Consider the savings function

Where e is a random variable with E(e) = 0 and Var(e) = (2e, 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. [if e is independent of inc, then E(e|inc) = E(e).]
(ii) Show that Var(u|inc) = (2e inc, so that the homoskedasticity Assumption SLR.5 is violated. In particular, the variance of sav increases with inc. [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.

Transcribed Image Text:

sav = B, + B,inc + u u = vinc e,