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Re: st: RE: control function with probit in first stage


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: control function with probit in first stage
Date   Fri, 13 Apr 2007 17:47:13 -0400

Deepak Hegde et al.--
Note that when
http://www.stata.com/meeting/5nasug/wiv.pdf
talks about the control function approach generalizing to nonlinear
models, I am referring to a nonlinear model in the *second* stage.
With a binary endogenous variable, you can use -ivreg2- (or even
-ivreg- I guess), or a standard control function approach, as
well--i.e. that fact that the endogenous variable is binary does not
affect consistency of the IV estimator.  The -treatreg- estimator
offers improved efficiency, however, and will show big differences in
small samples.  Another alternative appears in 18.4.1 of Wooldridge
(2002; http://www.stata.com/bookstore/cspd.html) as Procedure 18.1:

esto clear
sysuse auto, clear
treatreg pri wei, treat(for=mpg) r
esto treat
ivreg pri wei (for=mpg), r
esto ivreg
probit for wei mpg
predict ghat
ivreg pri wei (for=ghat), r
esto pr18_1
reg for wei ghat, r
predict vhat, resid
reg pri wei for vhat, r
esto pr18_1cf
esta

Note that the SEs in col 3 are correct, col 4 not so much.  (No
correction is required for an estimated instrument, but you must
correct SEs by hand when using the control function approach.)

If I've gotten anything wrong above, I trust Mark will correct it.

On 4/13/07, Deepak Hegde <hegde@haas.berkeley.edu> wrote:
Wooldridge (2002 p612) has a section on this.  Imbens (p3 of the below
linked file) has a short introduction too:
http://are.berkeley.edu/courses/ARE213/spring2006/lect18_06apr10.pdf, as
does http://www.stata.com/meeting/5nasug/wiv.pdf (p4)

The reason I am using the control function approach is because I am
explicitly interested in the coefficient/std errors on the residual (from
the first-step) in the second-stage regression.

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