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
n.j.cox@durham.ac.uk
LachZak@web.de
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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