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st: RE: RE: RE: instrumental variable nomenclature


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: RE: instrumental variable nomenclature
Date   Tue, 26 Aug 2008 12:42:42 +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: Monday, August 25, 2008 8:23 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: RE: instrumental variable nomenclature
> 
> 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.

If X is not observable, then you wouldn't say Z is an "instrument" for
it.  That's my understanding, at any rate, of the use of the
terminology.

Of course, you can go down the Humpty Dumpty Econometrics route

http://www.sundials.org/about/humpty.htm

but I'm not a big fan of that approach!

Cheers,
Mark


> 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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> > 
> 
> 
> --
> Heriot-Watt University is a Scottish charity registered under 
> charity number SC000278.
> 
> 
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-- 
Heriot-Watt University is a Scottish charity
registered under charity number SC000278.


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