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Re: Re: st: xtgee robust standard errors


From   "David M. Drukker, StataCorp" <ddrukker@stata.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: Re: st: xtgee robust standard errors
Date   Fri, 16 Aug 2002 11:35:32 -0500

In the continuing thread about robust standard errors after -xtgee ,
fam(gauss) link(id)-, Axel <A.Heitmueller@hw.ac.uk> asked:

> david, are you saying that xtgee using the robust option is similar
> to a hausman taylor iv estimation where one can use random effects
> despite x_it correlated with u_it in order to get estimates of time
> invariant variables?

No, when x_it and u_i are correlated in the model

 	y_it = B x_it + u_i + e_it
 
 		with 
		u_i ~ i.i.d over the panels 
		e_it ~ i.i.d over all the observations
		x_it uncorrelated with e_it 
		e_it uncorrelated with u_i 

-xtgee , fam(gauss) link(id)- will NOT provide consistent estimates of the
marginal effect of x_it on y_it.  In contrast, the Hausman-Taylor estimator
(Hausman and Taylor 1981) can provide consistent estimates of the parameter
B when x_it is correlated with u_i.  The Hausman-Taylor esimator overcomes
the correlation between the x_it and u_i via the method of instrumental
variables.

Still, there does exist a population parameter that corresponds to B for the
above model with x_it correlated with u_i, although I do not know how to
interpret it.  -xtgee , fam(gauss) link(id)- will estimate this population
parameter and specifying -robust- will provide consistent estimates of the
standard error.

If you are insterested interested in obtaining consistent estimates of B
that are interpretable as the marginal effect of x_it when x_it and u_i are
correlated, you should look into the instrumental variables estimators.
Baltagi (2001) and Wooldridge (2002) both give very good introductions to
these methods.

--David
ddrukker@stata.com


Baltagi, Badi. 2001.  "Econometric Analysis of Panel Data."  New York: John
Wiley and Sons.

Hausman, Jerry and Taylor, William. 1981. "Panel Data and Unobservable
Individual Effects", Econometrica, Vol 49 No 6: pp 1377-1398.

Wooldridge, Jeffrey. 2002. "Econometric Analysis of Cross Section and Panel
Data."  Cambridge, Massachusetts: The MIT Press.

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