Unequal Numbers of Observations and Partial Efficiency Gain: A Note

Efficiency gain from Aitken estimation in the seemingly unrelated regressions [Zellner (1962)] is not obtained when regressors are identical [Dwivendi and Srivastrava (1978)]. Swamy and Mehta (1975) show that there is efficiency gain from Aitken estimation when there are unequal numbers of observations, and a Monte Carlo study by Schmidt (1975) shows small sample evidence. Most recently, Farebrother (1992) deals with the model in the context of no contemporaneous observations. However, there has not been discussed estimation efficiency in the context of unequal numbers of observations and identifcal regressors. This note is to fill the gap by showing that the efficiency gain is only partial.