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st: RE: Several endogenous dummies, one instrument for each, in a binary model


From   "Nick Cox" <[email protected]>
To   <[email protected]>
Subject   st: RE: Several endogenous dummies, one instrument for each, in a binary model
Date   Fri, 30 Jan 2009 19:34:16 -0000

Just to get in before Kit Baum: it's a misunderstanding to think that
instruments map on to other variables one to one. That's not how
instrumental variables work. 

I don't have an answer the question. 

Nick 
[email protected] 

[email protected]

I'm estimating a series of probit models with several possibly
endogenous dummy variables. Following the suggestions by Angrist (2001):
Estimation of Limited Dependent Variable Models with Dummy Endogenous
Regressors: Simple Strategies for Empirical Practice, Journal of
Business and Economic Statistics, 19 (1) I'm using "standard" 2SLS.
However, there is a problem with my instruments...because I just have
one instrument for each of the endogenous dummies. The instruments are
not dummies (but regional-level percentages).
I was thinking about running regressions of the following type:
y1 = b0 + b1z1 + b2z2 + b3x3+....+u
where z1 and z2 are possibly endogenous dummies, to instrument just one
of the dummies (for instance, z1) and keep the other dummy (for
instance, z2) as a control without instrumenting it. As I said, the
instruments can just be used for 1 of the endogenous dummies. Are the
estimates on the instrumented dummy consistent in this case? Does anyone
know of any other procedure that I could use in this case?

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