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


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Estimating rare event logistic model (Relogit) with instrumental variable
Date   Mon, 9 Feb 2009 10:01:50 -0500

Marko Bender <Marko.Bender@wi.tum.de>:
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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