ECON 710 Final: ECON 710 UW Madison Final Exam 2017a

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31 Jan 2019
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Iv regression (a) b(cid:12) = (z 0x)(cid:0)1 (b) write. Z 0y = (pn i)(cid:0)1 (pn b(cid:12) (cid:0) (cid:12) = nxi=1. E(cid:16)b(cid:12) (cid:0) (cid:12) j z; x(cid:17) = e0@ nxi=1. = 0 zix0 i! (cid:0)1 nxi=1 ziei! ziei! j z; x1a i! (cid:0)1 nxi=1 i! (cid:0)1 nxi=1 zie (ei j z; x)! i! (cid:0)1 nxi=1 zie (ei j zi; xi)! E(cid:0)zieiejz0 i! (cid:0)1 nxi=1 i! (cid:0)1 i j zi; xi(cid:1)! nxi=1. E(cid:0)zieieiz0 i! (cid:0)1 i! nxi=1 i! (cid:0)1 nxi=1 i j zi; xi(cid:1) i = e(cid:0)e2. = nxi=1 where xiz0 xiz0 xiz0 xiz0 zix0 zix0 zix0 ziz0 i(cid:27)2 (cid:27)2. Notice that this is the variance conditional on both z and x: control function regression. (a) the reduced form equation for xi is xi = (cid:0)0zi + ui so. The de(cid:133)nition for "i is from ei = u0 expression on the right side, we (cid:133)nd i(cid:13) + "i so "i = ei (cid:0) u0 i(cid:13) .