st: RE: RE: ivreg2 and interaction terms

["Gars, Jared E" <jgars@purdue.edu>]

Thank you for the reply. I will look more into the id tests. They seem to be fine, I was just worried that the f stats of the instruments on the endogenous regressors were a little lower. I was under the impression that anything under 10 can be considered suspect but do not know much about how this applies to the use of two endogenous variables. 

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Millimet, Daniel
Sent: Wednesday, March 02, 2011 12:34 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: ivreg2 and interaction terms

1.  My understanding is that this is correct and done in practice quite frequently.
2.  Note, even with the interaction, your model is exactly identified even without using the interaction of dum with IV1 and IV2 as instruments.  So, you can see if the model is strongly identified even without using the 2 interactions as additional instruments.
3.  It also sounds like you are not gauging the strength of identification correctly when using 4 instruments and 2 endogenous variables.  To gauge strength, the F-stats from the individual first-stages is not relevant, rather you need to use the appropriate underidentification and weak id tests that view the model as a whole, rather than each first-stage individually.  Maybe this is what you meant, in which case I apologize.

Dann

**********************************************
Daniel L. Millimet, Professor
Department of Economics
Box 0496
SMU
Dallas, TX 75275-0496
phone: 214.768.3269
fax: 214.768.1821
web: http://faculty.smu.edu/millimet
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________________________________________
From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] on behalf of Gars, Jared E [jgars@purdue.edu]
Sent: Wednesday, March 02, 2011 11:19 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: ivreg2 and interaction terms

Statalist,
                This issue has been brought up before but I have not found a sufficient answer either theoretically or technically. Hopefully we can get a clear answer for people in the future that search the list.

I am regressing lnwage on a set of human capital characteristics (BMI, education, etc) where BMI is my endogenous variable.

Lnwage = a + b(BMI) + c(BMI*dum) + d(dum) + g(X) + e, where X is a set of exogenous regressors and dum is a binary variable to proxy the type of firm that the worker is in. (we are ignoring the endogenous choice of firm choice because there is very little evidence that it is indeed endogenous)

My intention is to capture whether returns to human capital vary across firm management in a transitional economy. So here I am allowing for a different intercept and slope for workers in more competitive firms.

Issues: I am using ivreg2, here is my input
xi: ivreg2 lnwage (lnBMI  lnBMI*dum = IV1 IV2  dum*IV1 dum*IV2 )   dum imr X    (IV1 and IV2 are my instruments)

So I believe the appropriate thing to do is to interact my exogenous dummy on the instruments in the first stage. Is this the correct approach in theory and/or practice? It seems to suck out the significance of my instruments. The F stats drop to around 5 for each.

I am not sure that this approach is correct or even really appropriate. Before you suggest just splitting them up, I am also doing that. However, the strength of my instruments diminishes significantly when the sample size becomes more limited.  I would like to be able to maintain the effectiveness of the instruments.


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