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Re: st: ivreg2 Griliches example instrument validity


From   "Mark Schaffer" <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: ivreg2 Griliches example instrument validity
Date   Fri, 15 Oct 2004 13:47:50 +0100

Hi Ralph.  To answer your questions,

Subject:        	st: ivreg2 Griliches example instrument validity
To:             	statalist@hsphsun2.harvard.edu
From:           	Ralph.Heinrich@unece.org
Date sent:      	Fri, 15 Oct 2004 12:05:51 +0200
Send reply to:  	statalist@hsphsun2.harvard.edu

> Hi,
> 
> I have been running the examples provided at the end of the documentation
> for ivreg2 using the Griliches data (Wages of very young men, JPE '76), and
> I have trouble interpreting the results of the tests for instrument
> validity. The model is
> 
> ivreg2 lw s expr tenure rns smsa _I* (iq=med kww age mrt)
> 
> The tests for joint validity of the list of instruments (Sargan, Basman,
> pseudo-S, pseudo-B, Hansen J in the case of GMM) all reject the null, ie
> the excluded instruments are NOT jointly valid. Is this interpretation
> correct ?

Correct.

> The orthog(age mrt) option further tests whether the subset (age mrt) of
> instruments is valid
> 
> ivreg2 lw s expr tenure rns smsa _I* (iq=med kww age mrt), gmm orthog(age
> mrt)
> 
> The C statistic rejects the null, implying that (age mrt) are NOT valid.
> Correct ?

Correct.

> At the same time the Hansen J for the UNrestricted equation now fails to
> reject its null, implying that the complementary subset of instruments (kww
> med) ARE valid. Is this interpretation correct ?

Correct.

> Now I ran the same regression with the orthog option on the complementary
> subset (kww med), ie
> 
> ivreg2 lw s expr tenure rns smsa _I* (iq=med kww age mrt), gmm orthog(kww
> med)
> 
> In view of the above, I expected the Hansen J on the unrestricted model to
> reject its null, and the C statistic not to reject its null. The former
> expectation is confirmed, but the C statistic does reject, implying that
> (kww med) are NOT valid. Is this not a contradiction to the Hansen J test
> result above, which seemed to suggest that (kww med) are valid ?

Here's the problem.  Roughly speaking, it appeared that (kww med) are 
valid and (age mrt) are not.  Then you tried testing the former using 
the C test.  However, to do this, you need to believe the 
complementary subset, (age mrt), is valid under both the null and the 
alternative, but you have evidence that it isn't.

The further evidence that using the (age mrt) instrument is badly 
specified comes from the relevance of the instruments.  (med kww) are 
strong instruments; the first-stage F=16. (age mrt) are weak 
instruments; the first-stage F=3, and hence the equation is verging 
on unidentified.

The C test is basically just the difference between the J from using 
all 4, and the J using (age mrt).  The latter specification is the 
one that is presumed to be consistent under the null and the 
alternative.  But the specification using all 4 is apparently 
misspecified, and so apparently is the specification using just (age 
mrt).  You can't get anything useful out of this comparison of two 
misspecified equations.

> Leaving aside the Hansen J results, the C results would suggest that none
> of the (two pairs of) instruments are valid. But when I ran the regressions
> with only (age mrt) and only (kww med) used as excluded instruments, ie
> 
> ivreg2 lw s expr tenure rns smsa _I* (iq=age mrt), gmm
> ivreg2 lw s expr tenure rns smsa _I* (iq=kww med), gmm
> 
> the Hansen J failed to reject the null in both cases , suggesting that both
> subsets ARE valid instruments ?!
> 
> So what am I missing here ?

I think what might be happening is that when (age mrt) are the 
excluded instruments, the equation is basically unidentified.  If you 
did 2SLS by hand using (age mrt), the iq_hat would be practically 
noise in the second stage regression.  Hence (kww med) won't satisfy 
the orthogonality conditions (will be correlated with the residuals) 
when you do your C test because, roughly speaking, the "economic 
content of iq" is still in the residuals (because iq_hat wasn't 
picking it up).

Caveat - the above explanation may get me in trouble with the RSPDS!  
(Royal Society for the Protection of Data Sets).

--Mark

> Thanks
> Ralph
> 
> 
> 
> Ralph Heinrich
> Economic Affairs Officer
> Economic Analysis Division
> UN Economic Commission for Europe
> 
> room 441
> Palais des Nations
> 1211 Geneva 10
> phone: 0041 22 917 1269
> http://www.unece.org/ead/ead_h.htm
> 
> 
> 
> *
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Prof. Mark E. Schaffer
Director
Centre for Economic Reform and Transformation
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS  UK
44-131-451-3494 direct
44-131-451-3008 fax
44-131-451-3485 CERT administrator
http://www.som.hw.ac.uk/cert

*
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