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st: RE: ivreg2/xtivreg2, clustering, and the covariance matrix of moment conditions


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: ivreg2/xtivreg2, clustering, and the covariance matrix of moment conditions
Date   Thu, 19 Feb 2009 16:50:48 -0000

Augusto,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Augusto Cadenas
> Sent: 18 February 2009 21:05
> To: statalist@hsphsun2.harvard.edu
> Subject: st: ivreg2/xtivreg2, clustering, and the covariance 
> matrix of moment conditions
> 
> Dear all,
> 
> when working with one of my panel datasets with -xtivreg2-, I get the
> well-known error message:
> 
> ***
> Warning: estimated covariance matrix of moment conditions not 
> of full rank.
>          standard errors and model tests should be 
> interpreted with caution.
> Possible causes:
>          number of clusters insufficient to calculate robust 
> covariance matrix
>          singleton dummy variable (dummy with one 1 and N-1 
> 0s or vice versa)
> partial option may address problem.
> ***
> 
> I saw this error message being discussed often here, but I was
> wondering if there is a simple rule that explains when this problem
> occurs. Can we relate it simply to the number of observations,
> clusters, regressors of the model?

Sometimes.  See Baum-Schaffer-Stillman, Stata Journal 2003 (sorry, on
the road, don't have the exact link).

> For example, I have N=8, T=12, a balanced panel (N*T=96), and want to
> have one cluster for each state (N), so M=8. The model I estimate has
> time and state fixed effects and only one regressor beyond that, so
> 1+7+11 coefficients to estimate. Is that because 19>8?

If you are using xtivreg2, then you probably estimating a fixed effects
model with 8 fixed effects and 11 time dummies.  The fixed effects are
NOT explicitly estimated - as usual with the FE model, they are
partialled out using the within transformation (demeaning).  Thus you
are probably obtaining 1+11=12 explicit coefficient estimates.

But your conclusion is basically correct.  Because 12 (number of
coefficients, var-cov matrix of moment conditions is 12x12) > 8 (number
of clusters, rank of the var-cov matrix of moment conditions), the
var-cov matrix of moment conditions is not of full rank.

> The other thing I'm wondering about is: why can Stata still compute
> standard errors in this case (even though they "should be interpreted
> with caution"), but can't compute the overid test in the case in which
> I have more than one instrument? (I tried both the perfectly
> identified and the overid case).

Because the overid test requires the var-cov matrix of moment conditions
to be of full rank and invertible.

You should investigate the -partial- option, as suggested by the error
message.  If you partial out your time dummies along with the fixed
effects, the var-cov matrix of (remaining) moment conditions will be 1x1
and you'll get your overid statistics.

HTH.

Cheers,
Mark

Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University
Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296
http://ideas.repec.org/e/psc51.html


> Thanks for your suggestions.
> 
> AC
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