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st: Re: robust estimation and singleton dummy


From   Christopher F Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: robust estimation and singleton dummy
Date   Tue, 1 Jul 2003 06:59:56 -0400

On Tuesday, July 1, 2003, at 02:33 AM, Vince wrote:


Mark Schaffer <M.E.Schaffer@hw.ac.uk> is estimating a model with an indicator
(dummy) variable that is 1 in only a single observation and 0 everywhere else
and he wants an explanation for some things he notices about the
variance-covariance matrix,
Thanks to Vince Wiggins for his cogent explanation of what is going on in this case (where the VCV becomes less than full rank). He and I corresponded offlist about the results I had posted
to Statalist using RATS, in which I found it strange that the robust standard errors did not agree, even in the case where the dummy (sorry, indicator) is excluded. We agreed that the difference in the latter case (e.g. regress weight length, robust) was a degrees-of-freedom issue. If one scales RATS' robust covariance matrix to divide by (N-k) rather than N, the two programs agree exactly.

With the dummy included, they do not; but inverting RATS' covariance matrix leads to a (slightly different) matrix of rank 2. Since RATS indicates that a generalized inverse is being used, and there is more than one way to generate a g-inverse, close in this case may be good enough (as it is in the case of horseshoes and hand grenades).

Kit

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