In a random effects model, define the composite error vit ai uit, where ai is uncorrelated with uit and the uit have constant variance 2it and are serially uncorrelated Define eit vit (i, where is given in (14 10) (i) Show that E(eit) 0 (ii) Show that Var(eit) 2it, t 1, , T (iii) Show that for t s, Cov(eit, eit) 0

Question: In a random effects model, define the composite error vit = ai + uit, where ai is uncorrelated with uit and the uit have constant

In a random effects model, define the composite error vit = ai + uit, where ai is uncorrelated with uit and the uit have constant variance σ2it and are serially uncorrelated. Define eit = vit (λi, where λ is given in (14.10).
(i) Show that E(eit) = 0.
(ii) Show that Var(eit) = σ2it, t = 1,...., T.
(iii) Show that for t ≠ s, Cov(eit, eit) = 0.

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