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st: RE: RE: instrumental variable nomenclature


From   "Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: instrumental variable nomenclature
Date   Mon, 25 Aug 2008 14:22:40 -0500

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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