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,...

i ii EeitEvit Av EVit AEv 0 because EVit 0 for all t VarVit 2 VarVit 2Var 2 ...

In a random effects model, define the composite error vit = ai + uit, where ai is

Question:

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.