Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 14

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) = ?2f , Var(vie) = ?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(uie,uig) = ?2f.

(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.

Step 1 of 5

We are given a regression model which is for the employee level. Here f is unobserved while v is error term specific to employee e.

The model given to us is