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Re: Re: st: xtgee robust standard errors


From   ddrukker@stata.com (David M. Drukker, StataCorp.)
To   statalist@hsphsun2.harvard.edu
Subject   Re: Re: st: xtgee robust standard errors
Date   Fri, 16 Aug 2002 10:13:04 -0500

Bo Cutter <wcutter@ucla.edu> asked:

> I am using the xtgee command to get robust standard error estimates for a
> random-effects panel data model. (i.e. xtgee..., family(gauss) link(ident)
> robust).  p.446 of manual S-Z (last sentence, first paragaph) has a sentence
> that implies these robust standard errors are correct even if the
> panel-specific effect is correlated with the regressors.  Can anyone tell me
> if I am interpreting this statement correctly ?  And do you know what the
> reference behind this statement is ?

And Bobby <rgutierrez@stata.com>, correctly noted that :

> Yes, this statement is true.  In general, the robust standard errors
> are a true indicator of the sample-to-sample variability of your
> parameter estimates even in mis-specified models.

> As for a reference, try

> Domowitz & White (1982).  Misspecified models with dependent
> observations.  Journal of Econometrics, 20, 35-58.

But it should be clarified that in this case -xtgee , robust- is providing
consistent estimates of the standard errors of estimates of population
parameters that are probably NOT what Bo wants from his model.

Let me explain via an example.  Consider 

	y_it = B x_it + u_i + e_it

where u_i is i.i.d over the panels and e_it is i.i.d over all the
ovbservations.  If x_it is correlated with the unobserved u_i then two
things are true:

	i) xtgee will not provide consistent estimates of the parameter B for
	   the model that assumes x_it is uncorrelated with u_i.
	   In particular, if x_it is correlated with u_i, the estimate that
	   -xtgee- produces for B cannot be interpreted as the marginal effect
	   of x_it on y_it.
	   
	ii) But there exists a true value of B in the mis-specified
	    model in which x_it is correlated with u_i.  The robust option
	    provides consistent estimates of the standard
	    errors of the estimate B in the mis-specified model.


--David
ddrukker@stata.com

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