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st: RE: instrumental variable nomenclature


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: instrumental variable nomenclature
Date   Mon, 25 Aug 2008 20:07:22 +0100

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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