st: RE: F-statistic on ivreg2 with Cluster option

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Juan Jose,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Juan Jose
> Sent: 20 October 2010 18:51
> To: StataList
> Subject: st: F-statistic on ivreg2 with Cluster option
> 
> Hi all,
> I have a specific question related to -ivreg2- with/without 
> cluster option since the instrument is at neighborhood level. 
> The issue is that F-stat with cluster option is very 
> different than the F-stat without cluster option. The 
> instrument it is still statistically significant, but at a 
> lower significance level (due to standard errors are higher). 
> For example, p-value changes from 0.063 to 0.099.
> 
> The two regressions I am running are the following (being the 
> only difference cluster option):
> (1) ivreg2 Y X2 - X14 (X1 = Z1), first robust
> (2) ivreg2 Y X2 - X14 (X1 = Z1), first robust cluster(neighbor)
> 
> Regression (1) has the following F-stat (being 461 the number 
> of observations):
> F test of excluded instruments:
>   F(  1,   445) =    36.77
>   Prob > F      =   0.0000
> 
> Regression (2) has the following F-stat (being 74 the number 
> of cluster):
> F test of excluded instruments:
>   F(  1,    73) =     4.70
>   Prob > F      =   0.0334
> 
> Given this different results about the F test of excluded 
> instruments, which one should I use? Seems to me that I 
> should that one with degrees of freedom related to the number 
> of observations and not that one related to the number of 
> cluster groups, but I might be wrong.
> Comments and suggestions are more than welcome!

This isn't an -ivreg2- question, but a general question about the
cluster-robust covariance estimator.  If you run a simple OLS regression
with -regress- with and without the cluster() option, you will get the
same difference in degrees of freedom showing up in the F-stat.

The Stata user's manual has a good discussion in Section 20.16 (Stata 11
manual).  The short answer to your question is that both F stats are
reported using the appropriate degrees of freedom, and in any case
degrees of freedom have very little to do with your decision of which to
use.  Under the null of iid errors, both F stats are consistent; with
errors that are clustered, only the cluster-robust F stat is consistent.
The difference between the two suggests that if you did a formal test,
you would reject the null of iid errors, i.e., you should use
cluster-robust.

--Mark

> 
> Regards,
> Juan Jose.
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