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st: RE: bootstrapping RE with small number of clusters

From   "Schaffer, Mark E" <[email protected]>
To   <[email protected]>
Subject   st: RE: bootstrapping RE with small number of clusters
Date   Thu, 31 Jan 2008 20:22:15 -0000


> -----Original Message-----
> From: [email protected] 
> [mailto:[email protected]] On Behalf Of 
> Lloyd Dumont
> Sent: 31 January 2008 00:36
> To: [email protected]
> Subject: st: bootstrapping RE with small number of clusters
> Hello, everyone.  As many of you know, I have been estimating 
> (using -xtreg- and the cluster option) a random effects model 
> on an unbalanced panel in which there are about 15 clusters, 
> most observed about 15 times.  That is, this is not the 
> typical situation in which in which the number of clusters is 
> significantly larger than the number of time periods.
> Two concerns:
> First, I am concerned that FE is more appropriate than RE.  
> That is a problem, because just about all the regressors I 
> care about are time constant.  (I think this may mean "tough 
> luck" for me, I realize.)

You're probably in "tough luck" land, I'm afraid.

The coefficients on the time-invariant regressors rely entirely on the
cross-unit variation.  In effect, you have 15 observations for
estimating however many such coefficients you've got.  Even if there's
only one, 15-1=14 degrees of freedom is not going to be very convincing.
If the #regressors>15 then RE is not possible at all.

> Second, I am concerned with the potential for small sample 
> bias in my variance estimates.  I thought a good way to deal 
> with this would be to bootstrap my standard errors (using 
> -xtreg- , the cluster option, and the vce(bootstrap) 
> options).  Now, I am a novice with the bootstrap, but my 
> initial attempts yielded confidence intervals, not 
> surprisingly, far less favorable than those yielded under the 
> normality assumption.  (This did not improve much as I 
> increased the number of reps.)
> So, does that just further demonstrate that my RE estimates 
> are inconsistent and that there is little I can do about it?

Sort of.  The problem isn't inconsistency, which is an asymptotic
concept. That is, estimates are consistent as something - here, the
number of panel units i.e. clusters - goes off to infinity.  The problem
is, rather, that 15 is not very far on the way to infinity.

Sorry I can't be more constructive.


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
email: [email protected]

> Or, is there a way to use the bootstrap to better determine 
> the actual/observed error structure, and then re-estimate the 
> model by imposing this "revealed"
> structure upon it?
> Thank you for your thoughts/suggestions.  Lloyd Dumont
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