System estimation for the one-way model: OLS versus GLS.

(a) Perform OLS on the system of equations given in (2.28) and show that the resulting estimator is pooled OLS \(\widehat{\delta}_{O L S}=\left(Z^{\prime} Zight)^{-1} Z^{\prime} y\).

(b) Perform GLS on the system of equations given in (2.28) and show that the resulting estimator is the random effects estimator \(\widehat{\delta}_{G LS}=\left(Z^{\prime} \Omega^{-1} Zight)^{-1} Z^{\prime} \Omega^{-1} y\) where \(\Omega^{-1}\) is given in (2.19).

1 P+ 1 (2.19)