretical view. However, if the Sargan test
> > fails to detect overidentification, this can only be
> > due to the fact that the selected instruments are quite weak...
> >
> > Best,
> > Andreas
> >
> > -----owner-statalist@hsphsun2.harvard.edu schrieb: -----
> > An: statalist@hsphsun2.harvard.edu
> > Von: "Justina Fischer"
> > Gesendet von: owner-statalist@hsphsun2.harvard.edu
> > Datum: 19.01.2012 23:22
> > Betreff: Re: Antwort: Re: RE: st: Spurious inference from endogeneity
> > tests
> >
> > nope.. the bias could turn the direction of observed influence - how do
> > you know then which one is correct (OLS or IV)?
> >
> > Rule of thumb is: better no instrument (OLS) than weak ones !!
> >
> > it is sufficient to provide good convincing arguments why you selected
> the
> > instruments; there is no need for theoretical models suggesting the
> > instrument explicitly. Let your phantasy work !
> >
> > Cheers
> > Justina
> >
> > -------- Original-Nachricht --------
> > > Datum: Thu, 19 Jan 2012 23:00:00 +0100
> > > Von: andreas.zweifel@uzh.ch
> > > An: statalist@hsphsun2.harvard.edu
> > > Betreff: Antwort: Re: RE: st: Spurious inference from endogeneity
> tests
> >
> > > Thanks for this clarifying remark.
> > >
> > > In addition, literature always stresses the requirement that
> > > IVs should be selected in line with theoretically motivated
> > > arguments. But economic theory may sometimes be limited in its
> > > capability to yield valid instruments. However, when instruments
> > > are therefore weak, I expect the bias of the IV estimator to be
> > > similarly large as the OLS estimator. Maybe then it would make
> > > sense to prefer one of the two estimators in terms of theory
> > > driven expectations as the lesser evil?
> > >
> > > -----owner-statalist@hsphsun2.harvard.edu schrieb: -----
> > > An: statalist@hsphsun2.harvard.edu
> > > Von: Austin Nichols
> > > Gesendet von: owner-statalist@hsphsun2.harvard.edu
> > > Datum: 18.01.2012 16:37
> > > Betreff: Re: RE: st: Spurious inference from endogeneity tests
> > >
> > > In re
> > > the poster's central question:
> > > "I have to conclude from my specification tests that my coefficient
> > > estimates from both OLS and 2SLS cannot be interpreted because 2SLS
> > > does not succeed in resolving the endogeneity problem?"
> > > I would answer yes.  Without better instruments, you have learned
> > > nothing from 2SLS, including whether OLS is biased or not.  The overID
> > > test is no good if you don't have strong instruments, since its
> > > failure to reject the overID restrictions could be due merely to the
> > > weakness of your excluded instruments.
> > >
> > > On Tue, Jan 17, 2012 at 6:44 PM, Justina Fischer <JAVFischer@gmx.de>
> > > wrote:
> > > > wow. I am deeply impressed :-)
> > > >
> > > > Let us hope the authors provide user-written Stata commands soon....
> > > >
> > > > justina
> > > > -------- Original-Nachricht --------
> > > >> Datum: Tue, 17 Jan 2012 18:41:27 -0500
> > > >> Von: Cameron McIntosh <cnm100@hotmail.com>
> > > >> An: STATA LIST <statalist@hsphsun2.harvard.edu>
> > > >> Betreff: RE: st: Spurious inference from endogeneity tests
> > > >
> > > >> The following papers will also be helpful:
> > > >> Murray, M.P. (2006). Avoiding Invalid Instruments and Coping with
> > Weak
> > > >> Instruments. Journal of Economic Perspectives, 20(4),
> > > >>
> > >
> >
> 111-132.http://www.eui.eu/Personal/Guiso/Courses/Econometrics/Murray_IV_jep_06.pdf
> > > >>
> > > >> Chao, J.C., & Swanson, N.R. (2005). Consistent estimation with a
> > large
> > > >> number of weak instruments. Econometrica, 73(5),
> > > >>
> > >
> >
> 1673–1692.http://gemini.econ.umd.edu/jrust/econ623/files/chao_swanson_econometrica.pdf
> > > >>
> > > >> Nevo, A., & Rosen, A.M. (2010). Identification with Imperfect
> > > Instruments.
> > > >> The Review of Economics and Statistics, Accepted for publication.
> > > >>
> > > >> Kolesár, M., Chetty, R., Friedman, J.N., Glaeser, E.L., & Imbens,
> > G.W.
> > > >>  (October 2011). Identification and Inference with Many Invalid
> > > Instruments.
> > > >> NBER Working Paper No. 17519. http://www.nber.org/papers/w17519
> > > >>
> > > >> Cam
> > > >> > Date: Wed, 18 Jan 2012 00:06:34 +0100
> > > >> > From: JAVFischer@gmx.de
> > > >> > Subject: Re: st: Spurious inference from endogeneity tests
> > > >> > To: statalist@hsphsun2.harvard.edu
> > > >> >
> > > >> > Hi Andreas
> > > >> >
> > > >> > for judging whether instruments are weak or not I would as first
> > step
> > > >> look into the first stage regression results, look at the Shea R2,
> > the
> > > F-test
> > > >> on the instruments, the single estimates....that tells you already
> a
> > > lot.
> > > >> Maybe use ivreg2.
> > > >> >
> > > >> > Maybe you have only one weak instrument in a set of instruments
> you
> > > >> should exclude  (so the set is then strong, even though one single
> > weak
> > > >> instrument may bias your results)
> > > >> >
> > > >> > Best
> > > >> >
> > > >> > Justina
> > > >> >
> > > >> >
> > > >> > -------- Original-Nachricht --------
> > > >> > > Datum: Tue, 17 Jan 2012 22:12:36 +0100
> > > >> > > Von: andreas.zweifel@uzh.ch
> > > >> > > An: statalist@hsphsun2.harvard.edu
> > > >> > > Betreff: st: Spurious inference from endogeneity tests
> > > >> >
> > > >> > > Dear Statausers,
> > > >> > >
> > > >> > > I am concerned with an endogeneity problem in my sample of 126
> > > firms
> > > >> when
> > > >> > > investigating the relationship between managerial disclosure
> and
> > > cost
> > > >> of
> > > >> > > capital effects. After running the ivreg28 command, the
> > > Cragg-Donald
> > > >> test
> > > >> > > F-statistic is 2.27, which indicates that my instruments are
> > rather
> > > >> weak.
> > > >> > > However, my model appears to be correctly identified, because
> the
> > > >> Anderson test
> > > >> > > statistic for the first stage equation yields a p-value lower
> > than
> > > >> 0.01
> > > >> > > and the Sargan test statistic is insignificant (p-value =
> 0.59).
> > > Since
> > > >> my
> > > >> > > instruments have passed the overidentification test, I run the
> > > ivendog
> > > >> command
> > > >> > > which is equivalent to a Hausman test. Again, the test
> statistic
> > is
> > > >> > > insignificant (p-value = 0.48).
> > > >> > >
> > > >> > > If I compare OLS and 2SLS, I find that only the former yields a
> > > >> > > significant coefficient of managerial disclosure in the model
> > > >> regressing cost of
> > > >> > > capital on managerial disclosure. Considering the specification
> > > tests
> > > >> above, it
> > > >> > > seems unlikely that 2SLS is an improvement over OLS. Thus I
> > assume
> > > >> that I
> > > >> > > can take the OLS estimates for causal inference. Is this
> correct?
> > > If
> > > >> yes,
> > > >> > > the point why I should not use 2SLS is likely due to the
> weakness
> > > of
> > > >> the
> > > >> > > instruments and the small-sample bias. So I have to conclude
> from
> > > my
> > > >> > > specification tests that my coefficient estimates from both OLS
> > and
> > > >> 2SLS cannot be
> > > >> > > interpreted because 2SLS does not succeed in resolving the
> > > endogeneity
> > > >> > > problem?
> > >
> > > *
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> >
> > --
> > Justina AV Fischer, PhD
> > COFIT Fellow
> > University of Bern
> >
> > homepage: http://www.justinaavfischer.de/
> > e-mail: javfischer@gmx.de. justina.fischer@wti.org
> > papers: http://ideas.repec.org/e/pfi55.html
> >
> >
> > *
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>
> --
> Justina AV Fischer, PhD
> COFIT Fellow
> University of Bern
>
> homepage: http://www.justinaavfischer.de/
> e-mail: javfischer@gmx.de. justina.fischer@wti.org
> papers: http://ideas.repec.org/e/pfi55.html
>
>
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--
Justina AV Fischer, PhD
COFIT Fellow
University of Bern

homepage: http://www.justinaavfischer.de/
e-mail: javfischer@gmx.de. justina.fischer@wti.org
papers: http://ideas.repec.org/e/pfi55.html

*
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```