Breusch and Pagan (1980) Lagrange multiplier test. Under normality of the disturbances, show that for the likelihood
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Breusch and Pagan (1980) Lagrange multiplier test. Under normality of the disturbances, show that for the likelihood function given in (4.15),
(a) The information matrix is block-diagonal between \(\theta^{\prime}=\left(\sigma_{\mu}^{2}, \sigma_{\lambda}^{2}, \sigma_{u}^{2}ight)\) and \(\delta\).
(b) For \(H_{0}^{c} ; \sigma_{\mu}^{2}=\sigma_{\lambda}^{2}=0\), verify (4.18), (4.20), and (4.22).
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