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RE: st: Re: why did IV estimation turn an insignificant included instrument variable in OLS to be significant in IV estimation?


From   "Jian Zhang" <jzh@ucdavis.edu>
To   "Rodrigo A. Alfaro" <ralfaro76@hotmail.com>, statalist@hsphsun2.harvard.edu
Subject   RE: st: Re: why did IV estimation turn an insignificant included instrument variable in OLS to be significant in IV estimation?
Date   Tue, 22 Aug 2006 23:23:23 -0700 (PDT)

Thanks, Rodrigo!   I remember that I read something, which is that the standard errors for IV 
estimators are always bigger than OLS (that is, the variance-covariance matrix of IV estimators 
minus the variance covariance matrix of OLS is always positive definite).  But I couldn't find any 
textbooks or materials discussing it.

Jian Zhang


> Jian,
> 
> Pretend that your model is:
> 
> y2 = b*y1 + c*x + e
> 
> if you estimate by LS then std error for b and c
> depend on the fit as well the std errors of y1 and x
> (you can check Marteen's question around 08/15)
> 
> LS+robust you add some of the structure of e,
> which makes the things more complex.
> 
> Alternative you can say that y1 is also endogenous
> therefore a IV estimator will be more appropiated
> you are adding some additional equation like
> 
> y1 = d1*z1 + d2*z2 + d3*z3 + w
> 
> Assuming that z's are valid instruments and taking
> whatever method of IV (2SLS, GMM, Nagar, LIML,
> Fuller, etc) your news std errors for b and c depend
> on several statistics and the std erros of z's and x.
> 
> >From above, your result is not an error. Now you have
> to think why taking y1 endogenous generates that x
> becomes significant(*).
> 
> Rodrigo.
> (*) Remember that significant is an inference that takes
> place after several assumptions: right distribution
> (IV estimators are Asymptotically Normal which
> means in large-large sample), right assumptions
> (validity of the instruments, omitted variables,
> specification of the model, etc.) and your personal
> choice of alpha (error type 1).
> 
> ----- Original Message ----- 
> From: "Jian Zhang" <jzh@ucdavis.edu>
> To: <statalist@hsphsun2.harvard.edu>
> Sent: Tuesday, August 22, 2006 7:53 PM
> Subject: st: why did IV estimation turn an insignificant included
> instrument 
> variable in OLS to be significant in IV estimation?
> 
> 
> Dear Statalisters,
> 
> I am implementing an IV estimaiton.    Compared to robust OLS estimation 
> results, I found that
> one INCLUDED variable changed from insignificant in robust OLS esitmation
> to 
> significant in IV
> estimation.  But, from what I understand, IV esitmators are supposed to 
> larger standard errors
> than OLS estimators.  If this is correct, the IV estimators are supposed
> to 
> be less significant than
> OLS estimators.    I wonder why this happened.  Is there anyone running
> into 
> the same problem
> and understanding it?  Thank you very much!
> 
> Best regards,
> Jian Zhang
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