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RE: st: Spurious inference from endogeneity tests


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Spurious inference from endogeneity tests
Date   Sun, 29 Jan 2012 13:57:56 -0000

Andreas,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> andreas.zweifel@uzh.ch
> Sent: 29 January 2012 13:00
> To: statalist@hsphsun2.harvard.edu
> Subject: RE: st: Spurious inference from endogeneity tests
> 
> Dear Mark,
> 
> The point is that if my model is exactly identified with 2 
> problematic regressors and 2 instruments, the Sargan test 
> drops out of the -ivreg2- inference. However, I get the 
> results from the first-stage test of the joint significance 
> of the IV, the Anderson-Rubin test statistic (p-value < 0.01) 
> and the Stock-Yogo Wright F-statistic exceeding 10 for the 
> two instruments. 

I don't see what the "point" is, to be honest.  These are two conceptually separate issues that relate to the two separate requirements for valid instruments in standard IV/GMM estimation: (1) exogeneity of instruments, which can be tested using an overid stat if the eqn is overidentified; (2) strength of instruments (weak or under-identification), which can be be tested using a Cragg-Donald or Anderson-type stat.

The A-R test stat reported by -ivreg2- to which you refer relates to the A-R approach, which I described in my previous post.  It using the A-R method to test whether 0 lies in the confidence interval for the endogenous regressor.

There is no "Stock-Yogo-Wright" statistic.  You are confusing the Stock-Wright S statistic (which is a close relative of the A-R test stat) with the Stock-Yogo critical values for the Cragg-Donald test stat (used to test instrument strength in standard IV estimation).

> To what degree do I need to doubt these test statistics 
> because of lacking robustness to weak instruments and use an 
> alternative approach instead? 

If your standard IV/GMM results suggest that you have weak or weak-ish instruments, you can consider using the AR approach or its relatives (-rivtest-, -condivreg-, the extension to K>1 regressors I sketched out, etc.) 

--Mark

> 
> Best,
> Andreas
> 
> -----owner-statalist@hsphsun2.harvard.edu schrieb: -----
> An: <statalist@hsphsun2.harvard.edu>
> Von: "Schaffer, Mark E" 
> Gesendet von: owner-statalist@hsphsun2.harvard.edu
> Datum: 29.01.2012 12:02
> Betreff: RE: st: Spurious inference from endogeneity tests
> 
> Andreas,
> 
> I don't know where you got the idea about trying to 
> artificially introduce overidentification, but it wasn't from 
> my suggestion about using the AR approach for >1 endogenous 
> regressors.  I referred to the AR "approach" to constructing 
> confidence intervals and sets.  The AR approach is what 
> -rivtest- and -condivreg- implement; ivreg2 does not 
> implement this.  All discussed in the Dufour article I 
> pointed towards.
> 
> The AR approach for one endogenous regressor is to find a 
> weak-instruments-robust confidence interval for the 
> coefficient beta1 on the endogenous regressors X1.
> 
> To test whether a specfic value for beta1 - say b1 - is in 
> the confidence interval, the AR approach is to do the following:
> 
> 1.  Create a new dependent variable y from the original dep 
> var Y and the endogenous regressor X1.  Specifically,
> 
> y = Y-b1*X1
> 
> 2.  Run an OLS regression with y as the dependent variable 
> and all the exogenous regressors and instruments as 
> independent variables.
> 
> 3.  Do a test of the joint significance of the IVs.  If b1 is 
> inside the confidence interval, they will be insignificant.  
> If b1 is outside the confidence interval, they will be significant.
> 
> The intuition is straightforward.  If b1 is close to the true 
> value of B1, then y has most of the impact of X1 purged from 
> it.  Since in that case y doesn't have X1 in it, the 
> instruments should be unrelated to y (after accounting for 
> the other regressors etc. etc.).
> 
> To construct a confidence interval, just do a grid search 
> over various values of b1.  (There's a shortcut for the 
> special case of iid, but a mechanical grid search always works.)
> 
> The AR approach has the drawback of wasting degrees of 
> freedom in the overidentified case, and -rivtest- and 
> -condivreg- implement more modern approaches that address 
> this.  In the exactly-identified case, the AR approach is the 
> same as these more modern approaches.
> 
> The AR approach for 2 endogenous regressors proceeds in the 
> same way, except that now you are purging Y of the effects of 
> both regressors:
> 
> y = Y - b1*X1 - b2*X2
> 
> And instead of a confidence interval you get a confidence 
> set.  That is, you find out whether (b1,b2) is in the 
> confidence set (the IVs in step 3 are not signif) or outside 
> the confidence set (the IVs in step 3 ARE signif).  And you 
> have to do a grid search over combinations of values for b1 
> and b2.  A hassle, but not too bad.
> 
> The above is useful if you want to use -rivtest- or 
> -condivreg- but can't because they handle only the 
> one-endog-regressor case.  The confidence set approach is the 
> K>1 generalization of these estimators.  But if you don't 
> want to use this approach to inference anyway, this won't be 
> of much interest.
> 
> --Mark
> 
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> > andreas.zweifel@uzh.ch
> > Sent: 27 January 2012 22:52
> > To: statalist@hsphsun2.harvard.edu
> > Subject: RE: st: Spurious inference from endogeneity tests
> > 
> > I am not sure if conducting the AR test in the K-regressor is the 
> > optimal solution to my problem. As I said, X1hat is a combined 
> > instrument for the endogenous variable X1, which has been 
> estimated in 
> > a preliminary regression on all available instruments Z. 
> Analogously, 
> > the interaction X1hat*X2 (X2
> > exogenous) will be the instrument for the endogenous 
> interaction term 
> > X1*X2. Using this approach to properly instrument the endogenous 
> > interaction term, I will obtain no more instruments than endogenous 
> > regressors by construction.
> > In other words, the model is exactly identified and testing for 
> > overidentifying restrictions will be redundant. I don't see why I 
> > should be worried as long as the weak instrument robust 
> Anderson Rubin 
> > test rejects its null ("H0: B1=0 and overidentifying 
> restrictions are 
> > valid") that the model is misspecified. Better still, weak 
> instrument 
> > robust inference might be of less concern if the F-statistic of the 
> > Stock Yogo
> > (2002) test to detect weak instruments yields a value of 
> >10 with two 
> > instruments, right? Of course I can run a specification test by 
> > computing additional instruments from forming the powers of 
> X1hat and 
> > X1hat*X2 to invoke the Sargan test statistic in -ivreg2-. However, 
> > what is the lesson to be learned from artificially introducing 
> > overidentification? In case the Sargan test statistic is 
> > insignificant, nothing will indicate that the model is 
> overidentified 
> > or misspecified.
> > Based on these results, I could eventually test whether the 2SLS 
> > coefficients substantially and systematically deviate from the OLS 
> > coefficients using a Hausman test and decide what to prefer for 
> > conducting statistical inference.
> > 
> > I hope the methodology described above satisfies the current 
> > state-of-the-art requirements for statistical inference. 
> This does not 
> > just mean that I am tired of using sophisticated 
> econometrics, but the 
> > goal of my research is to gain empirical evidence from data 
> analysis 
> > rather than evaluating the most complex tools available to solve 
> > presumably simple endogeneity problems.
> > 
> > Best,
> > Andreas
> > 
> > -----owner-statalist@hsphsun2.harvard.edu schrieb: -----
> > An: <statalist@hsphsun2.harvard.edu>
> > Von: "Schaffer, Mark E" 
> > Gesendet von: owner-statalist@hsphsun2.harvard.edu
> > Datum: 26.01.2012 23:05
> > Betreff: RE: st: Spurious inference from endogeneity tests
> > 
> > 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: owner-statalist@hsphsun2.harvard.edu
> > > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> > Suryadipta
> > > Roy
> > > Sent: 26 January 2012 00:06
> > > To: statalist@hsphsun2.harvard.edu
> > > 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
> > <JAVFischer@gmx.de>
> > > 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: andreas.zweifel@uzh.ch
> > > >> An: statalist@hsphsun2.harvard.edu
> > > >> 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
> > > >>
> > > >>
> > > >> -----owner-statalist@hsphsun2.harvard.edu schrieb: -----
> > > >> An: statalist@hsphsun2.harvard.edu
> > > >> Von: Suryadipta Roy
> > > >> Gesendet von: owner-statalist@hsphsun2.harvard.edu
> > > >> 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
> > > <JAVFischer@gmx.de>
> > > >> 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: 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?
> > > >> >> > >
> > > >> >> > > *
> > > >> >> > > *   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: javfischer@gmx.de. justina.fischer@wti.org
> > > >> >> > 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
> > > >> >> > *   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: javfischer@gmx.de. justina.fischer@wti.org
> > > >> >> 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
> > > >> >> *   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: javfischer@gmx.de. justina.fischer@wti.org
> > > >> > papers: http://ideas.repec.org/e/pfi55.html
> > > >> >
> > > >> >
> > > >> > *
> > > >> > *   For searches and help try:
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> > > >>
> > > >> *
> > > >> *   For searches and help try:
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> > > >> *
> > > >> *   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: javfischer@gmx.de. justina.fischer@wti.org
> > > > papers: http://ideas.repec.org/e/pfi55.html
> > > >
> > > >
> > > > *
> > > > *   For searches and help try:
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> > > 
> > > *
> > > *   For searches and help try:
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> > > *   http://www.ats.ucla.edu/stat/stata/
> > > 
> > 
> > 
> > --
> > Heriot-Watt University is a Scottish charity registered 
> under charity 
> > number SC000278.
> > 
> > Heriot-Watt University is the Sunday Times Scottish 
> University of the 
> > Year 2011-2012
> > 
> > 
> > 
> > *
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> > 
> 
> 
> --
> Heriot-Watt University is a Scottish charity registered under 
> charity number SC000278.
> 
> Heriot-Watt University is the Sunday Times Scottish 
> University of the Year 2011-2012
> 
> 
> 
> *
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> 


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