Re: st: bootstraping two stages together

["Danny Cohen-Zada" <danny.cohen.zada@gmail.com>]

Dear Professor Austin,

Did i understand you well that i should do the following: Run the first 
stage

y2 = b0+b1*x1+b2*x2+b3*z1 (z1 is an excluded instrument for y2)

then take the residuals of this equation - v2(hat)

Finally, I should estimate

y1  = a0+a1*y2+a2*x1+a3*x2+a4*v2(hat)           (where y1 obtain the values 
0,1,2)


If i am right, should i then also bootstrapt the standard errors.


Best,

Danny


----- Original Message ----- 
From: "Austin Nichols" <austinnichols@gmail.com>
To: <statalist@hsphsun2.harvard.edu>
Sent: Wednesday, June 18, 2008 6:06 PM
Subject: Re: st: bootstraping two stages together



> Danny Cohen-Zada <danoran@bgu.ac.il>:
> You have more to worry about than correcting SEs--that does not sound
> like a consistent estimator; see e.g. pp 12-13 of
> http://www.nber.org/family/WNE/lect_6_controlfuncs.pdf
> viz.
> "Plugging in fitted values for y2 only works in the case where the
> model is linear in y2"
>
> On Wed, Jun 18, 2008 at 12:47 PM, Danny Cohen-Zada <danoran@bgu.ac.il> 
> wrote:
>
> > Dear stata members
> >
> > I have a multinomial logit regression in which one of the covariates is
> > endogenous.
> >
> > More specifically, the model is:
> >
> >
> > 1) y1  = a0+a1*y2+a2*x1+a3*x2               (where y1 obtain the values
> > 0,1,2)
> >
> > 2) y2 = b0+b1*x1+b2*x2+b3*z1 (z1 is an excluded instrument for y2)
> >
> >
> > To run this model, i first estimate equation 2 and obtain expected y2 and
> > then plug it in equation 1 (which is a multinomial logit regression). In
> > this case, i know that the standard error of the estimated a1 coefficient 
> > is
> > not correct. I also know that i must bootstrap the two stages together 
> > but I
> > do not know how to do it.
> >
> > I will be thankful to anybody that can guide me in this issue.
> >
> > Danny
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