st: RE: on interactions of endogenous variables with an exogenous one and xtivreg2

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

Rado,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> rado645-bg@yahoo.de
> Sent: 03 July 2012 22:10
> To: statalist@hsphsun2.harvard.edu
> Subject: st: on interactions of endogenous variables with an 
> exogenous one and xtivreg2
> 
> Dear all,
> 
> I have an issue with a regression that includes endogenous 
> variable (x) and its interaction with an exogenous one (m). y 
> is the dependent variable and z is the instrument.
> 
> In this case, it was recommended to me to run two first stage 
> regressions: 
> 
> 1) x on z m and the set of control variables [where I have to 
> store fitted values (e.g. in a variable store1 ) ]
> 
> 2) x*m on z*m and the set of control variables  (without 
> including m in this regression)
> 
> [where I have to store fitted values (e.g. in a variable store2 )]
> 
> Next I have to move to the second stage: 
> 
> 3) y on store1 store2 m and the set of control variables
> 
> I would like to ask you whether conceptually this model is a 
> correct one in this case. For example m does not enter in 
> regression 1. Intuitively I would prefer to run the following 
> regression where F denotes the set of control variables: 
> 
> xtivreg2 y (x x*m = z z*m) m F
> 
> However m enters in both first stage regressions in this case. 

You are right to be suspicious about the recommendation you've received.  Your intuition is correct - you should estimate as you have specified just above, so that in effect m appears in all the first-stage regressions.  The Stata FAQ here

http://www.stata.com/support/faqs/statistics/instrumental-variables-regression/

explains why, I think.

> My second question refers to its estimation with xtivreg2. 
> From reading previous posts, I have also found that I cannot 
> store predicted values from the first stage with xtivreg2.

Actually, xtivreg2 with fixed effects won't produce predicted values of the dependent variable at all, whether first stage or second stage.  The reason is that the FE estimator doesn't allow estimation of the constant term.  There was a thread on just this point very recently:

http://www.stata.com/statalist/archive/2012-07/msg00053.html

Cheers,
Mark

> Is 
> there a possibility to overcome this limitation by using 
> another command to predict and store the RHSs from step 1 and 
> 2 so I can estimate this model? (I use  fixed effects and I 
> have to cluster by the panel id)
> 
> Best,
> Rado
> 
> 
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