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 \(\widehat{\delta}_{G L S}=\left(Z^{\prime} \Omega^{-1} Zight)^{-1} Z^{\prime} \Omega^{-1} y\) where \(\Omega^{-1}\) is given in (2.19).

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22-1 P+ Q (2.19)