Consider a model at the employee level,
yi,e = (0 + (1xi,e,1 + (2xi,e,2 + ... + (kxi,e,k + fi + vi,e'
where the unobserved variable fi is a "firm effect" to each employee at a given firm i. The error term vi.e is specific to employee e at firm i. The composite error is ui.e = fi + vi.e' such as in equation (8.28).
(i) Assume that Var(fi) = (2f, , Var(vi.e) = (2v, and fi and vi.e are uncorrelated. Show that Var(ui.e)
= (2f + (2v; call this (2.
(ii) Now suppose that for e ( g,vi.e and vi.g are uncorrelated. Show that Cov(ui.e, ui.g) = (2f.

(iv) Discuss the relevance of part (iii) for WLS estimation using data averaged at the firm level, where the weight used for observation i is the usual firm size.

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