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Re: st: bootstraping two stages together


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: bootstraping two stages together
Date   Wed, 18 Jun 2008 16:55:18 -0400

Danny Cohen-Zada <danny.cohen.zada@gmail.com>:
I think that's better than the first approach, but still not a
consistent estimator.  I don't know that anyone has derived one for
the multinomial logit case.  But if you are bound and determined to
proceed without showing consistency, then yes, use the control
function approach like so:

prog inconsist
 syntax varlist, y2(varlist) z(varlist)
 gettoken y x: varlist
 reg `y2' `x' `z'
 tempvar e
 predict double e, resid
 mlogit `y' `y2' `x' `e'
end
bs, reps(100): inconsist outcome xvars, y2(endogvar) z(instr)

But I think you could just run some -ivprobit- regressions instead...
g y0=(outcome==0) if !mi(outcome)
g y1=(outcome==1) if !mi(outcome)
g y2=(outcome==2) if !mi(outcome)

On Wed, Jun 18, 2008 at 4:42 PM, Danny Cohen-Zada
<danny.cohen.zada@gmail.com> wrote:
> 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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