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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

N/(N-k)

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....

--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
44-131-451-3008 fax
44-131-451-3485 CERT administrator
http://www.som.hw.ac.uk/cert

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