Consider the savings function sav 5 b01 b1inc1 u, u5

"inc.e, where e is a random variable with E1e25 0 and Var1e2 5 s2

e. Assume that e is independent of inc.

(i) Show that E1u0inc2 5 0, so that the key zero conditional mean assumption (Assumption SLR.4)

is satisfied. [Hint: If e is independent of inc, then E1e0inc2 5 E1e2.]

(ii) Show that Var1u0inc25 s2 einc, so that the homoskedasticity Assumption SLR.5 is violated. In particular, the variance of sav increases with inc. [Hint: Var1e0inc25 Var1e2 if e and inc are independent.]

(iii) Provide a discussion that supports the assumption that the variance of savings increases with family income.