st: RE: endog() option in ivreg2 for exactly identified models

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Vidhya,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of Vidhya Soundararajan
> Sent: 16 July 2013 21:43
> To: statalist@hsphsun2.harvard.edu
> Subject: st: endog() option in ivreg2 for exactly identified models
> 
> Dear stata list users,x
> 
> I have an exactly identified single equation model (three endogenous
> regressors and three instruments) and my standard errors are
> clustered. I want to test for exogeneity of all these three
> instruments using the endog () option in ivreg2.
> 
> These are a part of my results from ivreg2 command:
> -------------------------------------------------------------------------------------------------------
> --
> Hansen J statistic (overidentification test of all instruments): 0.000
> (equation exactly identified)
> -endog- option:
> Endogeneity test of endogenous regressors: 2.944
> Chi-sq(3) P-val =    0.4004
> -------------------------------------------------------------------------------------------------------
> --
> 
> My question here is: Can I interpret these results to accept the null
> that both IV estimates and OLS estimates are equal? Am I interpreting
> this right?

Yes, though "fail to reject the null" is maybe better.  If your estimates are very noisy, then you can fail to reject the null that the IV and OLS coefficients are the same not because they are very close, but because they are very imprecisely determined.

> 
> The reason I am wondering why not is that may be the endog option
> makes sense only for over identified models because the j-stat (and
> hence the difference in j-statistics of two models) is based on over
> identifying restrictions. This is probably not the case and endog()
> option can be used for exactly identified models as well.

That's right, the first statement is wrong and the second statement is right.  The case of no endogenous regressors (OLS or HOLS) is overidentified because there are excluded instruments, so you can get a Sargan or Hansen overid stat for it.  There's a discussion of this in the Baum et al. (2003) SJ paper cited in the ivreg2 help file.  See also below.

> But I just
> want to make sure. Any case, Stata does not give an error and I think
> I am probably interpreting this wrong. Can you please provide more
> help on this?
> 
> I understand that the test statistic reported here by ivreg2 is the
> difference of j-statisics of two models, one which treats all the 3
> endogenous regressors as exogenous and the other which treats them
> endogenous and uses the three instruments I provide to estimate a 2sls
> model.
> For the latter: J-statistic is 0 for an exactly identified IV model
> (which is my case).
> Former: The restricted model where the endogenous variables are
> treated exogenous, is the OLS. I am not sure what the J-statistic for
> an OLS model is. Is this 2.944 which makes the final statistic 2.944 -
> 0 = 2.944?

The interpretation is almost right.  The only point is that you are probably using robust, cluster, or some other option that means you are relaxing the iid assumption and getting a Hansen-Sargan (instead of just Sargan) J statistic.  In this case you are contrasting an exactly identified IV model with, not OLS, but what is usually called HOLS ("heteroskedastic OLS"), usually associated with Cragg.  It is a GMM estimator that is more efficient than OLS because it uses more orthogonality conditions than there are regressors (hence it's overidentified).  HOLS is also discussed in Baum et al. (2003).

HTH,
Mark

> 
> If I cannot interpret this test this way, are there other ways to test
> for the exogeneity of instruments (like in the Hausman test) in an
> exactly identified model when standard errors are clustered?
> 
> 
> Best,
> Vidhya
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