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).

NT 1-1 =NT(_1/un) i=1 t=2 NT 8L(0)/0 = NT i=1 t=2 L(0)/06 = (NT /26?)[1 - (IN & Jr)/(t)] (5.34)