Consider a model at the employee level,where the unobserved variable fi is a "firm eff...

Consider a model at the employee level,

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 = f1 + vi,e , such as in equation.

(i) Assume that Var(f1) = σ2f , Var(vie) = σ2v , and fi and vi,e are uncorrelated. Show that Var(ui,e) = σ2f + σ2v ; call this σ2.

(ii) Now suppose that for e ≠ g, vi,e and vi,g are uncorrelated. Show that Cov(uie,uig) = σ2f.

(iii) Let be the average of the composite errors within a firm. Show

(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.