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RE: st: RE: -endog- test under xtivreg2


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: -endog- test under xtivreg2
Date   Wed, 31 May 2006 21:08:50 +0100

Susie,

I'm the author of xtivreg2, so let me have a go at a response...

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Susie Enders
> Sent: 31 May 2006 20:08
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: -endog- test under xtivreg2
> 
> Please help!
> 
> I have been trying to proceed on this as suggested by Justina 
> (below), but am still stuck in what appear to me (perhaps 
> wrongly) to be a 'chicken-and-egg'
> problem. It seems that, for regressors which one fears to be 
> endogenous, on the one hand one needs to find appropriate 
> instruments in order to test whether they are in fact 
> endogenous, but on the other hand one must treat them as 
> endogenous and select appropriate instruments first. Is it 
> the case that, if you suspect a regressor might be 
> endogenous, you should first go through the whole process of 
> finding an appropriate/best instrument, and only then even 
> test if it is in fact endogenous?

I think this is a pretty accurate summary, except perhaps for the "best"
bit - see below.

> Would the following be a correct step-by-step guide of how to 
> proceed, with my dependent variable ROA and regressors a, b, 
> c, and d, of which I theoretically suspect d in particular of 
> being endogenous:
> 1) Experiment with various possible instruments for d, such 
> as l.d, l4.d, and e; by running the regressions
> .xtivreg2 ROA l.ROA a b c i.quarter (d=l.d) fe gmm
> bw(3) robust ffirst
> and repeating this using (d=l4.d) and (d=e).

Why experiment with using different instruments separately?  The simple
and conventional thing to do is to estimate using all your a priori
plausible (valid and relevant) instruments, and then see if they satisfy
the available diagnostics for validity (Hansen J test) and relevance
(first state F test and separate t tests).

> 2) Compare the Hansen J stats reported after the results. A 
> problem I have here is that the statistics are all zero as 
> the regressions are exactly identified. But if I had 
> statistics reported, would I be looking for the largest stat 
> as a pointer to the most appropriate instrument?

Very confused here.  The "if" doesn't make sense, since the
Sargan-Hansen J stat is always zero if exactly identified.  If it's
overidentified, i.e., you're using all the plausible instruments (see my
comment above), then the J stat is a specification test.  If the stat is
large, then you *fail* the test, because the null is that all the
instruments are valid, and a large J stat means you reject the null.

> Justina suggests looking at the F-stats of excluded 
> instruments, to be honest I don't see these, but there are 
> some F-stats in relation to the instrumentalised variable d 
> (pasted below).

What Justina suggested is exactly that.  The F stat is a test of the
excluded instruments in the first-stage regression of the instrumented
variable d on all the exogenous variables.  The F test is a test of
whether the excluded IVs are significant (relevant), and so you want
this stat to be big.  You should also look at the first-stage regression
output in full (i.e., use the first instead of ffirst option), and see
if the excluded IVs are individually as well as jointly significant.

> What exactly is it that I should be comparing 
> between regressions in order to choose the best instrument of 
> ones that I am considering? [continued below output...] 
> ===========================
> Variable Partial R2  Partial R2  F(1,17962)   P-value
> d        0.5041      0.5041      115.76       0.0000
> 
> NB: first-stage F-stat heteroskedasticity and autocorrelation-robust
> 
> Underidentification tests:
> Chi-sq(1)      P-value
> Anderson canon. corr. likelihood ratio stat.   
> 12631.56         0.0000
> Cragg-Donald N*minEval stat.                   
> 18306.78         0.0000
> Ho: matrix of reduced form coefficients has rank=K-1
> (underidentified)
> Ha: matrix has rank>=K (identified)
> 
> Weak identification statistics:
> Cragg-Donald (N-L)*minEval/L2 F-stat   18256.98
> 
> NB: identification statistics not robust
> 
> Anderson-Rubin test of joint significance of endogenous 
> regressors B1 in main equation, Ho:B1=0
> F(1,17962)=    0.24      P-val=0.6268
> Chi-sq(1)=     0.24      P-val=0.6264
> NB: Anderson-Rubin stat heteroskedasticity and 
> autocorrelation-robust ============================
> 
> 3. Once i have chosen the 'best' instrument (say l4.d), then 
> test whether or not the suspect variable is endogenous?

Again, some confusion here.  All you need is an IV specification that
meets the validity and relevance criteria.  You don't have to start
kicking out instruments unless you have good reason to do so, e.g.,
because the instrument is causing you to fail the J stat, or because
it's irrelevant.

> By specifying
> .xtivreg2 ROA l.ROA a b c i.quarter (d=l4.d) fe gmm
> bw(3) robust ffirst endog(d)
> And if the Ho on the endog test is rejected, this would mean 
> that d can in fact be treated as exogenous after all.
> 
> Would this be a correct way of proceeding? And where I am not 
> sure about the endogeneity of all regressors, how can I even 
> find the best instrument for one in order to test its 
> endogenity without knowing if the others are endogenous and 
> their appropriate instruments.

Dealing with multiple endogenous regressors can get messy.  Maybe you
should just try the above with a single endog regressor and get
comfortable with the procedures before looking at more complex models.

Hope this helps.

Cheers,
Mark

Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes

> I am feeling really confused about this and have been working 
> on it and reading the relevant literature but am struggling 
> to operationalise it. Any simple and practical tips would be 
> very much appreciated.
> 
> Debbie
> 
> --- J.Fischer@lse.ac.uk wrote:
> 
> > Hi
> > 
> > I am not an expert on instruments, but I suggest you
> > 1) first select appropriate instruments using the Sargan J 
> statistics 
> > and the F-stat on excl. instruments in the 1st stage 
> regression (use 
> > ffirst option)
> > 2) then test endogeneity ( Hausman Wu etc)
> > 
> > Justina
> > 
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Susie 
> > Enders
> > Sent: 24 May 2006 20:30
> > To: statalist@hsphsun2.harvard.edu
> > Subject: st: -endog- test under ivreg2
> > 
> > Hello,
> > 
> > I have a quarterly panel dataset on which I am running a 
> dynamic fixed 
> > effects model using the ivreg,gmm option (I have also tried using 
> > xtivreg2). I am not sure whether or not some of my regressors are 
> > endogenous and require instrumentalisation. I am trying to 
> test this 
> > using the endog option. My confusion is that the outcome from the 
> > endog test depends on what instrument one uses for the suspect 
> > variable. With some instruments the suspect variable appears 
> > endogenous, with others not. However, not even being sure 
> which is an 
> > appropriate instument, how do I establish whether or not 
> the suspect 
> > variable is endogenous in the first place and hence even 
> needing to be 
> > instrumentalised?
> > 
> > (I have already read the help files as well as the 
> > Baum-Schaffer-Stillman paper and tried searching on the list 
> > archives).
> > 
> > I have pasted below my specification and the relevant 
> portion of the 
> > output for 3 regressions, the only difference being the instrument 
> > used to instrument the suspect variable (d) which I am 
> testing whether 
> > or not it is endogenous. If I read the output correctly, in 
> regression 
> > 1 (in which the instrument is the same variable lagged 4 
> periods back) 
> > it seems that we reject Ho that the suspect variable
> > (d) is exogenous, ie
> > it does need to be instrumentalised. Regression 2 (in which the 
> > instrument is the one-lagged variable) doesnt even give an 
> output on 
> > endog. According to regression 3 (in which the instrument 
> is another 
> > variable, e) it seems we fail to reject Ho so the suspect 
> variable (d) 
> > is exogenous. How do I know whether or not it actually is 
> endogenous 
> > without
> > knowing which is the "right" intrument?   
> > 
> > A follow-up question would then be, if the suspect variable 
> is indeed 
> > endogenous and needs to be instrumented, how I decide which 
> instrument 
> > is best?
> > 
> > Regression 1:
> > ivreg2 ROA l.ROA a b c (d=l4.d), gmm endog(d) robust
> > cl(key)
> > 
> > Hansen J statistic (overidentification test of all
> > instruments):         0.000
> >                                                 
> > (equation exactly identified)
> > -endog- option:
> > Endogeneity test of endogenous regressors:          
> >  
> >                   9.550
> >                                                   
> > Chi-sq(1) P-val =    0.0020
> > Regressors tested:    d
> >
> --------------------------------------------------------------
> ----------
> > ------
> > Instrumented:         d
> > Included instruments: L.ROA a b c
> > Excluded instruments: l4.d
> > ---------------------------------
> > ===============
> > Regression 2:
> > ivreg2 ROA l.ROA a b c (d=l.d), gmm endog(d) robust
> > cl(key)
> > 
> > Hansen J statistic (overidentification test of all
> > instruments):         0.000
> >                                                 
> > (equation exactly identified)
> > 
> > Collinearity/identification problems in eqn. excl.
> > suspect orthog. conditions:
> >   C statistic not calculated for -orthog- option
> >
> --------------------------------------------------------------
> ----------
> > ------
> > Instrumented:         d
> > Included instruments: L.ROA a b c
> > Excluded instruments: l.d
> > 
> > ==========================================
> > 
> > Regression 3:
> > 
> > ivreg2 ROA l.ROA a b c (d=e), gmm endog(d) robust
> > cl(key)
> > 
> > Hansen J statistic (overidentification test of all
> > instruments):         0.000
> >                                                 
> > (equation exactly identified)
> > -endog- option:
> > Endogeneity test of endogenous regressors:          
> >  
> >                   0.925
> >                                                   
> > Chi-sq(1) P-val =    0.3362
> > Regressors tested:    d
> >
> --------------------------------------------------------------
> ----------
> > ------
> > Instrumented:         d
> > Included instruments: L.ROA a b c
> > Excluded instruments: e
> > ---------------------------------
> > 
> > Thanks so much for any help with this I am so frustrated!
> > 
> > Debbie
> > 
> > 
> > 
> > 
> > 
> > 		
> >
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