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Re: st: Estimating rare event logistic model (Relogit) with instrumental variable


From   Roger Harbord <rmharbord@googlemail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Estimating rare event logistic model (Relogit) with instrumental variable
Date   Wed, 11 Feb 2009 11:10:55 +0000

Just noticed that the discussion paper in Austin's first link below
was published in a journal last year:

Wilde J.  A note on GMM estimation of probit models with endogenous
regressors.  Statistical Papers
2008;49:471-484.<http://dx.doi.org/10.1007/s00362-006-0027-2>

On Mon, Feb 9, 2009 at 3:01 PM, Austin Nichols <austinnichols@gmail.com> wrote:
> This is probably a less straightforward problem than it first appears--see e.g.
> http://www.iwh-halle.de/d/publik/disc/4-05.pdf
> http://dx.doi.org/10.1016/S0165-1765(01)00623-1
>
> On Sun, Feb 8, 2009 at 12:51 PM, Stas Kolenikov <skolenik@gmail.com> wrote:
>> Murphy-Topel approach is one common way to adjust the standard errors,
>> see http://www.stata-journal.com/article.html?article=st0018. There's
>> been a special issue of Stata Journal on measurement errors --
>> http://www.stata-journal.com/sj3-4.html. There were papers addressing
>> some problems with instrumental variables estimation of GLMs, although
>> what some statisticians say an instrumental variable is (and hence
>> implemented in that software) might seem weird to an econometrician.
>>
>> The only thing that I personally know about rare events are population
>> based case-control studies where the slopes are estimated
>> consistently, and only the intercept might be off for some estimation
>> procedures. Is there much on top of that in terms of what you call
>> corrections for rare events?
>>
>> Gary King's procedures are about five versions of Stata old by now
>> (oh, those wonderful times without the -syntax- command!). I am pretty
>> sure that something of this kind has already been implemented under a
>> different name. -relogit- was not a great name, BTW, to begin with, as
>> my first thought was of a random effect logit (now existent as
>> -xtmelogit- in Stata 10).
>>
>> Anything that looks like a GMM can be implemented using Mata's
>> -optimize()- function, although that would require a good deal of
>> custom programming. For any sort of IV procedures, you have an
>> estimating equation that is essentially
>>
>> sum over observations ( residual times instrument times maybe a
>> weight/variance function )
>>
>> Square those sums, add them up -- and you have some sort of GMM
>> procedure, even though inefficient.
>>
>> On Sun, Feb 8, 2009 at 8:00 AM, Marko Bender <Marko.Bender@wi.tum.de> wrote:
>>> Dear STATA users,
>>>
>>> I would like to estimate a rare event logistic model (RELOGIT) with an
>>> instrumental variable.
>>> Is that possible in STATA?
>>>
>>> The problem is:
>>> - IVPROBIT does not correct for rare events
>>> - a "self constructed" two stage regression (1st stage: OLS; 2nd stage
>>> RELOGIT) does not deliver correct coefficients and standard errors
>>> - more flexible estimation procedures like CMP or GLLAMM do not allow to
>>> specify user written procedures like RELOGIT
>>>
>>> So does anybody know one of the following:
>>> - Is there a procedure existing to consistently estimate a two stage
>>> regression with user-defined estimation procedures (to include RELOGIT)?
>>> - How to do the regressions manually and to estimate the correct
>>> coefficients and standard errors?
>>> - Is a similar correction as implemented by RELOGIT available for probit
>>> results and could it be viable to correct the estimations of IVPROBIT?
>>>
>>> I would be really, really happy for any help you can provide.
>>>
>>> Regards,
>>> Marko
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