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

Exercise 6

In a random effects model, define the composite error vit = ai + uit,, where ai is uncorrelated with uit and the uit have constant variance ?2u and are serially uncorrelated. Define eit = vit- . where ? is given in (14.10).

(i) Show that E(eit) = 0.

(ii) Show that Var(eit) = ?2u t = 1,...., T.

(iii) Show that for t ? s, Cov(eit, eis.) = 0.

Step 1 of 6

Given that in the random effects model, the composite error is given by where is un-correlated with and have constant variance and are serially un-correlated

That means,

Now, consider where which is a constant

(i)

Since, in the random effect model, , where the composite error is given by

Since,

That implies,