# RE: st: Critical values for stock and yogo test when the clusteroption is used

 From "Schaffer, Mark E" To Subject RE: st: Critical values for stock and yogo test when the clusteroption is used Date Wed, 27 Feb 2008 15:18:44 -0000

```Danny,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> Sent: Wednesday, February 27, 2008 2:58 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Critical values for stock and yogo test when
> the clusteroption is used
>
> Dear Professor Austin and other statalist subscribers
>
> I only want to add that in the email today I clarified
> something that wasn't clear enough in the private mail
> yesterday. The points is that the results much differ if I
> use the clustered f-statistic instead of the regular one.
> The regular f-statistic is 158 which is extremely above the
> regular critical value (the critical values are between
> 5.53-16.38). This indicate that the instrument is extremely
> strong. However, if i compare the clustered f-statistic
> (5.26) to the regular critical values I may come to an
> opposite conclusion that my instrument is quite weak (it is
> only close to the 25% maximal iv size). Should i worry about
> the strength of my instrument?

The short answer is "yes", you should worry, and your intution below is
right.

The problem starts out just like the usual problem of using non-robust
SEs for inference.  If the disturbance is heteroskedastic or clustered,
the usual SEs are wrong, and usually [sic] you'll get SEs that are "too
small" and test stats that are "too big".  The same features of the data
that give you these test stats that are "too big" will give you a
first-stage F-stat that is also "too big", and so the Stock-Yogo
critical values will be wrong.

Where it gets complicated is that the S-Y critical values for weak
identification come from Monte Carlos.  My understanding is that if you
want the "right" critical values for cases where the standard S-Y iid
assumption is loosened, you have to specify how it's loosened, i.e., in
your case, what kind of clustering you've got.

That said, using a cluster-robust first-stage F stat with the S-Y
critical values is not bad and in the absence of anything better is
probably the best you can do.

It's also worth noting that the first-stage F-stat can also be used as a
test for *under*identification a la Anderson.  (See the paper by myself,
Kit Baum and Steve Stillman in the latest issue of the SJ, vol. 7 no. 4
2007.)  This is a test with an asymptotic justification and uses
standard critical values, and the robust first-stage F stat with this
standard critical values is fine.  Since underidentification is a lower
hurdle than weak identification, if you can't reject the null that your
equation is underidentified, you can pretty safely also fail to reject
the null that it's weakly identified.

Hope this helps.

Cheers,
Mark

Prof. Mark E. Schaffer
Director
Centre for Economic Reform and Transformation
Department of Economics
School of Management & Languages
Heriot-Watt University
Edinburgh EH14 4AS  UK
44-131-451-3494 direct
44-131-451-3296 fax
http://www.sml.hw.ac.uk/cert

> After all, i guess that as the
> clustered f-statistic is much lower than the regular one, the
> clustered critical value should also be lower? That is, don't
> we require to much when we compare the clustered f-statistic
> to the regular critical values.
>
> Best,
>
> Danny
>
>
> ----- Original Message -----
> From: "Austin Nichols" <austinnichols@gmail.com>
> To: <statalist@hsphsun2.harvard.edu>
> Sent: Wednesday, February 27, 2008 3:36 PM
> Subject: Re: st: Critical values for stock and yogo test when
> the clusteroption is used
>
>
> > All--
> > My reply (Tue, Feb 26, 2008 at 4:42 PM) to this
> interlocutor's private
> > email yesterday was:
> > ***************
> > Until someone redoes Stock and Yogo with various kinds of
> clustering,
> > you are stuck comparing your value to their table.  One
> reason no one
> > has done that is that different kinds of clustering might produce
> > different answers, so the critical values might be more
> > problem-specific, and you might have to run your own
> simulations for
> > your own case, using observed intra-cluster correlations in
> the data.
> > ***************
> > If anyone has a different answer, I'd be interested to hear
> it.  Note
> > that the ref for Stock and Yogo is in the help for -ivreg2-
> on SSC and
> > in http://www.stata.com/meeting/5nasug/wiv.pdf.
> >
> > On Wed, Feb 27, 2008 at 7:33 AM, Danny Cohen-Zada
> <danoran@bgu.ac.il>
> > wrote:
> >> I would be thankful to anybody that can give me an advice
> concerning
> >> the  critical values in the stock and yogo test.
> >>
> >>
> >>  I estimate the following IV model with the cluster option
> >>
> >>  ivreg2 y1 x1 x2 (y2 =  z1 ), ffirst cluster (x3)
> >>
> >>  (In my model I have only one endogenous regressor and one
> excluded
> >> instrument).
> >>
> >>  I know that the Stock and Yogo statistic assume conditional
> >> homoskedasticity  and independence. Since I use the
> cluster option I
> >> can not use the reported  stock and yogo statistic (f statistic on
> >> the exluded instrument)  and the  reported critical values.
> >>
> >>  I know that I can use the command ffirst to obtain the
> corrected f
> >> statistic  on the excluded instrument. It differ
> substantially  from
> >> the unclustered f  statistic (regular = 158, clustered=5.26, the
> >> regular critical values are in  the range 5.53-16.38). However, I
> >> still have a problem because I do not know  what the corrected
> >> critical values are (I guess that I can not use the
> regular critical
> >> values). If i used the regular f-statistic and the regular
>  critical
> >> values i find that my instruments are very very strong.
> This  picture
> >> is changed if i compare the corrected f-statisticto the regular
> >> critical values.
> >>
> >>  I would be thankful to anybody who knows how I can check that my
> >> instruments  are not weak in a regression where the
> cluster option is
> >> used.
> >> Specifically,
> >>  to which value should I compare the corrected f-statistic on the
> >> excluded  instrument obtained by the command ffirst.
> >>
> >>
> >>  Best,
> >>
> >>  Danny
> >>
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```