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st: RE: IV list in ivreg and ivreg2: procedure to test for endogeinity of added variable if one of the original variables is endogenous?


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: IV list in ivreg and ivreg2: procedure to test for endogeinity of added variable if one of the original variables is endogenous?
Date   Thu, 31 Aug 2006 17:09:41 +0100

Robert,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Vergeer, Robert
> Sent: 30 August 2006 12:24
> To: statalist@hsphsun2.harvard.edu
> Subject: st: IV list in ivreg and ivreg2: procedure to test 
> for endogeinity of added variable if one of the original 
> variables is endogenous?
> 
> Dear Statalist users,
> 
> While browsing through the Statalist archives, I found that I 
> am facing a similar problem as discussed below by Mark and 
> Eddy. Maybe I missed it, but I couldn't find a suitable 
> solution to the problem. Below I propose a possible solution.
> I am interested in any comments on the validity of this 
> solution (or other ideas to tackle this problem).
> 
> The problem concerns the limited control over the variables 
> used as instruments in the IV-regression.
> 
> I, like Mark, want to replicate, and then augment, a 
> regression performed by others. These others did - seemingly 
> erroneous - not deal with an endogeneity problem (say: for 
> variable X_OriginalEndogenous).
> Now, as I am interested in comparing an augmented regression 
> with the original regression, I don't want to deal with the 
> endogeneity problem of X_OriginalEndogenous, but I my 
> interest is with the coefficient of an added variable (say: X_added).
> I do want to test for the possible endogeneity of this added 
> explanatory variable X_added, but I do not want to use 
> X_OriginalEndogenous as an
> (included) instrument as it affects the overall validity of 
> all the instruments used to instrument X_added in an adverse 
> way (In my case, this leads to rejection of the validity of 
> the instruments).
> 
> To summarize:
> 
> The original regression, with which I want to compare my 
> augmented regression, reads:
> 
> Y = X_originalEndogenous, X_1, X_...
> 
> 
> My augemented regression, reads:
> 
> Y = X_originalEndogenous, X_1, X_..., X_added
> 
> 
> To test for possible endogeneity of X_added, I used:
> 
> ivreg2 Y  (X_originalEndogenous = INSTRUMENTS) X_1, X_..., X_added
> orthog(X_added)
> and used the C-value of the Difference in Sargan/Hansen test 
> as an indicator for the possible endogeneity of X_added. (So 
> that with this test, X_originalEndogenous is not used as an 
> instrument for X_added)
> 
> The I used:
> ivreg2 Y  (X_added  X_originalEndogenous = INSTRUMENTS) X_1, X_...
> And used the J-value to test for the validity of the 
> instruments (so X_originalEndogenous is not an included 
> instrument when I test for the validity of the instruments 
> for X_added).
> 
> Does anyone know if this procedure is valid?
> 
> Thanks a lot,
> 
> Robert Vergeer

In the orthog test in

> ivreg2 Y  (X_originalEndogenous = INSTRUMENTS) X_1, X_..., X_added
> orthog(X_added)

you are in effect contrasting

ivreg2 Y  (X_originalEndogenous = INSTRUMENTS) X_1, X_..., X_added

with

> ivreg2 Y  (X_originalEndogenous X_added = INSTRUMENTS) X_1, X_...

The difference is that in the first example, the orthogonality
conditions include X_added, so the J stat is a test of the orthogonality
conditions for INSTRUMENTS and X_added.

In the second case, they don't, so the J stat is a test of the
orthogonality conditions for just INSTRUMENTS.

In neither case are you using orthogonality conditions relating to
X_originalEndogenous.  So ... it's very clear - the
C/difference-in-Sargan/GMM distance test is a test of the extra
orthogonality conditions relating to X_added.

Note that the second specification is identical to your other equation,

> ivreg2 Y  (X_added  X_originalEndogenous = INSTRUMENTS) X_1, X_...

and thus the J stat for this equation is one of the two J stats used to
form the C stat.  (In fact, it's asymptotically but not numerically the
same - for details see the Baum-Schaffer-Stillman paper listed in the
references.)

In fact, the second specification needs to be valid for the C test to be
valid, since under the null of the C test, both INSTRUMENTS and X_added
are exogenous.  If the second J stat is large, it indicates that
INSTRUMENTS fail the orthogonality conditions, and therefore you can't
say anything about whether X_added are valid as well.

HTH.

Cheers,
Mark

NB: To save Nick the trouble, I notice that you posted this Q 3 times
yesterday, and I should point out that reposting of unanswered posts is
not, shall we say, "best practice".

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
 


> 
> 
> > Hi Mark,
> >
> > Thanks for your reply; please see my response below.
> >
> > Monday, April 19, 2004, Mark Schaffer wrote:
> >
> >>> Dear listers,
> >>>
> >>> When using ivreg or ivreg2 to do a 2SLS estimation, all the RHS 
> >>> variables except those explicitly specified as endogenous are
> > assumed
> >>> to be exogenous and valid IV. Call those the "included exogenous 
> >>> variables". However, I happen to have a case in which not all the 
> >>> "included exogenous variables" are valid IV, and I am asking
> > whether
> >>> users can have better control over the list of IV to be used in
> > the
> >>> 2SLS estimation.
> >
> >> I'm not sure this makes sense.  A "valid" IV is one that satisfies 
> >> the orthogonality conditions; this is synonymous with "exogenous".
> >> If one of your regressors isn't a valid IV, then it isn't 
> exogenous 
> >> and you need to treat it as endogenous.  This is the way that IV 
> >> works (or, in modern presentations, GMM with IV as a special case).
> >
> >> In your example, ln(P) might or might not be be orthogonal to the 
> >> disturbance term.  If it is, it's a valid IV and you can treat it
> > as
> >> exogenous; if it isn't, it's not a valid IV and you should 
> treat it 
> >> as endogenous.  It sounds like you lean towards the latter, which 
> >> looks like a reasonable way to proceed (so long as you have enough 
> >> other valid excluded instruments to identify the equation, 
> and they 
> >> are "relevant" as well as "valid").
> >
> >   ln(W/P) = a0 + a1*ln(P) + a2*y + B*X,
> >
> > It's correct that ln(P) is endogenous because the dependent 
> variable 
> > is ln(W/P)=ln(W) - ln(P),
> 
> This isn't necessarily the case.  It's quite possible that 
> ln(P) could be exogenous even though it's used to calculate 
> ln(W/P).  It depends on your priors and the data generating 
> process (and everything else).
> 
> > but the problem is that I do not want to deal with the 
> endogeneity of 
> > ln(P), and I don't want it to be part of the IV for the other 
> > endogenous variable, y,
> 
> I'm not sure what you mean here.  If ln(P) is an exogenous 
> regressor, then it's an "included IV" by definition.  Not a 
> problem for you.
> 
> > whose coefficient is the
> > ultimate concern of this study.
> >
> > I do not want to treat the endogeneity of ln(P) because (1) 
> the ln(P) 
> > variable is only to control for heterogenous preference, 
> and we do not 
> > really care about the coefficient of ln(P), (2) to the extent that
> > ln(P) are independent of y and X, the endogeneity problem of ln(P) 
> > does not have adverse effect on the coefficients of y and 
> X, (3) the 
> > work I want to follow/replicate does not treat its endogeneity 
> > (Carroll and Samwick, "The Nature of Precautionary Wealth", 
> Journal of 
> > Monetary Economics, 1997), and (4) good IV for ln(P) maybe 
> difficult 
> > to come by.
> 
> If the work that you want to replicate treats ln(P) as 
> exogenous, and good IVs for ln(P) are hard to come by, then 
> the decision to treat it as exogenous seems to be defensible 
> in your case.
> 
> As I said in my previous posting, either you treat ln(P) as 
> exogenous or endogenous.  There isn't any third way, at least 
> in IV-GMM.  It looks like either approach is legitimate in your case.
> 
> Hope this helps.
> 
> Cheers,
> Mark
> 
> >
> > I know this is a rather uncommon case, so I would appreciate any 
> > suggestion.
> >
> > Eddy
> >
> 
> 
> Ir. Robert Vergeer
> Department of Economics of Innovation
> TU Delft, faculty of Technology, Policy and Management
> 
> R.Vergeer@tudelft.nl
> TU Delft/ faculteit Techniek, Bestuur en Management Jaffalaan 5
> 2628 BX  Delft
> 015 2788928
> 
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Marcello Pagano
> Sent: maandag 7 augustus 2006 23:32
> To: statalist@hsphsun2.harvard.edu
> Subject: st: 2 parameter MLIRT polychotomous model simulation
> 
> I am trying to simulate 2-Parameter MLIRT polytomous models in Stata.
> Could someone pls suggest how I can do it? I came across 
> simirt program but I dont understand how to specify that each 
> item should have, say, 4 categories and specify its 
> discrimination parameter (because the rsm option cannot be 
> used with the disc option).
> 
> Could someone clarify/give suggestions please?
> 
> Thanks
> 
> Prathiba Natesan
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