Re: [Gretl-users] panel model residuals

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.