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st: Question about finite-sample adjustment for cluster-robust estimation

From   "Mark Schaffer" <[email protected]>
To   [email protected]
Subject   st: Question about finite-sample adjustment for cluster-robust estimation
Date   Mon, 07 Jun 2004 17:31:41 +0100

Hi everybody.  David Roodman and Kit Baum spotted a small bug in 
ivreg2 when the cluster-robust option is used - the F-stat differs 
from that reported by official Stata because the degrees of freedom 
adjustment is different.  (We'll post a bug fix shortly.)

But this led to a question of why official Stata makes the finite-
sample adjustment it does for cluster-robust estimation, and maybe 
there are some survey specialists out there who can explain it.

The manual (under Regress) states that if the option chosen is just
-robust-, the finite sample adjustment for the var-cov matrix is


where N is the number of observation and k is the number of 
regressors including the constant.

If the option chosen is -cluster-, then the adjustment is

(N-1)/(N-k) * M/(M-1)

where M is the number of clusters.

The intuition is clear enough - when the number of clusters is small, 
the standard errors can get big - but why M-1?  Why not, for example, 
M-k?  (The logic for this alternative is that the rank of the var-cov 
matrix is M-k when the cluster-robust option is chosen, and if M-k is 
small then the standard errors should be big.)  Does anybody know of 
any Monte Carlo evidence on this?  Inquiring minds want to know....

Prof. Mark E. Schaffer
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
44-131-451-3008 fax
44-131-451-3485 CERT administrator

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