Unbiased estimates of the variance components of the one-way SUR model.

(a) Using (6.6), verify that \(\widehat{\Sigma}_{u}=U^{\prime} Q U / N(T-1)\) and \(\widehat{\Sigma}_{1}=U^{\prime} P U / N\) yield unbiased estimates of \(\Sigma_{u}\) and \(\Sigma_{1}\), respectively.

(b) Using (6.13), verify that (6.16) results in unbiased estimates of \(\Sigma_{u}, \Lambda_{2}\), and \(\Lambda_{3}\), respectively.

Transcribed Image Text:

= ( + ,) 8 (IN & JT) + v (IN ET) = = 0 P + 8 (6.6)