ECON 710 Midterm: ECON 710 UW Madison Midterm 2011a
Document Summary
Sample answers: the coe cient (cid:13) 2 is the best linear predictor for e2 i given xi: the coe cient (cid:13) 1 is the best linear approximation to (cid:27)2(xi): they are the same. To see this explicitly, the foc for (cid:13) 1 is so that. The foc for (cid:13) 2 is so that. 2: (cid:13) 1 (cid:0)1 (cid:0)1, (cid:13) 2 (cid:13) 1 = e (xix0 i) (cid:13) 2 = e (xix0 i) E(cid:0)xie2 i(cid:1) i(cid:1) = e(cid:0)e(cid:0)xie2 i j xi(cid:1)(cid:1) Thus the conditions for (cid:13) 1 = (cid:18)1: substituing yi = xi(cid:12) + ei, Thus i i (xi(cid:12) + ei) i=1 x4 i i=1 x3 i ei i=1 x4 i i=1 x3 i yi i=1 x4 i=1 x3. 1 i=1 x4 i i=1 x3 i ei. By the wlln, if ex4 i < 1; then as n ! 1 n x4 i !p ex4 i : By the lie and e (ei j xi) = 0 then nxi=1.
