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

[Vidhya Soundararajan <vidhyahere@gmail.com>]

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?

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. 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?

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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