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RE: st: RE: RE: instrumental variable nomenclature


From   "Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: RE: instrumental variable nomenclature
Date   Wed, 27 Aug 2008 08:14:47 -0500

Stas - 

I don't understand your point about causality. It seems to me that
causality has a lot to do with the intrepretation of model error terms -
which would affect estimation -  but yes, my question was mostly about
nomenclature - thanks for your suggestion about checking out
"Measurement Error in Nonlinear Models" .

Al

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Stas
Kolenikov
Sent: Tuesday, August 26, 2008 1:06 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: RE: RE: instrumental variable nomenclature

Alan,

oh, screw the causality -- it is up to you as the researcher to think as
to how your X and Z variables are related, and interpret the findings.
If your question was about how to call those variables so that
economists will understand you -- then I think both Mark and I gave
pretty similar answers: you have a regression with a variable measured
with error (Z is the observed measure of X), and you must come up with
something else that's correlated with X, but not with the measurement
error d.

Note that econometric models usually assume linear relations. The
nonlinearities are far more difficult to deal with. Your main reference
will probably be Carroll and folks book
(http://www.citeulike.org/user/ctacmo/article/1761085). I think a lot of
their motivation comes from similar dose-response kind of stuff.

On Mon, Aug 25, 2008 at 2:22 PM, Feiveson, Alan H. (JSC-SK311)
<alan.h.feiveson@nasa.gov> wrote:
> Hi Mark, Stas -
>
> Sorry, I think I didn't explain the causative sequence properly. What 
> I should have said was that Z affects X through X = h(Z) + d, where d 
> is an error term independent of e. For example, Z is a dose and X is a
> (non-observable) effect. That's why I thought that Z would be an 
> instrument for X rather than the other way around. Does your 
> interpretation still with the above causative sequence?
>
> Thanks
>
> Al
>
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Schaffer, 
> Mark E
> Sent: Monday, August 25, 2008 2:07 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: instrumental variable nomenclature
>
> Al,
>
>> -----Original Message-----
>> From: owner-statalist@hsphsun2.harvard.edu
>> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Feiveson, 
>> Alan H. (JSC-SK311)
>> Sent: 25 August 2008 19:26
>> To: statalist@hsphsun2.harvard.edu
>> Subject: st: instrumental variable nomenclature
>>
>> Hi - I am looking for a name/title to describe the following 
>> simulatenous-equation model:
>>
>> This starts with a linear regression model Y = X*b + e, but X is not 
>> observed. However we know X is correlated with an observable variable

>> Z, with error term independent of e. So at this point, would it be 
>> correct to say this is an instrumental variable model with Z as an 
>> instrument for X?
>
> Not quite.  Say the "true model" is
>
> Y = X*b + e
>
> but you estimate
>
> Y = Z*b + u
>
> Z is an imperfect measure of X.  Say that
>
> Z = X*a + v
>
> This is the classic measurement error problem.  If you had an 
> instrument for X, you could get a consistent estimate of b using
linear IV.
>
> HTH.
>
> Cheers,
> Mark
>
>> Furthermore we also observe K = g(X) where g is a step function (for 
>> example, K follows an ordered probit model with X as the latent 
>> variable). So to get the nomenclature straight, can I say that this 
>> is
>
>> a nonlinear simultaneous equation model (one equation for Y given X, 
>> and one for K given X), with Z as an "instrumental variable for X"?
>>
>> Of course, how to estimate such a model is another story!
>>
>> Thanks for whatever suggestions (names or estimation
>> approach) you can provide.
>>
>> Al Feiveson
>>
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--
Stas Kolenikov, also found at http://stas.kolenikov.name Small print: I
use this email account for mailing lists only.
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