An LM test for first-order serial correlation in a fixed effects model. For (H_{5}^{b} ; ho=) 0

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An LM test for first-order serial correlation in a fixed effects model. For \(H_{5}^{b} ; ho=\) 0 (given the \(\mu_{i}\) are fixed),

(a) Verify that the likelihood is given by (5.40) and derive the MLE of the \(\mu_{i}\).

(b) Using (5.34) and (5.35), verify that the LM statistic for \(H_{5}^{b}\) is given by (5.42).

(c) Verify that for \(H_{5}^{a} ; \lambda=0\) (given the \(\mu_{i}\) are fixed), one obtains the same LM statistic as in (5.42).

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