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

 From "Schaffer, Mark E" To Subject RE: st: Re: why did IV estimation turn an insignificant included instrument variable in OLS to be significant in IV estimation? Date Wed, 23 Aug 2006 09:24:34 +0100

```Jian Zhang,

The other part of the answer is that you haven't said what you mean by
"significant".  Do you mean "significantly different from zero"?  Then
of course coefficients can become significant even if the SEs have
increased - the point estimate under IV can be further away from zero
than under OLS, taking confidence interval along with it.

--Mark

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jian Zhang
> Sent: Wednesday, August 23, 2006 7:23 AM
> To: Rodrigo A. Alfaro; 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?
>
> 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
> > *
> > *   For searches and help try:
> > *   http://www.stata.com/support/faqs/res/findit.html
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
> >
> > *
> > *   For searches and help try:
> > *   http://www.stata.com/support/faqs/res/findit.html
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
> >
> *
> *   For searches and help try:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>
>

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```