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RE: st: Spurious inference from endogeneity tests
From
"Schaffer, Mark E" <[email protected]>
To
<[email protected]>
Subject
RE: st: Spurious inference from endogeneity tests
Date
Thu, 26 Jan 2012 22:07:53 -0000
Andreas,
If you are feeling adventurous, you could try implementing the Anderson-Rubin (weak-instrument-robust) approach to the K-regressor case. I think it's discussed in Dufour (2003), "Identification, Weak Instruments and Statistical Inference in Econometrics" (full reference in the -ivreg2- help file references).
In the 1-endogenous-regressor case, the AR approach (which rivtest and condivreg extend) is to construct a confidence interval for the regressor beta_1. In the 2-endogenous-regressor case, the AR approach is to construct a confidence *set* for the regressors (beta_1, beta_2).
You could implement this by a simple grid search - a bit of a hassle, but not that bad.
HTH,
Mark
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of
> Suryadipta Roy
> Sent: 26 January 2012 00:06
> To: [email protected]
> Subject: Re: Antwort: Re: Antwort: Re: Antwort: Re: Antwort:
> Re: RE: st: Spurious inference from endogeneity tests
>
> Andreas,
> I see the problem. You are right; - condivreg- is not valid
> for more than one endogenous variable. My first reaction will
> be similar what has been probably suggested by another
> subscriber, i.e. to try using powers of x1hat and that of the
> product of x1hat and x2 to generate additional instruments
> for testing overidentification in -ivreg2- accompanied by
> -first- (/-ffirst-) option. If x1 is a limited dependent
> variable, then you might probably get even more creative by
> using a non-linear specification (or -rivtest- etc.) along
> with the usual linear model to generate different values of
> x1hat, and then interact them with x2 and see whether they
> retain sufficient independent information to be used as
> instruments. Or, trying out a log-log model (and/or log
> linear model) for x1 along with the linear model. Of course,
> one can check all the specifications checking the adjusted-r
> square, or the AIC/BIC following the -estat ic- command.
>
> Best wishes,
> Suryadipta.
>
> On Wed, Jan 25, 2012 at 5:49 AM, Justina Fischer
> <[email protected]> wrote:
> > Dear Andreas,
> >
> > finding suitable instruments (in terms of
> economic-theoretical coherence with the endogenous) is
> something this list does not aim at.
> >
> > best
> >
> > Justina
> >
> >
> > -------- Original-Nachricht --------
> >> Datum: Wed, 25 Jan 2012 08:40:54 +0100
> >> Von: [email protected]
> >> An: [email protected]
> >> Betreff: Antwort: Re: Antwort: Re: Antwort: Re: Antwort:
> Re: RE: st:
> >> Spurious inference from endogeneity tests
> >
> >> Hi Suyadipta,
> >>
> >> thank you for the suggestion to use -condivreg-.
> Unfortunately, the
> >> command works with one endogenous regressor only. However,
> I have two
> >> endogenous regressors due to an interaction of the original
> >> endogenous variable X1 and an exogenous control X2, i.e. my model
> >> looks like
> >>
> >> Y = X1 + X1*X2 + controls + e
> >>
> >> I have been recommended to estimate first X1 by instruments Zi
> >> (i=1,...n) to obtain X1hat, than form interactions X1hat*X2 as
> >> instruments to be used in the -ivreg2- command which then would be
> >>
> >> ivreg2 Y controls (X1 X1*X2 = X1hat X1hat*X2)
> >>
> >> (see http://www.stata.com/statalist/archive/2011-08/msg01496.html)
> >>
> >> This actually solves the endogeneity problem since the
> F-statistic of
> >> the weak instruments test substantially increases compared to the
> >> canned 2SLS procedure
> >>
> >> ivreg2 Y controls (X1 X1*X2 = Zi Zi*X2)
> >>
> >> where each basic instrument Zi is interacted with X2 yielding n
> >> combined instruments. So in total, I have 2*n instruments for 2
> >> endogenous regressors.
> >>
> >> In the special case of only one basic instrument Z1 (n=1),
> the first
> >> 2SLS approach and canned SLS just coincide because the model is
> >> exactly identified in both cases. However, to test whether the
> >> instruments are really valid you should have n>1
> instruments for one
> >> endogenous regressor. This yields another problem because in the
> >> first 2SLS approach there are always two endogenous regressors and
> >> two instruments by construction. Thus I can see no way how to test
> >> for overidentifying restrictions with this approach.
> >>
> >> I would appreciate any help with respect to a possible solution to
> >> that problem.
> >>
> >> Andreas Zweifel
> >>
> >>
> >> [email protected] schrieb: -----
> >> An: [email protected]
> >> Von: Suryadipta Roy
> >> Gesendet von: [email protected]
> >> Datum: 24.01.2012 13:20
> >> Betreff: Re: Antwort: Re: Antwort: Re: Antwort: Re: RE:
> st: Spurious
> >> inference from endogeneity tests
> >>
> >> Andreas,
> >> Along these lines, I would also suggest that you take a
> look at the
> >> condivreg command ( - findit condivreg - , the help file and the
> >> related papers) for detecting weak instruments. The Murray (2006)
> >> paper cited below is suggesting in those lines. The Stata journal
> >> references are Mikusheva and Poi (2003), Stata Journal 3:
> 57-70, and
> >> Mikusheva and Poi (2006), Stata Journal 6: 335-347.
> >>
> >> Best wishes,
> >> Suryadipta.
> >>
> >> On Mon, Jan 23, 2012 at 10:18 AM, Justina Fischer
> <[email protected]>
> >> wrote:
> >> > 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: [email protected]
> >> >> An: [email protected]
> >> >> 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
> >> >>
> >> >> [email protected] schrieb: -----
> >> >> An: [email protected]
> >> >> Von: "Justina Fischer"
> >> >> Gesendet von: [email protected]
> >> >> 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: [email protected]
> >> >> > An: [email protected]
> >> >> > 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
> >> >> >
> >> >> > [email protected] schrieb: -----
> >> >> > An: [email protected]
> >> >> > Von: "Justina Fischer"
> >> >> > Gesendet von: [email protected]
> >> >> > 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: [email protected]
> >> >> > > An: [email protected]
> >> >> > > 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?
> >> >> > >
> >> >> > > [email protected] schrieb: -----
> >> >> > > An: [email protected]
> >> >> > > Von: Austin Nichols
> >> >> > > Gesendet von: [email protected]
> >> >> > > 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
> >> <[email protected]>
> >> >> > > 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 <[email protected]>
> >> >> > > >> An: STATA LIST <[email protected]>
> >> >> > > >> 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: [email protected]
> >> >> > > >> > Subject: Re: st: Spurious inference from endogeneity
> >> >> > > >> > tests
> >> >> > > >> > To: [email protected]
> >> >> > > >> >
> >> >> > > >> > 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: [email protected]
> >> >> > > >> > > An: [email protected]
> >> >> > > >> > > 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?
> >> >> > >
> >> >> > > *
> >> >> > > * For searches and help try:
> >> >> > > * http://www.stata.com/help.cgi?search
> >> >> > > * http://www.stata.com/support/statalist/faq
> >> >> > > * http://www.ats.ucla.edu/stat/stata/
> >> >> > > *
> >> >> > > * For searches and help try:
> >> >> > > * http://www.stata.com/help.cgi?search
> >> >> > > * http://www.stata.com/support/statalist/faq
> >> >> > > * 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: [email protected]. [email protected]
> >> >> > papers: http://ideas.repec.org/e/pfi55.html
> >> >> >
> >> >> >
> >> >> > *
> >> >> > * For searches and help try:
> >> >> > * http://www.stata.com/help.cgi?search
> >> >> > * http://www.stata.com/support/statalist/faq
> >> >> > * http://www.ats.ucla.edu/stat/stata/
> >> >> > *
> >> >> > * For searches and help try:
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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: [email protected]. [email protected]
> >> >> papers: http://ideas.repec.org/e/pfi55.html
> >> >>
> >> >>
> >> >> *
> >> >> * For searches and help try:
> >> >> * http://www.stata.com/help.cgi?search
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> >> >> * http://www.ats.ucla.edu/stat/stata/
> >> >> *
> >> >> * For searches and help try:
> >> >> * http://www.stata.com/help.cgi?search
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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: [email protected]. [email protected]
> >> > papers: http://ideas.repec.org/e/pfi55.html
> >> >
> >> >
> >> > *
> >> > * For searches and help try:
> >> > * http://www.stata.com/help.cgi?search
> >> > * http://www.stata.com/support/statalist/faq
> >> > * http://www.ats.ucla.edu/stat/stata/
> >>
> >> *
> >> * For searches and help try:
> >> * http://www.stata.com/help.cgi?search
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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: [email protected]. [email protected]
> > papers: http://ideas.repec.org/e/pfi55.html
> >
> >
> > *
> > * For searches and help try:
> > * http://www.stata.com/help.cgi?search
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>
> *
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>
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