# Re: st: Re: why did IV estimation turn an insignificant includedinstrument variable in OLS to be significant in IV estimation?

 From Jian Zhang To statalist@hsphsun2.harvard.edu Subject Re: st: Re: why did IV estimation turn an insignificant includedinstrument variable in OLS to be significant in IV estimation? Date Thu, 24 Aug 2006 12:45:10 -0700 (PDT)

```Thanks, Rodrigo and Mark!  Your comments really help!

Best regards,
Jian

On Wed, 23 Aug 2006,
Rodrigo A. Alfaro wrote:

> Jerry Hausman in "IV Estimation with Valid and Invalid Instruments"
> available in his webpage at MIT (http://econ-www.mit.edu/faculty/)
> has a model where you can see what you think. Variance of IV
> is greater than LS, for that check the model, theorem 1 and (2.5).
> But note that the model only have 1 endogenous variable as
> explanatory. In that particular case, your guess is true... but as
> Mark pointed the estimation of beta should be different. A particular
> case is when sigma_eu=0 which proves the inefficient of IV in that
> particular case, but if sigma_eu!=0 therefore your LS is inconsistent
> reason for why you are dealing with the IV estimator. R.
>
>
> ----- Original Message -----
> From: "Jian Zhang" <jzh@ucdavis.edu>
> To: "Rodrigo A. Alfaro" <ralfaro76@hotmail.com>;
> <statalist@hsphsun2.harvard.edu>
> Sent: Wednesday, August 23, 2006 2:23 AM
> Subject: RE: st: Re: why did IV estimation turn an insignificant included
> instrument variable in OLS to be significant in IV estimation?
>
>
> 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
> >
> > 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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