On Sun, 20 Dec 2015, Sven Schreiber wrote:
> After a little bumbling around
> it became apparent that, given a balanced panel, the Stata ui values
> differ from the above by a multiplicative constant, and after a bit more
> trial and error it emerged that the constant is
>
> 1 - (1 - \theta)^2
>
> where \theta is the GLS coefficient. So (for a balanced panel) we have
>
> ui_stata = (1 - (1 - theta)^2) * pmean($uhat)
>
> Can anyone supply an econometric rationale for that formula?
I think the point is to split up the means such that the estimated
variance of the group effects (which enter in theta to make the GLS
feasible) will be justified by that split. However, I am not sure at all
whether this split would always be unique, i.e. whether another
"allocation" of the means among the two error components (and differing
across groups) would also be possible. In other words, whether the
variance restriction is identifying by itself.
It's a signal-extraction argument. Basically that would be the conditional
expectation of u_i given $uhat, and therefore an unbiased predictor.
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Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
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