re:st: Re: 3SLS with different instruments for different equations

[Christopher Baum <kit.baum@bc.edu>]

<>
As I said in my post   http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1103/date/article-963.html 
all three equations are indeed exactly ID.  And all three Ys are OBVIOUSLY endogenous -- that's why they are on the LHS, with other Ys on the RHS!
I don't understand your semantic confusion in this regard. A system of three simultaneous equations involves three endogenous variables, and what you hve written down has no recursive structure. Ergo, you have three endogenous variables, and three reduced form equations, each with a Y on the LHS. 

What you are trying to do is to state that the regression of Y2 on all the instruments should include Z1 but not Z2. I don't know whether the Zs are the same as your IVs in an earlier message; I suppose so. But if you look at the equation for Y2:

Y2 = k0 + k1*Y1 + k2*IV1 + k3*X1 + k4*X2

it is exactly ID, so it needs one instrument. The only available instrument is what you were calling IV2 (and now Z2?) and so there is no way to estimate an equation for Y2 that does not make use of Z2. If you did it would not be ID. The same goes, symmetrically, for Y3. I said in my earlier posting that you could not do anything with 3SLS or GMM that involved placing additional exclusion restrictions (such as leaving a variable out of the instrument list) because you have all exactly ID equations. I stand by that diagnosis. and think trying to do this with GMM is a waste of time. Linear GMM is just a more general case of 3SLS, just as linear IV-GMM is just a general case of 2SLS.

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
                              An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
   An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html




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