Introductory Econometrics 4th Edition by Jeffrey Wooldridge

تمرين 4

Consider the savings function
where e is a random variable with E(e) = 0 and Var(e) = a2g. Assume that e is independent of inc.
(i) Show that E(u/inc) = 0, so that the key zero conditional mean assumption (Assumption SLR.4) is satisfied. [Hint: If e is independent of inc, then E(e/inc) = E(e).]
(ii) Show that Var(u|inc) = a2Jnc, so that the homoskedasticity Assumption SLR.5 is violated. In particular, the variance of sav increases with inc. [Hint: Var(e/inc) = Var(e), if e and inc are independent.]
(iii) Provide a discussion that supports the assumption that the variance of savings increases with family income.