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


From   andreas.zweifel@uzh.ch
To   statalist@hsphsun2.harvard.edu
Subject   Antwort: Re: Antwort: Re: Antwort: Re: RE: st: Spurious inference from endogeneity tests
Date   Mon, 23 Jan 2012 15:59:27 +0100

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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> > *
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> > *   http://www.ats.ucla.edu/stat/stata/
> 
> -- 
> Justina AV Fischer, PhD
> COFIT Fellow
> World Trade Institute
> 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
World Trade Institute
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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