In the continuing thread about robust standard errors after -xtgee ,
fam(gauss) link(id)-, Axel <[email protected]> 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
[email protected]
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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