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
> 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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